*Everyday Mathematics* Listserv Archives

Want to see other questions Everyday Mathematics teachers have had about the curriculum throughout the years? Check out these topics, with teacher questions and answers provided.

These questions and answers are from the UCSMP-EL listserv archives. This archive is a work-in-progress; if you spot any errors, please email emvlc@uchicago.edu.

### Question

I was wondering what the protocol is for the reading of directions in the written assessments for Grade 2 students. I do not have any students who are below grade-level in reading, but I wondered if any of you do, and if so, do you read the directions for the written assessments to them? I looked in the Assessment Handbook, and there is no directive regarding this. I know that if a student has an Individualized Education Program that specifies the reading of directions, they can be read. I wondered what you do with students who do not have Individualized Education Programs in Second Grade but who are unable to read the directions in the Everyday Mathematics written assessments. (10/15/11)

I have no problem modifying administration to meet the needs of your students. We want to assess the mathematics and if the directions are inhibiting a teacher from getting at what math the child knows, I suggest they read the directions to them. (10/17/11)

I taught Second Grade last year. I read each question on assessments. I had many low readers. (10/17/11)

### Question

I'm looking for a norm-referenced (standardized) math test that aligns well with Everyday Mathematics. The questions on the test should provide a reasonable measure of the topics we teach. In the test-publishing industry this is called "content validity." I have used the following instruments and found them lacking in content validity because our children generally score much higher on the tests than classroom teachers report: Wechsler Individual Achievement Test; Key Math Inventory; Woodcock-Johnson Tests of Achievement-III. (04/05/07)

Have you tried the Test of Early Mathematics Ability-3 (TEMA-3)? It works well for kids up to about age 8. (04/14/07)

A special education teacher in my school used a test called Key Math Diagnostic Assessment by Pearson. She used it in another district and found that it gave a clearer, more specific view of the student. (04/14/07)

While the Key Math Diagnostic Assessment is a diagnostic test, its strength is not assessing conceptual development. There are some that I believe are better for determining conceptual development. I think the issue with the content validity may not be as highly aligned as some other instruments that are just now becoming available. (04/14/07)

I use the Key Math Diagnostic Assessment frequently, as it is the required test our system uses to identify students for Title I services. I find it a useful tool to identify strengths and weaknesses in a child's mathematical understanding. The test results do, at times, differ greatly from what the teacher is seeing in the classroom. However, I find this helpful information. This begins a conversation about what is happening in the classroom that may be inhibiting the child's ability to learn. When I test students, it is in a one-on-one environment with ample time allotted. Sometimes the problem lies not with their math skills but with the learning environment and the student's learning style. (04/14/07)

### Question

Just wondering if anyone's district/staff has had a discussion about when to allow students to use manipulatives/fact sheets/etc. on assessments. The assessment handbook identifies using various manipulatives as part of the grade-level goals, but our staff is wondering about how/when to wean kids off the manipulatives. We have 3 competing opinions right now: 1) kids should be actively encouraged to use the same strategies during the assessments that they use during the activities/games/math boxes; 2) kids should not be using the manipulatives on assessments (depends on grade level to some extent); 3) kids should be allowed to use the manipulatives if they ask, but should not be directly told get them out at the beginning of an assessment. (02/20/09)

From my experience, students will stop using manipulatives when they're ready. I would make manipulatives available for those who want to use them, but I wouldn't require them to ask (some students won't ask if they don't think anyone else is going to do it and that student may need them). (02/20/09)

I think students should be allowed to use any manipulative available. They will fall back to where they are comfortable. However, many state assessments do not allow their use. What we have done is teach students how to tear scratch paper into "manipulatives." One example is to tear an arrow to help select the correct answer choice when turning a certain number of degrees. This type of activity seems to help students who have difficulty drawing a picture. (02/20/09)

### Question

This is our first year of full implementation of Everyday Mathematics. Has anyone been able to utilize the assessments from the End-of-Year Assessment for Kindergarten and find a way to streamline them a bit to make it easier for a teacher to administer? The Mid-Year Assessment took the teachers a significant amount of time to administer. (04/08/10)

Spend no more than 10 minutes on the test per day, which is about 3 questions. Otherwise, the students are overwhelmed and exhausted, not to mention that it is nearly impossible for the teacher to work with one student for more than an hour at a time! We also made the questions more specific (assigned values and specific numbers to compare) so that we could compare the results across the grade level and so that they aligned more closely to our state standards. (04/08/11)

In our district we paired down the questions assessed. Our Kindergarten teachers collaborated with our First Grade teachers to determine which test questions needed to be assessed in order to have the best information on students' math skills as they exit kindergarten and enter First Grade. We found that the original assessment was too lengthy to fit into our half-day Kindergarten program and took away valuable teaching time when administered in its entirety. So far, the kindergarten teachers have been more successful giving the assessment, and the First Grade teachers find the information given to them valuable. (04/09/10)

### Question

I'm trying to understand the publishers' expectations regarding Everyday Mathematics Kindergarten Number and Numeration Goal #1. Based on the Everyday Mathematics materials, it's fairly clear that Kindergarten students are expected to do the following by the end of the year: Count on by 1s to 100; Count on by 2s with number grids, number lines, or calculators; Count on by 5s and 10s with number grids, number lines, or calculators; Count back by 1s with number grids, number lines, or calculators. However, the materials don't seem to answer these questions: Should Kindergarteners be able to count on by 1s to 100 with and without number grids, number lines, or calculators? What target should teachers use in measuring Kindergarteners ability to count on by 2s? The Suggestions for End-of-Year Periodic Assessment Tasks in the Assessment Handbook does not provide any guidance on this. What target should teachers use in measuring Kindergarteners ability to count on by 5s and 10s? The Suggestions for Mid-Year Periodic Assessment Tasks in the Assessment Handbook states: "Look for the child to count on to at least 50 by 10s and by 5s." But the Suggestions for End-of-Year Periodic Assessment Tasks doesn't provide a target. Is it still 50? What target should teachers use in measuring Kindergarteners ability to count back by 1s? The Suggestions for End-of-Year Periodic Assessment Tasks states: "Look for the child to count back by 1s from a number beyond 10." Does this mean that a child has met this part of the end-of-year learning goal if he can count back by 1s from 11? This is our district's first year using a standards-based program, and I want to be sure I'm using the correct standards when I assess and record student progress toward goals. (02/06/08)

I taught Kindergarten for many years. I think if the materials don't give a clear target, you could go with your state's benchmarks. For instance, in my state the content level expectation is to count by 2s and 5s to 30, so that would be my target if Everyday Mathematics doesn't give one. I found when I taught Kindergarten that the Everyday Mathematics goals were more stringent than the state benchmarks. I expected them to be able to skip count to 30 without the numberline, but to count higher using the numberline/grid. (02/06/08)

### Question

Our district is looking for assessments to help identify mathematics deficiencies for students brought to our Intervention and Referral Services teams. In language arts literacy, we use Dynamic Indicators of Basic Early Learning Skills (DIBELS) to assess students reading fluency. Does anyone know of a math assessment that can be used to determine a student's deficiencies in mathematics. Someone mentioned using mid-year and end of the year tests. Our problem is, if we have a 5th grader functioning at a 2nd grade level, we would have to administer many tests to determine this. Is there a single instrument that can be given to determine a student's math level? (10/19/09)

Continental Press and Coach sell simulation tests (grade specific) that can be used as baselines to determine an entry level. (10/20/09)

We use the Key Math Diagnostic Assessment by Pearson. It does take some time to administer, but it gives a very detailed picture of the student in many areas. It can be normed by grade level or age. The specific areas covered are numeration, algebra, geometry, measurement, data analysis and probability, mental computation and estimation, all math operations, and problem solving. (10/20/09)

Our district is just beginning to implement the Response to Intervention model, and we administered AIMSweb screeners this fall. I have not found the computation screener to be of any benefit to me. I attended a math conference recently and was introduced to America's Choice and their program called Mathematics Navigator. It is diagnostic in nature and is able to pinpoint certain concepts that students are missing. (10/20/09)

We use Group Mathematics Assessment and Diagnostic Evaluation (GMADE). It is a standardized, norm-referenced diagnostic math assessment. Raw scores are converted to standard scores, stanines, percentiles, etc., which are helpful when trying to determine where students are functioning in mathematics in relation to their peers. It is normed for age and grade, fall and spring. Support materials are available too. It isolates weaknesses in areas of Concepts & Communication (Number Sense), Operations and Computation, and Process and Applications. It is our second year using this for Response to Intervention and we are having good results. (10/20/09)

### Question

I use the Open Response items, but I provide a practice in class first. (Regarding the Assessment Assistant CD, is there a third edition CD yet?) I clearly state the rubric for grading and demonstrate on the overhead how to meet the rubric items. I send them home, with the other parts of the unit assessment at the end of the unit, with the rubric and an indication of what the child did. I warn the parents that these are hard and that the kids didn't do these last year, so they are new to them. I teach second grade. I expect third grade will use them and I want my kids to have a clue as to how to do them! I find them very challenging for second grade, but worthwhile. My kids actually seem to like them now that we've done a few. If we didn't do the practice together, though, I don't think they would do well unless they were working together on it. I like hearing what other people are doing with the Open Response. It is something I'm not quite settled with and it's good to read other approaches to them. (04/01/08)

I think there have been many good suggestions for guiding students through the process of learning to answer Open Response questions. Modeling is really important here. I also would encourage teachers to make an overhead of a couple of the level 2 or level 3 responses (the student samples in the Assessment Handbook) and work together to edit them to be level 4 responses. This helps them focus on what makes an excellent response, and it is non-threatening, as it is not their own writing so it is less personal. Also, if you are not using the writing and reasoning prompts with the Math Boxes, I would encourage teachers to use those so students can become more comfortable with small writing tasks as they build towards the more complex Open Response provided at the end of the unit. (04/22/08)

### Question

I am interested in how Fourth Grade teachers dealt with checking the accuracy of students' responses to the Unit 4 Open Response question (Lesson 4.11). Recall the 12 runners that had to be divided into three closely matched teams of 4? Did teachers go through and add up the times for each students' teams to check accuracy? If you have 20 students, or more, wouldn't this take a long time? I know that there is more to the question than accuracy of adding decimals, but surely that is part of it. (One can't just make an answer key of the various combinations students might have come up with, because, if I did my math right, there are 34,655 different possible ways to make 3 teams of 4 out of the 12 runners.) (02/05/09)

Here's how I solved this problem: I let the students use calculators. Why, you ask? Well, in our high stakes testing, students are often allowed to use calculators for word problems. That's because the high-stakes test is testing their understanding of word problems, not their calculations. I had noticed that I rarely give my students a calculator during tests, so I decided to do that more so they will get comfortable with the idea. So I assume they got the calculations right, and I am just checking how close the total times are. (02/08/09)

### Question

I am interested in what classrooms are doing with the Open Responses. How do classroom teachers scaffold this activity for students? How do the different grades approach this activity? Please share the different options you have seen in classrooms. Specifically, to math coaches, when teachers feel that the Open Response is too difficult for students and they only give it to their high students, what is your response and how do you support them? (08/25/11)

Usually, students are having trouble with the format of writing to an Open Response question. If students are not familiar with this type of assessment they need scaffolding. First a simple, generic rubric should be available to all students. Introductions to the Open Response assessments should be several grade levels below the students. This way, students can become familiar with the "Explain your Strategies; Defend your Solution" strategies without being bogged down by the math. Going over the benchmark responses with your students is crucial. Once the students feel comfortable with the Open Response format, I have always allowed them to work in pairs to discuss the problem for about 15 minutes without writing. After that, they work on the written response individually. Believe it or not, I still received totally individual responses. Keep in mind, this is real life. Engineers do not solve problems in isolation. I think it is more important that students learn to write to Open Response questions than it is that they solve the math involved correctly. Thorough explanations and defenses of solutions should be highly valued. You can always modify the Open Response questions to differentiate (up or down) for your student population. (08/25/11)

I am a Fifth Grade teacher, and I use the Open Responses at the end of each unit. Students receive one extra credit point just for making a good attempt. Then, I use the rubric to determine whether a student's response earns them 2, 3, or 4 extra credit points. It teaches my students to attempt such questions even though they seem too difficult. They often surpise themselves and receive more than one extra credit point. (08/25/11)

I use the strategies given in the guideline for solving number stories in the Fourth and Fifth Grade program. Then I help students break down the problem. What is the question? How do I approach it? We usually look at 4 areas to earn points: correct answer, show your work (draw a diagram, provide calculations that help solve the problem), use words to describe understanding (using proper terms and descriptions), identify the specific element of the Open Response problem for the unit. For instance, in Grade 4, Unit 2, landmark data is the key element. Students need a graph of jelly beans (+1 pt), a data set constructed with 11 students (+1), and an explanation that has maximum and minimum and determines median and mode (+1). The graph should be complete and match the data set (+1). By helping students identify 4 areas they are more successful in earning points. (08/26/11)

There is a video of an interesting Open Response question in a Fourth Grade classroom at the Virtual Learning Community (VLC) website: http://vlc.uchicago.edu/resources/201. Be forewarned, the video lasts an entire lesson. However, you can get a great deal out of watching a portion of the video. In order to access this video, you'll need to join the VLC. You can access information about the VLC, which is sponsored by the Center for Elementary Mathematics and Science Education at the University of Chicago, the home of the Everyday Mathematics authors, by clicking on the "ABOUT" tab at http://vlc.uchicago.edu/about. If you decide to join the site, click on the red HOME tab at the top of the page and then click on JOIN. After you sign up, you'll receive an email confirming your membership. If the email does not appear within an hour, please check your junk or bulk email folder to see if it landed there. Once you receive your confirmation, log into the site and away you go. (08/26/11)

As a math coach, I often do this lesson with classes. I prepare PowerPoints so that I can project the rubrics from the Assessment Handbook and some of the student work that is also included in the Assessment Handbook. Initially we work the problem together. Then we check the rubric to see how we did and look at other ways students responded. We also might look at some of the examples that received partial credit and make suggestions on how to improve them. On subsequent units I let the students make first attempts on the problem in pairs or teams and then we look at the rubric and the students improve their answers. Then the students will respond individually and self-correct using the rubric. We never use these for a grade, but as a district we do expect teachers to do them after each unit and use them as teaching option if that is what the students need. One more observation I have is that often teachers did not think they could offer the students the use of manipulatives to solve the problem. I encourage the students to use their tools, so if the problem is about money take out the coins. (08/26/11)

I work with K-4 students and teachers, and we have found the Open Responses most helpful as an instructional opportunity rather than as an independent assessment. We encourage teachers to model parts of the most difficult tasks and guide tasks that need further clarification as students work together to solve them. For some tasks, we have created organizers that help support the breaking down of a task into smaller parts. Another strategy is to work through a part of the task together, and then ask the students to complete another part independently. Of course you can differentiate how much support to give groups of children, with independent completion the goal for your higher achieving students. But we do think all students need to be exposed to the Open Response type of work so that their reasoning skills get put to work. (08/26/11)

### Question

I am just looking for some brief info regarding Open Response items. We feel they are valuable exercises, but struggle with finding the time for them. How do others use them? Are they basically a whole separate lesson/day? Do you use them on the Assessment days? (01/04/11)

We use Open Response on one day and then the Oral/Slate and Written Assessment on the second day. We've also given our teachers some flexibility with the Open Response. Some must be done independently, but others can be done as partner/small group activities or even whole-class activities. For those, many of the teachers have found success with a 10/10/10 approach, where students work on an Open Response for 10 minutes individually, then 10 minutes in partners, and then 10 minutes as whole-group discussion. We've found if you really stick to four lessons a week, you will still have time for two days of assessment, and maybe even a day of review prior to the assessments. (01/05/11)

### Question

Our school is really having a hard time getting students to do Open Response questions. I was wondering if anybody had any resources of maybe some graphic organizers or techniques they use to help students format their answers to Open Response. I have worked with the Exemplars a bit, and the students work out the problem but then can't put their thought process down in writing. (02/26/07)

Students can be encouraged to communicate their thinking by drawing pictures and using numbers before formulating words. Often these visual images help students select their words and describe their thinking in writing. Teachers can assist by modeling written explanations with help from the class. (02/26/07)

One of the first things I work with teachers on is having students verbalize. Get students to talk more, to "talk" their explanations, not just on specific extended response questions but overall in the classroom. When I was in the classroom, the students had a weekly challenge which started out having to restate the question in their own words and ended with a written explanation (of course showing/labeling all their work and showing a check for their work or solving the problem using a different strategy/approach in between). The written explanation started with "The problem solving strategy I used was . . . " and continued with a general formant of "First I . . . because . . . Then I . . . The reason I . . . " I used this in Grade 8 and coordinated with my English Language Arts teaching partner. In a self-contained classroom the teacher could use the constructed response for math and ELA. In general I found that students really need lots of practice with lots of feedback on what was done well and where they could improve. Also included in the written explanation was a requirement of the use of five math language words. (02/27/07)

We use Formula Writing by Janet Cosner. She has a website that you can Google to order her books. (02/27/07)

### Question

I teach Fourth Grade and my class is really struggling with open number sentences. We have discussed how the variable is like a question mark, but they can't seem to figure out how to solve it. We have related it to fact triangles and gone over how to put the numbers in the triangle but they still are struggling. Any suggestions? (11/20/09)

I found that many of my 4th graders really didn't understand how the addition/subtraction fact triangles worked and were unable to work a number model back into the triangle. It took lots of practice, but now the kids can use the fact triangles correctly, and it tells them exactly what to do to find the variable. Make sure students can fit a number model like 10 - 3 = 7 correctly into a triangle before you try it with the variables. (11/20/09)

Explain to the class that the equation is like a balance scale, even draw a picture of a scale. For example, 5 + 4 = ___ + 3. Tell them to do the side that has the two numbers to get the answer, then tell them the other side has to equal the same, so 3 + what = 9? (11/20/09)

You could try setting up on the chalkboard or posterboard: ____ + ____ = ____ + ____ . Using index cards with numbers, fill in three of the blanks: 2 + 7 = ____ + 1 Then do it wrong a few times and guess and check. Does 2 + 7 = 5 + 1? Does 2 + 7 = 12 + 1? Does 2 + 7 = 0 + 1? Be sure to let the students correct you, which will be fun. If they don't see it is incorrect, show them one that is: 2 + 7 = 8 + 1 = 9 They could then break into pairs to either complete problems you've filled in three of the blanks or make up their own. You could even break the numbers down into tallies instead of digits: || + ||||||| = ____ + |. (11/20/09)

### Question

I would love to know if the authors consider Open Responses to be formative or summative assessments? (11/17/09)

I think of "formative" or "summative" as referring to how the data that is gathered is used. Roughly speaking, if teachers use information they get from assessing their students' responses to some task or question to plan further instruction, then they are using that information formatively; if they use the information to assign grades, they're using the data summatively. So whether an item is formative or summative depends on how the information from that item is used rather than on the item itself. In Everyday Mathematics, we tend to give a lot of leeway to teachers to decide how they want to grade. As the Assessment Handbook says, because local assessment systems are based on local norms and values, it would be impossible to design a system that would apply universally. But the authors of Everyday Mathematics recognize that many teachers are required by their districts to give traditional grades. And although it is impossible to design a single grading system that will work for everyone, there are some broad principles to follow: Grades should be fair and based on evidence that can be documented. Evidence for grading should come from multiple sources. Grades should be based on content that is important. They should not be based only on the content that is most easily assessed. The grading system should be aligned with both state and local standards and with the curriculum. In Everyday Mathematics, we do give some guidance about what we consider "fair to grade," meaning that we think that items that we label "fair to grade" have had sufficient instruction and practice that the children have had sufficient opportunity to master them. Of course, people can and do differ about what's fair to grade, so these are only guidelines. I asked the person who wrote many of the Open Response items what she thought about the question below, and she said she didn't think the Open Response tasks were "fair to grade" since they require more than mastered content and skills. They often require the application of a variety of skills--some maybe mastered and others maybe not. When we wrote the Open Response items, we wrote problems that were tied to unit content, but did not focus only on skills and concepts that should be mastered. The Open Response problems also require organizing and writing in a way that can be a bit of a stretch. Many of our assessment tasks serve as learning opportunities as well as assessment opportunities. We designed the Open Response problems with this in mind. A number of schools have reported that the Open Response items are challenging for their students. This may be due in part to the fact that the tasks are relatively new to the program, and so students have not had a lot of experience with representing their thinking and explaining their strategies as these tasks demand. In some cases, schools have created additional opportunities for developing the skills that the Open Response tasks help develop and assess. (11/20/08)

### Question

Our district would love to hear how others are using the Open Responses that come with each unit. We were thrilled to have these as an addition to the 3rd edition, but our students are struggling with them. (03/27/08)

If your students are not familiar with this type of question, begin with questions from much lower grade levels and work up. Be sure they understand how to write to a rubric before infusing more difficult mathematical concepts. (03/27/08)

I am considering using Open Responses as a posed problem to be done in pairs rather than an end of the unit assessment. It would provide students the opportunity to problem solve, an experience that is not a major activity in this program. This would be more in keeping with a constructivist philosophy and could lead to a good strategy discussion. Sharing the variety of ways students use to solve these problems would be a good way to focus on understanding concepts rather than purely learning processes. (03/27/08)

In Second Grade, I have the students work independently, then talk with a partner and finally we discuss the solutions with the whole class. (03/28/08)

We looked at the mathematics embedded in the task and the standard requirement for that specific skill (skills) and adapted the task to meet the standard for the grade. We kept the task as-is for our higher performance pupils. Another factor to consider is wording of the task. These responses tend to be very wordy. This can cause a lot of distraction for our struggling and ELL students, especially if they cannot read. (03/30/08)

If you have access to the Assessment Assistant CD, you can make a "practice" test with the open response questions. This CD allows you to change the numbers and I also like to change the names. I use my name and the students' names whenever possible. Then we practice how to answer the questions. I give the original Open Response for the test. I feel that this teaches the students how to answer this type of question and then gives them practice with a very similar problem. (03/31/08)

I strongly encourage you to use the Open Responses as they were designed to be used. The students will catch on quickly if you use them after each unit. Since this is a new routine for the 3rd Edition, naturally the students are new at this. Next year, if your students have practiced all year, they should be fairly proficient at the process. At the beginning of the year, I did let them "practice" with a similar problem that I got off the Assessment Assistant worksheet builder. This seemed to help them be prepared for the the problem on the assessment. (03/28/08)

### Question

We too are wondering about practice for the Open Response problems at the end of each unit. It seems that these problems just pop up without practice or preparation. Am I missing something in the teacher resources or lesson plans? Can one of the developers address this issue? (12/31/07)

You can create problems that look very similar using the Assessment Assistant CD. (11/01/07)

This is our second year with Everyday Mathematics, 3rd edition. We like Writing/Reasoning in the Math Boxes for short daily practice. (11/01/07)

The Everyday Mathematics authors believe teachers need to have a variety of assessment tools and techniques to choose from so students can demonstrate what they know in a variety of ways and teachers can have reliable information from multiple sources. From page 21 of the grade-level specific Assessment Handbooks, "The Open Response problems at the end of each unit are linked to one or more Grade-Level Goals emphasized in the unit. They provide additional balance in an assessment plan as they allow students to: become more aware of their problem-solving processes as they communicate their understanding, for example, through words, pictures, and diagrams; apply a variety of strategies to solve longer tasks; further demonstrate their knowledge and understanding through application of skills and concepts in meaningful contexts; and be successful on a variety of levels." The "practice and preparation" for these problems can be found in the unit itself. Again, the Open Response problems are linked to one or more Grade-Level Goals emphasized in the unit. This, of course, doesn't mean that students won't be asked to use some previously acquired skills as well. The problems give students the opportunity to apply the Grade-Level Goal mathematics in complex or new situations. Additionally, in terms of "practice and preparation," the unit-specific section of the Assessment Handbooks, each Open Response problem has suggested implementation strategies, modifications for meeting diverse student needs, and suggestions for improving open response skills. Finally, please keep in mind that all of the Open Response problems were field tested with students using the second edition of Everyday Mathematics. (11/05/07)

The Open Response problems are designed to be contextual problems involving the application of skills and concepts from the unit. Much of the preparation for these problems is in the class discussions, the explanations required for many journal page problems, the Exit Slips, and the Writing/Reasoning prompts that appear within the unit. Let's take a look at the Open Response problem in Unit 1 of Grade 4 as an example. For this task, students sort polygons into groups according to polygon properties. Please refer to pages 55-59 of the Grade 4 Assessment Handbook. The stated focus of the problem is: Describe, compare, and classify polygons using appropriate geometric terms [Geometry Goal 2]. I'll provide a few examples of activities within the unit that use similar skills and strategies. Lesson 1-2: Students discuss characteristics of line segments, lines, and rays. In a Math Log or on an Exit Slip students explain the difference between a line segment and a line. Students are encouraged to include drawings and symbols as part of their explanations. Lesson 1-3: Students use straws and connectors to construct triangles and quadrangles. They describe the properties of and compare the quadrangles, as well as identify the types of quadrangles. In Problems 1 and 2 on Study Link 1-3 students are asked to draw examples of rectangles and trapezoids. Problem 3 includes the following question: How are the polygons in Problems 1 and 2 similar? How are they different? Completing Part 3 activities will also prepare students for the unit's Open Response problem. For example, the Readiness activity in this lesson asks students to sort pattern blocks according to rules. The last problem on the page asks students to make up their own rule and then sort the blocks according to that rule. In the ELL Support activity, students use a Venn diagram to compare and contrast the attributes of different categories of quadrangles. Lesson 1-4: As part of the Math Message, students complete a Math Masters page titled "Properties of Polygons." They are shown 5 polygons and told, "All of these have something in common." They are shown 5 different polygons and told, "None of these has it." Six polygons are shown in Problem 1. Students are asked to circle the ones that have "it." Problem 2 asks them to describe the property that all of the circled polygons have in common (four sides). Finally, students are asked to use a straightedge to draw a polygon that has this property. Further along in the lesson students develop definitions for the terms parallel, intersecting, and perpendicular. They also describe characteristics of parallelograms and classify quadrangles based on side and angle properties. On journal page 11, students complete statements such as: Squares are [always, sometimes, never] rectangles. Explain. Lesson 1-5: Students construct convex and concave polygons and develop definitions for these terms. On journal page 12 students are shown examples of polygons and figures that are not polygons. They are then asked to describe what a polygon is and why one of the figures on the page is not a polygon. The Enrichment activity in the lesson gives students a similar experience with kites and rhombuses. There are three more lessons in Unit 1, but I think I'll move onto Unit 2 where the focus of the unit isn't so narrow. Before doing so, however, I'd like to mention one of the Modifications for Meeting Diverse Needs that is suggested for Unit 1's Open Response problem. Many of the activities in the unit provided the opportunity for students to work with the actual shapes. One suggestion for implementing this problem is to make and cut out an enlarged version of each of the polygons that appear in the Open Response problem. Students are then able to physically move the cardstock polygons into and out of groups. While this modification may not be necessary for all students, it may allow others to be more successful with the problem. For the Open Response problem in Unit 2 of Grade 4 (Assessment Handbook, pages 63-67) students analyze data landmarks, create a matching data set, and make a graph. The stated focus of the problem is: Create a bar graph [Data and Chance Goal 1] and Use the maximum, minimum, range, median, and mode to answer questions [Data and Chance Goal 2]. Again, let's take a look at a few of the activities within the unit that use similar skills and strategies. Lesson 2-5: Students guess, estimate, and then count the number of raisins in 1/2-ounce boxes. The data is recorded on a tally chart. Students then use the data display to determine the maximum, minimum, range, mode, median, and mean of the data set. During the class discussion, students are encouraged to talk about the distribution of the data in their tally charts. Terms like 'clumps,' 'bumps,' 'holes,' and 'way-out number' are acceptable. Lesson 2-6: Students use stick-on notes to construct a line plot to organize and summarize data about the sizes of their families. They find the minimum, maximum, range, mode, and median for the data set. The median is determined by removing stick-on notes from the line plot and lining them up in ascending order. Students remove stick-on notes, two at a time (one from each end) until only one or two notes remain. Questions for class discussion include: How are the landmarks reflected in the shape and distribution of the data in the line plot? Where are the clusters, bumps, holes, and far-out numbers? Are the median and mode for family size the same? Lesson 2-7: The Writing/Reasoning prompt that goes along with Math Boxes, Problem 4 states: Shaneel said, I can draw a rhombus, rectangle, square, or kite for Problem 4. Do you agree or disagree? Explain your answer. While the prompt does not address the skills or concepts in the Open Response problem, it does provide students with practice in explaining their reasoning in writing. Lesson 2-8: Students measure their head sizes to the nearest half-centimeter. They determine the maximum, minimum, range, mode and median of the data and then display it in a bar graph. They use the data to answer the following question on journal page 46: How would the landmarks help Ms. Woods, a clothing store owner, decide how many baseball caps of each size to stock? Now let's take a look at one of the Modifications for Meeting Diverse Needs. It suggests that students write the landmarks on stick-on notes and then place the stick-on notes in a line plot. Students then can move the remaining blank notes to make the landmarks in the problem true. This strategy for working with landmarks mimics the one used in Lesson 2-6. Again, not all students may need this modification, but it may be beneficial to some. Regarding whether or not students can be successful with the new Open Response problems in the third edition of Everyday Mathematics, I don't agree that the "only solution is to supplement." As demonstrated in the examples above, much of the preparation for these problems is in the classroom discussions, the explanations required for many journal page problems, the Exit Slips, and the Writing/Reasoning prompts that appear within the unit. The authors believe that these embedded features, along with the Implementation Tips, Modification for Meeting Diverse Needs, and Improving Open Response Skills suggestions, provide students with adequate preparation to tackle these problems. How students respond to the Open Response problems can provide a great deal of information about students' communication skills and is another source of formative assessment. I'd suggest giving the above exercise a try with your grade-level team. Pick a unit and the corresponding Open Response problem. See what connections you're able to make between the two. Think about the Key Concepts and Skills in the unit as well as the strategies students use to solve problems. Take a look at the Implementation Tips, Modifications for Meeting Diverse Needs, and the Improving Open Response Skills suggestions to see how they relate. (11/06/07)

I am currently the western region curriculum specialist for Wright Group/McGraw Hill. I would like to share some information concerning problem solving as it relates to the program and as it relates to state testing, at least in the state of Washington. Everyday Mathematics gives all students a balanced curriculum that is rich in real-world problem solving. Problem solving is embedded within the mathematical content strands and not taught as a stand-alone process. Students build and maintain basic math skills, including automatic math fact recall, while they develop higher-order and critical-thinking skills. The Everyday Mathematics 3rd Edition further enhances this philosophy and is the culmination of many hours of research and field testing by the University of Chicago School Mathematics Project authors. These changes will provide teachers with stronger lesson and content support which will translate into better lessons, and students who have a stronger understanding of mathematics. Students will have stronger problem-solving skills, computation skills, and basic math knowledge than if they used a different program. Everyday Mathematics is a rigorous mathematics program and has the expectation that all students can be better mathematics students. Through the lesson support provided to teachers, and the years of research and development, this program provides students with a program that makes math more accessible and fun at the same time. In the Teacher's Reference Manual in the chapter on Problem Solving, the philosophy of Everyday Mathematics is clearly defined. To quote the authors, "In Everyday Mathematics, problem solving is broadly conceived. Number stories, the program's version of word problems, have their place, but problem solving permeates the entire curriculum. Children solve problems both in purely mathematical contexts, such as What's My Rule? tables, and in real situations from the classroom and everyday life. Children also create and solve problems using information from materials, from you, and from their own experiences and imaginations." Everyday Mathematics focuses on four different ways of approaching a problem: concrete, visual, pictorial, and symbolic. From as early as Kindergarten, students are taught to approach problem solving by looking at what do you know, what do you want to find out, what do you need to know, solve the problem and then check to see if your answer makes sense. In each unit organizer, there is a section on Problem Solving that suggests the problem-solving strategies that might be useful in that unit as well as listing the lessons and the activities in those lessons that reinforce teaching through problem solving. In taking a look at the Third Grade curriculum, I found that students are reviewing and using the problem-solving guide that is used throughout the program beginning in Unit 2. This guide is explained in-depth on page 228 in the Teachers Reference Manual. The guide is based on the general problem-solving guidelines that were developed by George Polya, the mathematician that is renowned for his work on problem solving. Students are exposed to this guide from Kindergarten and use it throughout to help them with the process of problem solving. In the third edition of Everyday Mathematics, having students construct written responses has been incorporated into the program not only through the Open Response question at the end of each unit in the Progress Check lesson, but also within the unit lessons with the writing/reasoning opportunities. By using these features of the program throughout the year as well as the multiple choice questions that are included within the Math Boxes, students will be prepared for the format that the Washington Assessment of Student Learning. Students will be practicing these question types throughout the entire year rather than just when exposed to test prep materials that are often used in the weeks or month preceding the test by many classroom teachers. Math Log C master on page 288 of the Assessment Handbook as well as Exit Slips provide masters that can be used to collect your students explanations of how they solved problems that have writing/reasoning opportunities. You could also use these masters to have students explain their thinking when solving other problems within the student journals if you feel your students need more practice in this area of assessment. By teaching the program as it is intended, students will gain the skills necessary for successfully solving problems not only in the context of an Everyday Mathematics lesson or on a state assessment but in real life situations that they encounter. We have found districts that have shown the greatest gains in student achievement have fidelity to the program. (11/08/07)

### Question

I am curious to know how Kindergarten teachers using Everyday Mathematics (3rd edition) are assessing their students and how often. Does anyone use the checklists? It seems like a lot of work and our teachers feel they would be assessing for long periods of time to fill out profiles. (01/08/09)

Our teachers have used the baseline. They do that in September and do the Mid-Year Assessment at the end of January. They have found it to be very valuable. One way to manage it is to do five students a day or simply take one task per day and use the checklist. It is manageable. (01/09/09)

In our school we do the EM Kindergarten Baseline, Mid-year and End-of-year assessments. We find the student information garnered well worth the time put in. To make the process more efficient we have created Teacher Assessment Kits. The kit is specific to the assessment at hand. The necessary manipulatives are in big ziplock bags, numbered by task and placed in order in a portable plastic tote. Throughout the year we can readily use the appropriate kit to assess individual students for intervention and/or placement. (01/10/09)

We do the Mid- and End-of-Year Assessments, but we modified them. Attached is what we created. It still requires one-on-one time and may take 15-20 minutes. But for most students, it takes less.
(01/12/09)

Modified EDM Mid-Year Assessment- K.pdf

Modified EDM End-of-Year Assessment- K.doc

### Question

Our school has decided to go with the 4-point rubric system of assessing students. Will the online assessment generate reports using the 4 point rubric or will it convert this to A and N ( making adequate process or not making adequate progress)? (11/14/07)

The online Assessment Management System allows you to record both Making Adequate Progress/Not Making Adequate Progress as well as 4-point scoring. To create usable reports, the system REQUIRES the Making Adequate Progress/Not Making adequate Progress designation; it is OPTIONAL to enter the 4-point detail score. The system does not convert a 4-point score to an "A" (Making Adequate Progress) or an "N" (Not Making Adequate Progress); the 4-point score is to be entered as supporting detail for the Making Adequate Progress/Not Making Adequate Progress scoring. The way to transport saved tests is to export them. If you have the test generator installed in school and at home, you can do the following on Computer #1: 1) Create and save a test; 2) Go to File and select Export; 3) In the Export dialog, click the Browse button and navigate to your thumb drive; 4) Click the Export button. On Computer #2: 1) Connect the thumb drive; 2) Launch the Management program; 3) Go to File and select Import; 4) In the Import dialog, click the Browse button and navigate to the thumb drive; 5) Select the file; 6) Click the Import button. That should make it available in the Worksheet Building workspace. (11/14/07)

### Question

I am looking for a math pretest for beginning first graders. An end-of-year Kindergarten test would also work. Does anyone have anything they can share? (11/10/11)

The 2012 Common Core State Standards Edition has a Beginning-of-Year Checklist. It includes counting on and back, identifying coins, knowing a tool for telling time, creating patterns, and organizing sets of objects. (11/10/11)

### Question

Does Everyday Mathematics provide beginning, middle, and end-of-the-year assessments for Kindergarten? (09/09/09)

Yes, in the Assessment Handbook for Kindergarten you will find Baseline (beginning of the year), Mid-Year, and End-of-Year Assessment for Kindergarten. There are recording sheets as well as suggestions for assessing. (09/09/09)

Yes, but it is not a paper and pencil task. You can find the specifics in the Assessment Handbook. (09/10/09)

### Question

I am a math coach in Seattle Public Schools and in charge of a project to identify exemplary methods and teaching examples of how to differentiate a typical lesson. This would be outside the realm of merely plugging in the readiness piece or enriching for a particular segment of a classroom. In essence, the question is how to properly pretest and target specific groups within the classroom, then how to manage a lesson as a classroom teacher in such a way that the key concepts are properly introduced, but the experiences or options to explore the concepts are differentiated. How does this look? How is this best managed? (12/05/08)

At the recent National Indian Education Association's (NIEA) 39th Annual Convention in Seattle, there was a presentation that would answer some of your questions involving exemplary methods, teaching examples, differentiation outside the realm of plugging in what is in the book, and assessment. The presentation was titled "A Math Partnership that Leaves No Child Behind." Some of the presenters were from the Marysville School District. Dr. Kyle Kinoshita, Executive Director for Teaching and Learning was a co-presenter representing the administration from that school district. (12/05/08)

I teach EM in centers, similar to the previous reply, but I'm the only teacher in my general ed classroom. I teach the math message and mental math to the whole class, then split the class into three groups: Math Boxes, Math Games and Teacher Center. At teacher center on Mon-Thurs I teach the bulk of Part 1 for each lesson, differentiating my approach and instruction for each group (below grade, at grade and above grade). Then on Friday I conduct either a formative or summative assessment in place of the math message/mental math and during the teacher center I either re-teach concepts that kids still don't get or push kids who are mastering all math concepts. Our math block is 60 minutes. I have 28 students and teach the lesson in one room, self contained general education, 4th grade. I teach the whole group for about 15 minutes, then do three rotations of centers for 15 minutes each. Sometimes if it is a hard concept, I'll teach the same lesson for three days and meet with groups for a longer period and have a longer whole group lesson (ie 30 mins whole group, 30 mins with one diff. group one one days, rotate for three days so I can see each group). I can stay on track with the EM pacing guide for the most part, although there are times when we're a week or two behind. Then I catch up by making decisions about which lessons to teach more quickly or to combine into one. If I only had 42 minutes, I'd teach the whole group in 15, then two groups for 12-15 minutes each (appx). I would maybe break my class into 4 groups and meet with groups 1&2 on day 1 and groups 3&4 on day 2 or split my class into two groups and meet with them both on day 1. This means that you'll need two days for each lesson, so you might consider how to combine two days' worth of lessons (don't forget that you have review days and game days built into the EM pacing calandar, so it might not be too bad if you have to do it this way). (12/06/08)

I have taught EM in an inclusion setting for 4 years. My support teacher and I have organized lessons this way. We divide the class in half, roughly middle-high, and middle-low. While I teach part 1 of the lesson to the higher group first, the resource teacher further divides the other lower half into 2 groups: one group doing Math Boxes with her to help, and the other group playing a math game. They switch after 15 minutes, while I continue Part 1 of the lesson with the 1st group, including the journal pages that might go with it. Then we switch and do the whole thing again for the next half of the class. The good part is that games are played daily, and students who need support with one Math Box or other have small group attention. (12/05/08)

This is a great plan for differentiating if you have a resource teacher in your room. We have a full inclusion model, but I have no math support in my first grade classroom. This is our first year with EM. Does anyone have any working models for classrooms with only one teacher (particularly primary grade classrooms with nonreaders)? I am frustrated with the problem of trying to re-teach and reinforce for so many struggling students while other students are waiting but are not yet able to move on to practice or other tasks without an adult to supervise. When struggling students have trouble with early lessons and concepts, playing the games reinforces their errors. For example, when we play Coin-Dice the children who are still struggling to recognize the difference and value of the coins are not correctly exchanging coins. I have limited them to either dimes and pennies or nickels with pennies, but it is still confusing to them. (12/08/09)

Step one is pretesting the concepts in order to drive your instruction. (12/07/08)

### Question

I would like some feedback on pretests. Does anybody else pretest? Because the Everyday Mathematics program spirals and doesn't offer a pretest, I am wondering what others are doing who use this program. (12/14/07)

I teach First Grade and have the students do a pretest before every unit. This helps me guide my instruction and give extension work to those who already know the concept. Our school has an Assessment Assistant CD from EM that has problems for each unit. We made our pretest from that CD. (12/15/07)

Some teachers in our district are considering the previous year's End-of-Year Assessment as a pretest. Instead of giving the whole test, teachers may choose items they feel are most valuable. Either way, the idea is that the previous year's test gives a better picture of what a student knows. (08/18/08)

Check the Assistant Assessment CD for the Everyday Mathematics 3rd edition. There is a pretest on this CD for the 2nd edition. This is the only place that I know of that offers a pretest. (08/18/08)

I've given the Second Grade End-of-Year Assessment to my Third Graders as a pretest for the past several years. While I don't use the information to group them, it lets me know which concepts they've got solidly and which I will need to spend more time on. It also reaffirmed the fact that EM works. Most children really did retain the concepts. In addition, if I see a trend, I communicate with the second grade teachers that they may want to spend more time on that concept. Finally, I do share the assessments in November at parent-teacher conferences. Especially since we are in the first years of EM, I want parents to see how the program is working for their child, and give suggestions for what they may want to work on at home. (08/20/08)

I have had teachers use the Mid-Year or End-of-Year Assessments for the current grade to give an idea of what students know and allow teachers to plan for differentiation within their math groups. Students are told to try to answer as much as possible and skip what they do not know so that they are not frustrated. (08/25/10)

The Developmental Math Group has a math assessment for Pre-Kindergarten through Grade 2. They just wrote readiness forms for Kindergarten through Grade 3. If you are interested, you could contact them at dmg6@mac.com or go to their website at developmentalmathgroup.com. (08/10/10)

### Question

What do you use at your school for a Universal Screening Tool for Math? Our grades 2-5 are going to be using AIMSweb and my principal is wondering what 1st Grade should use and if Kindergarten should be screened at all. (11/12/09)

We use the Northwest Evaluation Association Measures of Academic Progress (NWEA MAP) at the end of the first semester and second semester in Kindergarten, and then three times a year for Grades 1-7. Grade 8 has beginning and middle of the year assessments, except for those students who are in Tier 2 or 3 (Response to Intervention). They get an end of the year assessment as well. (11/12/09)

Our district is piloting Assessing Math Concepts (AMC) with Kindergarten, first and second grades. We are using the Palm version, so data collection is really quick. Reports can be generated to identify specific areas of need and recommend concise interventions. AMC targets only numeracy, and we like what we see so far. You can see it at mathperspectives.com or didax.com. (11/12/09)

We use AIMSweb and it is not that great. We use Math-Curriculum Based Measurement (M-CBM) for Grades 1-3 and Math Concepts and Applications (M-CAP) for 4-5. I think the Early Numeracy is good, but our district doesn't test Kindergarten until January. Just be prepared to do lots of progress monitoring and entering data in the computer. (11/14/09)

### Question

A consultant came to our school to help us through our first year with Everyday Mathematics. She suggested we give 70% to part A (summative) and 30% to part B. Others have told us not to even count part B for a grade because it is formative. How have other schools dealt with this for Grades 3-5? (11/19/08)

Our consultant suggested 75% for Part A and 25% for Part B. Then after others told me that we shouldn't be scoring Part B, the consultant said that if the children weren't performing well with Part B, teachers may not want to score it at all. (11/20/08)

It is almost a pretest of future skills, if I understand Part B correctly. We use Part A for summative. We also add practice for the open responses and some adaptations for kids if needed. We look at Part B before we teach the unit and see what we might need to supplement. We use it for the communication grade. It's interesting that some think it should be formative. (11/20/08)

I grade part A and make it worth more points, like 4 or 5 points per problem/blank. I try to get close to 100. For Part B, I grade it like a homework assignment and make everything worth 1 point. I also grade the Open Response and it is worth 4 points, just like the rubric. (11/20/08)

I grade both Part A and Part B. If counting Part B helps a student's grade, I include it. If it hurts the grade average, I don't include it. (11/20/08)

### Question

Are there any districts out there that do standards-based assessment for skills evaluated by performance on tasks within the Student Math Journals? If so, would anyone be willing to share their checklists? (01/08/08)

We are in the process of doing this in our grade level. We began with the checklists for each unit. We looked at the goals (not including the formative assessment) and found where those skills were practiced in the Math Journals. If a skill was in the Math Journals more than once, we looked at the last time it was practiced in the unit (thinking it was more likely to be mastered by that point in the unit). Then we wrote the page number (and, if applicable, the problem or Math Box number) right on that form. Then we counted the number of skills that we found were practiced in the Math Journals (usually not all the skills from the Progress Check are in the Math Journals for that unit) and came up with a rubric for a grade. For example, in Grade Four Unit Four we found 11 skills that were practiced in Math Journals. So we decided 9-11 skills mastered would be an "A", 7-8 a "B", and so forth. Towards the end of each unit, we collect the Math Journals to grade what we call a "Journal Check". We only do this once a unit. To make it a little more manageable, I put a sticker on each Math Journal. So on a Monday I might say, "Today I am doing a Math Journal check on the flower stickers." Those kids pile their journals on my desk and I correct and return them the next day. (01/08/08)

### Question

In the 3rd edition of Everyday Mathematics, what is the difference in Part A and Part B of the progress check? Also, how do you use each part and grade each part? (10/15/08)

Part A is the summative section and provides you with information on how the children are progressing to their grade-level goals. I include this section in my grading. Part B is the formative section and can be used for long-term planning. The Assessment Handbook mentions that Part A can be looked at like the Recognizing Student Achievement (RSA) activities and Part B is much like the Informing Instruction notes in the lessons. (10/15/09)

Part A of the Progress Check is a test of what students were expected to master during the unit. Part B is more formative; it contains items and content to which students were exposed but not expected to master; or in some cases, Part B will contain a preview of material to come. Our teachers use Part A for an achievement grade; the score for Part B cannot hurt the grade, but can help if students do well. We found we need to educate our students and parents so that neither would be upset if a child did not do well on Part B of the assessment. (10/15/08)

### Question

Does anyone know if children are considered automatic with their basic addition, subtraction, and multiplication facts if they can complete a 50 basic fact quiz in three minutes? (01/17/08)

We usually count four seconds per problem in second grade if it's a written test. Three seconds to think of the answer, one second to write it. (01/17/08)

Latest research shows that every child should have 3 seconds to give the answer to any fact. That means students should never be given less than 5 minutes for 100 facts. This research also shows that those who use number sense to quickly arrive at a sum or product fair better than their peers who try to memorize. When number sense is used for fact acquisition student can better apply the facts to extensions. So I would say any child who can give the answer to 50 facts in three minutes will do very well as long as these are not memorized facts that will evaporate over time when not used constantly. (01/17/08)

Everyday Mathematics considers facts automatic if students can answer them within 3 seconds. I give 30 problem quizzes in 1 1/2 minutes. (01/17/08)

### Question

Does anyone know of a district that has re-identified the Math Boxes for Everyday Mathematics, 3rd edition? We have them identified as Beginning-Developing-Secure from the older edition and some of the teachers in our district are looking for this information to go with the new edition. If it is out there we would like to see if we can get a copy. (07/02/08)

The new edition has goals that are identified by red stars in the teacher's edition. All the Math Boxes are already done for you! Beginning-Developing-Secure is no longer used, only Adequate Progress and Not Adequate Progress. Red stars indicate goals that need to be met. (07/02/08)

### Question

Does anyone know where I can find a list of when Everyday Mathematics expects mastery of each skill? I have a teacher who wants to know at what point each skill is expected to be mastered specifically for Second Grade. (11/05/09)

One of the tools that I have found useful to determine how EM develops concepts over time is the Looking at Grade-Level Goals chart found at the end of each unit section in the Differentiation Handbook. Using this chart (for 2nd Grade Unit 1, it is on page 55) with the assessments give you a good idea of which unit a concept is taught and/or practiced for the last time. (11/05/09)

### Question

Does anyone use a math assessment wall to track student progress? In our district we have a reading assessment wall for Grades K-4 that is a large visual showing student progress through reading levels, etc. This year the district would like math to be part of the assessment wall. Has anyone done anything like this? (10/21/07)

Because of space, I use colored folders. I provide one folder for each teacher with the names of students on little cards so all of one class fits in a folder. We track their 6 week benchmark scores. I divide each folder into the grade bands, and then tape each student's card in the appropriate place. It's a great visual that I can take to grade-level meetings to show exactly where each student is on that benchmark. I also write in small numbers at the bottom of each card what the grade was, so that we can tell at a glance if a child is improving or remaining steady. (10/22/07)

### Question

I really miss the Beginning-Developing-Secure goals. Does anyone have these for the new edition for Grades 1-5? (05/18/09)

There have been several questions sent to the list over the last couple of days regarding the third edition of the curriculum. I'd like to make a couple of comments on some of the issues people have raised. One of the most important things to know is that the third edition of Everyday Mathematics remains true to the philosophy of the first and second editions. And, in alignment with our development principles, the third edition incorporates the latest educational research as well teacher feedback from the second edition. One area of change that some people have asked about concerns Beginning-Developing-Secure (BDS). In order to better explain some of the changes surrounding BDS, I'd like to backtrack a bit and discuss the evolution of EM's learning goals. Students using Everyday Mathematics are expected to master a variety of mathematical skills and concepts, but not the first time they are encountered. When Everyday Mathematics was first published beginning in the 1980s, the Beginning, Developing, and Secure labels did not exist. Feedback from users of the first edition indicated that some teachers were uncomfortable moving through the curriculum ("trusting the spiral") because they didn't know where a particular skill or concept fell in terms of the curriculum. They weren't sure whether a lesson was a first exposure or a last chance for a particular skill or concept. The terms Beginning, Developing, and Secure were introduced in an update of the first edition in order to help teachers feel more comfortable moving through the curriculum. These terms were then applied to the learning goals in the second edition. The main function of the Beginning, Developing, and Secure labels in the second edition was to provide information about the curriculum's treatment of a topic. If a learning goal was marked as Beginning (B) at a certain point in the curriculum, teachers were to understand that instruction at that point was an exposure to the skill or concept. Developing (D) indicated that the curriculum had provided prior treatment of the skill or concept, but further instruction would occur in subsequent lessons. If a learning goal was marked Secure (S) at a certain point, the curriculum would provide additional opportunities to practice and apply the skill or concept, but lessons would no longer be devoted to it. A secondary function of the BDS labels was to indicate individual students' levels of mastery of skills and concepts. These two separate uses of the same system of labels have led to problems. Feedback from users of the second edition challenged the authors to look more closely at the BDS labels on learning goals. For example, teachers asked thought-provoking questions such as the following: If a learning goal is labeled as Beginning or Developing at a certain point in the curriculum, then at what point does it become Secure? If a learning goal is labeled as Developing in Unit 1, does that mean it is still considered Developing at the end of the year? How do the learning goals connect across the grade levels? Why are there more Secure learning goals at some grade levels than others? If a child does not demonstrate proficiency with a Secure learning goal in Unit 2, when will I have the opportunity to check back to see if progress has been made? What should the majority of third graders (or students at any grade level) be able to do by the end of the year? The third edition of Everyday Mathematics addresses these questions in part through the introduction of Program Goals and Grade-Level Goals. Program Goals are the threads that weave the curriculum together across grades. These goals are organized by content strand and are the same at all grade levels. The goals express the mathematical content that all children who study K-6 Everyday Mathematics are expected to master. The level of generality of our Program Goals is quite high which is appropriate for goals that span Grades K-6. They don't provide guidance at the level of specificity that teachers need at each grade level. The third edition, therefore, has another set of goals that clarify what the Program Goals mean for each grade level. There are about two dozen of these Grade-Level Goals for each grade, K-6. They are all linked to specific Program Goals. These Grade-Level Goals are guideposts along trajectories of learning that span multiple years. They clarify our expectations for mastery at each grade level. Everyday Mathematics is designed so that the vast majority of students will reach the Grade-Level Goals for a given grade upon completion of that grade. Students who meet the Grade-Level Goals will be well prepared to succeed in higher levels of mathematics. The primary function that the BD S system served in the second edition, letting teachers know where they are in the curriculum's treatment of a topic, is met in several ways in the third edition. First, as outlined above, there is an explicit and well-articulated goal structure that spans all grades and provides detailed information about exactly what is to be mastered at each grade. Second, the Learning in Perspective tables found in every Unit Organizer and popular in the second edition, have been enhanced in the third edition. Third, the Teacher's Lesson Guide alerts teachers to lesson content that is being introduced for the first time through Links to the Future notes. These notes provide specific references to future Grade-Level Goals and help teachers understand introductory activities at their grade level in the context of the entire K-6 curriculum. Finally, the new grade-level specific Differentiation Handbooks include tables that show in which unit each Grade-Level Goal is taught and practiced within the grade. Similar tables also appear at the back of each Teacher's Lesson Guide. Unlike the Differentiation Handbook tables, these Teacher's Lesson Guide tables span several grade levels. The secondary function of BDS in the second edition, as a rubric or scale for assessing students, is also met in several ways in the third edition. Every lesson, for example, now includes a Recognizing Student Achievement (RSA) note, which identifies a task from the lesson, links that task to a specific Grade-Level Goal, and provides specific benchmarks teachers can use to judge whether students are making adequate progress toward meeting that goal. The Progress Checks in each assessment lesson have also been reorganized so that teachers can easily identify which items are assessing material students can fairly be held accountable for and which items should be used as formative or baseline assessment only. Each assessment lesson also includes an Open Response item for which a task-specific rubric and annotated anchor papers are provided in the grade-level specific Assessment Handbooks. The BDS labels are not part of the third edition of Everyday Mathematics, but the spirit and functions of BDS live on in the Program Goals and Grade-Level Goals and in the structure and features of EM 3.0. The disappearance of these labels does not reflect a change in the Everyday Mathematics approach, but rather an attempt to make that approach easier to understand and implement. We hope you will enjoy learning more about the third edition in the months to come. For additional information, please contact Wright Group/McGraw-Hill. (05/19/09)

The third edition does not use the BDS labels. Instead, grade-level goals are defined in terms of what should be mastered by the end of the year. The Recognizing Student Achievement (RSA) tasks in each lesson provide criteria for expected performance at that checkpoint-time in the year. (02/03/10)

The last page for each unit in the Differentiation Handbook has the grade-level goals broken down into "taught," "practiced," and "not a focus" for each unit. This might help. (02/03/10)

### Question

I really need suggestions for grading while using Everyday Mathematics. Do you check the Assessments in a traditional way (one point per question)? Do you use a traditional point system in your grade book, or do you look at the goals as a whole? We are going into year two, and the grading system we tried last year was cumbersome and not compatible with our computerized grade book. (07/11/09)

Our district has opted to use the rubric which is found in the Assessment Handbook. For the Recognizing Student Acheivement (RSA) problems and Progress Checks, we use the rubric. Then we get the average for our final grade for each quarter. This has worked very well for us. (07/13/09)

I use many of the Math Boxes as a "quick check" and assign 4-6 points. Students complete the first box, come to me to check, then complete the rest of the assigned boxes. In my gradebook I label the indicator, and it transfers nicely to our online grading system. The point value for each unit test varies based on the focus of our district's indicators. (07/13/09)

Grading has finally become quite easy for me in EM after a few years. Because the Math Boxes are paired, I go over the first one on the overhead after they have finished it and grade the paired box. If it is a red starred item, I make them do that first. I have also started using hint sheets this year using the blank Math Boxes at the back of the Differentiation Handbook. I grade out of 100 points. For tests I grade part A only. (07/13/09)

### Question

I'm wondering if any other school districts are struggling with grading. I have tried to convince my grade level that we should report out the way the program intends (using Adequate Progress and Not Adequate Progress), and they are convinced that they should still be using Beginning-Developing-Secure (BDS). Has anyone else run into this problem? Shouldn't the program be used as it was intended? (10/14/09)

I agree with those rejecting the Adequate Progress/ Not Adequate Progress system. I don't think that it tells parents very useful information. So, I'm using the tried and true BDS system (10/14/09)

This is our 2nd year with Everyday Mathematics. We have also struggled with how to grade, or report progress on report cards. We are currently using M (mastery), D (developing), and I (needs improvement) in Grades K-2 in order to be consistent with our reading literacy reporting. This has required teachers to develop rubrics or guidelines regarding what is enough progress for Mastery or Developing. Some teachers wish to go strictly by the assessments: either the student mastered the skill or not. Others wish to use the Recognizing Student Achievement problems as in indicator of Mastery, even if the student did not get the test question right. This has also caused some grades to re-write some assessments to be sure that a skill is assessed by more than just one item. Then the teachers decide if 2 out of 3 questions correct is Mastery or Developing, etc. for that topic. I guess the bottom line is that ours is still a work in progress, and we would also be interested in hearing what others do, especially K-2. (10/15/09)

### Question

Do the Grade-Level Goals tell me what should be mastered at each grade level? In other words, I want to know what a kid has to learn this year. Experience and exposure aren't enough. What are they expected to know-know before the next school year? (12/11/09)

The Everyday Mathematics Grade-Level Goals document in the Assessment Handbook is really comprehensive, very specific, and gives both a lateral and vertical view of yearly goals and how the ideas grow. (12/11/09)

Are you using the 3rd edition? The Assessment Handbook, page 37, gives the Grade-Levels Goals from Kindergarten to 6th Grade. It gives the content strand and the overall program goals. The grade-level goals define the specific learning goals for that grade level. Each grade-level poster lists the program goals. The grade-level goals (numbered) also list what a student is expected to know at the end of the year. (12/11/09)

### Question

In the second edition of Everyday Mathematics, there were Math Boxes considered Secure. Are there such Math Boxes in EM3? How do you tell which ones are Secure? (11/09/10)

The Teacher's Lesson Guide has red stars that indicate which goals needs to be met. A red star is a goal that must be adequately met. (11/10/09)

### Question

Is there anyone using Everyday Mathematics in New Jersey that incorporates formative assessment? (01/14/08)

Part B of the unit assessment is formative. (01/14/08)

You can use the Assessment Assistant CD to give you pretests. You can clone the actual questions and change the presentation. You can also align with your state standards. I find this to be a very useful tool. (01/14/08)

### Question

My district is looking to break down the goals that are established, developing, and secure for each grade level. Does anyone have any information that would aid in doing this? This is a new series for us and our teachers have expressed that they would "feel better" if they knew each level of skill attainment and at what points throughout the year they were expected to be secure with them. (12/18/07)

The Scope and Sequence Charts in the back of the Teacher's Lesson Guides may be helpful to you. (12/18/07)

### Question

Our teachers in Grades 3-5 are having trouble coming to an agreement on how to use Part B on unit assessments. Specifically, 5th Grade teachers feel that Part B items are often easier than Part A items. In addition, they feel that based on the lessons/activities, there are often items in Part B that students should have mastered. Therefore, they are scoring the items on Part B, not just using it as a formative assessment. They all know the philosophy of the separation of Parts A and B, but do not feel that the assessments accurately reflect the intended uses for the separate parts. Does anyone have any input regarding the difficulty/contents of Part B in Grade 5 versus other grade levels? Have you heard anything like this from colleagues? (04/08/10)

We have struggled with a similar situation. Some of our teachers were uncomfortable not grading Part B. The spiral nature of the curriculum and the formative nature of the assessment is why teachers sometimes feel that students should get credit for Part B. The credit should be in the fact that when students can show they have mastered some of Part B that the teacher will not re-teach this material, but treat it as review and probably not spend as much time on it. They should not get hung up on the difficulty. Just the opposite. In many cases they should be disappointed if some of the problems are not relatively easy for the students. The teachers really need to think of the two parts as two distinct entities, despite the titles. This might help separate the two. Part B really is the preview of the next unit, not the end of the current unit. If this was a reading program, you could think of the items in Part B that the students do understand as the content anchors, the building blocks on which the instruction is going to build. This is no different for mathematics. We do ask principals to collect unit assessment data, but only Part A. This has also helped to reinforce the difference between the two parts. Slowly, we believe that our teachers are getting more comfortable with not counting Part B as an assessment. (04/08/10)

The problem teachers face is that in many instances the Part B questions actually are based on the material that was taught in the unit being assessed. In fact, we have identified many Part A questions that were barely addressed in the current unit. Our grade level tries to decide beforehand which items we will count as summative assessment, based on our instruction rather than Parts A and B. (04/08/10)

Part A includes concepts the students should have mastered. Sometimes these are concepts from previous units, not only the current unit. For instance, if Unit 5 is on fractions, most of the fraction concepts will be in Part B of the test. In Units 6, 7, 8, and 9, students will practice those concepts through Math Boxes and other journal activities. On the Unit 9 test, Part A could very well have fractions, as by that point, students are expected to have mastered those concepts. Back in Units 5-8, fractions were still on part B, until students had sufficient practice with concepts. I never count Part B on a test since those are concepts that were taught, but at the current time, students are not expected to have mastered. The mastery comes later and then the concept moves up to part A. (04/11/10)

### Question

The Kindergarten teachers in my district have been working on a pacing guide, benchmarks, and report cards for Everyday Mathematics, 3rd edition. We have worked through the pacing and benchmarks are now wrestling with assessments for each grading period. We are finding that each of our 16 Kindergarten teachers assess the benchmarks in a different way. So we are looking for input. Is there an assessment tool in EM that would help us in this area? How are you doing with consistancy of assessment in your districts? Is anyone aware of research that would help us as we institute guidelines for Kindergarten assessment? (05/14/08)

There are awesome checklists (Beginning-of-Year, Mid-Year, and End-of-Year Assessments) in the Assessment Handbook with prompts for teachers to use as they work with the students. (05/16/08)

### Question

Does anyone have a list of the Secure goals for grade levels K-6? I am a special education resource teacher who has to write goals for the next school year. We have only begun to use this Everyday Mathematics this school year. (01/08/07)

Check the back of a Teacher's Lesson Guide. Each grade level lists the goals for the grade before, current grade, and grade after. They differeniate Beginning, Developing, and Secure goals by shading. (01/17/07)

### Question

We are currently looking at making the transition from the 2nd edition to the 3rd. I have looked at the new edition and even tried a few lessons out. My biggest questions come in the area of assessment. Is there anyone out there that has made the transition and found the assessment to be easier, harder, or just different? I saw that the Beginning, Developing, and Secure designations have gone away and the new way of assessing makes very good sense to me. Is the online assessment management system worth it? This really intrigued me, but the cost seemed rather high. If there is anyone using this tool could you let me know what you think? I like the idea of having all of my data online, but am worried that it may be hard to use myself, but even harder to train inexperienced computer users. (12/06/07)

We switched to the third edition this fall. The assessment was the main selling point for us. In my First Grade class, I try to assess some concept everyday. Sometimes it might be a journal page, a Mental Math problem, or an Exit Slip. It seems like a lot of work, but it really gives you a great picture of each child and their strengths and weaknesses. I will admit the assessments were a little daunting at first, but at this point in the year they seem to flow fairly easily. Most of the trouble comes with organization! Each teacher needs to experiment and find what out works for them. But I highly recommend the third edition. There is a big red star when you are assessing a skill. You can't miss it. (12/06/07)

Our Second Grade team decided to change our documenting of the daily assessment piece (which, by the way, is very valuable!) by comparing it to what is exactly assessed for our district report cards. We looked at the Ongoing Assessment, focused on the Recognizing Student Achievement (RSA) pieces, and now only record the lessons and test items that correlate with our report card. While we use all pieces for our instruction, it has certainly helped with organization and bookkeeping to stop recording the information we don't need for report cards. As an aside, we found the online assessment tool to be more work than just using the checklist provided in the back of the assessment book. (12/07/07)

We are in our first year of implementation. The assessment, I think is better. You have the Open Response at the end which is amazing. Plus, the Differentiation Handbook is the best part of the series. As for the online assessment piece, it makes more sense to save money. You can do everything it does with materials in your kit. However, the online Student Reference Book is amazing! (12/07/07)

### Question

What do you use for progress monitoring in math? (01/12/11)

Math Recovery probes for the lower groups and AIMsweb for everyone three times a year. (01/12/11)

### Question

I continue to be frustrated with Recognizing Student Achievement (RSA) assessments that are in the program. I teach 5th Grade and in lesson 4.2 Partial-Quotients Division Algorithms are taught for the first time in 5th Grade. In the lesson, examples are provided with a one-digit divisor and a three-digit dividend. When you refer to the Student Reference Book they also provide only one-digit divisors and three-digit dividends. Then when it comes to the RSA on page 101, there are two-digit divisors and four-digit dividends. Where is the practice before children are assessed? Why are they not taught two-digit dividends before an RSA? My main complaint is that this skill is skimmed and not taught. Why is the book set up in this manner? Are other schol districts supplementing long division and spending more time on it to ensure children's success? (10/11/10)

You've brought up two different issues here. The first is about RSAs. We went through as a team and picked the RSAs that we thought 1) were well-taught in the lesson AND 2) were a skill we thought students should have mastered by that lesson. We ended up with 3-5 RSAs per unit. We count these as "quiz grades" and check them by collecting Math Journals at the end of each unit. Lately, our math consultant has suggested we even phase some of these out and, instead, use the Writing/Reasoning questions provided in some lessons as a better indicator of understanding. We are in the process of developing rubrics to assess these. The other issue you brought up is the tendency of Everyday Mathematics to take a skill "one step further." I love this aspect of the program because it challenges our top students to generalize what they have already learned. In the case of an RSA that has problems that go "above and beyond" what you think has been taught or should be mastered, it is usually not all the problems. So we use a rubric to grade these. Students who can do only one-digit divisors, for example, would get a "B." Students who can go beyond grade-level expectations and solve problems with two-digit divisors would get an "A." Two-digit divisors ARE introduced in fourth grade, but not expected to be mastered yet. (11/12/10)

Partial-Quotients Division Algorithm is taught in Grade 4 using 1- and 2-digit divisors. Lesson 4-2 is a review of the algorithm. I believe that the RSA is to assess that the students can demonstrate the process, which they should ideally recall from the previous year. This algorithm is focused on throughout Unit 4. For students who are still struggling after Unit 4, I would focus additional practice and games on division rather than halt the program all together. As for only having 1-digit divisor examples before completing the journal page, I would make a note to include a couple of examples with 2-digit divisors during the lesson for next year. (11/11/10)

### Question

I was wondering if there is anyone out there that does the Recognizing Student Achievement (RSA) part ofEveryday Mathematics lessons differently than how the books calls for it? I have been making up short-cycle assessments for each lesson geared toward the same questions in the RSA part so I can generate more data and practice gearing up for the end of the unit assessment? (12/10/08)

Our teachers have made "exit slips" so students can write their responses or work for the RSAs. Some teachers write out the problems, others cut and paste them onto paper, and others have type them. Regardless, the teachers collect the RSAs to evaluate student progress. (12/11/08)

### Question

Should the Recognizing Student Achievement (RSA) tasks for each lesson be considered formative assessment or summative assessment. (11/02/07)

These are considered summative assessment. (11/02/07)

### Question

We are looking for ideas on how to streamline the data collected by the red-starred Recognizing Student Achievement (RSA) tasks in each lesson. I know there are the record charts provided by the Everyday Mathematics program, but is there anyone who has a different way of keeping track of these that has been beneficial? Our goal is to create leveled groupings based on the data from these red stars. (02/17/11)

We've taken a stab at this. These documents identify the red-starred items in each lesson. You can ignore the row at the top. It's an effort to link these items with our state's (Michigan) grade-level content expectations. If you aren't familiar with Excel documents, click on the tabs at the bottom of the page to move through the units. We did not create one for Kindergarten, and we don't use EM in sixth grade. [attachment included in original email.]
(02/19/11)

Grade 1.xls

Grade 2.xls

Grade 3.xls

Grade 4.xls

Grade 5.xls

### Question

Our district is in the first year of implementing Everyday Mathematics. We are discussing how to format report cards to align with the curriculum. Do other districts have report cards that describe units/objectives from EM? (01/28/09)

Our school lists the EM program goals on our report card. The program goals are the same for every grade level so the math section of our report card looks the same for every grade level. If you look at your Grade-Level Goals poster, the program goals are in bold print (there are 15 program goals total divided between the 6 content strands). For example, under the Number and Numeration strand there are three program goals - 1) Understands the meanings, uses, and representations of numbers; 2) Understands equivalent names for numbers; and 3) Understands common numerical relationships. Each grade level then has different/specific grade level goals that are listed under these program goals on your poster. Every day as I am teaching the lesson I use the checklists from the Assessment Handbook to record how the students did on the Recognizing Student Achievement (RSA) task for that day and then the checklist for the Progress Check at the end of the unit. The checklists have the content strand and grade-level goal number listed right on it so if you look at your poster you very easily see which program goal it falls under and therefore which section of our report card it would fall under. It has worked very well for us. (01/29/09)

### Question

Does anyone have end-of-unit progress reports detailing for the parents how the students performed on each concept in the unit (Secure, Developing, Needs Improvement)? We are looking into creating them to send home after each unit, and I would like to see what other schools have done. (05/04/11)

In the back of the Assessment Handbook, there are Individual Profile of Progress reports for the unit as well as a breakdown of the unit test questions. It's a checklist of standards correlated with each lesson. You can download podcasts from iTunes that teach how to use them. (05/04/11)

### Question

Has anyone developed comprehensive assessments to be used quarterly to determine proficiency levels over a span of units for report cards? My district is requesting such assessments, and I am having difficulty getting them developed due to the within-grade and between-grade spiraling. (10/20/10)

Is your report card standards-based? If it is, then use the report card to guide what your quarterly exam would contain for math content. If it is not, use the common core math standards or your state standards for your grade and pluck out the matching concepts in Everyday Mathematics that you taught that quarter. If you need to include the spiral items, limit them to 20% of the exam. Then develop your assessment using just those standards that you plucked out for that term. (10/20/10)

### Question

I am interested in getting some input into how those of you using the 2007 edition are going to be doing report cards. Are you using a checklist? Are you using Beginning, Developing, Secure? (09/24/07)

I am also wondering what others have planned on doing with their report cards. One dilemma I have is that my administration wants me to identify the learning goals that would match the Secure skills from the second edition so that all of the 6th grade report cards look very similar. This is a difficult task. For instance, if the 2nd edition report card has 14 Secure skills then I need to have 14 Secure skill for the 3rd edition report card. I was able to get through quarter 1 and 2; however, quarter 3 is very challenging. The Secure skills need to be identified so that we can use the math report card to identify students who have attained "honor roll status." One of the presenters at the Capital Area Intermediate Unit showed me a report card that was drafted by some co-workers. They set it up with the strands (as headings) and then listed the learning goals that went with each strand in the units that were taught in a quarter. There a two columns, one for Adequate Progress and one for Not Adequate Progress. (09/25/07)

This year at our school, we are doing a standards based report card, which we are calling a "Progress Report." So, we are using the Progress Check checklists along with the Recognizing Student Achievement (RSA) checklists as part of our assessment. We are only recording how the kids do on Part A of the Progress Check since that is the summative part. Also, as for Math Boxes, we have examined each Math Box page to determine which skills are assessed in each problem. We only record those problems that cover skills that have been covered. The rest of the problems are for formative purposes only. Also, problems that assess skills learned in future units are only used for formative purposes. And we only assess the second Math Box of the pair. So we are really only assessing 4 - 5 Math Boxes in an entire unit which makes this more manageable. It may seem like a lot of work but the parents will see exactly which math skills their students are consistently being successful on and which skills they need help with. The only change from the EM program is that we are using four levels, not two. Our levels are 1) consistently demonstrates skill; 2) developing skill; 3) experiencing difficulty with skill; and 4) not currently demonstrating skill. (09/25/07)

### Question

My district adopted Everyday Mathematics about 5 years ago. They have been struggling with how to assess EM for report cards. They have tried to make the old report card fit the new math program, but it really isn't satisfactory. I wondered if anybody would be able to send me a report card, or tell me how you assess it? (10/10/11)

We are using a standards based report card and the attached benchmarks give teachers an idea of what constitutes meeting or exceeding the standards.
(10/11/11)

Kindergarten SBR Math Outline.doc

Grade1 SBR Math Outline.doc

Grade2 SBR Math Outline.doc

Grade3 SBR Math Outline.doc

Grade4 SBR Math Outline.doc

Grade5 SBR Math Outline.doc

This has been an ongoing discussion at my school. We are leaning towards using the program goals and content strands (found on posters), which are the same for each grade with obvious differences in level of expectation for grade-level goals. Our math portion of the report card used to include all the goals assessed within a unit, but it was so long. Now we're hoping to streamline and though we'll keep track of student performance using the Individual Profile of Progress, we will use this more detailed info in our conferences rather than putting all of it on the report card. (10/11/11)

We took the Everyday Mathematics goals (grades K-4) and turned them into lines on our report card so that every starred assessment and unit test question (not used as a formative assessment) had a landing spot. I attached the document we use. I can't tell you how successful this report card is. We only started using it at the beginning of this year. We assess each line of the report card with a +, *, or - symbol and give an overall math grade of advanced, proficient, basic, or below basic.
(10/11/11)

Report Cards.xls

### Question

Our teachers are struggling with organizing all of the collected data to formulate report card grades. Our grades for the report card are based on the Everyday Mathematics Grade-Level Goals. It seems that to get an accurate grade for a student on a specific goal or skill, teachers have to look in so many places (Recognizing Student Achievement, Math Boxes, written tests, oral tests, Math Messages, observations, etc.) Does anyone have a system for organizing all of the data? Is there a spreadsheet that works or other hints to help? (01/23/08)

The Online Assessment Management System addresses these concerns. (01/23/08)

I am a second grade teacher in Philadelphia and I am using a spreadsheet to grade the activities giving the different weights. I can enhance it I am sure. (01/23/08)

### Question

We are using the Standards-Based Progress Report (SBPR). Teachers are struggling for a grade from Everyday Mathematics to put on the SBPR. Any ideas? (10/24/07)

We use a standards-based reporting system, and I encourage teachers to use option two found on page 27 in the Assessment Handbook as another way of grading. We are currently using EM, 3rd edition so I have aligned the unit tests to correlate with our state standards, and Part A is graded on a conversion chart to calculate a rubric grade. Our standards-based reporting system allows teachers to use several options for inputting grades so the Adequate Progress and Not Adequate Progress can be translated to a checklist in out system. (10/24/07)

### Question

We have been using Everyday Mathematics for a couple of years now and we were doing OK with a report card based on Beginning, Developing, and Secure. Now we have the new version and we have no idea how to come up with a grade. (08/30/07)

In the Assessment Handbook there is a page called, Options for Recording Data on Checklists. In my 4th grade book it is on page 27. There is an option for defining Adequate Progress on a 4 point continuum so that you have some flexibility with how you report how students are doing. In our district our report card has descriptors (Emerging, Progressing, Achieving, Extending) and the rubric in the assessment book is going to be very beneficial to our teachers. In the Frequently Asked Questions section, one of the questions defines what Adequate Progress means, and that was also helpful for our teachers to read and understand. (07/31/07)

We used EM, 3rd edition this year. My recommendation is to keep your Beginning-Developing-Secure (BDS) alignment active as you transition to Adequate Progress-Not Adequate Progressmeet. EM2 and 3 align very well so BDS will still work since you already know the program. I appreciated the "facelift" and "upgrades" in EM3 but I do miss BDS, especially in assessment conferences. (07/11/07)

### Question

I'm curious as to what other districts that are unable to purchase the 2012 edition of Everyday Mathematics are doing. I know they provided us with unit/lesson changes and additions, but they did not tell us exactly where the change was in the lesson. What are other districts doing to incorporate the changes of the Common Core State Standards (CCSS) to the 2007 edition and have you taken out lessons in order to add in the changes, such as the Algorithm Projects? (10/03/11)

There is a crosswalk on the everydaymathonline website. It aligns both the Math and ELA Common Core standards for all grade levels. It is fantastic. In order to view it, you need to have your username and password to the online site to login. (10/03/11)

### Question

Has anyone seen a correlation between the new Common Core State Standards (CCSS) and Everyday Mathematics? (11/23/10)

Yes, Wright Group has one. Contact your rep. (11/23/10)

Many of you have inquired about the Common Core State Standards and Everyday Mathematics. McGraw-Hill Education and the Everyday Mathematics authors are currently reviewing the Common Core State Standards and each grade level. We are working on a plan that includes both a correlation and the creation of any additional content by grade level needed for the program to completely align to the Common Core State Standards. Since EM is a research based program it takes time to complete this task. Both the final correlation and any additional content needed will be available by Spring of 2011, if not sooner. Initial alignment information will be available this fall. Please stay in touch with your sales representative for information moving forward. (06/28/10)

In terms of the entire set of Common Core State Standards, we believe that we are going to proceed by taking each of the grade-level standards and developing local, quarterly sub-goals. We will then develop local formative assessments to measure each of the quarterly sub-goals. It is an ambitious project that we believe will take 2 - 3 years to complete. With EM we will also have to identify where the Common Core State Standards are found within the EM curriculum and make adjustments accordingly. (06/26/10)

### Question

I am looking for pacing guides for the new Common Core State Standards (CCSS) edition. Does anyone know where I can find them? (10/17/11)

They are on the Grade-Level Goals Poster. (10/17/11)

I have also attached a pacing chart for the new CCSS edition, which will also show the number of lessons at each grade level.
(10/17/11)

EM-CCSS Edition Pacing Guide.pdf

### Question

Thank you for providing the document called Everyday Mathematics and the Standards for Mathematical Practice on your website. We have found it to be very helpful, and we are particularly interested in the Guiding Questions (beginning on page 11) but see that they are only available for units 1 and 2. When will they be available for units 3 and beyond? (11/07/11)

We spent time this fall field testing the Guiding Questions for Units 1 and 2. We are in the process of examining the feedback and looking at the current structure. We will write Guiding Questions for the rest of the units at each grade and make these available as soon as they are ready, hopefully in early 2012. (11/09/11)

### Question

I help out with schools districts each Spring to plan a math enrichment day based around a theme. It is for 4-6th Graders, and we have around 200 attend. We have done the following projects so far: building a bridge, making a quilt, and spending a million dollars. Does anyone have any other suggestions? The students work in small cross-grade level groups to complete the projects and have approximately 5 hours to finish them. (12/19/08)

You might want to look into the book One Hen, which talks about microfinance for children. There is a website that links to it, and I know that other people have done roll playing with junior high students. Additionally you may want to look at Opportunity International's information on their micro loans. (12/19/08)

How about making a tesselating geometric faux stain glass window to cover a main window in the school. You can use clear overhead transparencies, permanent sharpie markers, and the geometry templates along with a small tesselating pattern that all levels can do. (12/19/09)

### Question

Any ideas for adapting the hundreds grid for a blind first grader? She is not yet proficient with Braille. (02/15/08)

I haven't tried it, but could you trace the numbers with puffy paint? (02/15/08)

What about Wikki Stix? If you haven't heard of this product before, it is a wax-covered yarn that can be manipulated into any shape and will attach to paper. Here is a website you can check out for more information: http://www.wikkistix.com/sightimpaired.htm (02/17/08)

For the person looking for information on adapting the 100 chart for a blind student, I asked a friend who works with a blind student about what she did for this child in first grade oncerning the number grid. This is her response: The 100's chart is a visual tool, but I do believe we adapted it for A. I used a large piece of Braille graph paper and sticky Braille paper, Brailling the numbers, cutting and then sticking on the graph paper. The main reason for doing this was probably because everyone else would have one. It probably would be helpful, but if the child is not proficient in reading Braille, quite difficult. Hopefully they are working with the abacus, as that is a very important tool for learning math for a student with visual impairments. Forces them to learn their 10's factors quickly! (02/19/08)

### Question

My first grade team is very concerned about their students who are lower-functioning. They feel that these learners have difficulty with the fast-paced spiraling curriculum. Just when they start to understand a concept, they quickly have to shift gears and end up frustrated. I tried to reassure the teachers and give them suggestions for scaffolding and differentiating, but since I have not taught this program to younger children, I wasn't sure what else to say. (01/06/10)

Make sure they are using the games suggested in the program. It is in the game playing that the students get their skill practice and reinforce their understanding of number facts. (01/06/10)

I agree about the games as a critical tool for understanding. However, children struggling with concepts and knowledge need to be assisted so that they are not practicing errors during games. I like to pair them with someone who can help them during the game, give them props to help them more accurately play the games. For example, with coins, I tape coins (heads and tails) on tag board with the coin name and value written along with the coin and laminate this. This way, the children who struggle with identifying coins and remembering their values can play games like Penny-Nickel Grab, etc. Another way to help these students succeed is to add to the Mental Math problems you know they can solve and call on them to answer these questions. (01/07/10)

Tell them to trust the spiral. Each concept will be presented at least five times before mastery is expected. They are not expected to completely understand a concept the first time it is presented. It is simply an introduction and students will revisit it over and over before they are expected to completely understand it. (01/06/10)

I teach 2nd grade and we have the same struggles with some of our students. I pay close attention to the Math Box pages because they repeat the information learned in previous lessons and that gives us chances to revisit skills that may not have been retained when first introduced. Passage of time and maturity helps, and you may find that a student who struggles with a concept has finally picked it up a month later when working a similar problem in a Math Box. The skills book is also excellent for giving extra practice on specific skills, especially for those who need extra practice and more time to absorb the information. But, bottom line is that the spiraling curriculum works, but a critical component is that the student remain in that same school environment from one year to the next, staying with Everyday Mathematics. (01/06/10)

Everyday Mathematics isn't really designed to be an intervention for really struggling students, so if you have students who are really below grade level (and may be being tested for special ed, etc), it may be lacking in resources. However, one approach that is brought up quite a bit is using the Readiness activities in part three to preteach topics. In that way, students will have better background coming in. (01/08/10)

We are using Math Addvantage to assess and do interventions for primary and intermediate students who need remediation that includes multiplication and division. Intensive training but excellent. (01/08/10)

### Question

I will have a student who will need to respond to all Math Journal items and Study Links on a computer. Is there already a disk that has the pages ready for this application? (06/15/11)

We have this exact same issue and have been struggling to find an answer. Just yesterday, we learned that there is something called Book Share which is a subscription service that works with curriculum for this very purpose. Contact your special education department for guidance. (06/16/11)

You can scan the journal pages and create a word document or use Smartboard or Promethean technology for the student. (11/22/08)

I might look into scanning it into a program like Kurzweil. In our state, we are able to access Assistive Technology Teams that can assist teachers in finding ways to provide accommodations that students need. They do not need to be eligible for Individualized Education Program (IEP) services to access this team. Another thing to consider is whether the student has an IEP or 504 plan, where you could consider the student eligible for the National Instructional Materials Accessibility Standard (NIMAS). (11/25/09)

You might look or contact Infinitec (www.infinitec.org/). They have many types of assistive devices and programs with their target being students with disabilities. They may even have what you need. (05/19/10)

Our assistive technology teacher uses Adobe LiveCycle Designer 8.0 to add numeric and text fields to pdfs so kids could enter answers on the computer, then print out their completed sheets. (06/20/10)

### Question

I am looking for any research that has been done in regards to using the Everyday Mathematics program with special education students. (09/04/07)

There were no responses to this question.

### Question

I have taught with Everyday Mathematics for a few years now, but am struggling in teaching my class of 29 second graders (a number of them are "at-risk"). I have tried 1/2 and 1/2 (1/2 with me and 1/2 doing Math Boxes and math games then flip-flopping), whole class on carpet (bringing Math Message booklets and Math Journals), working together on the projector (ELMO), and whole group at seats using the ELMO. (09/07/07)

The largest class of 2nd or 3rd graders that I ever taught was 26, but here are some ways I tried to differentiate: * use cooperative group seating arrangements so that your more at-risk students are mixed with more capable students. Games, journal pages, and Math Boxes can be completed cooperatively with support. * teach Part 1 of the lesson with the whole class, circulating and monitoring. Then, as you assign either independent journal pages or Math Boxes, pull a small group of at-risk students to a separate table to work with you. More capable students can be identified as "checkers" to help on- or above-grade level students while you are occupied. On- and above-grade level students can also work on journal pages with partners while you have your small group separated and working with you. * use enrichment activities from Part 3 of the lesson to create yet another small group that can work independently while you support the less capable students * play games a minimum of 60 minutes a week. Use games as entry task or center time, include 10 minutes at the beginning or end of 2-3 lessons a week and include the 20 minutes of games that are introduced in the lessons. If your students are seated in a good mix, they can play with their table partner quickly without loss of instructional time. (09/07/07)

### Question

I would like to hear comments from Everyday Mathematics teachers and consultants regarding the unilateral decision by the Special Education Department in my district to pull all special education students, K-12, with learning disabilities from EM and put them in Saxon. I think that especially with the enhanced differentiation component in the 2007 edition there is no need to do this and fear that this will mean they will require pull-out math for the rest of their schooling as they will have missed all the EM instruction, routines, vocab, etc. What do other school districts do? (09/12/07)

Our Special Education Department uses EM, either with pull-outs in the resource room or ed-techs in the classroom, depending on the child. (09/12/07)

Our district attempts in all cases to use Everyday Mathematics for exactly the reasons stated. They need to be involved in the routines of EM to have success. (09/12/07)

I have one word for your special education group--EQUITY. They have totally lost that when they choose to change a program and instructional style that is different than the main population. Many special education groups choose procedural/non-application style programs because they either a) don't understand the way our number system works so they themselves rely on rules vs. logic or b) they still believe everyone in special education can't reason beyond basic rote. Neither is acceptable and will show up very clearly on your testing data. Speaking of data, it would be smart for these folks to research the data of Saxon schools and National Assessment of Educational Progress (NAEP) results and compare this to EM results. It is hard for me to believe anyone in your state Department of Education would support this decision as it smacks a bit like bias and moves back to pull-out vs. push-in. Maine is one of the leaders of math reform, and this is not a reformed move. My own experience in one school is that a 4th grade student showed eligibility for special education support, but found that EM methods were easier to use and produced more correct solutions than the expected traditional algorithm taught in the resource room. This happens over and over in my tutoring experiences. I have even helped high school teachers understand the workings of algorithms and the sensibility of them, so their students can regenerate their formulas and rules on their own. I apologize for my tone, but find that this question still surprises me. Having used Saxon and EM, I know there is no comparison. I also know that all students can do and appreciate math--not just arithmetic. (09/12/07)

I so whole heartily agree with the previous message about EM and special education. I have witnessed over and over how understanding works ever so much better for special education children than drill and kill. This is not surprising as it is the same for all children. Many of our special education teachers here in Anchorage use EM. How in the world are we preparing students in special education to return to the classroom where EM is being taught if our special education teachers do not use it as well. In schools where teachers are willing to arrange all math at a grade level at the same time and cooperatively plan so they are all on the same lesson (sure helps with the pacing), I recommend the students stay in the classroom for the presentation of the lesson with all other children. The special education teacher should vary the room she is in for the presentation. Then based on the difficulty of the topic the special education children may or may not be pulled out. If they are pulled out, the pull-out time is broken into 3 fifteen minute periods. Part I should be used for sticking with the goal and vocabulary of the lesson even if it means the same goal from a lower grade level. Part II should be used for filling in the potholes. These are mini lessons or EM games to pick up holes in learning from previous years. Part III should be used to pre-teach vocabulary and the main ideas for next lesson so that the students will have an edge in class the next day. (09/12/07)

For the past two years, I have been an inclusion teacher in 4th grade. The resource teachers come to my room to service their students. All of the resource students are placed in one class for each grade, then into an overflow class. Usually the ones who require the most hours are in one class, and the ones requiring fewer hours are in the 2nd class. The results we have gotten with supporting students using only EM in the classroom are phenomenal. Our resource students scored a whopping 40% higher than the rest of that subgroup in our very large county in standardized testing in math. For several years the support teachers grappled with whether the students needed an additional program or if supporting EM with re-teaching and differentiating instruction in small groups would work. Using EM works. When you remove the low performing students from classroom instruction, you take the big picture away from them. The resource kids hear the same large group lessons that everyone else hears. Many times they can be successful in conceptual areas that do not relate to their area of weakness. They feel part of the whole class. There are so many benefits to keeping them in the classroom. The extra hands (teachers) give me more time with the high performing students, we all teach everyone. (09/12/07)

You may want to visit the following website from the What Works Clearinghouse (WWC): (http://ies.ed.gov/ncee/wwc/reports/elementary_math/eday_math/effectiveness.asp). The WWC rates interventions as positive, potentially positive, mixed, no discernible effects, potentially negative, or negative. The rating of effectiveness takes into account four factors: the quality of the research design, the statistical significance of the findings (as calculated by the WWC), the size of the differences between participants in the intervention condition and the comparison condition, and the consistency of the findings across studies (see the WWC Intervention Rating Scheme). The WWC found Everyday Mathematics to have potentially positive effects on math achievement. According to the website, Saxon is listed as having "no discernable effects." (http://ies.ed.gov/ncee/wwc/reports/elementary_math/sesm/index.asp). I hope this information in addition to the other wonderful information that has been posted will help you in your dialogue with your district. (09/20/07)

### Question

Do any of your districts use different resources with your learning support/Tier 3 students besides Everyday Mathematics? Do you know of a curriculum that is directly related to EM, but is geared to this population? (02/24/10)

Our district is in the implementation phase of Help Math, a software program designed to meet the needs of the English Learners population. The company (Digital Directions) claims that their program also supports the learning needs of struggling students. (02/24/10)

I am one of the many consultants that train for McGraw-Hill for Everyday Mathematics, as well as an intervention program called, Number Worlds. There is a correlation that was created by McGraw-Hill for Number Worlds to EM. I am actually working independently as a math coach for several school districts in OH and 2 of them use EM along with Number Worlds. We have watched Tier III students grow with the use of both programs. (02/24/10)

### Question

Does anyone have any suggestions on how to effectively co-teach (special education and regular education in one classroom) Everyday Mathematics during a 45 minute class period? What is the role of each teacher? I was just wondering what teachers who have been there have done in the past. (08/27/07)

I worked with a special education teacher and she would do a preview with students. She would make sure the students had vocabulary and would do a mini lesson before the full instruction happened in the classroom. It was very helpful and the students felt successful as they were able to answer some of the questions. She would also accomodate their learning styles by using manipulatives when necessary to build concepts. She also differentiated their Math Boxes and tests to match their number range. (08/27/07)

I have taught an inclusion class for the last 2 years. I had 90 minutes, as recommended by the EM program. After the warm-ups (Math Message, Mental Math), the class split in half. I taught Part 1 of the lesson to the higher performing students (on the floor in my large meeting area), while the resource teacher was overseeing and supporting games and Math Boxes at 2 different tables. I took 30 minutes for Part 1, but the games and Math Box tables switched after 15 minutes. Then after 30 minutes, the halves of the class switched, and I taught Part 1 to the lower students, while the other half of the class did Math Boxes and games. It may sound complicated, but it worked really well. My resource teacher was a planning wizard. This routine would change occasionally if the lesson was more appropriate to large group work, such as the compass work in the beginning of 4th grade. (08/28/07)

### Question

Does anyone have some ideas I can pass along to my Reading Recovery (RR) teachers? We've adopted the 3rd edition of Everyday Mathematics this year. To quote one of them, "I keep finding that I am modifying, adjusting, and adapting the EM materials constantly or using other materials. I am hoping to find a school district that successfully serves its Individualized Education Program (IEP) students with EM so I am not re-inventing the wheel." (04/23/08)

We have a teacher of the gifted in our district who somewhat informally compacts the curriculum. She gives the end of unit tests to her students and then determines which concepts and skills she can skip or skim over and which need more focus. She also uses Exemplar problems aligned to the Units. (04/24/08)

I do not understand this approach. I find that almost every EM lesson teaches, reviews, and/or introduces several skills, including many which aren't assessed on the specific end-of-unit assessments. While I agree that this approach would work well for traditional math programs, which offer one lesson on adding fractions, another lesson on subtracting fractions, etc., I don't see how EM lessons can be skipped based on pre- or post-assessments. (04/24/08)

I am a teacher of 4th and 5th grade highly and profoundly gifted students. We have those kids in a self-contained classroom. We teach 4th grade students out of the 5th grade math book and then the 5th grade students out of the 6th grade math book. Basically we skip an entire grade level (4th). These kids need only 3-4 repetitions to learn a new concept. We are in the middle of trying to figure out how to put together a solid pre-test to give us a better understanding of what the kids know and what they do not know. Presently, I have at any given time about 1/4 of my class working on a more complex activity related to the lesson I am teaching if they pretested out of the lesson. Even if they have demonstrated success in the pre-test, I still make them do the homework for the night (normally the Study Link) which helps me be more comfortable with their understanding level. We are not happy with this method and are looking for a better method. I don't want to compromise EM spiral philosophy, but these kids only need a few repetitions to master the material. (04/26/08)

You all may want to check out a newly released intervention program from Wright Group/McGraw-Hill called Pinpoint Math. (04/24/08)

### Question

Does anyone have suggestions on how to prioritize journal pages for students who are slow to finish or struggling learners? Or strategies to help those students get the paper and pencil work done faster? I know to look for the assessment items with the red star and make sure kids do those. But I have a cluster of low-performering students who often cannot finish their assignments in the time alloted in my school day. This is especially true if I pull them to work with them on the skill for the day. They have no time left for the Math Box page if I do the other pages with them. How can I decide which things to cut back on or how to get them up-to-date with their assignments? (11/01/08)

I would suggest reducing the amount of work. Not every problem on every journal page needs to be completed. The goal of every lesson is in the objective (located on the first page of each lesson), and the work all helps aim the student at that objective. If your students need extra processing time, they may also have problems with the written parts. In some cases you may be able to scribe for them or ask them questions about what they are doing to see if they are advancing towards the goal. I find that these types of learners do better by picking up the pace and doing other activities besides written work. (11/03/08)

I have my students highlight the priority boxes with the skills we have identified as ones they should be able to do NOW. The boxes we don't highlight should be left to last. That way, if they don't get something done, it will be something that will be taught again in later lessons. (11/03/08)

### Question

How are Special Education and Title I people in your districts using Everyday Mathematics, 3rd editon? (03/05/09)

Our special education tried the program, but decided their students couldn't do it. Our special education uses Triumphs. (03/05/09)

The district I used to work for is still using the second edition, but for some of the special education classes they would use the materials from the grade level below. They made really good use of the correlation chart that tells you what lessons in the previous grade correspond to the present lesson. So while they were following the grade-level goals, they often would use the lessons from the previous grade. (03/05/09)

EM3 is our adopted K-6 math program to support our aligned curriculum. It is assumed that ALL students will have access to that curriculum. We have only variations/accommodations on it. Our Individualized Education Program (IEP) subgroup in grades 3-5 made the No Child Left Behind (NCLB) target last year, even though it was higher. (03/05/09)

1. Do the readiness activities. 2. Look in the teaching manual at what goals must be attained and focus on those. 3. Use study hall or other time throughout the week to reteach concepts. 4. Incorporate other hands-on projects. For instance, when discussing supplementary and complementary angles have students take pictures of angles in the school/community and make a PowerPoint of their findings. 5. Give students a weekly check-up and have those that are "getting it" pair up with those that are not and they can be the teachers. 6. Shorten assignments, as long as they are practicing all required concepts. 7. Only have students do certain problems on Math Boxes that are part of the current unit or that they should have already mastered. 8. Use games to help get a concept across. 9. Do an example together and then have students work in partners on a similar problem. 10. Post online math games to a website for students to play at home. 11. Read the problems aloud. 12. Focus on the big picture and really hammer at those concepts! 13. Incorporate unitedstreaming and teachertube videos to reteach concepts or get students ready. (03/06/09)

I have taken the EM "Critical Building Blocks for Struggling Learners" and created a resource handbook for supporting EM in the regular classroom. Initially it went to special education staff, but it is also being used by math tutors and aides, graduation coaches, and after school program staff. The four building blocks are: 1) daily exposure to the number grid; 2) daily fact power practice; 3) repeated practice with EM templates ("What's My Rule?," Name Collection Boxes, and Frames and Arrows); 4) Mental Math. I added EM algorithms as a fifth section. I then cross-referenced these five areas with every lesson, game, home connection, and black line master at each grade level. Attached is a pdf of this list.
(03/06/09)

Resources_.pdf

### Question

I have a fifth grade special education teacher who is wondering how to help her autistic, very low-level boys. She has three in her class, and does not now how far down to drop the level of instruction so that they will realistically benefit. They have very low reading comprehension, and their math skills range from Kindergarten to early second grade. What resources are out there from Everyday Mathematics that will help these students and their teacher? (09/19/07)

I taught EM to an autistic boy two years ago. He was a first grader at the time, and we primarily worked through the first grade EM book. However, I learned very quickly that he had an enormously difficult time with any concept that was not presented to him physically whenever possible. He had to touch and manipulate things over and over to be able to connect with them. Even very basic addition and subtraction problems had to be continuously modeled for him, or he had to have the counters to work with when doing adding and subtracting problems. He never really moved past the need to have these items. I did introduce some Touch Math techniques with him, which helped the addition and subtraction. For the 5th grade teacher you are working with, I would recommend really keeping things as concrete as much as possible and for as long as possible so the students can attach meaning to the concepts. In addition, if it were me, I would use the lower level EM manuals to provide instruction closer to their current academic level. You could use the 5th grade curriculum as your starting point, but work backwards down the curriculum as far as you need in order to build on the skills where they currently are and to make the instruction more concrete. She will probably need to get her hands on some lower-level math journals, at least to make copies from, or use the Assessment Assistant CD to build her own materials. (09/20/07)

### Question

I teach a self-contained room for emotionally impaired K-2 children. Currently, all my students are in second grade, but they are functioning below grade level. I started the year teaching the first grade Everyday Mathematics curriculum, but as the year has progressed, two students are falling behind. One is finding it too easy (but is not quite ready for the 2nd grade material), and the rest are doing just fine with the normal pacing. How can I set up my math time to meet all of these needs? The EM lessons are so involved that I don't see how I can teach 3 separate lessons each day. I thought about having part of the group do math games while I teach the others. However, due to their behavior issues, they don't work well independently at all and find games extremely challenging and can lead to fighting, cheating, and angry outbursts. (11/18/09)

In the teachers manual, there are usually extensions that students can do if they already know the concept or caught on really quickly. One of my students already knew time to the hour, half hour, quarter hour and minute, so one of the activities was to have the student make a book about time. I had him draw him during certain times of the day using different types of time (hour, half-hour, etc.). (11/19/07)

I teach a "cross-categorical" special education room. I am currently "only" teaching two grade levels of EM at once, but last year I taught three grade levels in an hour. I did have an aide, but what worked best for me was to have the students work in stations. They did 20 minutes of direct instruction with me, 20 minutes of Math Journals or other seatwork, and 20 minutes of games either with the aide or on the computer. It was really hard for me to schedule lessons and games and Math Journal pages or worksheets so that I hit everyone's independent working ability level, but we got into a routine, and it seemed to work for us. Sometimes I spread the Exploration lessons out over 3 days as the "independent work time" or with the aide, while I went on with the other unit lessons. That helped us keep on pace a little. I also had a student to whom I taught 1st grade EM one year when he was a 2nd grader and then again the next year when he was a 3rd grader. That was a really good plan for him and I could see a lot of growth in him the second time through things. Because of his extremely low IQ, that made so much more sense than sending him on through the 2nd grade curriculum when he obviously was not ready. You could maybe have your other students doing "non-math" things during the time you are doing direct EM instruction with a small group. Whatever those "non-math" things are would depend on what skills your kids are best at doing independently, reading or spelling work for instance. Then, you could schedule a Math Journal time or something like that where everyone is working on their own level, but all at the same time so you could supervise and help as needed. It would spread your math time out, but I know for my special education kids, it's sometimes a challenge to keep them thinking about math things for an hour anyway. (11/21/07)

### Question

I teach first grade and have a student who is struggling with the Everyday Mathematics program because of fine motor control. Currently I am able to adapt for him by having him dictate answers to work in Math Boxes, journals, etc. I am not able to do this all the time and it takes away from independent or partner practice. With writing he uses a computer to type his work, which has helped tremendously. His family and I are looking for ways to make EM more accessible using the computer. He is able to play many of the games on the computer, as well as practice addition and subtraction problems using Math Facts in a Flash. He is missing out on the spiraling practice, though, by struggling with the journal. Has anyone found effective ways to move this daily practice to the computer? (04/12/07)

You might be able to scan pages into the computer and make them a word document or photocopy the pages and enlarge them for hard copy use. (04/13/07)

### Question

I'm a math coach. The Kindergarten teachers at my school have enjoyed the scaffolding within the Everyday Mathematics program. However, new students and some special needs students are having difficulty keeping pace with the program. Does anyone have any differentiation strategies that I can share with my colleagues? (11/01/07)

Math coaches can familiarize themselves with Section 5 in the Management Guide of the Teacher's Reference Manual-Early Childhood which is devoted to differentiating instruction in EM. In addition, coaches can emphasize the importance of Kindergarten staff exploring the Section Opener together when planning for the month. Teachers can incorporate the suggestions made on the Differentiated Instruction pages which refer specifically to ELL, Readiness, Connections, Extra Practice, Centers, and Technology support, in their respective lesson plans. Finally, Part B offers many teaching options which address individual needs. The Teacher's Guide to Activities also provides many highlighted planning tips in the margin, along with Adjusting the Activity notes throughout lessons which offer continuing notes on differentiating instruction. (11/01/07)

### Question

I'm teaching 5th Grade math this year to three sections of students. These students may be ability grouped. At my school, only 20% of students are proficient in math, according to the state tests. Will Everyday Mathematics be "too much" for my kids, the majority of whom are coming to be below grade level? (08/11/07)

I've only taught EM for one year, but I don't think it will be too much for them as far as the skills go. The skills are appropriate and the way they are presented is great for all levels of learners. By fifth grade, though, those who don't have the background of knowing their multiplication and division facts will be at a disadvantage, but those skills are still practiced some. I personally think the problem may come in with the amount of work required of them. Quite often, the lower level students are at a lower level because of the poor study habits they have used throughout their school years. It is a vicious cycle: It takes them longer to do their work so they aren't as likely to do it, so the work becomes harder and harder as they get further behind. You know the cycle. The necessary Home Links don't get done, the last of the journal isn't completed, etc. The games, at least, will help them because they are done in class and are a fun way to practice the content. Is there after-school tutoring that the students could go to? Could they stay after school with you to work on their skills or homework? Is there some way they could have some extra, supervised time during their school day to work on their Home Links or journals? If they have internet access at home, would they play the games online? Could you send home the family game kit? (08/13/07)

### Question

My resource room teachers working with struggling students would like a list from K- 5 of all the Multiage Classroom Companion Lessons so that they don't spend time searching through each volume and grade. Does Everyday Mathematics have this available? Or has anyone else made a list themselves? (11/19/09)

See attachment.
(11/19/09)

5th Grade Multiage Classrooms Companion Lessons.xls

### Question

Our Academic Intervention Services (AIS) program is K-5 in our elementary building is serviced mainly by 3 teachers. Our schedule is made up of an array of structures. We ability group Everyday Mathematics in grades 2-5, so each of us have a low group of 10-15 kids with an aide or another teacher. We also have Special Education teachers servicing at the low levels. Two of us push-in to a primary class for one period and teach. The rest of our day is made up of pulling students out of the classroom on a rotating schedule. We service kids on a needs basis. We see most kids only once a week, but in a small group ranging from 1 - 3. Some students I see all the time, while other students may only be seen for a small period of time on a specific topic. It makes for a crazy, always changing schedule! Next year we will be cut to 1 1/2 providers, so I'd love to hear how other school district run AIS math. Does anyone use the computer lab as a resource? If so, is there a specific program you use for support? I do recommend that if you have a choice, pushing into primary classrooms (reaching problems before they develop fully in the upper grades) should be part of your program. It has been a positive experience and an avenue that has really benefited the kids. (02/28/08)

My district has no math or reading support for Response to Intervention (RtI) right now, except for Title I schools. I would be very interested in knowing just how other districts are funding their math and reading specialists to help with all this extra intervention. (02/29/08)

We have recently hit upon a strategy for Response to Intervention (RtI) that we are excited about using. Because of the nature of EM, we decided that having a different program for Tier 1 or Tier 2 intervention would confuse the struggling students even more. Therefore, we utilize EM for these two tiers of intervention. Twenty minutes each day is set aside for RtI. In second grade, we are using the Readiness portion of Part 3 to support our Tier 1 RtI learners and the compatible EM first grade lesson to support Tier 2 learners. Tier 3 learners are completely pulled out and have a separate curriculum, so we do not service them in our classroom. I also have the gifted and talented students in my classroom. A typical Math Activities session - as I have named it for my second grade students - is planned thusly: Enrichment Group: Grade 2 EM Part 3 Enrichment activities (Independent work); Practice Group: Grade 2 EM Part 3 Extra Practice activities OR compatible activities to practice skills (Independent work); Tier 1 Intervention: Grade 2 EM Part 3 Readiness activities OR Math Game to support skills (with classroom assistant); Tier 2 Intervention: Grade 1 EM compatible lesson (can be found in planning section of Teacher's Lesson Guide). We have used the Assessment Assistant CD to create pretests for each unit based on the grade level goals. At this point, this is our only way of collecting data. We are still working on finding a better way to do that so we can track progress by looking at a chart or grid. I'd be interested in anyone's thoughts on that! It's a start, and we really think it's on the right track. The EM material is all there and very good. You may have to find some supplemental materials if Part 3 doesn't have Extra Practice or Readiness, but not very often. (02/29/08)

I have been doing math remediation for 15 years. Currently, a teacher assistant and myself serve students from K-6. This year we have intensified our support for Kindergarten so that we can do more early intervention. Our program is very multifaceted in order to meet the needs of our students. Each year we meet with the classroom teachers to discuss times for push-in or pull-out opportunities. In order to accommodate all our classes, I work in 30-minute periods. I try to schedule at least one pull-out per week so that I can work in small groups with manipulatives close by. During this time, I try to either reinforce what they have just done in the class, or I preview a skill or game that they will encounter in the next couple days. The students really enjoy learning ahead of time and can often become the "go to" person during whole class instruction, which they love. There are a lot of great activities listed in the EM Teachers Lesson Guide in Part 3 of the lessons that I use more and more frequently for pre-teaching or reinforcement. I keep of checklist of secure skills for each grade level so that I can track how students are progressing in those important areas. I also occasionally schedule the computer lab to allow students to play EM math games. If I do this, I try to focus on one game that supports the unit they are working on and help them with strategies. I also have a math lab at the end of each day and students can come and get more individualized help with classwork or homework. This period also works well when students have been absent and need to make up work. (02/29/08)

Our school has used EM for many years, and this year we developed a Math Lab for K-2 students. Weak skills are identified through baseline assessments in the beginning of the year and unit assessments throughout the year. I see small groups of kids all needing the same skill usually 3x a week, which involves an EM lesson, more practice, and games. When the skill seems secure, I give an exit slip which is the same or similar to the initial problem on the unit assessment. The groups are flexible and revolving, depending on the needs of the students. I have worked out a schedule with the 16 classroom teachers, and take the kids when they are not having math in the classroom. So far this intervention seems to be working very well. (02/29/08)

### Question

Our district is in the process of adopting the Everyday Mathematics program in Kindergarten through 5th grade. Recently, some of our special education teachers questioned the program's appropriateness for children with Autism Spectrum Disorder (ASD). Specifically, they're concerned about the many transitions in a typical EM lesson. How are other districts dealing with this? Have others found EM to be the appropriate program for children with ASD? What modifications have they made to help children with ASD be successful? (05/07/08)

I am speaking as a 2nd grade teacher of a child that is on the autism spectrum. My district is not "dealing with this" as you put it. It is up to the teacher. He is a bright child child who does very well in all other academic areas. However, math frustrates him on an almost daily basis because of how abstract it can be. Some modifications I've made are to try to find one-on-one time when I can, use small group instruction, and supplement different areas (especially with time and money). EM does not correlate with our state's Grade Level Content Expectations (GLCE) and the district report card, so I focus mainly on the objectives that he should be secure with on the report card. He may miss items in the Math Journal that are not on the report card in order to receive a little bit more practice on items that are on the report card. (05/07/08)

### Question

We have a blind student who will need modified Everyday Mathematics materials next year. Does anyone how to access these materials? (05/30/07)

We have a third grade child who is going blind. We enlarge all of his materials. That works for him. (05/30/07)

### Question

What are some suggestions for our teachers who are working with learning support students that are several grade levels below their on-grade level counterparts? Based on the Individualized Education Program (IEP), we have a group of students who are being pulled, and we are not sure whether to keep them at EM 6th grade materials or to instruct them using the grade level material that matches their ability. Any suggestions would be appreciated. (09/04/08)

I have been teaching 6th grade EDM for 5 years now. With the third edition of the series, a readiness section is included (I honestly can't remember whether it was in the 2nd edition). I use these activities to preteach my strugglers the day before the lesson (or if time did not permit me to meet with them the day before, I work with them while the rest of the students are working on the math message). I find that it helps to tap their background knowledge of the concept being addressed and boosts their confidence as well. I use this with all of my students who are struggling, not just kiddos in Sped. I have used material from other grades in the past, but especially for sixth graders who are self-concious about being labeled to begin with, I find that bridging the gap between what they know and don't know is more effective. (09/04/08)

I teach a group of 2nd and 3rd graders on IEPs doing pull-out instruction on EM. I have one hour for this and an aide. My 3rd graders work in the 3rd grade book, two of my 2nd graders work in the 2nd grade book, and one is working in the 1st grade book. (He worked through the 1st grade book with me last year, too, but mastered so little of the content that it didn't make any sense for him to go into the 2nd grade book this year. We are able to "skip through" some of the very basic things, but overall, I am sticking pretty close to the 1st grade lessons for him again.) I try to keep my students working in the grade level book for the grade they are, but sometimes that just isn't going to be the best use of time for my students. But, regardless of what grade level manual I am teaching from, I end up modifying many things along the way to fit the needs of each child. What I have done for the past several years is to divide my EM hour into 3 twenty-minute blocks of time and we do rotations. During one station, I teach the lesson for the day to one of the groups. Primarily I focus on Part 1 of the lesson. Sometimes I get to Part 2, but not always. At another station, my students either play the EM math games on CD on my computers, or they play an EM math game with a partner. If there is a game that goes along with the lesson for the day, they play that, but we frequently pull in other games as well for review. For the third station, the students work on the Math Journal pages that go along with the lesson for the day. Of course, all of this is pretty flexible, because sometimes it's easier for the aide to play the game with the whole group instead of having them play alone, or sometimes the Math Journal pages take longer than I expected and we don't get to the games that day. This system has worked reasonably well for me so far. This is probably the 4th or 5th year that I have taught EM to multiple grade levels at the same time during an hour. I do a lot of adjusting of the curriculum to fit the specific needs of each student. I change Math Journal problems for students who aren't ready for a particular skill. For example, my 2nd graders can generally solve the "Whats My Rule?" problems when the rule is given, but they can almost never figure out the rule themselves. So, for those problems, I either fill in the rule or I create a separate worksheet for them with the same skill but at their level. I have a 3rd grader who works very slowly, but is fairly accurate, so he almost never has to do the same amount of problems as the other students in his group. I try to follow as closely as I can to the time schedule of the regular classroom teachers, but I am usually behind them. I have taken a workshop specifically in differentiating instruction for the EM curriculum. That was fairly helpful. One of the good things about EM, especially for the younger students is the use of routines. For example, if you get your EM time set up so that the first 3-5 minutes are spent doing the same routine every time, I've found that those skills become a part of student knowledge pretty quickly. For example, right now my 3rd graders are having a terrible time with putting 4-digit numbers in order from smallest to largest, and they are also really struggling with knowing "10 more" or "10 less" than a number. So, every morning, the first thing they do when they come to my room is grab their dry-erase boards and markers and spend about 3 minutes on the "board work" that I put on my chalkboard dealing with one of those two skills. I try to pick things that come up frequently in Math Boxes. One of my biggest frustrations with EM and the spiral curriculum is that my students usually have a very difficult time "jumping around" from topic to topic within a lesson. For example, one lesson in first grade covers Frames and Arrows, adding on a number grid, and skip counting on a number line. The next day, the lesson may cover skip counting on a calculator, subtracting on the number grid, and then penny-nickel exchange. That's too much for my students to wrap their minds around each day and not enough continuity. In the spiral curriculum, you also have to be comfortable with the fact that you do not teach to mastery every time you have a topic covered in a lesson. For special education students, this can be good, because our students don't usually "get" mastery on the first time something is introduced. At the same time, it's frustrating for them to have to switch topics repeatedly within one lesson. This is primarily why I focus on Part 1 of the lesson and make sure that within a unit I am putting most emphasis on the "starred skill" goals in that unit. When I am working with the 3rd graders, I will often look into the 2nd grade manual to come up with ideas for games that build on skills that the 3rd graders are weak in. The 3rd grade manual gives examples for each unit of where specifically to look in prior and future grade levels to make connections easier to find. As with any math series, you can also make adjustments for things like place value. If the lesson calls for teaching and ordering numbers with 5 or 6 digits, we may just work with numbers with 3 or 4 digits or whatever is appropriate for those students. Another thing that I do with my third graders a little is allow use of a calculator for some of the activities. My students are probably never going to memorize their multiplication and division facts (let alone addition and subtraction), but if they can read/hear a "word problem" and know what operation to do to solve the problem, then I am happy with that, and then they can use their calculator. We don't do this every time, but often. I do introduce the alternate algorithms that EM focuses on, but I do not require them to solve a particular problem by a specific method. I usually end up making all of my own quizzes and unit assessments that both hit the main goals of each unit and that addresses the particular needs of each of my students. (09/10/08)

### Question

Our district behavior specialist approached me yesterday with two separate issues. I would love some input on how to support these students with Everyday Mathematics. 1) Our students with Autism Spectrum Disorder (ASD) are really struggling with the transitions with EM. Moving from slate (Mental Math/Math Message) to group learning and manipulatives for Part 1 instruction, then to the Math Journal, and finally games is very overwhelming to them. Generally, our students without these types of special needs are flourishing and seeing great success with EM. However, I would love some ideas on how to help students who struggle with transitions and the frequent change of topics/materials. For more information, our schools are full inclusion, so these students participate in the general population math class (sometimes with/sometimes without a resource teacher). 2) Some of our general population and advanced placement students are also struggling with the EM curriculum. For students who have perfectionistic tendencies, moving on to a topic before full mastery can be devastating for them. We have a few students who have really shut down because they are overwhelmed with the spiral, which often doesnt teach to mastery immediately. Has anyone found a way to support these students with EM? (11/12/10)

Using cards that students can turn over as flip cards help students transition (on one side the card says slate work with a time frame indicated, on the other side the card says math instruction). The use of classroom routines can help, for some ASD students a daily checklist helps them transition. One teacher who has had several perfectionist students has the perfectionist students work together to compare answers as a means of support (11/12/10)

### Question

I'm wondering what resources people use when compacting 2 years of material into one? I am primarily looking at a group of 3rd graders who will skip the grade 3 book and move straight into the grade 4 book. Similarly, a group of 4th graders skipping to grade 5. Does anyone have a document prepared that helps the teacher with this transition? Are there good online resources people have used that are helpful? (07/22/10)

Begin fourth grade in the third grade year, and then complete grade 4 and all of grade 5 in the fourth grade year, so that in fifth grade the students are doing all of the grade 6 curriculum. We only do this with our top 5%. They can keep up with the accelerated pace. (07/22/10)

We have the 4th graders skip the 4th grade year and go right to fifth grade. We spend more time in the factors and multiplication facts as well as mathematical thinking at the beginning of the year. We also spend a while with the long division to help them get comfortable with that. By the end of the year, we whiz through the last couple of chapters and have 2-4 weeks left of the year for fun projects. (07/22/10)

### Question

Our district does Everyday Mathematics, K-5. EM was made for full day Kindergarten. Our Kindergarten is half day. Is there anyone out there that uses the EM for half day Kindergarten, and if so, did you take out lessons or do you teach every lesson? (10/14/10)

We have the same situation at our school. Our school has agreed to teach 80% of the curriculum. I present part of every lesson. I do the core activity and the routines each day (survey happens once a week, jobs changer happens once a week). I rarely get to use the Minute Math book, however we do play lots of number sense games, such as I Spy and other quick math games during spare moments. I teach about 4 lessons a week and have a parent helper twice a week help us to play games and do more involved activities. I do some of the teaching options on some days. At our school we do not give homework in kindergarten, so I also omit those activities; however I send them home, so families can choose to do them if they are interested. I also pick and choose parts of the projects. We had an EM consultant come and talk to our school about the program. I was advised to do the main activity and try to do 1 option for each lesson, as well as the routines. (10/14/10)

### Question

Does anyone have any experience or suggestions with compacting curriculum in grades K-2? We have a small group of students doing some compacting in Grade 3 and doing some enrichment, and now our Gifted & Talented staff want to do something similar K-2. (05/03/11)

I have been teaching EM for 12 years now, in two different districts at several different grade levels. This year, after earning my gifted certification, I really delved into compacting. I have second and third grade students in my math class. (A high second grader and a high third grader from another class come to my third grade class just for math.) Anyway, I start my lesson with the whole class with a slate activity. After a brief teacher led lesson, I split my students into ability groups based on a unit pretest. Each group has journal pages to complete at their desk, a game at the carpet to practice fact mastery (all EM games are very easy to differentiate and if played daily really help with fact mastery), and a teacher-led center where I can really differentiate. The children rotate among these three stations in groups of 4 to 6. Heres an example of yesterdays lesson: Teacher center: students in the high group learned to add integers using spiders and snakes and then were able to compute a solution to a number model such as (-9) + 12 = 3; students in the low group used a number line to add integers; students in a third group were still having trouble with a previous concept in the unit, so I added that to their small group lesson. Game: students played Name That Number. The higher groups had to use at least two operations and four cards. Journal: All students completed Math Box pages (this is so vital for everyone with the spiraled review). Many of my lessons come from the projects in the Teachers Lesson Guide, Open Response questions, and the Enrichment section. I also love the Internet when planning for this type of differentiation. (05/04/11)

### Question

My administrators want us to compress the Everyday Mathematics curriculum so that the students will complete this year's work by March (when we do the state test) and then start the next year's curriculum in April so that the following years students will complete the curriculum in time for the state testing of that grade. This means that every year the students will all start the following year's curriculum in April. However, Kindergarten will have to compress their curriculum every year. EM is already a tough curriculum. I am a Kindergarten teacher and I know this isn't appropriate for kindergarten but I also think it isn't appropriate for any grade. It certainly isn't taking into account individual needs of the students. Does anyone have any research/information that we can use to support our opposition to this idea? (08/28/07)

I think a much better idea would be to align the EM program with the state tests, and determine which skills on the test will not be covered in the chapters taught before March. Then teachers can jump ahead to those particular skills and be sure that they are addressed. I think if you do this, you will realize that there are very few new skills taught in the latter chapters, thus illuminating the need to compress. Sounds much easier than having each teacher teach two different grade levels and making sure they have all the necessary materials, etc. (08/29/07)

### Question

The gifted/talented teachers in my district have asked me to present a 30-40 minute session to a group of about 35 classroom teachers on compacting the Everyday Mathematics curriculum. Do any of you have knowledge or experiences that you would be willing to share related to compacting EM? (02/27/07)

We compact EM for some of our high ability students, either individual lessons or sometimes an entire unit. First of all, we give unit pretests to see which lessons within a unit a student has mastered and then compact those lessons. We look through each lesson and consider which parts/problems are repetition of previous concepts learned, and typically cut out most of that. Since it is a spiral curriculum, we don't cut out all the repetition though. We do brief reviews and then move on. For the journal pages of a mastered lesson, we will only have the students do the most difficult problems. Many times there are numerous problems that deal with the same concept/skill. Gifted students typically need to do something 1-2 times before they "get" it, so we might have them do 4 of 10 problems, make sure they understand the concept, and then not require them to do more in that page/lesson. Then, depending on the student/class/unit, we will either have them move onto the next lesson, or we will bring in some related materials that take the concept a step further. We try to use the enrichment opportunities from the curriculum as much as possible, but sometimes our gifted kids need more of a challenge. This is a process that we feel has to be fairly individualized. We really have to know where a kid is at before we'll compact, and we observe carefully while they're moving through the compacted lessons. We have often flexed kids in and out of compacting within one given unit. (02/28/07)

In the August 2006 issue of National Council of Teachers of Mathematics (NCTM) publication, Teaching Children Mathematics, there is a fabulous article about how one school provided for their highly capable math students. The article is titled "Differentiating the Curriculum for Elementary Gifted Mathematics Students." (02/28/07)

### Question

Does anyone know of any interactive websites or computer programs that help elementary students, especially English Language Learners (ELLs), develop math vocabulary? (05/13/08)

This one is awesome! http://www.amathsdictionaryforkids.com/ (05/14/08)

Harcourt's Multimedia Math Glossary http://www.hbschool.com/glossary/math2/index_temp.html A Maths Dictionary http://www.amathsdictionaryforkids.com/ Math Words http://www.mathwords.com/ Very complex (and amazing): Connecting Mathematics http://thesaurus.maths.org/mmkb/view.html?resource=index (05/14/08)

### Question

I have a second grade teacher looking for parent resources written in Spanish. Any help? (11/09/11)

This link will take you to parent help (Spanish option) for second grade: http://everydaymath.uchicago.edu/parents/homework_help/2nd_grade/ (11/09/11)

You can find the family letters here: http://everydaymath.uchicago.edu/educators/grade_specific/ (11/09/11)

Here is the link for the Spanish and English Family Letters. Many teachers want to send the Family Letters through email for those that have email or link them on their website. They are also on the new eSuites. http://everydaymath.uchicago.edu/parents/family_letters/ (11/09/11)

### Question

Does anyone know of a way to translate Home Links/Study Links to other languages, or has anyone done this? I am thinking for kids whose parents are not fluent in English. Maybe this is more of a challenge at the younger levels? Has anyone experienced this in their program? (10/05/09)

You can do it in many languages if you purchase the eSuite. (10/05/09)

### Question

I am an Instructional Coach at an elementary school that will begin a dual immersion program next year beginning with 1st grade and adding 2nd grade the following year. Half of the students would be English speaking and the other half Spanish. One model we are looking at has students learning Language Arts in English and Math in Spanish. We are using the Everyday Mathematics program. I would be interested in any comments/concerns regarding this model, and if anyone has had experiences similar to this. (12/03/08)

We have done that. It has been successful. We sometimes do math homework in English and do some test prep in English. We do English Language Arts, Spanish Language Arts, Math in Spanish. This is 3rd grade and up. Below that English is only a small percentage of the day and done orally. They begin English reading in 3rd grade. (12/03/08)

We tried that for several years and found that the math suffered a lot. The conversation, problem solving, and instruction was too much for the students to handle in Spanish, because math is more than just numbers or computation, and the students couldn't converse. We have switched to doing the math in English, and that has made a huge difference. The same has also been true with the Japanese immersion program, so they are also doing the math in English now. Once they have a strong enough language base (middle school) it was not a problem, but the model is also different in middle school. (12/03/08)

I teach at an International Baccalaureate (IB) elementary school in Colorado. We have had an immersion program for 11 years now serving 1st through 5th grades. In our immersion track, we teach Language Arts and Social Studies in English and Math and Science in French. (12/03/08)

### Question

Our district has 6 students in Grade 3 for whom we feel it would be beneficial to accelerate through the program. The goal is for them to have completed grade 6 at the end of grade 5. Because it is only 6 students, we are struggling with how to schedule this. Are there any schools that have already put such a plan into place or is there anyone who might be able to suggest how to handle this? We are trying to not have one teacher have to have two different math courses going on simultaneoulsy. (06/23/09)

At our school we have sending and receiving classes. Those classes have their math periods blocked and math is taught at the same time. Our fifth graders then are bused to the middle school. This sending and receiving system works well. Consideration is made with regard to days that there are field trips or grade level activities. In those cases, alternate assignments are planned and are completed in their homeroom. (06/23/09)

### Question

I am wanting some ideas for students in grades 3 and up who are identified as gifted and are finishing everything in each class period with time to spare. I have suggested that the teachers use the Everyday Mathematics projects. Is there anything else that some of you are using with these students? (11/04/11)

I taught in a grades 3/4 gifted classroom for several years. I used the Enrichment section of lessons and also some of the projects for my students. I also had other challenging packets I made for them that were not from the program. (11/02/11)

In the 2007+ editions, you should encourage teachers to use the Writing/Reasoning prompts on a regular basis. They connect with and extend the Math Boxes and require mathematical thinking and expository writing. Students might need modeled lessons of how to respond to the prompts initially, but they are a great enrichment and extension and can be incorporated into assessment as well. (11/05/11)

### Question

I teach Everyday Mathematics with three groups of 5th graders (90 minutes each with small class sizes). Math is the only subject I teach, so I have the time and energy to put a lot into my planning and assessing. Anyhow, I have a couple of students in the grade level who are just ridiculously above the rest of the group. These students not only scored "Advanced" on the end of year 4th grade state test last year, but they have already scored in the Advanced range for 5th grade math on the baseline assessment. Essentially, they are already beyond proficient for this grade level, and we have only been in school two weeks! What should I do with these students? I am not willing to draft them as assistant teachers, as I am paid to teach and they are not, and I'm not willing to rely solely on the infrequent Enrichment opportunities in Part 3 of selected lessons. I should also add that at least 30% of the grade level struggles tremendously with EM. (09/10/07)

One thing I was hoping to be able to fit in this year is to have some of the students script some of the games and video tape portions of it to show strategies. For example, in Factor Captor, the students could show the pros and cons of using the prime numbers and why they chose one number above another. (09/11/07)

While you will obviously have extensions for them, I would not rule out the wonderful advantage of allowing them to help others. Let's never forget the best way to learn is to teach, and it could be a wonderfully rewarding experience for them. (09/11/07)

You could get the advanced students going on a virtual math team <http://mathforum.org/vmt/teachers/orientation.html> or just working with the Problems of the Week at Math Forum <http://mathforum.org/>. The cost for one teacher is $25. Students can submit their solutions online, and it provides great practice in the complex problem solving and writing about mathematical thinking that isn't always part of the EM program. Another source of good, more complex problems is the Brain Teasers site from Houghton Mifflin <http://www.eduplace.com/math/brain/>. If you have some computer access for these students, there are many other great sites available (for students above and below grade level), like the National Library Virtual Manipulatives and Shodor Interactivate <http://www.shodor.org/interactivate/>. (09/11/07)

I would put them on a webquest. There are some really cool ones out there. Also keep them involved with your students who are struggling. Sometimes they can explain their thinking and other students lights will come on! (09/11/07)

I usually have my advanced students stay with us for the teacher directed part of the lesson, then I allow them to finish the Math Journal pages on their own, while the rest of us are working together or in small groups. Then I have them play a game with another advanced student. After that, I have mini lessons that I have developed from the Minute Math book. There are some very difficult questions and problems included in that. Also, I have something called "versatiles" that I purchased online. They are math activities that the kids love. (09/11/07)

If these advanced students have truly mastered all of the EM skills and objectives at Grade 5, you may want to look at EM for 6th Grade. I bought the 6th year Teacher's Lesson Guide and Student Math Journals for 2 students in my class. I didn't go straight through the 6th Grade book with them, but made their instruction match what the rest of the class was doing. For almost the entire year, this was fairly easy to do. For example, when the rest of the class worked on exponents, those two worked on more advanced ideas and the negative exponents which are taught on the 6th grade level. You have to manage it the way you might do for a split grade class, matching the one grade's work to the other's. If they are truly that gifted, they should need just a little bit of teaching from you, and if your classes are small you can manage this. Also, since you have more than one student, the small group can work together on some of the concepts. A word of warning: I have had students who were very gifted, but in checking carefully, I found that they often do not have all of the vocabulary and terms necessary to communicate mathematically or to do well on state testing. (09/11/07)

### Question

I was just wondering what teachers are using to meet the needs of their more advanced students in Sixth Grade who are preparing to take Pre-Algebra or Algebra in Seventh Grade. I am aware of the Differentiation Handbook and the Enrichment activities offered with the third edition but I don't feel that that is enough. Do others feel the same way? (02/24/10)

I use the Pre-Algebra problems of the week on mathforum.org (connected with Drexel Universtity) to strech the more advanced 6th graders. It costs $25 for the year. (02/25/10)

I teach 5th Grade, but my teaching colleague teaches 6th Grade math. We are in a program for highly and profoundly gifted kids. We teach the kids in the grade ahead program, but also find we need to extend those really mathematically talented kids. Really talented kids do so much better when they have big ideas to help them organize their world and all the new learning they are putting on top of existing understanding. We use M cubed for fractions. M cubed has a book for algebra you might want to look at. We mainly use Ed Zaccaro's books. He has one on Algebra. (ISBN-13: 978-0-9679915-2-8 or ISBN-10: 0-9679915-2-8) that I think will be a winner for you. We also create many of our own extensions. (02/26/10)

### Question

I am going to have a very gifted child in my class this year. His mom said he was bored with the Everyday Mathematics presented to him last year. He has already skipped a grade level (2nd grade). What do you suggest? (08/22/08)

Give him the Enrichment section of each lesson. (08/22/08)

I teach a class with highly and profoundly gifted kids. What I do is give the kids a pretest for every unit. Then I compact the lessons so they do a unit in about a week to a week and a half. Then I have a related activity to follow. Out of all of this, the pretest is the most important in my mind. If you don't have a pretest available, just give the end-of-unit test for the pretest. Just don't give them the answers for that test so it will be at least a little valid at the end of the unit. If you have a specialist in your district that person might be able to help you to fill in the gaps with the lessons/projects after each unit. I continue to modify the program each year. (08/22/08)

Use Exit Slips and Math Logs to have him write down his problem solving techniques and thinking. Use prompts to encourage him to explain his work with specific Math Boxes. Look to Part 3 of every lesson for Enrichment activities that he can do alone and with partners. If you do not have access to EM3 Open Response assessment, look for the Alternative Assessment options in the EM2 Assessment Handbook. Use a rubric to score his responses so he can see your expectations and if need be, work to improve his performance. Modify games so he will be challenged (i.e. for Name That Number, add a zero to every number card so that he is mentally calculating with 2 digit numbers). Keep track of his performance on the 'preview' activities in the Math Boxes. It will help you plan his instruction for the upcoming unit. (08/22/08)

The Projects section is filled with wonderful, challenging, hands-on ideas that may just be perfect for this child. Talk to last year's teacher to see if the projects were done, and if not, those could also be part of his portfolio. This is such a rich program that there is ample material for all types of students. (08/23/08)

### Question

Can anyone recommend a supplemental program for gifted learners, Grades 1 to 5? (09/03/09)

Everyday Mathematics (2007) has a wealth of resources for the mathematically gifted student. This includes, but is not limited, to ideas in the Differentiated Handbook, the Projects, Open Response items, and modifications to Games. If one organizes these resources into a menu (see Carol Ann Tomlinson's work on gifted learners), students may select from a list that matches the current unit, regardless of their grade level. Be cautious regarding students who may be able to quickly respond to basic facts but are less capable of explaining their thinking. (09/03/09)

As a classroom teacher of gifted learners, I agree that Everyday Mathematics has material to accommodate those kids who are maybe only one standard deviation above the mean. For those kids who really get math, what is available in Everyday Mathematics is not sufficient, at least not in my classroom. I would recommend you first look at the books by Ed Zaccaro. He gets that gifted learners need to look at things that happen around them. He spends much of his time helping the kids to organize their thoughts in many different ways. I would also check with The College of William and Mary. Dr. VanTassel-Baska is absolutely brilliant and has helped the gifted education folks immeasurably. I use one of Dr. Dana Johnsons units on bases that my fourth graders just love. They also have a Geometry unit that is absolutely astounding. Both Zaccaro and The College of William and Mary get to the heart of the joy and beauty that comes with playing in mathematics. My kids never make less than two years of growth in one year. (09/04/09)

A few helpful programs are IXL, ALEKS, and Sunshine Math. (10/03/09)

Exemplars are wonderful to use. They are aligned with EM units (look under 'alignment' on their website). Several of our teachers of gifted students have used them with good results. Many of our general education teachers also use Exemplars when they can. (09/10/09)

### Question

I am looking for ideas and strategies for differentiating for higher level learners in Everyday Mathematics. Some of our students (especially those in the intermediate grades) are slightly bored with the core instruction. These are mostly our gifted students, and they do have an excellent grasp of what's being taught. What are some ideas for pushing them, aside from having them play games all of the time? This is our first year, so teachers are hard-pressed for time to get through the lessons as it is, so I need some good, practical, and easily implemented ideas. (12/12/08)

I really like the Groundworks series also published by Wright Group. Titles include Reasoning About Measurement, Reasoning with Numbers, Reasoning with Geometry, Reasoning with Data and Probability, and Algebraic Thinking. The set of books cover each one of the five National Council of Teachers of Mathematics (NCTM) standards, and are available for different grades. I use these with gifted students who love the additional challenges in these books. (12/12/08)

I have used the Family Math series published by Equals/Lawrence Hall of Science. The volume for middle school level worked well in centers for advanced 6th graders and the Family Math Volumes I and II have activities at many levels. (12/12/08)

### Question

I have a parent asking for summer work for her daughter entering second grade. She is at a very high level. I hesitate to give her anything from the Everyday Mathematics CD, as she is likely to get that next year in class. The last thing she needs is redundancy. Any ideas to challenge her in a big way and keep her interest level up? (04/28/08)

Are you using the new EM edition? I am asking because I was thinking about suggesting something along the lines of the Open Response questions. You could generate a list of questions that follow that format or use the actual Open Response questions if you didn't this year. It is great that she is high in math but it might be nice for her to explain her thinking. You could even ask for copies to be sent to you when she returns to school in the fall and use it for sample models for next year's group. (04/28/08)

It sounds like she would benefit from some additional rich problems. Two books from the National Council of Teachers of Mathematis (NCTM) that would be helpful for you to find some things for her are: Children are Mathematical Problem Solvers and Exploring Mathematics through Literature. (04/28/08)

Playing the EM Games can be both fun and challenging. Make copies of the directions and game sheets and send them home for the summer. Also, if your school district has the EM games online, she could challenge her skills that way. Introducing her to some of the second grade games may be the answer. (04/28/08)

Have you already used the Enrichment activities from Part 3 of all the lessons with this student? If not, I'd suggest going through all the 1st Grade lessons and selecting enough to give this student 1-2 per week. Then, perhaps put them in a calendar format. If you know you'll see her next year, maybe 'cut a deal' with the student and have her keep the completed work in a folder to bring to you in the fall for a special treat. Throw in playing certain games each week/month also. Then, the folder could contain the manipulatives for the specific games you suggest. Or, tell them how to make a math deck out of a deck of cards. I would also review the Explorations from the past year. You might consider including some of these as summer activities as well. And, how about the projects? She might enjoy making delightful boxes. If you make 2, you can fit one inside the other like a gift box and you can make them in various sizes. EM actually makes prepared Family Games Kits that would be perfect to send with a child over the summer. The parents can actually purchase the kit from the Wright Group website (www.wrightgroup.com). Finally, check out the alternative assessment ideas in the Assessment Handbook. I know you're not assessing this student, but it might give you some good ideas for more open-ended activities to include that require higher order thinking skills. To that same end, I would consider making Name Collection Boxes, "What's My Rule?" and Frames and Arrows copies using more advanced numbers and/or computations. I believe there is also a section in the Teachers Lesson Guide that refers to popular children's games that help develop math skills, such as Racko and Yahtzee. (04/28/08)

### Question

My district is currently in the process of adopting the new Everyday Mathematics, 3rd edition program. It is a wonderful program for my first graders, and they are really enjoying it. However, I have a problem. I have a student in my room who is gifted in math and is preforming at beginning third grade level. How do I incorporate his needs into my classroom? He needs more than differentiating the First Grade curriculum. He needs Third Grade curriculum, but due to maturity issues it would not be appropriate for him to go into a Third Grade classroom for instruction. Because we devote so much time to math, I feel it is difficult to find the time in the day to teach the hour or more of math to the rest of my class, on top of trying to meet the needs of this one student. Is there anyone who has been in this same situation, and how have you been able to meet the student's needs? How has the administration in your building supported you in determining how to best meet the student's needs? (10/08/07)

I would suggest using a number of the Open Response assessments and activity opportunities that EM3 provides to challenge this student. Look for the Writing/Reasoning prompts that accompany many of the Math Boxes. You can find reference to these in the Teacher's Lesson Guide Unit Organizer in the section about Math Boxes. There are also blank blackline masters at the back of the Differentiation Handbook that can be adjusted for any level. There are blank Name Collection Boxes, Frames and Arrows, and more. Another idea would be to go to the Projects section at the back of the Teachers Lesson Guide and either use one or two projects for the student to do independently or develop a similar project as an extension to the ones that are there. Finally, I would use the Open Response tasks in the Assessment Handbook to challenge the student to think critically and to illustrate and write his response. You may want to vary the challenging work you give the student to include both paper/pencil, exploration activities, and long term projects. Be sure to include activities that incorporate the use of manipulatives like pattern blocks and geoboards. (10/08/07)

### Question

My school district uses Everyday Mathematics, 3rd edition and is thinking of having a select group of students skip 5th Grade math and go directly to 6th Grade math. We are interested in seeing if any other districts have found success with this model. If so, how did you reinforce the skills that the students may have missed because they did not use the 5th Grade materials? (04/18/08)

My district uses this model of acceleration for 3rd, 4th, and 5th Grade students. Our initial screen is through standardized testing which creates our pool of potential students. Then we give the End-of-Year Assessment for the grade level they would be skipping (ie. an incoming 4th Grader would take the 4th Grade EOY). We base our invitation to participate in accelerated math on a score of 75% or better on that assessment. Our experience is that there is very little remediation that needs to occur with regard to the content in the year skipped. These students have a solid understanding of mathematics and can make up any lost ground very quickly and easily. We identify students in the spring of the prior year, so students can be cluster-placed among a few classroom, and then pulled at the same time their class is having math. This serves as less of a disruption to teachers and students. (04/18/08)

In my district we compact the Fourth, Fifth, and Sixth Grade curriculum into two years. Students begin this compacting in an accelerated math group in Fourth Grade, and by the end of Fifth Grade they have completed Sixth Grade math. We feel this is preferable to skipping an entire year of the curriculum. (04/18/08)

### Question

Our district is in our first year using Everyday Mathematics. We have a history of pretesting and accelerating students. That has been put on hold this year in favor of more differentiation, as we feel all students needed to learn the routines and vocabulary in EM. Teachers are starting to ask about next year, however. Do any of your districts accelerate students through EM? If so, do you use the End-of-the-Year Assessments to determine which students might need this, or some other diagnostic tool? A special population we are trying to service is a small group of students who will be 5th graders next year. We are trying to collect data to see if the 6th grade EM is appropriate, or if Transition Math is a possibility. (04/28/09)

I would recommend moving the students into Transition Math to give them the strong pre-algebra foundation since they are accelerated. (04/29/09)

### Question

If anyone has specific ideas on how to level homework for the high level learners (to enrich and extend on the skill rather than skip to the next grade) please advise! (10/07/10)

Have you tried Exemplars? They might be exactly what you are looking for. (10/12/10)

Have you used the Writing/Reasoning prompts to challenge your students? What about using the Assessment Assistant CD to create more Open Response opportunities for your high achievers? Have you tried changing the difficulty level on the games as suggested in the Differentiation Handbook? I think the blackline masters in the Differentiation Handbook can offer plenty of challenge, if you want a paper and pencil format, since you plug in the level of difficulty yourself. (10/13/10)

### Question

We have an interesting dilemma here. We have one 4th Grade student who is exceptionally gifted in math. I tested him on 4th Grade skills and was convinced that he was not going to learn anything new using the 4th Grade Everyday Mathematics, so we moved him into a 5th Grade classroom. He is doing very well in 5th Grade. The problem is that this is a K-5 building, so we are not sure what to do with this child for next year. We are fortunate that we have the 6th Grade EM to use. However, we have no one to deliver the instruction. The gifted teacher and I only spend 1 day a week each in his building, and his classroom teacher certainly cannot deliver an entire curriculum to just one student. Is there anyone out there who was faced with a similar situation? (03/21/07)

I would suggest using the Learning in Perspective page and the Multi-age companion lessons for each unit. In that way the student will be working on skills that the class is working on, but on his own level. (03/21/07)

I teach Fifth Grade, and one year we had one student who had done the Fifth Grade EM in the Fourth Grade. I used the Sixth Grade EM with him by giving him a weekly lesson for the 4 or 5 lessons each week. He then worked on his own, using the CD to check his book. As the classroom teacher, I checked in with him every other day to see where he was at. He would come to me if he had problems; otherwise, he worked independently except for that one lesson a week. It wasn't the best way to teach the program, but it was the best I could do that year. Whenever I had a volunteer come in, they also worked with him and the one-day a week Gifted/Talented teacher also checked on him. (03/21/07)

An option to this type of situation, above and beyond using the differiented activities or the projects would be to match lesson type using the scope and sequence of unit lessons which appears at the beginning of each lesson. In that way he would be working on the same skills, but at a parallel level of concept use and understanding. I did this for both below-grade level and the above- grade level when I was a Grade 4 classroom teacher. (03/21/07)

Our K-5 school set up an after-school enrichment class for several 4th and 5th graders who were ready for 6th Grade instruction. A classroom teacher worked an extended day to meet the needs of these students. It worked out really well for meeting the students' needs, but it did present challenges for the regular classroom teacher during math instruction. I think it would be tricky to do this with only one student. (03/21/07)

### Question

Are there any pretests to see if students know the material in any given chapter. I know there are a couple of questions at the end of the tests, but not enough. The games are easy to separate by levels. Other than simply looking at their class performance during classroom activities and informally placing them in groups, how are other people separating the students into instructional levels? Now we're making up our own pretests, which is a pain. And are there other ideas for enrichment besides the projects and the occasional Enrichment problems? Or is this program being primarily taught to the whole group at once? (02/05/09)

We're using the Assessment Assistant CD to create pretests for each unit. Our students are separated into instructional levels for each unit based on the results of the pre-tests. (02/05/09)

### Question

I am a math coach in Seattle Public Schools and in charge of a project to identify exemplary methods and teaching examples of how to differentiate a typical lesson. This would be outside the realm of merely plugging in the Readiness piece or enriching for a particular segment of a classroom. In essence, the question is how to properly pretest and target specific groups within the classroom, then how to manage a lesson in such a way that the key concepts are properly introduced, but the experiences or options to explore the concepts is differentiated. How does this look? How is this best managed? (12/05/08)

At the recent National Indian Education Association's (NIEA) 39th Annual Convention in Seattle, there was a presentation that would answer some of your questions involving exemplary methods, teaching examples, differentiation outside the realm of plugging in what is in the book, and assessment. The presentation was titled "A Math Partnership that Leaves No Child Behind." Some of the presenters were from the Marysville School District. Dr. Kyle Kinoshita, Executive Director for Teaching and Learning was a co-presenter representing the administration from that school district. (12/05/08)

I teach EM in centers, similar to the previous reply, but I'm the only teacher in my general ed classroom. I teach the math message and mental math to the whole class, then split the class into three groups: Math Boxes, Math Games and Teacher Center. At teacher center on Mon-Thurs I teach the bulk of Part 1 for each lesson, differentiating my approach and instruction for each group (below grade, at grade and above grade). Then on Friday I conduct either a formative or summative assessment in place of the math message/mental math and during the teacher center I either re-teach concepts that kids still don't get or push kids who are mastering all math concepts. Our math block is 60 minutes. I have 28 students and teach the lesson in one room, self contained general education, 4th grade. I teach the whole group for about 15 minutes, then do three rotations of centers for 15 minutes each. Sometimes if it is a hard concept, I'll teach the same lesson for three days and meet with groups for a longer period and have a longer whole group lesson (ie 30 mins whole group, 30 mins with one diff. group one one days, rotate for three days so I can see each group). I can stay on track with the EM pacing guide for the most part, although there are times when we're a week or two behind. Then I catch up by making decisions about which lessons to teach more quickly or to combine into one. If I only had 42 minutes, I'd teach the whole group in 15, then two groups for 12-15 minutes each (appx). I would maybe break my class into 4 groups and meet with groups 1&2 on day 1 and groups 3&4 on day 2 or split my class into two groups and meet with them both on day 1. This means that you'll need two days for each lesson, so you might consider how to combine two days' worth of lessons (don't forget that you have review days and game days built into the EM pacing calandar, so it might not be too bad if you have to do it this way). (12/06/08)

I have taught EM in an inclusion setting for 4 years. My support teacher and I have organized lessons this way. We divide the class in half, roughly middle-high, and middle-low. While I teach part 1 of the lesson to the higher group first, the resource teacher further divides the other lower half into 2 groups: one group doing Math Boxes with her to help, and the other group playing a math game. They switch after 15 minutes, while I continue Part 1 of the lesson with the 1st group, including the journal pages that might go with it. Then we switch and do the whole thing again for the next half of the class. The good part is that games are played daily, and students who need support with one Math Box or other have small group attention. (12/05/08)

This is a great plan for differentiating if you have a resource teacher in your room. We have a full inclusion model, but I have no math support in my first grade classroom. This is our first year with EM. Does anyone have any working models for classrooms with only one teacher (particularly primary grade classrooms with nonreaders)? I am frustrated with the problem of trying to re-teach and reinforce for so many struggling students while other students are waiting but are not yet able to move on to practice or other tasks without an adult to supervise. When struggling students have trouble with early lessons and concepts, playing the games reinforces their errors. For example, when we play Coin-Dice the children who are still struggling to recognize the difference and value of the coins are not correctly exchanging coins. I have limited them to either dimes and pennies or nickels with pennies, but it is still confusing to them. (12/08/09)

Step one is pretesting the concepts in order to drive your instruction. (12/07/08)

### Question

I am looking for ideas to teach Everyday Mathematics in small instruction groups for part of each day. We are hoping this will better help with differentiation and ultimately improve understanding for our students. I appreciate any ideas. (11/16/09)

In EM there is a built-in small group opportunity. Dividing the class into three groups, you can have one group working on Math Boxes, one group playing the games, and one group receiving small group instruction. I taught a whole group for fifteen minutes, then broke mine into groups, with the groups rotating every 15 minutes or so. We have sixty minutes for math, so it works well. If I saw problems with any Math Box, I could have the group bring the journal to the small group instruction and use that time to work with any calculation errors and misconceptions as well as target instruction to work on weak areas for that particular group. (11/16/09)

I too use small group instruction with EM. I teach both 1st and 2nd Grades, so I have two 1st Grade groups and two 2nd Grade groups. I have 4 stations every day: me, Math Boxes, and then stations 3 and 4 vary (EM game, differentiation activity from the Differentiation Handbook, computer math activity, secure skill, or some other game). When the kids are with me, we first go over their Math Boxes from the previous lesson, and then I work with them on the current lesson. I love it and so do the kids. (11/17/09)

### Question

Most of the grade levels at our school flexibly ability group for math instruction. One grade level in the middle of the others prefers not to do this. Our test scores indicate that ability grouping is a successful strategy. Our students like it, and the parents in our district support it. Are there schools that are doing ability grouping using Everyday Mathematics and are finding success with it? (05/12/11)

Tracking in math is much worse than tracking in reading. If you put a child in a slower track in math, they will never catch up! In a few cases here in Anchorage, teams group by unit. The children needing more time for understanding in Geometry are different from the the children needing more time for computation. Even when this format is used, every teacher stays with the pacing chart and every teacher in the team is teaching the same lesson on the same day. Some will be going deeper for understanding and some will be getting an enriched version, but when the year ends, every teacher in the team finishes the program on the same day and no child is left finishing only one journal. (05/12/11)

We have some teachers who would love to split the students in their grade levels into groups at the beginning of the year and take them as far as they can go during the year. They have a hard time understanding that this does not enable children to move among the groups and that they may have real struggles with some concepts and a strong understanding of others. It's great to hear that teachers, if grouping, are doing it based on the concepts introduced in each unit. Some of our teachers have been working hard this year to use small group instruction (with students grouped according to need based on our common assessments and/or the multitude of assessments, formal and informal, in EM) after the whole group lesson. They see great advantages with this system. The one stumbling block that they all face is the time to do everything well. (05/12/11)

I have to respectfully disagree to a certain extent. I teach 1st Grade in a Title I school. I still have a small group of children who, even with interventions, are still working on the basics such as counting by 1s, 2s, 5s, and 10s to 110, and naming and identifying coins. My district does not test for special education before 2nd Grade (except extremely rarely). It is very difficult for them to do what the rest of the class is doing in math. This is why I love the guided math approach. I model it on "to, with, by." I change groups at the end of each unit, and they are flexible. I have had students go from group 2 to 4. (05/12/11)

We have started flex grouping in Grades 3-5 primarily to help differentiate for high achieving students that do not meet our Gifted and Talented (GT) criteria. We have several students in each grade level who are at about the 95th percentile on the Northwest Evaluation Association (NWEA) Measures of Academic Progress (MAP) tests but do not qualify for GT services. These students were taking pretests and scoring 80% at the beginning of a unit. We modify the EM curriculum for these students by flex grouping and then compacting the unit for which they tested high to a length of 5 or 6 days. For the rest of the time in that unit they work with materials from the grade level above that cover the same content as the original grade level unit. It is relatively easily to do that because of the spiraling. So, all of the students spend the same amount of time on the content, but some work from the grade level above for about half of the unit. If they pretest out the next year, they can spiral up again. If they do not pretest out the next year, then they are actually doing the same material twice. That is OK since they havent yet mastered it. We pretest each unit. Next year, we are striving to work with this model in Grades 1 and 2 as well as 3-5. Two challenges have surfaced. One of them is building scheduling. We have about 4 classrooms per grade level, and for this to work best they all need to teach math at the same time. The other challenge is that the top students have left the room and taken some of the leadership. However, the students remaining are not a slow group, they are a simply a group that has not already learned 80% of the content for that unit. We are finding so far that it is easier to deal with that than differentiating the top end with challenging material on a regular basis. (05/13/11)

### Question

Should schools using Everyday Mathematics ability group kids for math groups? Why or why not? Our teachers are really struggling with this. They think we should be ability grouping our classes and our administration is under the impression that leveling or grouping is not an accepted practice. (09/17/09)

I do this to a certain extent in my classroom. I teach a 1st/2nd split. I have 4 groups for math (2 for 1st and 2 for 2nd). I have them somewhat divided by level so that I can provide enrichment for the higher kids, and reinforcement for the younger ones. I have 4 centers each day: me, Math Boxes/worksheet, and the last two are either a game or computer math. This is the first year that I have done it this way, and both the kids and I love it! (09/17/09)

Our school created an "Honors" homeroom. They use a different math program. There have been pros and cons to this. The other EM classes still have some strong students who really get a chance to shine and assist in small groups with those who struggle. I have noticed more of a need for guided instruction than independent work though because of the new dynamics in each class. Because the gifted students end up not being in the EM classes, they aren't leveled or tracked in the traditional sense, but they are more homogenous than in the past. (09/17/09)

This summer I spent quite a bit of time researching various ways of leveling as well as looking for results. We had been leveling with 2 levels and tried a few teachers doing heterogeneous grouping last year and wanted to know what others were finding. One of the things that we heard is that the teachers who had been teaching struggling students noticed a big difference in their class participation and in their own feelings about how class went. When there is a group of students who feel they never get it, they tend to not ask questions and if everyone around them is in the same boat there are not a lot of peer role models for them. When there was mixed grouping, the overall flow of the class changed, suddenly there were students asking questions and students who never asked were realizing that they werent alone when something was unclear and started asking questions as well. In that light, there was success and the struggling students did better in the mixed grouping. We are also providing interventions for all students depending on the needs of the student. With leveling the needs of two classrooms are different which puts more of a burden on individual teachers for the interventions. However, because the interventions apply to the majority of the class they are easy to do whether skill or concept based. With leveling, the classes are taught to the higher students and interventions provide the extra support for those who need it. With the mixed groups, were finding that the class is taught to the middle so some require intervention support and some have their interventions in the way of enrichment. Those who need enrichment are more the students who can work independently; while others in the class are receiving support interventions. This does create a problem as the intervention needs change on a daily basis. We arent using the EM Projects as enrichment in school, but they are used outside of school. Some of our enrichment is to experiment with the games and look closer to see how they work and develop strategies, while some of the support interventions come from the need to enhance basic skills (which may be vocab or various things from the readiness activities). For those using a Response to Intervention (RtI) model, most of these we consider in-class or Tier 1 are available to all students and are very focused on the immediate needs or for the upcoming lessons. (09/18/09)

### Question

The school that I teach at has two classrooms of 3rd, 4th, and 5th Grades. We have been using Everyday Mathematics for approximately 8 years. We are considering taking all 100+ students and grouping them according to where a beginning of the year assessment would place them. Then they would be in EM curriculum at the grade level that they are functioning at, not necessarily their grade level. The reasoning behind this is that even with modifications, differentiation, and utilizing Part 3 of the lesson, we continue to have some students who are one to two years behind grade level. It is not making much sense to some of the teachers to keep pushing them through the program, not having mastered any of it. Has anyone out there tried something like this? (05/27/10)

EM just came out in the last few months with an Assessment Handbook that had Beginning-of-Year Assessments for all grade levels. (05/27/10)

### Question

We are beginning to take our Everyday Mathematics games and level them by adding a simplified version and possibly more challenging versions. Has anyone out there begin doing this? And do you have any suggestions or samples? (05/21/09)

There is a great guide at the beginning of each Teacher's Lesson Guide that might help. It's called Games Correlation Chart. It can be found on page xxxii. You can see at which grade levels the game is taught, which will help to differentiate it. You could go to that grade level and see how it is taught or look at the chart and go up or down a grade level to find a game that is similar. Also, the Games Section of the My Reference Book (MRB) or Student Reference Book (SRB) will differentiate the game sometimes. (05/22/09)

### Question

We are working on flexible groupings with Third Grade in Everyday Mathematics. At this point we have three groups which are ability based and change frequently. The whole class receives the core of the lesson and then students are broken up into their groups. If you have had success with this, could you please share what occurs in each group during the break out sessions? I'm working with an on-level group and am struggling with the teacher expectations during my group time vs. student needs. If you group students with different teachers, do you follow what the teacher wants done in the group or do you plan the group based on what you assess the needs to be? (09/13/11)

We have seen marked improvement on state testing scores in classrooms using this model.
(09/13/11)

Model.pdf

### Question

We will have about 45 Fifth Graders next year in two homeroom classes. I will teach math to both groups. We have the option to keep each homeroom as it is, or level the two classes. Which do you think is best? If we do level the kids, we will retest after every unit to see if groupings need to change. (08/11/08)

I've done it both ways. This year our Sixth Grade team is going to try it with mixed grouping. Iin the Fifth Grade class I was in last year, we did some leveling but we didn't do it evenly. We based it on the state testing, the higher 2/3 were in one math class and the other 1/3 was in the other class. This way there were about 30 more independent students in one class and 18 students who needed additional support in the other. We had 3 groups of this. There were pros and cons to both ways we've done it. On the pro side of things, you have fewer problems of losing people as you can pace the day appropriately. However, we did find that we had more discipline issues in the smaller class. Personally, I like having a mixed group and not leveling the students. I found that it works better for my students and me. (08/11/08)

The research is pretty straightforward on the "pros and cons" of ability grouping. When you narrow the populations, you limit the impact of positive role models, both skill-wise and behaviorally. There are better ways to differentiate instruction within mixed ability groups that are far more effective than grouping kids by test scores. In EM3, there are very good resources for differentiation. (08/12/08)

### Question

We have a new Fourth Grade student who is very capable in all areas. She is a very high reader but is lacking in math. This is due to the lack of exposure in her old school. For example, she was never taught to skip count. She has been given the First Grade End-of-Year Assessment for Everyday Mathematics and did okay. We are looking to do 6 weeks of intervention with this student in hopes that she will make great gains since she is very capable. What suggestions do you have on how to spend this intervention time? Should we focus on one topic and follow it through all the grade levels to fourth? Or skip around? (09/19/08)

I have had students come into my classroom that do not have the Everyday Mathematics background, and what I have done is partner them up with another student. Give it a month or two and they will assimilate into the program. They will start to understand the rules and routines and the spiral in the program is so effective for these new students. (09/19/08)

### Question

We have one or two students who are currently in the Third Grade classroom for Everyday Mathematics. As the end of the year approaches, the classroom teacher and special education teacher have put out the idea of having these students repeat Third Grade EM again next year. As the math coach for our building, I'm not sure I agree with this idea as they will completely miss out on the Fifth Grade program before entering middle school. Has anyone else encountered a similar problem? Did you send the students on to the next grade level with extra support or keep them back in math? (03/23/10)

I teach K-4 special education and have been a part of both self-contained math instruction and inclusion instruction with EM. I have only had one instance in 4 years where I had students repeat a year of EM. In this instance, I did a full year of self-contained EM instruction with two conduct disorder (CD) 1st Graders. At the end of the year, neither had mastered more than a scant handful of the end-of-the-year skills. Because I was going to be their math teacher again the following year, and because it was a self-contained situation, I went ahead and spent their 2nd Grade year repeating the 1st Grade EM curriculum. In those areas where they had already mastered the skills, I looked to the 2nd Grade book for the next level of instruction. I was pleased with the results and felt that it was a good fit in my situation, but I don't think it is a blanket cure for everyone. Are the students you are talking about identified as special education with Individualized Education Programs (IEPs)? Do they have a Specific Learning Disorder (SLD) or Conduct Disorder (CD)? Are they participating this year in Everyday Mathematics in the regular classroom with their same grade peers? What would that look like next year? Would they be special education fourth graders going into a regular education third grade classroom for math? I have had special education students who struggle with EM in the regular classroom setting. In general, either I give them extra support or an aide goes into the classroom during their math time. It is also good to remember that the items written into student IEPs will drive the focus of their curriculum, so even if they are in the regular class and struggling with concepts, you can make adjustments for them within the classroom setting and with assignments and such in order to help them meet their IEP goals while benefiting from what they can from the full scope of the EM curriculum. (03/23/10)

I would recommend mapping out a long-term plan for this child that goes way beyond repeating 3rd Grade. What will you do in 5th Grade? What is the plan for when they enter middle school? What is the plan for getting them eventually caught up? Or is the plan to keep them a year behind indefinitely? Personally, I would advocate using the 4th Grade curriculum, but making use of the correlation chart that gives the corresponding lesson in the 3rd Grade curriculum. Take full advantage of the spiral, focus on the same concept the 4th Graders are working on, but draw on the 3rd Grade lesson to scaffold. (03/18/10)

I would advise moving him on in EM and be prepared to differentiate instruction as needed. Even though the student will not be able to do all the work at the next level, because of the spiral in EM, he should be successful with parts of it and he will at least get exposure to some of the more difficult concepts. (03/23/10)

I developed an alternative for struggling students. Rather than trying to reconstruct the entire spiral and thus locking students into being a year or two behind grade level, I took a list of 4 critical building blocks as well as the Algorithms and compiled a list of all the resources available at each grade level. It's attached if you'd like to see it.
(03/25/10)

Resources.pdf

### Question

Can anyone recommend an early childhood intervention program that supports Everyday Mathematics to use with struggling Kindergarteners? (06/16/11)

Number Worlds level A or B. It lines up with EM. (06/16/11)

I would suggest that you investigate Math Perspectives. The diagnostics lead into appropriate work to do with the child. (06/16/11)

I would suggest Moving With Math-Extensions Kindergarten. (06/16/11)

### Question

Are there any schools that use Everyday Mathematics with their primary students and also use a supplementary program for the lowest students? This can be for Response to Intervention (RtI). Do you find the other program is helping those students be more successful than by just using the EM program alone? (03/18/10)

Next year, we are planning on using Number Worlds as well as EM for our lowest students. (03/18/10)

We use Number Worlds as a Tier 3 intervention, with students who are far enough behind their peers that they are not likely to catch up. It replaces EM for their math program. We use Pinpoint Math as a Tier 2 intervention for kids who need some extra help to keep up with their peers. They do it in addition to EM. They are tested to find areas of weakness and meet in small groups to address those lacking skills. (03/18/10)

There are several school districts in central Ohio are who are using the Number Concept Activity Book to help struggling math students in the primary grades. This is a book that lists essential number concepts young children need to be successful in math. (03/18/10)

### Question

I am facilitating a workshop regarding differentiation and interventions. I am looking for something in this area that I can give the teachers that they can immediately use in their classrooms. I would appreciate any ideas. (02/24/11)

I've attached a resource I developed. Remember to use the games as differentiation and intervention tools. I've also attached the K-6 games sorted by strands. Additionally, we've had impressive results with Pinpoint Math as a Tier 2 intervention supporting EM. [attachment included in original email]
(02/25/11)

Resource 1.pdf

Resource 2.pdf

### Question

I am looking for ideas and curriculum for math intervention. Our school uses Everyday Mathematics. I am looking for materials for Grades K-5 (05/02/08)

I think one of the best things you can do is use the EM materials for summer school. There is no need to purchase anything else. Look at Part 3 of the lessons. It has great Reteaching, Practice or Enrichment ideas. The Projects would be fun for the students and a great learning experience as are the Explorations. If you have a specific concept that you want to focus on, find those lessons in the program. I also recommend games, games and more games. What better way to practice concepts by bumping them up or down for the students. (05/02/08)

Last summer our school purchased Groundworks from Creative Publications. We purchased them for our Title I teacher, but have also found uses for them in the regular classroom. There are books for Grades 1-7. Each grade has a book for geometry, a book for reasoning with numbers, a book for algebraic thinking, a book for reasoning with data and probability, and a book for reasoning about measurement. If you have an EM catalog, the books are in the back few pages. In the 2008 catalog, they are shown on pages 58-59. We like these books because they are very student friendly and promote mathematical thinking. They blend well with EM, too. They may seem a bit expensive, but you are allowed to copy from the masters. I see that they sell student sets on the web, too. (05/05/08)

We have been using the EM Skills Link books for review and the EM games for extra practice. We are also looking at using Math Recovery in conjunction with EM for the students that need more intense intervention. We have discovered that it is vital to establish whether the student has number sense or not, which Math Recovery has a great assessment for. (05/02/08)

### Question

I was wondering how people are implementing Response to Intervention (RtI) Tier 2 and Tier 3 with the Everyday Mathematics program. Specifically how are teachers monitoring students' understanding of concepts as well as checking in with students' progress towards understanding those concepts? (08/12/09)

As I understand it, all students in Tier 2 and Tier 3 would have accommodations and modifications based on their specific strengths and weaknesses. There isn't necessarily a materials list or specific resource list because each student would need to have their curricular needs/assessments designed for them. I've never had a remedial program for students who struggle with math. There is some differentiated material provided by EM, but if that doesn't meet the child's needs you have to work with your school resources personnel to adjust lessons and materials or add support staff assigned to that student. I wouldn't revert to old material, but I might utilize lower grade material when it is appropriate. (08/14/09)

Tier 2 and Tier 3 students should be served through the games and the Extra Practice and Readiness activities offered in Part 3 of the lesson. The Differentiation Handbook has great advice on how to manage this and meet specific needs. (08/13/09)

The third edition of EM has many improvements. In my opinion, the newly added differentiated instruction component is by far the most significant improvement. This can be used to map a course for the Tier 2 and Tier 3 students for Response to Intervention (RtI). And as always, EM provides looking back (and looking ahead) to make for easier teacher referencing by skill. Using off-grade material should be a good habit to cultivate, not one to shy away from. If your teachers have saved their old (prior to 3rd edition) Teacher Resource Packs they could have the prior (and next) grade level for reference. For most student needs, there is more than enough within the program to not have to consider looking elsewhere. (08/18/09)

### Question

I was wondering if anyone has seen Number World or Pinpoint Math in action or has any feedback on them. My elementary school is pulling and using Part 3 from the lessons for Tier 2 intervention, in the form of before-school Title I groups. We are also using Part 3 for differentiated instruction once or twice a week (depending on the grade level) on what used to be a catch up day on our pacing calendars. We have an hour for math daily. Our special education is inclusion as much as possible, but for those students who are more than a year behind we were looking at Number Worlds and Pinpoint Math as a Tier 2 intervention during school hours. Any thoughts? (08/27/09)

We used Pinpoint Math last year with our Tier 3 students with great gain, especially wih 1st and 2nd Graders. (08/27/09)

Number Worlds is awesome. We use it with our extreme kids. It uses more manipulatives to teach basic concept knowledge. Also, it has more practice pages on one concept instead of tackling two or three concepts at once. We are also looking into purchasing Pinpoint Math, which has progress monitoring built into the programs. (05/12/09)

You might look at Number Worlds or Do the Math. (05/12/09)

### Question

Our district is trying to create a list of possible intervention programs that fit well with the Everyday Mathematics program. Does anyone know of any such programs? (05/10/06)

Another intervention program we have used is Moving With Math Extensions. (05/12/07)

### Question

Tennessee has recently changed the process for students who are referred for a Specific Learning Disability (SLD). The State requires that in order for a student to qualify for SLD, there must be documented interventions provided for the student using research based interventions. In reading, we use Dynamic Indicators of Basic Early Learning Skills (DIBELS) data, progress monitoring, and Voyager intervention in order to compile this documentation. However, we do not currently use anything but Everyday Mathematics for our math curriculum. Does EM have intervention programs that we can use in this way or does anyone else have a suggestion for what to use? Has anyone come across this problem before? (01/04/08)

There is DIBELS for math now, but I realize other alternatives might be less expensive. (01/04/08)

We also use DIBELS, progress monitoring, GRADE (Group Reading Assessment and Diagnostic Evaluation), and an intervention program (Sidewalks, which goes with our literacy series ReadingStreet) for our literacy/reading program. We just adopted EM this year and are hoping to put together a similar intervention approach for students who are below grade level for math. We are piloting the Number Worlds intervention materials (also from McGraw Hill and aligned with EM) and administered the GMADE (Group Math Assessment and Diagnostic Evaluation) assessment at the beginning of the year. We would like to find a DIBELS-type assessment for math but so far have not found anything. I would love to know more of the "math DIBELS" that was mentioned. (01/07/08)

I'm thinking that the math 'DIBELS' might be a reference to mCLASS: Math. We are piloting this assessment with K-3 teachers. We use Personal Digital Assistants (PDAs) for the DIBELS and Wireless Generation has this product at their web site. It only assesses Number and Numeration, not any other strand. We've encountered some problems as the program was not finished when we began in the fall. We are not ready to endorse it yet, but it is interesting. K-1 assessments are done one-on-one with data entered in the PDA and then synced with the website. Grades 2-3 are whole group paper-and-pencil tasks. Teachers then enter scores at the website to get class profiles. (01/07/08)

Here is a link to AIMSweb that has the DIBELS-type assessment for math. The TEN (Test of Early Numeracy) is for K-1 and looks at early number concepts, missing number, oral counting, quantity discrimination, etc. We are beginning to use this to identify children who need interventions at the primary level. AIMSweb also has computation probes. Another website to get information on Curriculum Based Management-types assessments is Interventioncenteral, by Jim Wright. Both links are below. http://www.aimsweb.com/products/cbm/en-cbm/description.php http://www.interventioncentral.org/htmdocs/interventions/cbmwarehouse.php (01/07/08)

As a ten-year user of EM, I have learned about the importance of assessing and then helping students learn the essential concepts that they are missing. Two other teachers and I spent six years researching and writing the Developmental Math Assessment (DMA). This assessment matches the concepts that are presented in the EM program. The DMA, like the Developmental Reading Assessment (DRA), is a classroom-based assessment. It is not a stand-alone program. It is intended to empower teachers, improve teaching, and most importantly increase student learning. Of course, the authors believe that improvement in student learning starts with well-prepared teachers. The authors wrote the DMA to help teachers know what to assess, what to teach, how to know if kids know what you teach (what grade level they are performing on), and what to do if they know it or if they don't. Each assessment is written on an appropriate level of difficulty based on age-appropriate state and national standards as well as current research in mathematics. The assessment ranges from: (e) Emergent (3 year olds) with a prenumber non-intrusive child oriented assessment; (pk) Pre-Kindergarten assessment of essential number concepts; (k) Kindergarten assessment of number concepts to know if children are ready for Kindergarten curriculum and a developmental assessment that includes operations as well as number concepts to help determine the appropriate instructional level; (1) First Grade assessment to determine if children are on-grade level and a developmental assessment that includes operations and number concepts; (2) Second Grade assessment to determine instructional level in number concepts and operations and an assessment looking at a variety of other important math concepts. Each assessment section is color coded by age/grade for ease of teacher orientation. Teachers really only need to know their own grade level section. Hopefully this makes the assessment more teacher-friendly. If you are interested in looking and reading more about this assessment, you can visit www.developmentalmathgroup.com. (01/09/08)

### Question

We are currently looking into math intervention programs that align (somewhat) to Everyday Mathematics. Has anyone found a math intervention program that they would recommend? (01/11/10)

We have been previewing Pinpoint Math, published by McGraw Hill, and it seems to be a very good match to supplement EM and aligns to New York State standards quite well. (01/11/10)

### Question

We have been using Everyday Mathematics for 4 years and are really seeing progress by using it. However, with Response to Intervention (RtI) coming into the picture we are looking for a good progress monitoring assessment to use with the students. Something fairly simple and quick that isn't necessarily linked to an intervention program already. Is there anything like this that others are using already that they would recommend? (11/13/07)

I have started collecting some of the Response to Intervention (RtI) and Progress Monitoring (PM) resources I've found on several wiki pages. All have some resources and research information. Math Intervention (http://cesa5mathscience.wikispaces.com/Math+Intervention) Progress Monitoring Workshop Links (http://mentorshare.wikispaces.com/Workshop+Links) Curriculum-Based Measurement (CBM) Tools http://mentorshare.wikispaces.com/Tools+%26+Forms (11/13/07)

Our district is piloting mCLASS:Math. It is a Wireless Generation product, and seems to have potential for K-1 (and eventually K-3) students. We have had great success using their Dynamic Indicators of Basic Early Learning Skills (DIBELS) product for our reading efforts, and because our K-2 teachers are adept at using the handhelds and web reports for progress monitoring in reading, we are hopeful that their skills will transfer to the mCLASS:Math product. Our start has been a little bumpy. It is a new product and is just rolling out this year. However, it seems to have potential. You can download a one hour webcast by going to this site and clicking on mCLASS:Math. www.wirelessgeneration.com (11/14/07)

### Question

What are districts doing for intervention for struggling students? If you use Everyday Mathematics, do you modify the program? Do you use other programs/resources? If a student is taken out of EM for awhile, is it difficult to transition them back into the program? (01/11/11)

We have 60 minutes of core math time per day where Everyday Mathematics is used. Then we have an additional 30 minutes of intervention time. The struggling students use math recovery. Students do not miss anything because every student goes to an intervention group. The high flyers do talented and gifted type of activities. The on-level students play EM games. The kids who are behind go to the intervention group that fits them. Kids who struggle with multiplication go to one group, kids who can't structure numbers go to another group. In Sixth Grade we have 6 groups. The groups are taught by classroom teachers, Title I teachers, special education teachers, etc. We do the same for reading. The core reading/language block is 60 minutes. Then there is 30 minutes of intervention groups. The lower groups are progress monitored every two weeks. (01/11/11)

In our building, math intervention typically involves 30 minutes, 3 times per week of intervention. This is usually a combination of pull-out and push-in, depending on scheduling constraints. I usually have pull-out during my small reading group time on days when those children are not receiving direct, small group reading instruction from me, but doing a reinforcement activity for a Secure skill in reading or math. This works out well. The children either complete the reinforcement activity when they return or take it home. Since it is reinforcement and not new material, it makes for a quick homework assignment. The intervention is based on Everyday Mathematics; however, some skills are targeted for mastery rather than spiraled. After the students are done, I have them write a review of the game by filling in the blanks. I played ______. I thought it was ________ because__________. Additionally, I encourage a spirit of competition with oneself by going "Above and Beyond" and have a math center that allows for that. Once the students are secure in a skill, they know they can continue to challenge themselves in that area or others. For example, if by mid-year they are Secure in writing to 100 without error, then they are free to continue as high as they like. If students have mastered all the coin names and values, they can play the Money Exchange Game with a friend. If a student has mastered number collections to 7 and they want to continue on with 8, 9, 10, they can. I use a composition notebook, as a math journal, to keep quite a bit of their work and for them to use as a resource. There is a plain 100s chart glued on the front inside cover. In the back I have 100s charts that helps them practice counting by 5s, 10s and 2s. It is not uncommon to see a child sitting and practicing the skill without any prompting. They value the journal as a resource. Geometric shape pictures that go along with the week's theme are also easily made more challenging. In the beginning of the year, the students are told they must use each a shape at least once, to make an ocean picture, for example. When the picture is completed they fill out a sheet where they record how many times they used each shape. For more of a challenge, I raise the minimum number of shapes, and have them spell the shape names. However, I rarely need to do that officially. Students tend to do so on their own if they are more advanced. (01/12/11)

### Question

Does anyone know where I could find review sheets and study guides for each unit for third grade (third edition)? (10/03/09)

Do you have the assessment CD that comes with the program? I have been able to easily create extra practice sheets for units with it. I also use the Skills Links workbook that comes with the program. (10/05/09)

The best use of the Assessment CD is to make mini-assessments, as needed, to give the teacher extra evidence of student understanding of particular learning target(s). Making review sheets that look similar to the next day's test send messages that do not improve student learning: 1) The learning for the unit stops at the unit-end assessment or "test," with no future opportunities for improvement, and 2) students' evidence to date does not count, and 3) students can only succeed on a "test" if they complete an identical test the night before. Another point to consider is moving the traditional "review day" before the assessment to a "differentiation day" the day after the assessment. The latter does not slow down pacing, and is targeted to students' individual needs. The Assessment CD would come in handy in designing small group tasks on this day. If a teacher is assessing students daily, using the Recognizing Student Achievements within the program, she knows who will or will not be successful on the unit-end assessment. A review day may mask students' weaknesses. Instead, the teacher should use the unit-end assessments as one more piece of evidence of student understanding for particular learning targets. And where there is still weakness, look for future Math Boxes, etc., for intervention without changing the pace of the program. (10/05/09)

### Question

My students had a great deal of difficulty with Study Link 9.7 (fourth grade). Lesson 9.7 is about working with population data and ranking it. It is somewhat tedious but not very challenging. The class enjoyed doing it as busy work. However, Study Link 9.7 is about ratio and percent and is very challenging. I don't see the correlation between what we did in class and with the Study Link. My students were very puzzled. (04/02/08)

One of the Key Concepts and Skills cited in Lesson 9-7 is "Order data reported as percents." I would agree that this aspect of the lesson wasn't the most challenging. Another of the Key Concepts and Skills cited is "Interpret 'percent-of' data." This gets at the concept behind the data that the students have been asked to order. For example, in the Math Message, students discuss what is meant by a statistic such as "21% of the population in the United States is 14 or younger." Later in the lesson students discuss what is meant by statistics such as a 2.0% growth rate for Haiti in one year or a _0.1% growth rate for Italy. All of this work with percents ties into the focus of Unit 9 - links among fraction, decimal, and percent names for numbers, with a special emphasis on percents. Unit 9 follows up on the work students did with fractions in Unit 7 - work such as finding the fractional parts of sets and regions. So now we move to Study Link 9-7. Students are asked to use population data from the 10 least-populated countries in the world to estimate answers to problems. Here are some thoughts as to how students might approach the problems given that the focus of the unit is on the link between fraction, decimals, and percents. 1. The population of Liechtenstein is about __% of the population of Dominica. From the table students know that the population of Liechtenstein is about 33,000 and the population of Dominica is about 69,000. Think about it in terms of a fraction and then make the conversion from a fraction to a percent. 33,000 is about 1/2 of 69,000. 1/2 is equivalent to 50%. If the numbers seem too large for some students to work with, consider the Study Link 9-7 Follow-Up which states, "Some students may note that when working with populations rounded to the nearest ten thousand, they only have to consider the first two digits." 2. What country's population is about 33% of Liechtenstein's population? Students know the population of Liechtenstein: 33,000. They know that 33% is about 1/3. What's 1/3 of 33,000? Find a country in the table with a population close to 11,000. 3. The population of Vatican City is about __% of the population of Palau. Consider the strategy used to solve the Writing/Reasoning problem on page 761 of the Teacher's Lesson Guide. 4. The population of the 10 countries listed is 314,900. What 3 country populations together equal about 50% of that total? 50% is equivalent to 1/2. 1/2 of 314,900 is about 155,000. Find three numbers in the table whose sum is about 155,000. 5. The population of St. Kitts and Nevis is about __% of Nauru's population. From the table students know that the population of St. Kitts and Nevis is about 39,000 and the population of Nauru is about 13,000. The population of St. Kitts and Nevis is about 3 times that of Nauru. Students can think about this problem in a similar way as they thought about the yearly growth rate in Haiti. (The Teacher's Lesson Guide referenced Student Reference Book, page 300 as a model for thinking about this problem.) Keep in mind that many of the Math Boxes problems in this unit focus on problems such as the ones in the Study Link. For example, Problem 1 on Math Boxes 9-7 offered the following: 10% of 50 = __ 5% of 80 = __ 20% of 40 = __ __% of 16 = 12 __% of 24 = 6 Last thought__I just finished reading "Open and Closed Mathematics: Student Experiences and Understandings" by Jo Boaler (Journal for Research in Mathematics Education, 1998, Vol. 29, No. 1, 41-62). Part of the study includes a discussion on student performance on contextualized questions. I thought about the study immediately as I compared the Math Boxes problems to the ones that were posed on Study Link 9-7. It might be worth a quick read. I hope this is helpful. (04/02/08)

### Question

Does anyone have any tips for the sunrise/sunset chart with the time change? (11/07/07)

Yes, record the times as they reflect the change. The "blip" is a great problem to pose and discuss. It's a real situation- the kids understand what happened outside. This is real data you can help them understand and relate to. (04/08/08)

I have been using one for about 10 years and never had any problems. Provided there have been no significant changes with the charts that are being included with EM3, completing the chart is quite easy. At the bottom you can fill in the blanks (I usually start with 5:00 and count by half hours.) At the top I count each bold vertical line by 10 minute intervals. This should allow you to fill in the hours that are appropriat for when the sun comes up and when it sets. (@ 5 - 9 AM and @ 5 - 9 PM) This should work fine if you start after Standard time begins and use this routine until Daylight Savings time begins again in the spring. That is plenty enough to show how much the length of our day changes. (11/21/07)

I think the problem may be that if you go 5:00 - 9:00 on both sides (sunrise and sunset) as shown in the book, in some states, like Maine, you can not chart the sunset after the end of Daylight Savings Time due to the fact that sunset occurs before 5:00 PM. One suggestion would be to label the sunset side starting at 4:00 PM and going to 8:00 PM, the other would be to double label the chart at the top so that the students would see both 5:00 PM and 4:00 PM on the same line. Then just talk with them about the artificial time change. (This was a suggestion made to us by the EM rep at our last inservice day when this same issue was raised. I plan to use this method next year....I think it makes more sense, plus it will keep the hourglass shape EM wants to show the students.) (11/21/07)

### Question

Does anyone know if there is an online version of the Student Reference Book for grades 3_6? We don't have enough SRB's for each student to have his or her own, so they need to have something they can reference at home. (09/06/07)

There is an online version of third edition, but you have to pay for it. (11/09/07)

### Question

Does the 3rd edition have a separate Home Link booklet for students homework or does it need to be copied by the teacher? (08/06/07)

3rd grade does have a separate Home Link booklet that you can purchase. It comes at an additional charge, and does not come as part of the student pack. You also have the option of copying the Home Links from the Math Master's book. Make sure you look at the Home Link before you copy it, just to be sure you want to send it home. (08/06/07)

Yes, the 2007 edition does offer a Homelink consumable workbook. They sell for approx. $5, which I feel is worth it, especially if you have had to make your own copies in the past. You can find them at http://www.wrightgroup.com/index.php/programcomp?isbn=007608972X. (08/06/07)

### Question

Does the whole number line need to be displayed in the classroom? (08/17/08)

I display mine around the top of two of my walls. I think EM suggests either putting the whole number line up at once or one number at a time as the year progresses. At least for first grade. (08/18/08)

Here in Hungary we give the prior year's end-of-year test at the start of the new year... Meaning, in the first weeks of second grade we give the kids the first grade end-of-year test again. Although they've just done it 60 days before, it's actually quite informative to see how much the kids have retained over the summer. Among the reasons we do not do the second grade test at the start of second grade is that we can fairly predict the kids' performance--poor in most cases--so it doesn't inform our instruction much. Also, it's perhaps easier to say at the outset "Everyone, we're going to have a test you may remember from the end of last year," than to say "Everyone, you probably won't score too well on this test, but don't get discouraged..." (08/19/08)

### Question

Help! I am very frustrated with my number line. First, I have a small classroom without a lot of wall space, and I don't think I can post the entire number line. I can fit -23 to 48 with no problem. Second, I don't understand the rationale behind having a basic number line in the 5th grade. I have read the Teachers Reference Manual, but it didn't elaborate on the number line's purpose for upper grade students. I think the negative numbers are fine, but positives all the way to 180? In the FIFTH grade? Please enlighten me. (08/20/07)

I posted my number line around the top perimeter of the room similar to a wallpaper border. I posted -35 to 100. (08/20/07)

The number line makes a nice visual in the room, but you DEFINITELY do not need the whole thing. I too teach 5th, and I agree the negative numbers are very useful at this grade level. (08/20/07)

Someone shared this idea once on this list (I'm sorry I don't remember to whom I should be giving credit here)... When you have your number line way up high in the room, you can use a flashlight pointed at the number line to highlight answers and movement/direction for adding/subtracting. I thought that sounded like such a great idea. (08/21/07)

I teach fifth grade, and when we started the program last year the sixth grade teacher and I did not order the number line. Later I wished that I had one, ordered it, and put it up. Most of the students used it for the negatives and moving back and forth between the negatives and positives. It was an extreme pain to put up, partly because I put it as high as I could reach with the ladder so as not to take up space that I already use, but I do believe it was worth it. Even if you can't put up the whole number line, my opinion is that it would be good to start with the lowest numbers and go as far up as you can. (08/21/07)

### Question

I am finding it very difficult to keep up with the copies that all the grades (K_5) need to implement the lessons. We are going through literally thousands of sheets of paper and hours upon hours to make the copies. Is anyone else experiencing the same problem? Does anyone have any suggestions to reduce the amount of duplicating necessary? (10/25/07)

We found it more cost effective to buy the Study Link books. They are around $4.95 each and have every Study Link and every family letter in them. At another school, we had some parent volunteers who would come in as "math helpers". I didn't have any, but I know of other teachers who would send their helper to make copies for the week. It won't help you save a tree, but it saves some time. (10/26/07)

Yes, we have experienced the same challenge, but we have negotiated a price with a local copy place. They keep a copy of the Math Masters and duplicate what teachers want. Actually, they only duplicate the Home/Study Links and the Family letters. Teachers have them copied for the year, so they just have to pull out what they want as they need it. The company delivers them to the schools in the fall. Other copies are made at school. We rationalize that we save money on our school copy machines, to say nothing of giving teachers more time to plan math rather than stand by the copy machine. I also believe it assures that teachers use all the material in the program (so easy to forego a Home Link if you don't have time to copy it). (10/26/07)

Purchasing the Home Link/Study Link is more cost efficient than copying, although that probably won't help you for this budget year. Parent volunteers are a good source. As mentioned, after you purchase the Home Link books, you are only left with an occasional Math Master. I have laminated most of the Math Masters in a few sets, and use them with vis a vis or whiteboard marker. (Especially the Exploration materials, you only need enough laminated for a small group as the kids rotate.) Game directions are better laminated and one per table (Kids don't read them anyway!). If you can take the time to read through and understand what the copies are for, you can probably reduce them. This is hard if you are just going by the "Advance Preparation" of each unit. Now that we have the Home Link book, my math copying is minimal! Hang in there, it will get better. (10/26/07)

### Question

I am thinking someone sent out something a while ago comparing the new 3rd edition to the 2nd edition, listing all of the great changes in EM3. I looked through the archives but couldn't find it. Does anyone remember this and have it saved? (02/20/09)

One of the most important things to know is that the third edition of Everyday Mathematics remains true to the philosophy of the first and second editions. And, in alignment with our development principles, the third edition incorporates the latest educational research as well as teacher feedback from the second edition. In the second edition, the terms beginning, developing, and secure were used to describe both learning goals and student performance in relation to these learning goals. Feedback from users of the second edition indicated that using the same terms to describe both the curriculum and student performance was confusing. As in previous editions, students using Everyday Mathematics are expected to master a variety of mathematical skills and concepts, but not the first time they are encountered. The third edition of Everyday Mathematics addresses the development of concepts and skills within and across the grades through the introduction of Program Goals and Grade-Level Goals. Program Goals are threads that weave the curriculum together across grades. The level of generality of the Program Goals is quite high which is appropriate for goals that span Grades K-6. Grade-Level Goals clarify what the Program Goals mean for each grade level. There are about two dozen of these Grade-Level Goals for each grade, K-6. The Grade-Level Goals are all linked to specific Program Goals. They clarify our expectations for mastery at each grade level. Everyday Mathematics is designed so that the vast majority of students will reach the Grade-Level Goals for a given grade upon completion of that grade. While the Grade-Level Goals reflect the core of the curriculum at each grade level, they do not capture all of the content that is addressed each year. This remaining content builds and supports the foundation for meeting successive Grade-Level Goals. In the third edition of Everyday Mathematics, each lesson contains a Recognizing Student Achievement note. These notes highlight specific tasks from which teachers can collect student performance data to monitor and document students' progress towards meeting specific Grade-Level Goals. These tasks include Mental Math and Reflexes problems, game record sheets, Math Boxes problems, journal pages, and Math Log or Exit Slip prompts and are labeled with a magenta-colored star in the Teacher's Lesson Guide. Each Recognizing Student Achievement task for a given Grade-Level Goal provides a snapshot of the student's progress with respect to that goal. The selected tasks have nothing to do with whether the content is being introduced for the first time or is familiar to children. Students who are making "adequate progress" as defined by a Recognizing Student Achievement note are "on a trajectory to meet the Grade-Level Goal." Such students have successfully accomplished what is expected to that point in the curriculum; they are on track to reach that Grade-Level Goal. The level of performance that is expected in October is not the same as what is expected in April. If students continue to progress as expected, then they will have gained proficiency with the Grade-Level Goal upon completion of the year. There are many reasonable ways to evaluate student performance on the Recognizing Student Achievement tasks. One approach would be to note whether a student has met the criteria for making adequate progress or not. This approach includes the most essential information, is simple, and over time would provide a great deal of useful information about student progress. A more elaborate approach would be to use a four-point scale to evaluate student performance on these tasks: 4: Students are making "adequate progress" as indicated by the assessment note, but in fact already demonstrate a sophisticated and well-articulated understanding of the concept or skill being assessed. 3: Students are making "adequate progress" as indicated by the assessment note. At this point, students demonstrate a developmentally appropriate understanding of the concept or skill being assessed. 2: Students are not making "adequate progress" as indicated by the assessment note. Students partially completed the problem or problem set or the problems are only partially correct. At this point of exposure, students demonstrate an understanding of the concept or skill being assessed that is marginally short of what is expected. 1: Students are not making "adequate progress" as indicated by the assessment note. The problem or problem set is incomplete or incorrect. At this point of exposure, students demonstrate an understanding of the concept or skill being assessed that is significantly short of what is expected. The Everyday Mathematics curriculum continues to aim for proficiency with concepts and skills through repeated exposures over several years. The Teacher's Lesson Guide alerts teachers to content that is being introduced for the first time through Links to the Future notes. These notes provide specific references to future Grade-Level Goals and help teachers understand introductory activities at their grade level in the context of the entire K-6 curriculum. The grade-level Differentiation Handbooks also include tables that show when lesson content is revisited throughout the curriculum. (02/20/09)

My main concern with doing away with the Building, Developing, and Secure (BDS) terminology is that teachers who are new to EM will think every lesson has to be taught to mastery. If they do that, they will never get through the year. We also appreciated the B, D, & S based on the brain research the last 20 years. My students always asked if the lesson was a seed planting, weeding and watering, or harvesting lesson. It made a difference how we approached the lesson. We are moving towards a performance based report card and will be using a system similar to B, D, & S to describe a student's progress towards goals that should be secure (in the case of the new edition – grade level goals). That need not change. The wonderful lessons of EM are still the same. If you are moving over to the third edition you still have the B, D, & S information. As to my concern about the new-to-program teachers knowing how much emphasis to put on the lesson I think the red star is the big clue. If I find the red star on just one math box in the lesson, my supposition is that the lesson is a beginning or developing lesson. However, if I find the red star on one or two of the actual lesson pages, I'm feeling pretty sure this is an important lesson. I know I can check this out by looking at the Checking Progress to see if the topic is to be assessed in Part A which is the summative section. If I find the topic is Part B, I know the assessment must be formative so I can use it to guide where I am going with the topic. (02/20/09)

### Question

EM3 lists books in different units that can be used to enrich instruction. For example, Grade 3 - Unit 3 lists several books in the Unit Organizer under Connecting Math and Literacy. Two of the books are linked directly to lessons (3.1 and 3.5) while the 3 other books listed are not tied to a particular lesson. I am hoping that somewhere, there is a complete list for each grade level of these books. Does anyone has such a list, or know where I can get one? (12/10/07)

A list of literature can be found in the Home School Connection Handbook. (12/11/07)

I don't think that you can order the literacy connections directly from Everyday Math. We ordered the literacy connections through the company; Knowledge Industries Inc. They have put together a set per grade level that go along with the EM series. (12/11/07)

I gave a list of books that I wanted ordered to the librarian and she ordered them for the entire school. They are kept in the library. (12/11/07)

I received this newsletter recently and thought that this topic was covered quite nicely. You can see the discussion given by Marilyn Burns at this link: http://www.mathsolutions.com/index.cfm?page=3Dnl_= wp2&crid=3D250&contentid=3D754 (12/12/07)

I love EDM, but I really hate the "use a calculator" answer. I'm also tired and it's progress report time so I'm being a bit grumpy. With the majority of the algorithms used in EDM, the student is learning what is really happening and not a set of rote steps. When I learned long division with decimals we moved the divisor's decimal point to the right to eliminate it. As we did, we counted places. Then we moved the decimal point in the dividend "up" to the quotient area and slid it to the right the same number of places. In EDM we enforce number sense, in particular composition and decomposition of numbers. When working with fractions (EDM07, grade 5) we learn about equivalent fractions and multiplying/dividing the numerator and denominator by the same number which will give us an equivalent fraction. Why not draw the connection that a division problem is a fraction is a ratio. If I multiply the numerator and denominator or dividend and divisor by the same number, I have the same problem and the same ratio. THEY ARE THE SAME. So, to get rid of my decimal point, just multiply both the divisor and dividend by powers of 10 (more reinforcement of place value, powers of 10, basic number facts). Granted, it would create bigger division problems for them to do, but I also think it would show a deeper understanding of division and the relationship to fractions and ratios. Additionally it can help show why dividing by a decimal may yield a large number. I'm not complaining about the program, but I do wonder why it isn't presented like that. It seems that it stays with the philosophy and gets rid of the "use a calculator" answer. Just curious. Examples: 1 / 0.1 = 10 / 1 = 10 4.5 / 0.9 = 45 / 9 = 5 15.5 / 5 = 155 / 50 = 3R5 10.8 / 0.09 = 1080 / 9 = 120 (12/12/07)

### Question

I send home the Home Links as we complete each lesson, which seemed to be the way the EM program was developed. I have heard of other teachers sending them home the week ahead or the week later (5 at a time) or sending 2 home (back to back copies to save paper) prior to one of the lessons being taught. Just wondering what others do. (12/29/07)

Speaking as a parent first and teacher second (using EM), I feel the Home Links should be sent home as the lessons are completed. I don't know of many children who appreciate homework let alone 5 pieces at once. (Even if teachers allow time for completion, I believe a "packet" is too much... especially for the primary grades.) The Home Links are a great "practice" tool to be used following the lesson. (12/29/07)

I too used to send home Home Links on a daily basis. I now send them home 1 unit at a time. In my newsletter each week, I have a section showing which lesson is covered each day. At the beginning of the year, I tell families that it is okay to work ahead if need be (as some nights can be very busy), but students should never be behind. We go over them the following day which helps students to see the importance of them being done on time. This has worked really well for me in both 2nd and 3rd grade:) (12/29/07)

I also teach first grade and have found that they are too easy in some cases so I do supplement with other work. I send them home only when I feel they need extra review/practice. I do not send them home with every lesson. When I do send them home, I send them home after I have taught the lesson. However, the second grade teachers in our school send them home for the whole week and tell parents what day to do each one. (12/30/07)

### Question

I was curious if there were other Kindergarten teachers who have experienced the same situation I have with my Everyday Math Home Link letters... the Home Links do not coincide with the lessons. Has anyone explored this or actually gone through the letters and put them in an order that goes with the lessons taught? It seems odd to me to not have them coincide with the lessons if the parents are to do this at home to reinforce what we are doing in the classroom. (08/28/07)

Read in your Resources for the Kindergarten Classroom in the section pertaining to Home Links and you will see that their suggested use is one per week. They are not meant to match exactly as they do in the upper grades. (08/27/07)

### Question

I was wondering when the Wright Group would be posting the 3rd edition Morning Message for all grade levels. They did this for the 2nd edition. (08/16/07)

Wright Group has posted them. You need to click on the 2007 Edition and then from the drop down menu in the upper left-hand corner click on Math Message and follow the directions. (08/16/07)

### Question

Is the Student Reference book (SRB) available online so families can use it at home without kids taking the book home? (11/14/08)

The online Student Resource Book is available to parents and students only if schools or districts subscribe to the on-line service. Once the school or district has subscribed the teachers can register themselves and their students, only then can the students and their parents have access to the SRB online. (11/15/08)

### Question

Our district has recently adopted Everyday Mathematics and we have had one short training. Now I don't know where to even begin. Here are the questions I have so far (I teach second grade and we will be using the third edition.) 1. What do the tool kits have in them to begin with? 2. How many of each game do you make? For example, do I make enough for the class to play these together? (6 copies of each game?) 3. What are your ideas for storing your games, manipulatives, tool kits, etc.? 4. What is the best piece of advice for teachers who have never used EM? (06/11/07)

I will just answer to how some of us have done the tool kit in our district. I would give each child a zip lock bag to keep in his or her desk. (The bag would usually need to be replaced by mid-year). In this bag I would put a clock face, some counters, the small ruler, a marker for the slates (if you have a response board), real coins in a small container, and then let the tool kit grow from your class lessons. Games: I didn't make any games. But some teachers do. Your second-grade does have a student reference book that has a game section and it has all the games that you will introduce. You can make a decision from that section of the book. (We work from the second edition, so I am not familiar with the new second grade reference book. Our edition has a game section in the student book.) Your teacher materials will have everything you need for the games. Most of them just take a number generator (spinner, cards, or number cubes) and a recording sheet. It just depends on how fancy you want to get. Storing: I kept my manipulatives out on shelves so all students could have access to them whenever they might need them. If I were in a room without shelves, I would find a way to have them out for their use. The items you do not use all the time, just keep in a container where you have easy access. Best advice: Have fun with this math. It is a great curriculum for teaching math. I will say it won't make much sense to you until about mid-year, then it becomes easier to teach. Read your lessons every day before you teach. It seems like it is scripted, but it really is not. You need to know what you are teaching. So reading it and thinking about how you will present the information will be really important to do. You can't just "wing it." I will promise you that you will not want to go back to traditional math programs once you have learned to teach EM. (06/12/07)

I teach second grade also and have used EM for 5 years. I tried the tool kits for a year and found them unwieldy. So I have all of the materials needed for each unit on a cart and pass them out as we need them. It keeps their desks freer and it does not take that much time away from the lessons. I do have them bring in their own coins to keep in their desks. I made several of each game as they came up(parents helped) , so when we had a games afternoon I could rotate them through centers. The best pieces of advise I got when I started were to three ring bind everything... that way you can take one unit home in a small binder each night to go over the lesson. I found this wonderful, as the books weigh a ton! Don't even try to do part 3 (I did) because you will inevitably run out of time! I love the program and find that if done properly it does improve math scores and math understanding. (06/12/07)

My name Amy Dillard and I am one of the authors of Everyday Mathematics. It's fantastic to see experienced EM teachers like Paula offering suggestions to those new to the program. I'd like to throw in my two cents regarding Part 3 activities and the Third Edition of Everyday Mathematics. The Differentiation Options in Part 3 include optional Readiness, Enrichment, Extra Practice, and ELL Support activities that can be used with individual students, small groups, or the whole class. The activities build on the Key Concepts and Skills highlighted in Part 1 of each lesson. You can use them to supplement, modify, or adapt the lesson to meet students' needs. As the children in your classroom are new to Everyday Mathematics, I'd suggest that you read through the Readiness activities that appear in most lessons. These activities introduce or develop the lesson content to support students as they work with the Key Concepts and Skills. These new Readiness activities were designed to be used with some or all students before teaching the lesson to preview the content so students are better prepared to engage in the lesson activities. I agree with Paula that it can be challenging to decide which children in your classroom might benefit from these activities, but I encourage you to use your professional judgment and assessment results to make these important decisions. Consider using the Part 3 Planning Master which can be found at the back of the Differentiation Handbooks to help you plan how you will use the Part 3 activities for a given unit. (06/12/07)

2. When I first introduce a game I make enough for a class set with partners (18 kids, 9 games) 3. I make five copies that I laminate and store in file folders for the kids to play whenever they have time. The kids grab the folder and the tools they need to play with a partner. The tool kits are pencil boxes, this works really well. It is expensive the first year, but you can reuse them year after year if you train the children how to take care of them. Then they store their boxes in a wooden shoe storage box. It has slots for 12 boxes and the tool kits work great. (06/12/07)

You place in each toolkit, a template, tape measure, and a calculator. Number of games to make depends on class size, but the rule of thumb is 1 copy for 4 students. Rules for the games are in student's journal and reference book. Best Advice: Read the entire Unit Organizer before teaching the lessons. Follow the lesson design; always do part 1 and 2. Part 3 is for Differentiation and you will not use it all the time. The Routines and Games are a very important, do not skip them. Mental Math and Reflexes are good slate activities, read about them in you Teacher's Reference Manual. Teach the curriculum as designed: follow whole group, partners, and small group. Expect noise, it will be the excitement of learning. (06/13/07)

I have used EM for many years in first grade. I use plastic shoe boxes with lids for the tool kits and have one per table of 4 kids. At first the tool kits are empty. As the year progresses and I introduce a game or a new tool we put the new item(s) into the kit. At free choice time kids choose one tool or game we already played in class. For example, they had the Everything Math Deck in their kits, so they had several games to choose from. They also had their templates, their tape measures, dice, etc. As for the games, when we first began using the series we made a set of games for the kids to use and take home on a rotating basis. We included a direction card and all the items needed to play the game in a (yellow) cardboard box with a handle. Our kids loved taking a game home to share with their families. If they didn't return the game, they could not get another the next trade in day. As I recall, we traded every Friday and Monday. Some years we had parent volunteers who came daily, so they could trade each morning or three times a week. We also made a collection of read aloud math themed books with manipulatives which we circulated among the kids. At one time we had both going. It got a bit crazy, but it also got the kids doing constructive activities in the evenings with their families. We began doing the exchanges after most outdoor activities like soccer were over for the year. (06/13/07)

### Question

This can be EM related or not, but I am looking for multiple choice math practice for 5th grade students. Anything close to grade level involving picking a multiple-choice answer will work. (02/23/10)

Check these ones out. http://www.internet4classrooms.com/grade_level_help/test_taking_assistance_fifth_5th_grade.htm Mike, just noticed you are from MN. Go to MDE and download the MCA practice tests. (02/23/10)

If you go to the PA section of the Department of Education's website, there are numerous multiple choice practice tests. They are listed under Pennsylvania System of School Assessment (PSSA), item sampler. (02/24/10)

The California version of the Teacher Assessment Assistant has California Standards Practice Tests that are multiple choice in PDF form. It is designed solely for multiple choice practice. (02/23/10)

You can use the Teacher's Assessment Assistant CD to create multiple choice tests tied to the EM chapters or goals. It's a pretty easy process. (02/23/10)

### Question

We had an in-service with lots of teacher-made materials to look at (not make and take) and there was an idea using a laminated file folder as a student resource. The folder had a number grid to 110, a number line, geometric shapes with names and several other things that I can't recall. What would you add as a resource for 1st graders? I think a ruler would be difficult to use if it was stationary on the page. (08/15/07)

I include a picture of various coins--penny, nickel, dime, quarter, half-dollar and a dollar bill--and the monetary value of each in my folders. (08/15/07)

I made a copy of the number grid on colored cardstock then laminated them. The kids used these as book marks in the math journals and with dry erase markers for various units. I also made one to send home to use with homework. (08/16/07)

I've seen that Reference File Folder in the past also. There were "reference frames" such as Parts/total diagram, Frames and Arrows and What's My Rule. You might also have an addition fact table. However, these are also on the inside cover of the Student Journals. If you are using 3rd Edition EM, all of this is in My Reference Book. (08/15/07)

A colleague and I also saw these folders at an EM conference. We chose to laminate ours and use them as resources with our assistants. Students can use wet erase markers (Vis-a-Vis) and practice the different reference frames as needed. You could include things like number lines, blank clock faces, and Frames and Arrows. They are a wonderful resource! (08/15/07)

### Question

The kindergarten team at my school is interested in acquiring the 2007 edition of Everyday Mathematics. I'm wondering if someone has used both the 2004 and 2007, and if so, is there a major difference between the two, and are there more materials necessary to execute the 2007 edition? I am hoping we can order the 2007 edition teacher's guide and nothing else. (11/05/09)

I have used both 2nd and 3rd editions of EM and to my knowledge, no new manipulatives needed to be purchased. Below is a comparison that my predecessor compiled when we decided to switch to the 3rd edition. Items available in English and Spanish Adjusting the activity shows learning styles It appears that there are more student pages dedicated to practice The parent letter at the beginning of the unit has vocabulary and answer to Study Links, but now answers to links are on a separate page. ELL support in Differentiation Handbook More writing and reasoning Math Master Book in chronological order rather than grouped by section Technology Link available on internet or CD ROM No Introduce, Develop, Secure Page at the beginning of the unit on differentiated instruction In color Tells you what to assess with pink stars Assessment Handbook- Assessment Overview for each unit along with a list of modifications for written assessments and sample student answers Home Connections Handbook now divided into Early Childhood, 1-3, and 4-6. Used to be K-6 Math Boxes tell you which lesson the math boxes are paired with. Example: Lesson 4-1 is paired with Lesson 4-3. The Skill in problem 6 previews Unit 5 content. Kindergarten Now has center activity cards Section on ongoing daily routines all together rather than spread throughout the book. Assessment- tells you where to assess Each unit has a page on differentiated instruction Provides a list of terms you should use with the students Improved Assessment Handbook More Math Masters You have an Early Childhood Home Connection Handbook Resources for the Kindergarten Classroom Book (Themes Activities, Family Letters, etc.) My 1st Math Journal Book for Students (11/05/09)

I think the 2007 version is much better. You should probably also get the black-line masters book. The center charts for children to work at centers are great. So getting the resource kit is really best. You can manage without the journals for kindergarten. Some teachers like them; most would rather not use them. (11/05/09)

Our K teacher used the 2004 edition prior to updating to the 2007 edition this year. She loves the fact that it is much more sequential and easily used in the classroom. I'd get the teacher resource kit at least, so you'd have all of the components and make your own decision as to the student journals. (11/05/09)

I actually worked in three EM editions. The 2007 one is wonderful. It truly brings respectability to the "K" math program. The alignment of the program is also similar to the other grades. It still emphasizes morning routines but for the newer teacher shows how to differentiate instruction while using, how to allow the routines to change as the childrens' knowledge expands. There are LOTS of GREAT changes. Changes (for the good) have also been made in the resource book, which is loaded with resources. Assessment will be very different . The Assessment Handbook addresses these changes and lays out a whole system that will assist the teacher in informal and formal assessment. Contact your EM representative and see if you can't take a healthy look at the whole prpgram. I would say, if you are making the change, do it right. The children and all of you will benefit. (11/05/09)

Our kindergarten teachers far prefer the 2007 edition for all the reasons that prior postings have listed. I strongly recommend investing in the whole teacher's kit. The major reason is that the Assessment Handbook provides really important tools for assessing and reporting student progress. In particular, the Baseline, Mid-Year, and End-of-Year periodic assessments are so rich. And the price difference between the teacher's guide and the whole kit is not great. (11/05/09)

### Question

Can anyone give me specifics on what the differences are between the 2nd and 3rd editions for Kindergarten? (03/08/07)

My name is Debbie Leslie and I am one of the authors of 3rd edition /Kindergarten Everyday Mathematics. Below I am re-posting a response I sent to an earlier query about 3rd edition KEM from January. If it doesn't answer your specific questions, I'm happy to provide additional information. Although we changed the overall structure of KEM with the 3rd edition, we maintained the principle of having a program that is robust and rich enough for full-day Kindergarten programs, but also flexible enough to be used comfortably in half-day programs. One of the goals of the 3rd edition revision was to help teachers implement the program more consistently across both types of settings. I see that Barb Smart already posted a very informative response to your question, and -- as you can see from my response below -- I concur with all that she wrote. As you may know, in 3rd edition KEM there are 126 numbered activities, each consisting of Part A (Core Activities) and Part B (Teaching Options). The expectation is that both half- and full-day teachers will do the activities in Part A in each numbered activity in the /Teacher's Guide to Activities/. These include: * the Main Activity (the first and longer activity), and * the Revisit Activity (the second and shorter activity, which is a repeat -- sometimes with modification -- of an earlier Main Activity) Half- and full-day teachers will likely differ in the extent that they use the Teaching Options (Part B in each numbered activity). The Teaching Options are optional and can be used any time after the Main Activity. Teachers in full-day programs will likely be able to do more of the Teaching Options activities than teachers in half-day programs. That said, we expect that all teachers will find some Teaching Options that fit well into their program and schedule, since the Teaching Options often link to other curricular areas or can be done in the Math Center or another classroom Center. They can be very useful for integrating mathematics into daily activities, thereby helping both half- and full-day teachers "find" more time for math in their busy days. Another place where half- and full-day teachers may differ is in their use of the Projects. There is one project at the end of each Section in the Teacher's Guide, or a total of 8 projects in KEM. Each project includes several activities. Like the Teaching Options, the projects are optional and teachers can pick and choose from the activities that comprise them. Here again, full-day teachers will probably be able to use the projects more fully than half-day teachers, but half-day teachers will also likely find some project activities that they would like to integrate into their programs. A related point regarding pacing: all teachers should aim to do about 3-4 numbered activities per week (including the Main Activity, the Revisit Activity, and any Teaching Options they select), which means completing about one Section of the Teacher's Guide per month (4-5 weeks). This will comfortably take them through the entire Teacher's Guide during the school year. For more information and discussion about half-day and full-day programs, you might also see page xxxi of the Kindergarten /Teacher's Guide to Activities/ and Section 1.7 (pp. 10-11) in the /Early Childhood Teacher's Reference Manual/. The Section Openers at the beginning of each Section also provide useful information for planning and pacing. (03/09/07)

### Question

Is the new kindergarten edition (third edition 2007) written for full or half day kindergarten? The new version does not seem to identify core activities. Previously, we used this information to direct teachers in planning full or half-day kindergarten classes (half day kindergarten sessions would use core activities; full day would use core activities in the morning and non-core activities in the afternoon). (01/08/07)

The Kindergarten EM3 program is designed for use in full and half day programs. Teachers initiate all or most of the Routines as the year begins. The daily activities (126 total) are grouped into 8 Sections - 14 to 16 activities plus an optional Project - with a Section Opener that provides useful overview information. Each Daily Activity includes two parts: A Core Activity is a main activity plus a revisit activity and B Teaching Options. All teachers (full and half day programs) should teach the required Part A Core Activities, and then make selections from the Teaching Options. Projects and Theme provide even more math activities. I have worked with a couple pilot groups this year and the full day program teachers report that they do all of Part A and most of the Part B while the half day program teachers find they do all of Part A and make selections from Part B. You'll find more information about this in the Introduction section of the KEM3 Teacher's Guide to Activities under Instruction, p. xxxi - xxxiii. Read that through ... then look at a few activities and I'm sure your question will answer itself as you'll see the many ways teachers can build their mathematics program ... starting with a Part A Core Activity. (01/08/07)

As you look at the new Kindergarten lesson plan, Part A of the lesson is called "Core Activities." The caption has just been moved from the margin to the actual point of use. Part B gives teachers options for differentiating the lesson or extending for the whole day environment. (01/12/07)

### Question

How different are the 2004 edition Grade 1 Math Journals from the 2007 edition? Will I be able to teach using the 2004 Teachers' Guide if the students have the 2007 journals? Is there a list somewhere of which lessons have been moved or changed? (08/07/08)

The 2004 Math Journals are still advertised for sale at www.wrightgroup.com. http://www.wrightgroup.com/index.php/componentsale?isbn=0075844419 http://www.wrightgroup.com/index.php/componentsale?isbn=0075844427 (08/07/08)

### Question

I have been assembling my Elementary Mathematics games this summer and have run across one that I need help with. The game is in the 3rd Edition and is called Base 10 Number Game. The directions say to start a "bank" with 20 longs and 40 cubes and put 1 flat on your mat. The directions then say to roll the dice and put the same number of cubes as there are dots on the dice back in the bank. If you start with a flat, how can you put cubes in the bank? (07/02/08)

The base 10 Trading Game helps children understand that a flat is a whole thing but it can also be broken into parts. So before the kids can put cubes back into the bank s/he must break the flat into longs and the longs into cubes as needed. In this game the students are asked to see and understand the parts that compose the flat. (07/03/08)

Since they start with a flat, if they roll a 3 they have to first change the flat into 10 longs, and then one long into 10 cubes. So they can then take away the 3 cubes. They finish the first roll with 9 longs and 7 cubes. (07/03/08)

You will find that this trading game is the best way to help 2nd graders understand subtraction regrouping. They also play the game using dollars, dimes and pennies. As far as assessment, this year I assessed my students once a month. I would take one week and assess 4-5 students a day. I found that was more manageable. (07/04/08)

### Question

Does anyone have a list of the grade level goals and the games that correspond with each goal? Or does anyone know if this would even exist? (09/15/09)

I'm glad this question came up because this is our first year with EDM3 and we're still working on making best use of its new features. I didn't find exactly what you're looking for, but I figured out how I could get there: Step 1. In the beginning of each Teacher's Lesson Guide there is a Games Correlation Chart. That will lead you to a strand. Step 2. Find a lesson in which the game is played. Then look at the Learning Goal associated with that part of the lesson. Example Step 1. For second grade, TLG I it's on pages xxxii and xxxiii; the Number Grid Game is under Patterns. Step 2. In second grade, the game is played (among other times in the year) in Part 2 of lesson 1.8 to give students opportunities to use patterns on the number grid. On the opening page of the lesson (page 51) it notes that among the key concepts and skills is, "Identify patterns on the number grid [Patterns, Functions, and Algebra Goal 1]." The questions I still have are: Are there other, more direct ways to get there? Might a game encompass more than one learning goal? (09/15/09)

In the beginning of each Teacher's Lesson Guide there is a game correlation chart. The chart lists all of the games and what grade level the game is played. It will also list what lesson you will be playing that game. The chart also informs what skill and concept areas are covered with the game you are playing. Also, at the beginning of each unit is a section called "Practice through Games." You will find a chart listing the games and the lesson when it should be played along with the skill being practiced along with the goal; i.e., Grade 2, Unit 1: Lesson 1.4. The student will be palying Coin Top-It. The student will be working on counting (Operations and Computation, Goal 2). (09/15/09)

### Question

Has anyone played the Fishing for Digits game? It is new in the Fourth Grade. I have not been able to figure out how to use the record sheet. (09/22/07)

I tried the fishing for digits game about two weeks ago and found it a great game to enhance large number place value and mental math. We chose not to use the record sheet on the first try and my students were quite successful. I passed the word along to other fourth grade teachers in my building NOT to bother with the record sheet when first playing the game. A few of my students who struggle with mental math used small sheets of scrap paper to simply make notes to themselves and visualize what they needed to do on the calculator. (09/22/07)

I think I finally figured it out...let's see if this works. For those who haven't played, Fishing for Digits is a place-value game that uses the calculator. Students put a random 6-digit number into the calculator and play with a partner. On the record sheet, each player records their own number (I think you would need to use a divider so the other player cannot see your number). Player 1 goes 'fishing' for digits and asks, for example, "Do you have a 4?" If the answer is no, both players keep their same number (and record it in the first blank of Round 1...the directions actually say that Player 1 adds 0 and Player 2 subtracts 0. If the answer is YES, then Player 1 adds the value of the digit to his number and Player 2 subtracts the value of the digit from his number and they each record their new number on the first blank of Round 1. Then it is time for Player 2 to fish for digits. They repeat the steps and record their new number on the second blank of Round 1. Basically, each round has 2 turns (one for Player 1 and one for Player 2) and that is why you have 2 blanks for each round. After 5 rounds (which is really 10 turns) the player whose calculator has the larger number wins! (09/26/07)

### Question

Does anyone know where I could locate a chart that lists when we play each game? I found a place in the Teachers Lesson Guide where it lists the first time the students play the game (Games Correlation Chart), but I would love to know when we will play each game in the future. For example, we just played Dollar Rummy for Lesson 3-5. Is there some place I could look to see when/if we will play it again? (11/02/09)

I made a chart that lists when each game is called for in a lesson. There is also a chart for the literature connections. This is for the 3rd edition. (11/03/09)

If you look at the Unit Organizer under Ongoing Learning and Practice it will list Practice through Games. We have the third edition, so I don't know if that makes a difference. (11/03/09)

### Question

I am in charge of planning a Family Games Night (K-6) next month. I have read all the suggestions in the Home Connection Handbook, but am looking for more ideas. What games have others played? How did you manage it? How long did it last? Prizes? Refreshments? Etc. (10/22/08)

I have been part of several Family Math nights--food is always a requirement. Feed them and they will come. Games, prizes - raffle tickets one per family. I have had the parents play the games with their students so that they can play them at home, trying to house regular decks of playing cards or dice that are readily available. I have done it where they stay in their childs room the whole time - 1 hour, or rotate every 15 to 20 minutes playing each game, or changing rooms to get exposure to games at other levels. (10/22/08)

Our Family Math Night has evolved into more than games but when we just played games we had as many EM games as we could set up at tables around the cafeteria. We had families move from table to table through out the evening. We had several of the games reproduced for families to take home with them. The home packets contained any materials necessary to be able to play the game - directions, board, dice, counters, playing cards, etc. We also had commercial games available that they could purchase themselves from a store such as 'Toys R Us' that related to math. When we first started we had raffles but after a year or two we didn't much like this because a handful of students were over the top happy while the large majority were disappointed. In doing this for many years now, we've found that every family being able to take home a few games is better. We usually include a pencil and math sticker or some such simple item. We decorate the cafeteria with balloons - National Council of Teacher's of Mathematics (NCTM) has "We Love Math" balloons which we then supplement with less expensive ones from a party store. The evening is from 6:30 - 8:30 including an introduction and wrap-up (with a feedback form). We serve juice boxes and baggie of 2_3 cookies. We used to serve coffee/tea but clean up was time consuming and usually there would be a spill or two. The evening consists of "stations". One station is games, another uses a variety of manipulatives, another is 'teaching' station for a particular concept (last year I did coordinate geometry using 4 shower curtains taped together to make a floor model of the 4 quadrants). Another station was math through literature (math read-alouds were done). Our stations vary a bit from year to year. Each station is numbered 1, 2, 3, 4, etc. As families arrive they're given a large large envelope with the order they will be attending the various stations (ie. 1, 2, 3, 4, or 2, 3, 4, 1 etc.) As they progress from station to station they collect something from each station to take home that related to than station. It's a great nightterrific turn out for grades K_6. We've not been as successful with grades 7-8. (10/22/08)

Name that Number and the Top-It games are easy to do and don't require anything special, just a deck of cards. Name that Number is a game that can be used in the very early grades and all the way through 6th grade, increasing in complexity as you add more operations, the use of parentheses, powers of numbers and even the order of operations. Fantastic game! In my experience, when you offer some type of refreshment, you get a better turn out. Some schools have instituted a passport type system in which you need to get a certain number of "stamps" or initials from presenters as participants experience various games before enjoying the ice cream or other refreshment. These are very powerful, positive experiences for both students and teachers. (10/24/08)

We did some parent nights in the past. Now that we have been using the program for years we haven't done one in a while. We set up the lunch tables in the gym with buckets of materials in them. We had many game sheets on the tables. As the parents entered, we told them to choose a spot to sit in for the first game. After everyone was set, we gave them about 10 minutes to play a game. Then, we would have them rotate. This was with a parents only session. It was fun to see them get so competitive. Some of the games we played were multiplication baseball, wrestling, factor bingo, beat the calculator, top-it games, just to name a few. This was a very powerful tool. The parents had a blast. The evening was for about an hour. The thing was, when all the other parents who didn't come heard about the night, they wanted to know when we were going to do another. I have done a family night with my class. I had the kids pick their favorite games we had materials for about 10 different games. I set it up the same as our parent night, with buckets and materials around on the tables. The kids played games with the parents. Everyone had a great time. (10/22/08)

Our 3rd grade team (3 teachers) had our "Math with the Experts" activity day/evening last Tuesday held in our gym. The students were the experts and taught their parents 5 of the EM gamesNumber Top-It, Multiplication Baseball, Roll to 100, Pick a Coin, and Name That Number. We offered two sessions, 3:30-4:40 and 6:30-7:30. The students participated in only one of the sessions. We offered two session to help accommodate parents who work evenings etc. The only refreshment that we offered was a Tootsie-Pop halfway through the sessions. Families completed a 4 game rotation during the hour; switching to a new game every 15 minutes. Our team created take-home bags for each student/family. The bag included one of each of the following: deck of cards, EM deck of cards, ruler, tape measure , calculator, dice, $ bag with $15 in plastic coins and $1400 in paper bills, and a book related to math (e.g. Shark Swimathon, Lemonade Stand, Betcha!, etc.). Each book is a Math Start Level 3 book connected to a math concept. We also included a card stock, laminated copy of the directions for each of the 5 games as well as any score sheets/mats needed for playing the game. This is our second year of offering this fun family activity. I am thrilled to say that we had 93% attendance. The students had an opportunity to shine and show just how much they really know about numbers. The take home kit is really about helping families create game nights of their own and ensuring that our students have no excuses for not completing their Home Links due to lack of math materials in their homes. It requires preparation (take home kit) and some funds. The students and parents really enjoy the teaching/learning that takes place. It's really fun for the teachers too! (10/25/08)

### Question

I have to teach a workshop for the teachers in my building on Everyday Mathematics games. How can I promote using the games, especially when many teachers are giving up on them due to time constraints? (08/11/07)

Are the teachers in your building trying to play the games after each lesson? If so, you may want to let them know about doing one "Game Day" a week. I use this in my classroom and love it. I teach a lesson each day, Monday through Thursday. Then, on Friday, I focus on games. This seems to work well for me. Keep in mind, if there is a lesson where you will be introducing a new game, I will do that as part of the lesson and not on the Game Day. (08/12/07)

Maybe if you have the teachers make up the games so that they have them ready for use. I make up the games and keep them in large oversized envelopes with the rules taped to the front of the envelope. I keep everything (except for the math cards) in the envelopes. I than have students work in groups. I give different games to different groups so that they can work on skills that need improvement. I often do this on Friday so that we can have a review time. Sometimes I pair up lower students with helpful higher level students so that they can help the lower level students. I may have 4 to 6 different activities going at one time. After a time I have students rotate to different groups or different partners. Not sure that helps, but I think if teachers think of the games as a time to review and help students with missed work or skills that need improvement it might help. Also having the games made up ahead of time is a great help. (08/12/07)

My suggestion would be to set up one Key Game per grade level and have teachers rotate in mixed-grade teams from game to game. Have posters at each game site to encourage teachers to make notes about the kind of math skills that the game allows students to practice. This should encourage some discussion and remind teachers how powerful the games are for students. (08/12/07)

The games are the tools that help students reinforce and practice skills being learned. They are as necessary to the program as the study links. My first year with EM, I did not use the games effectively, and found my students did not retain the skills as well as I would have liked. The second year, I made a commitment to use the games and found that students retained the information learned at a much faster rate. The games are much better than the old "Drill and Kill." Our district recommends games and "catch-up days" once a week. (08/13/07)

Our school implemented a GREAT way to get all games in... It is mandatory that 1st thing in the am, between the first & second bells, the ENTIRE school has math game time. It also helped out GREATLY with attendance because the kids wanted to be there early to get lots of play time in. (08/12/07)

I would suggest the first 10 minutes of each day be given to working with the EM games in the classroom. It gives those students who arrive early something to do and everyone seems to get to school on time knowing this is "game time"...it is what I did in my Kindergarten classsroom. I rotate 5 games throughout the week. At the beginning of the school year it is free exploration with different manipulatives, then activities at calendar at least 3 times, then moved to games in the a.m. Good luck! The games are ESSENTIAL to the program!! (08/12/07)

### Question

I would like to help teachers in my K-4 school set up consistent game days so they can incorporate a steady diet of EM games into their curriculum. Like many others, they feel there is not always enough time to get to the games. How do other teachers use the games routinely in their classrooms? One example I have seen is having grade-level classes rotate between rooms, with each room having a different game to play. Any other great ideas like that one? (09/15/08)

I made a chart that lists when each game is called for in a lesson. There is also a chart for the literature connections. This is for the 3rd edition. (09/15/08)

Wednesday nights were game night for my class. Instead of getting a written assignment, they had to play a game and get a weekly sheet signed saying that they played. (they also had a home link). Then at the end of the quarter I would give that sheet a grade based on the signatures. (09/15/08)

Some teachers here have tried doing "game days" instead of when they come up in the lesson. I've been trying to get everyone to do the games when they come up so that they're in context and not simply "a game". For us, sometimes this does mean that a lesson runs into the next day, but we try to keep them so that they're done with the lessons. Sorry, I hate to be negative, but just doing them later on didn't work as well for us. (09/15/08)

Another model is to have games as a center, providing other problem solving opportunities or activities, meeting with the teacher in small groups and/or completing partner work as other centers. Sometimes teachers also need to be reminded that games are an opportunity for all, not just an option for those that complete their "seatwork". (09/15/09)

I had a time set aside every day for games. We usually didn't get to the game in the lesson, so we always played that during our 10-15 minute game time. I set mine up after recess so the students could get everything set up before they went out to recess. The key is to have partner lists up so you can just choose one of the lists to use and tell the students what game they are to play. I found that during a game day my students actually didn't have the attention span to play for long. Breaking up the time you have into shorter sessions is far more effective and students will use the time better. Instead of a game day, I had a day of differentiation. I would pull small groups aside to preteach or reteach skills, while the rest of my students were finishing journal pages or working on the extra practices or enrichments from Part 3. I would switch these groups after 10 or so minutes, and pull another small group. (09/15/08)

Most Fridays are used as a game day in my second grade classroom. I set up about 6 different stations each with a different game. I have parent volunteers come in and help monitor each station. Students rotate through each station spending about 10 minutes at each one. The station that I monitor is one that involves reteaching or enrichment depending on the week's lessons. Throughout the week though I try to have the students play the game along with the lesson as well but having Fridays set aside help if we didn't get to it. Other second grade teachers do something similar to this as well. (09/15/08)

### Question

My principal asked me to find a really good, fun math game for a class of 30 third graders. She doesn't want an Everyday Mathematics game. She will use it with the class while she gives the teacher a "gift of time" (she will give the teacher a break). Does anyone have a super, great math game for a whole class that is engaging and will take about 45 min.? (12/18/07)

Dollar Words by Marilyn Burns is fun. Each letter of the alphabet is worth $. A = 1 cent B = 2 cents C = 3 cents, and so on up to $0.26 for Z. First challenge the kids to find the value of their own first names. Then challenge them to come up with a word that has the highest value. A great homework challenge is to find words that equal exactly one dollar. We have made collections of Dollar Words that lasted quite a while. (12/18/07)

It takes a little time and organization, but calendar bingo is great fun. Gather discarded calendars (it is better if it is from various years). Each student gets a month. Create a list of questions whose answer is 1-30 or 31. (How old is your mother - 20 years; how many years old are you; How many siblings do you have? what is 3X3;etc.) Play bingo! (12/19/07)

Some good choices. (Most, if not all, are from Marilyn Burns.) For small groups: -Race to the hexagon -Pathways game(addition) -Pathways game (multiplication) For entire class: -The game of Pig (probability - play with partners, than graph results as a class.) (12/18/07)

### Question

Some of the teachers in my building feel that they have a difficult time getting through the entire Everyday Mathematics curriculum in one school year, so the first thing that they "throw out" are the math games. Does anybody know of any articles or research that explains the importance of playing the games on a regular basis and what it can do to improving scores that I can share with some of my teachers? (07/31/07)

If the teachers are not getting through the program it is probably because they are spending too much time on beginning and developing skills lessons. It was explained to me this way . . . If the skill is beginning it will come up many more times in their EM so teachers should make this a green light skill. Introduce it and go on. If it is developing they students will see it again so make it a yellow light and don't spend much time on it. But, if the skill is a secure skill, then it needs a red light. Stop and make sure your students get it. This gets the teachers through the book with time to spend on games. I don't know what articles there are but I do know this was a problem for our first-year teachers. (06/01/07)

### Question

The discussion here at the American International School of Budapest went from "We should have a family math night!" to "Why not a math spirit week?" to "Why not have January be Math Month, with Art and Music integrations, Science, PE, and Literature!" So January is going to be Math Month at the lower elementary. I'm the committee coordinator for this proposed celebration and I would sure appreciate hearing what you have done on Math Nights, Math Weeks, and Math Months at your schools! (11/14/07)

One thing we did was have the students become the teachers and teach their parents how to play math games during our 'math night'. We also created a bunch of manipulatives (K-2 - laminated clock faces, number grids, etc.) to give out to parents so they could help their children with homework and math skills practice. We even gave out 'travel' size games, manipulatives, and practice ideas because we found that parents/students were driving around after school hours to sporting events and activities. (11/14/07)

### Question

This will be our first year with Everyday Mathematics and I would like suggestions about how others package and send games home as well as how often they are sent. (07/11/09)

I send home a 2-pocket folder at the beginning of the year for games, once a few have been introduced. I then send home the directions and game board copies as I introduce them. Students are responsible for keeping these folders so that when I assign a game for homework they have it right there. (07/13/09)

I have a set of see-thru bookbags that I ordered (Lakeshore). I would suggest that you use something more study than ziploc bags. I have 8 bags. I set up 2 games per bag. Included in the bag are directions (either laminated sheets or placed in page protectors), majority of the game materials which I place in snack size ziploc bags (such as coins, dice, game cards, etc.) and a little rhyme that encourages the families to return the game bag the next school day. I have a checklist sheet to keep track of who has taken a game home. Usually I pull names to begin the process, then that child passes the game on to another student. If there are items that need to be replaced I have been lucky enough to have the students remind me or each other. Prior to beginning this process I send home a letter or include in my newsletter the goal, purpose, and value of the game bags. Also, rather than using some of the EM manipulatives I purchase or ask parents to donate additional math items such as dice, dominoes, etc. (07/12/09)

We are using heavy-duty (6 mil. ply) plastic zip loc bags for games & sending materials home. The 10x13" holds laminated instructions & the bag is sturdy enough for manipulatives, game cards, dice, etc. They are a "bit" pricy - but we also use these for our Science Readers 6-packs. You can probably get together with others or as a site and order in bulk. Uline company sells them: http://www.uline.com/cls_uline/Uline-Products (07/12/09)

### Question

We are new to Everyday Mathematics and are hosting a Family Math Night in a few weeks. I would love to hear your ideas for themes as well as booths or stations. (09/17/09)

We hold a parent math workshop in the fall with the focus being how to help your child learn their basic math facts. This allows us to explain/introduce how different today's math class looks and why and emphasize how important meaningful fact practice is. We go over fact families and triangle cards and teach the fact games like Top It and Beat the Calculator and discuss how to help them develop strategies, not just rote memorization (but that they must get to automaticity). Our Family Math Night is mid-late winter and is organized completely around the Everyday Mathematics Games. We had parent volunteers help organize an EM Game Center for each classroom so that all materials are in one hanging file box. When they did, they made one extra set for Family Math Night (with printable cards for the games so we don't have to worry about losing pieces of our Everything Math decks at the event). We set up 4_6 copies of most of the games in our cafeteria and let the students teach the parents. If it is a game they haven't gotten to yet, all of the directions and materials are right there. Then they have the rest of the year to play at home. Our PTA also provides money for us to purchase door prizes and estimation items (jellybeans, jump rope (length), balls (circumference), and bubbles (volume). Your ticket to the door prize raffle is an evaluation sheet to help us improve for the following year. (09/18/09)

When we do Family Math Night, each teacher takes a game of their choice to teach the parents. The parents then rotate to each of the six teachers and play the games with their child. (09/18/09)

The last responder made great points, but I would add to that. You won't have time to do it in four hours, but I would stress how important it is to be familiar with the games and manipulatives. They can do that on their own, but it's critical that they are fluent in the games ahead of the kids. Also, occasionally there weren't enough materials in our kits to do small groups as called for in the manual. For example, we didn't have enough attribute blocks to have each group make attribute trains, so we did this whole group and now I've added more attribute blocks for this coming year. (08/09/09)

### Question

Does anyone have any suggestions on what to say to parents when you send home Math Journal 1? I feel the need to explain that not every problem was tackled, not every page is finished, and some pages werent assigned because we did them together or in another way. (02/20/08)

I came upon 2 letters that I've used in the past years. Maybe one of them would work for you. Dear Parents, Attached is your child's math journal. The journal serves as a source for students to learn concepts from the daily lessons, as well as to practice previously taught skills. There are various ways that we use the journals in class. Often students work together with their peers while a teacher walks around the classroom to help. Sometimes we complete problems as a class and other times students work independently so that we can check their progress. You may keep the math journal at home and use it as means for reviewing skills. Some pages are not complete or corrected. The pages with Math Boxes are the best ones for students if they are looking for some extra practice. You could even make up new problems on a separate sheet of paper based on the ones in the journal. Happy problem solving! (02/20/08)

This is the one we just put together for second grade. You're welcome to revise it to your liking. Dear Parents, Attached is your child's math journal. The journal serves as a source for students to learn concepts from the daily lessons, as well as to practice previously taught skills. There are various ways that we use the journals in class. Often students work together with their peers while a teacher walks around the classroom to help. Sometimes we complete problems as a class and other times students work independently so that we can check their progress. You may keep the math journal at home and use it as means for reviewing skills. Some pages are not complete or corrected. The pages with Math Boxes are the best ones for students if they are looking for some extra practice. You could even make up new problems on a separate sheet of paper based on the ones in the journal. Happy problem solving! (02/20/08)

I always send journal one home, and have never had any parent issues. At our open house I explain to parents that the journal will come home in January, and not all pages will be complete. I suggest that the child finish these pages at home over the summer, or if the parent wants to help their child with skills and concepts. As far as other children at home, if one wants to complete problems undone, or begin to peruse what will be learned as they enter into 4th grade, yippee! (02/20/08)

### Question

I received the following message from a Second Grade teacher and wondered if anyone else has noticed this discrepancy. Our math teaching manuals do not always match up with our students' journals. I attempted to use the Mobiwrite today but realized it that page 69 in the Student Journal was different. We are wondering if there are more instances of these discrepancies? If so, does EM have plans to correct the disks or change the student materials to ensure that they align? (11/30/10)

The EM author team at the University of Chicago maintains an online error report form at http://everydaymath.uchicago.edu/error_report.shtml We check the reports that come in and, when necessary, request reprint corrections from our publisher, McGraw-Hill School Education Group. Without knowing the specific mismatch, it's difficult to say if this is an error or if you might have the wrong version of the journals. If you think you have the wrong journals, you should probably contact your sales rep. (11/30/10)

Make sure you have the correct CD's for the series you are using...the pages are diffferent. (11/30/10)

### Question

Does anyone have any suggestions for the clock-making activity in Unit 2, Lesson 6 of grade 1? One teacher used a ready-made clock instead of all students making one. (10/14/10)

I use a combination of clocks. We make the paper ones, often using card stock, so the children can do the first lesson with only the hour hand. We make the second paper one with both hands to take home for practice since so many families only have digital clocks. I then use "Judy" brand practice clocks for use in the classroom. (10/14/10)

When I modeled the clock lesson for our first year EM teachers, I went to Wal-Mart and bought the least expensive battery clock they had that was kitchen sized. I unscrewed the back and popped off the second hand and minute hands. I put the clock back together and that way I can move the clock from the back for the lessons / practice that use only the hour hand. I taped the minute and second hands to the back because with the clock model I happened to get those hands easily came off and I can put them back on just by disassembling and reassembling the clock. It worked really well. I think that the clock was less than $10.00. (10/14/10)

The beauty of the clock connected to that lesson is that it only has the hour hand; this increases student understanding of time and allows them to be more successful, especially early on. I think that it is genius, so make those clocks. (10/15/10)

I use bobby pins to distinguish between the hour and minute hand. I usually buy them in different colors as well, if I can find them. If you cut the clock face out and lay it on top of the dessert plate and then put a small hole in the center, the bobby pins will slip in through the hole with one half on the front of the plate and the other on the back of the plate. They are tight enough that they don't move unless you move them. This is a quick and cheap way to make a great working clock for each student to use for practice. Eleanor Rodie Vigo County Elementary Math Liaison (10/15/10)

### Question

This is our first year using Everyday Mathematics in our school. We were curious if any other K teachers have come up with a better more efficient way to create the sticks needed for games. (11/03/11)

I made them the first year, and had the kids help put the beans on the popsicle sticks. They are holding up well. (11/03/11)

Some teachers in my district drew the beans on with sharpie markers. (11/03/11)

When we were learning what "5" is in Section 1, the children did the attaching. The sticks were saved and then used for lesson 5*10. Another year I had the children glue 5 nickels(cardstock). When they earned the 5 sticks, they are traded for the raft with a quarter glued on (11/03/11)

Try small stickers instead of beans on the popsicle sticks. (11/03/11)

### Question

I am thinking of putting some Everyday Mathematics games together so each of my students can take home a sort of "kit" of activities for use at home, and then return it to me in June at the end of the year. (I send home game directions regularly, but I think I might get a better response if I included everything all together - spinners, cards, etc., laminated, ready to go.) Some of the games I thought of for my second grade students are Number Grid Difference, Clock Concentration, Array Bingo, Addition Spin, and Im still working on some more. (It's vacation week for us here and I don't have my manuals at home to reference.) One thing my kids can use more practice with is two- digit addition and subtraction. Does anyone have a good idea on how to make 10's and 1's for use at home? We have base 10 blocks in the classroom, but not enough for home use. I have used laminated tag for these in the past, but they are so difficult for the kids to pick up and use that I'd rather find something easier for their fingers to hold onto. Does anyone else do something similar to sending games home, or have other game ideas? In particular, besides Beat the Calculator, which requires three people, I'd love some games that practice basic math facts. (I am thinking of including a set of laminated fact triangles, thinking that they'd be nicer for the kids to use than the paper copy ones that go home on a Home Link at the beginning of the year.) (02/26/08)

I have made 10s and 1s by using milk bottle twist off tops and toilet paper rolls. I haven't done this in a long time, but 10 caps used to fit perfectly into a toilet paper roll. (02/26/08)

How about gluing beans to a tongue depressor? I think you can fit 10 beans on one. (02/26/08)

Plastic canvas works very nicely for hundreds, tens, and ones. You can find this at any craft store for a reasonable cost. It also makes great place value blocks for the overhead or Elmo. I would recommend that you get the largest grade you can find. Send home a half sheet of it and have the first family cut up the (hundreds), tens and ones, then have them put the pieces into a snack bag for storage and return with the game. After they enjoy the game it will be ready for other families to use. (I would include a place value mat with the game - it is usually very helpful.) I have also found that "tens frames" work well. (02/26/08)

We used to make "bean sticks" for tens and ones. Get a big bag of dried beans and craft sticks. The kids can glue 10 beans onto each popsicle stick, and they can have a handful of beans for the ones. (02/26/08)

How about beads on pipe cleaners? (02/26/08)

### Question

As we are getting started, many teachers have been asking me about the Number Grid. I have seen some Everyday Mathematics classrooms that have a certain way of coloring this number grid to make it more student-friendly. For example, coloring down the 5s column red and the 10s column blue. I have looked through the teacher manuals and reference manual, but have not found anything suggested by EM regarding this question. Does anyone have more information regarding this? Does EM suggest such a system for the number grids? (07/28/10)

Highlighting tape. Have you seen that? It is a roll of tape that is colorful and transparent. It sticks on, but peels off easily and can be reused a few times before losing its stickiness. That worked great for me. (07/28/10)

I have not ever seen anything from EM specifically about coloring the number grid, especially with the goal of making easier for students to use. Many activities exist to help students see the patterns in number charts. EM grade 4 or 5 has an enrichment activity about the "Sieve of Eratosthenes," and there are interactive "sieves" as well. This is the classic upper-elementary/middle school number chart activity. With the current series, you could also search the Interactive Teachers' Guides for "grid" and see where the number grid is addressed at each grade. If this has been a recurring question, you could use the number grid as the focus for a cross-grade look at Number and Operations. Such strand traces are a great PD opportunity. Perhaps if you have PD time, you could guide the search with grade levels teams and then have them share. Trust the spiral! Although I haven't updated it recently, I collected EM resources for participants in a math grant that you can find here: http://cesa5mathscience.wikispaces.com/K-6+Series (07/28/10)

My EM trainer displayed a Number Grid for First Grade that had the 10 and 11 colored, 20 and 21, 30 and 31, etc. She mentioned that it was an aid for students as they swept down the number grid so that it would help them keep their places. Each "set" of numbers had the square outlined in a different color. (07/28/10)

I work with a color coded number grid, so the eye can more easily connect the right side of the paper/chart to the left side, as the eye tracks downward or upward as the need may be. However, this year I had two color blind studentsone couldn't see red, orange, or yellow, and the other couldn't see blue. I found it is not really true that color blind children see gradients of gray and I don't think the color coding of the chart was helpful for these children. I did find that subtle, patterned backgrounds in various black and white patterns helped when we made the "probability spinners," so a textured/patterned background might help color blind children with the Number Grid. (07/29/10)

After using EM for many years, I would like to make a suggestion regarding the coding of the number grid .To make it meaningful, build it WITH the children as the year progresses and use different colored post-it tape which is NOT permanent and easily removed if the grid is laminated. When counting by 10's , 2's, etc. the children can have the pieces of tape and build the grid as you count. Do the same for patterning on the grid. As early as "K", you can find children in their group time counting by 2's, 5's. etc. and applying the tape. You will probably hear, "What would it look like if we count by 3's!?!?!?" As you teach the use of the Number Grid, have the children color in their own copy of a minature Number Grid of their own. I post a child's colored Number Grid for each of the concepts. By not having a HNumber Grid with lots of coloring, each of the smaller ones highlights the concept you are teaching. I also like the idea of splurging on a pocket chart so the children can build the patterns with the numerals in hand. If laminated, you can still use the post it tape. Hope you and your students have as much fun using the Number Grid as I have! (07/28/10)

If you feel the need to mark the return sweep for the number grid (this is recommended in "K" and 1st grade), beside using the removable post-it tape, you can place small matching stickers (your choice or the children's, or little colored dots) placed just OUTSIDE in the margin of the Number Grid. Again a reminder, don't do this in preparation for your children. Do this with the children so they begin to own and understand what is being done to the number grid. It is possible to confuse some children with a number grid that is tooooooooo busy with stuff. (07/28/10)

### Question

Can anyone help me with a trick to keep your place on the number grid? I have a few children who cannot remember where they started or where they are going. If they add 46 +22 they need some kinds of markers. Any ideas? (01/17/08)

Renee, check in the First Grade TLG...I dont know the lesson number off-hand, but the directions are there. (01/18/08)

I use transparent colored bingo chips. Students can place the chip on the number and still read what is beneath it, then use fingers to move along the grid. (01/18/08)

I laminate number grids for students. We use dry erase markers or Vis a Vis on them and circle where we start and where they will end. Then they actually are able to write as they hop. Then each time they can erase and have a clean slate for the next problem. (01/18/08)

In my special ed classroom, this happens ALL the time. Here are some of my solutions...My students use number grids that are just copied from the inside of the math journal, so they are 8.5x11 in size. I slip them inside a page protector for student use. My students are allowed to use various things to mark their place on the grid. I have small plastic animals that they use for counters or game pieces, and they like chosing an animal to move along the number grid. Another thing I like is small foam circles or squares. Those are more tactile (and quieter) for those students who need the touch of the object to reinforce. Pretty much anything small can be used as a counter...a foam packing peanut, a penny, a dry bean, etc... Another way we often mark our place is by using a dry erase marker to circle the answer. The dry erase marker writes easily on the page protector and wipes off easily with felt pieces that we use for erasers. They underline the beginning number, so they remember where they started if they lose their place and circle their final answer so they can remember what they landed on. If you use smaller individual number grids on each child's desk, they can be easily laminated...and then you can use the dry erase marker method on those small grids as well. You could also use a small square of colored overhead transparency so that the number is highlighted. Even just a colored index card with a small square cut out of the center can be used as a 'mask' to emphasize the number that the student needs to write. Another thing I did was to enlarge a number grid onto legal-sized (or larger, if you can find it) cardstock. I made two copies the same size, laminated them both, then cut all the number squares out individually on one of the copies. I then put small velcro tabs on each of the number squares on the intact number grid, and on the backs of each of the small individual number squares. (Does that make sense?) Now, I have a number grid where every numbered square is easily removable. We actually use this for a bunch of different activities. But, as with your example, if I had a student who lost his/her place when finding the answer, I would just have that child use my velcro number grid, find the answer, pull off the number square, and put it next to the problem they are writing the answer for. When they are done, it just gets stuck back in place on the grid. This was, admittedly, a lot of work to make, but I am glad I did it. I only have one, but it would be good to have more than one version of this number line. Maybe a parent volunteer could help you assemble some! Do you have the last/first numbers of your grid color coded? That will help some students with tracking where to go next after they get to the end of a row. For example, on my big classroom grid, I colored with a highlighter in the following way... 0 & 1 stay white, 10 & 11 are both green, 20 and 21 stay white, 30 and 31 are both blue, 40 and 41 stay white, 50 and 51 are both green etc... (using the same pattern of white, green, white, blue...) This way, if a student is adding (or subtracting) along and come to the "decade number"say 30 (which is blue), they know to jump down to the beginning of the next row that starts with blue (31). All the indididual desk number grids and the 8.5 x 11 ones that I put in page protectors are "coded" in the same way. (01/18/08)

I have used overhead counting chips at the starting number; the children can see the number under the chip. For students who juggle the chips around (so it doesn't work) I place a number grid under the grid on the unifix cubes 10-by-10 grid. That keeps counters in place. The question made me imagine a computer program that allowed a student to click on a number on the grid and drag to the ending number, thus highlighting all the unit squares between and including the starting and ending numbers. It probably exists. (01/18/08)

This is something like what you describe: National Library of Virtual Manipulatives K-2 Number & Operations http://nlvm.usu.edu/en/nav/category_g_1_t_1.html Look at Number Line Arithmetic and Number Line Bounce for example. (01/18/08)

### Question

How do you teach using a slide rule to a whole group? Also, the end of unit assessment says that students may use their slide rule. How can we expect students to use the slide rule if it is not taught to mastery? (08/25/07)

I use the overhead of the slide rule provided in the Math Masters, but this doesn't get the method across clearly enough. I have my students work in pairs to help each other while I give step-by-step instructions. I always have to go from group to group helping them directly until they get the hang of it. What I find useful is to put a number line on the floor using duct tape from about _15 to +15 and have the students "walk the line", as I call it. This method is described in the 6.8 lesson, and I've had many students prefer this to using the slide rule. (02/19/10)

I know that some folks don't like the slide rule lesson, but I have at least 1-3 students per year that are spatial learners. Having the slide rule solidifies the addition of fractions, but also really helps with negative numbers. Agreed, it is unusual. That being said, I had to use a slide rule in college (way back in the 70s) so I sort of get it and like that method of computing. (02/23/10)

As the math coach, I teamed up with the 5th grade teacher for this lesson. It went very well with most of the kids catching on quickly. The extra set of hands and eyes was the key. This is our first year of EM and our kids already had a pretty good grasp of fractions from 4th grade. I don't know how this might have gone with a class already in the EM program, but I would expect it to be better if anything. Most of the kids stuck with the traditional, but a few really liked and used the slide rule. I think this lesson could be taught as a whole group if you're comfortable with that. Another possibility is for the teacher to initially teach a small group beforehand who can then be team leaders, teaching to small groups with the teacher facilitating and helping as needed. It could also be taught as the teacher-led small group in a class of 3-4 groups that rotate thought activities: math journal/math boxes, games, computation practice, enrichment, etc. The lesson may look scary at first, but it is actually quite "doable" as the kids would say. (02/21/10)

I put a sample slide rule under a document camera. I could not have taught this lesson without using the camera. None of my students used the slide rule during the end of unit assessment. It felt like a wasted lesson, although it was insightful (but that's about it). (02/20/10)

### Question

I am getting materials ready for the grade 4 lesson on angles and polygons. I bought regular drinking straws and chenille sticks. Works okay but the straw diameter is a little large for the connectors. What do you suggest as an alternative? (08/09/09)

If you can return the drinking straws, or exchange them, I would suggest coffee straws. They are usually available at bulk food stores like Gordon's, and they're thinner. That way if you want them to construct permanent models, they can use Elmer's glue on the pipe cleaner tips, and they can even be suspended from the ceiling for display. Most of the time, I could use both items from year to year. Cut the pipe cleaners in 1 inch segments and they're easier to put more than one in a straw to construct 3-D models. (08/25/07)

I use the flexible straws without connectors. Students can slit the short end of each straw from the end to the bend with a pair of scissors. To connect the straws, insert the short end of one straw into the long end of another. For 3-D shapes you can wrap the connecting edges with a little scotch tape. (08/25/07)

I found narrower straws from a bartender at one of my favorite restaurants. I mentioned that I teach math and that I needed them for a geometry lesson with my students. The bartender happily gave me a box which lasted me the school year. Note: These are not stirrers or the very narrow mixed drinks straws. I've since found all sizes of straws at Smart and Final (a discount supply store in Los Angeles). (08/25/07)

### Question

I am the math coordinator and teacher at an International School in Germany. We use Everyday Mathematics but we do not teach the American money or measurement system. Does anyone else have this issue and if so, what supplemental materials do you use to teach metric units and the Euro? It gets very time consuming to modify every lesson and unit test. (03/25/09)

I have used EM at international schools for four years in grades 5 and 6. I think for the grades where using money is more of a focus (grade 2, I believe), it may be better to continue to adapt lessons and assessments to incorporate the local currency. You could also just use American money, but always provide visual aides that inform students what a dime, quarter, penny, and nickel are. The math skill behind teaching money is the counting by 5s, 10s, 25s, so it doesn't really matter what currency you use. Using local currency just makes it more meaningful to the students. In grades five and six, I teach my students how to use an inch ruler as I found it helped them apply and understand fractions. I had them complete conversion problems (ex: oz. to lbs.), but I never required them to remember the rates. I always provided those. This gave them practice in the skill of conversion of units. (03/25/09)

I taught overseas as an elementary teacher and for a short time with some administrative responsibilities. We always used the local currency to some extent. It only made sense for us to do the local currency since the local currency is what the students can get some practice with outside the school. That is the only thing all of the students have in common. With the other nationalities, it makes no sense to learn the American money unless you go to an American school. European Council of International Schools (ECIS) must have a website that allows teachers to talk with one another about these issues. If nothing else the chair of the math committee for ECIS will be able to give you names of people who have addressed this issue for their schools. (03/25/09)

### Question

I am trying to budget for paper, card stock, and lamination film for next year. We will be implementing Everyday Math for the first time. Can anyone tell me an estimated amount of materials that are needed per class, school, or any way that you have ordered it? (02/23/09)

One thing we did was to purchase the Home Link/Study Link books for our students, which helped a lot with budgeting. If you dont have these, you will need to plan on copying the Home Link/Study Link for each lesson and the checking progress for each unit for each student. There are also parent letters for each unit which are available online with the online EM games or you can budget to make paper copies of those. In addition, we use the Self-Assessment for each unit from the assessment handbook. Your teachers will probably also need the assessment checklists from the assessment handbook for record keeping. So maybe for each unit count the number of lessons (for each Home Link/Study Link or Self Assessment) and add 3 or 4 for the Progress Check. The first year we tried to make copies and slide them into sheet protectors for anything that was not consumable from the Math Masters book such as directions for explorations, games, etc. as well as options from Part 3 of the lesson that we might use in a small group or center setting. That still works well for us. The sheet protectors can also hold any cards or sheets you might need for a game and they also are interchangeable if with a new group of students you find different activities work better. (02/23/09)

### Question

I would like to make a function machine for my 1st graders. Does anyone know of a way to do this? (02/23/09)

I made one from a 1/2-gallon milk carton. Sealed the top with masking tape. Cut 2 rectangular holes on one side, one near the top and one near the bottom (roughly 1 inch by 2-3 inches). Taped a rectangular piece of paper on the inside to create a little chute (roughly the width of the carton and long enough to reach both holes. Covered the whole thing with contact paper. I used a pattern that I got from a workshop. It was very easy to make and the cost was very minimal. My kids loved it when we were introducing What's My Rule? Problems. There is room in between the two slots to put a sticky with the rule on it after they discover what it is. They quickly figured out that I had the output number on the reverse side, but still had tons of fun with the activity. (07/07/09)

We made one in our teacher workshops out of the animal plates and a small paper bowl. You know the plates that have the animal face and the ears? We cut a rectangle at the top and one at the bottom; we used the same one over and over for a template. Then we stapled the paper plate to the paper bowl and ta-da... a function machine. The bowl has enough of a curve that the card slides out the bottom, (sometimes with a little manipulating necessary.) One of our math coaches made one out of plastic needlepoint canvas, and pipe cleaners and decorated it. It was in the shape of a cereal box. They are so cute. She also put a curved piece on the inside so that the card would slide right out the bottom. She made me one and his name is Nathaniel Number Muncher. (07/07/09)

### Question

My kindergarten teachers have asked about the best way to use the thermometers for the Kindergarten routines. Do you put them outside? On their windows? What have others done with them? (07/07/09)

I put our classroom thermometer (that is color-coded with the color zones) between a window and screen. The children can easily read the temperature color zone each morning from our classroom by simply going to that window. It works great. (07/07/09)

### Question

My question is what where to store manipulatives and materials. If in cupboards, how does a substitute teacher locate them? (04/25/08)

My materials were usually out and visible, so I rarely had this happen. But here are a few suggestions; * perhaps you could put a sketch or a diagram of your classroom with the location of materials in your plan book * label your cabinet doors so everything is easy to find * be sure a neighbor teacher knows your system so he or she could assist, or * write a note in your Teacher Lesson Guide telling where things are in the Materials list at the beginning of each lesson. (04/25/07)

I leave all of my manipulatives in labeled bins and out for students to explore at free times and when they need them during math time. (04/25/07)

### Question

We are starting our first year of implementation and I am looking for classroom management ideas such as color coding the Everyday Deck of Cards and storing them in travel soap dishes. (06/02/09)

I buy pencil boxes to use as the tool kits. If you watch sales, you can usually get them for fifty cents apiece. Make sure to take a shape template along with you to double check the size. I tell the children that they are responsible for taking care of their tool kits. Every student has an ID number that coordinates with everything in his or her tool kit. That way if a shape template is on the floor we know whom it belongs to. Film canisters also work very well for storing money. Everything the children need throughout the year fits great in the pencil box. I only start out with a few items at the beginning of the year. We do a lot of training about how to use and care for the materials. As the items come up in the units we had it in the tool kits. (06/02/09)

I do not do the tool kit. I have manipulatives in plastic shoe boxes labeled: cards, dice, cubes, pattern blocks, etc. I have enough boxes of the pattern blocks and cubes for each group of 4. When we need items for games, I just take them off the shelf and kids come get what they need. I velcroed the template into the back of the Student Reference Book (SRB). I put the one side on the "back" of the template, so it lays flat for measuring and using stencils. Each template is numbered as well as each SRB. (Kids get class number at the beginning of the year.) I also bought the stretchy book covers when they were on clearance at Target this past fall. They have really saved the SRB covers. (The template actually slides right in there and really no need for the velcro, but I had already done the velcro.) (06/02/09)

### Question

When Frames and Arrows was introduced, the rule always included whether we were counting up or back. Now we are seeing in some math boxes count by 5's or count by 2's. It only mentions the direction when counting back. Are we to assume that if it is not mentioned we are to count up, or should we explore both possibilities? For example, if the rule is count by 5's and the first frame is 20, then the next frame could be 25 or 15. (12/05/07)

My name is Rachel McCall and I am of the authors for the Third Edition of Everyday Mathematics. You are correct to assume that if we don't specifically say "count back" then our expectation is that children will count forward. Often more than one frame is filled to reinforce that. However, in a case like you mention below in which the rule is 'Count by 5s' and only the first frame is filled, either answer would be acceptable--as long as the child fills all of the frames in the same manner and is able to justify his or her work. So, while I would expect a child to fill the next frames with 25, 30, 35, etc., a child who filled the frames with 15, 10, 5, etc. should not be penalized. (12/05/07)

### Question

I was discussing Everyday Mathematics with some other EM teachers. We would like to see more boxes on the math boxes dedicated to the current unit's skills. It seems like they need more practice before the Progress Check lesson. We know the spiral is important and has really helped to maintain the skills through the grade levels. Do any of you struggle with this? Do you make additional practice sheets to give the students more opportunity to practice the tested skills during a unit? (11/23/09)

Sometimes I use the blank math box page to make additional practice boxes. (11/24/09)

Some of the teachers in my district are using the 'Skills Links' books for this purpose. They are a separate purchase and teachers are being very selective about the pages they use. Also, the Algorithms handbook provides extra practice with algorithms. Another resource is the Assessment Assistant CD, which allows you to make your own practice sheets. (11/24/09)

While EM encourages teachers to use the games as practice, I always like to give students pencil and paper practice. It is only a few problems, like the Study Links. I began using EM in 1999. When I first started I would spend a lot of time cutting and pasting worksheets together. They have added so much to the curriculum that I don't find myself having to create worksheets or practice activities. I use the Assessment Assistant Worksheet Builder and the Everyday Math Online website. The online site gives you access to the Skills Link practice worksheets and the Algorithms Handbook practice worksheets. (11/25/09)

I find that the best "practice" is the games!! Play the games for at least 15 min per day. They are meant to be the practice part of the program, where other programs use worksheets. Then the math boxes can be used as a mini-assessment. (11/24/09)

### Question

How do teachers manage math boxes in your setting? Are they collected and corrected by teacher every day, corrected by students, etc. How do teachers use math boxes to plan for instruction? Are they used as homework? (09/21/07)

I no longer pull a grade off of math boxes. I use them as more of an informal assessment. Each student works on the individual cell, then the team members share the individual answers. The team then discusses the different answers (if there are any), and then I call on a member of the team to share the team's agreed upon answer. This tends to alleviate any embarrassment for a wrong answer. I also pick at least one or two cells a day for the students to share strategies on the white board so all learners can see how the problem was solved. I leave the pages intact until the journal is complete and then send it home all at once. This way the students can grade their own journals, and correct answers that were missed. I can watch the class as a whole and see who is missing what cell, and that can further drive my instruction. If I want an individual grade, I utilize exit slips, which give me a better idea of who is missing what concept. (09/22/07)

I use Math Boxes in many different ways. First of all, I usually have the students do them after the Math Message, since I often need a "buffer activity" between that and the lesson. It's usually done after Part A in the lesson manual. We go over the Math Boxes together, with the students correcting their own or a neighbor's using a colored pen, pencil or marker. I differentiate Math Boxes using a laminated chart I keep in the front of the room. It has 6 boxes arranged like a typical Math Boxes pages. I have laminated squares that either have an "H" (for "have to dos") or a "C" (for "choice to do"). I attach the squares using velcro to indicate which Math Boxes the students have to do, and which are choices. Choice boxes are harder review skills or skills that have not yet been introduced. In terms of correcting Math Boxes, I look at them as part of weekly "Journal Checks". Prior to the first day of school, I divided my class into 5 groups for the five days of the week. Then I put stickers of the same color/design for each group. For example, group one (Monday group) would have red stickers, group two (Tuesday) green, etc. At the end of Math class I'll collect the Journals of that group. This means I am looking at each child's Math Journal once a week, but I don't have an overwhelming amount to look at each night. I don't really use the Journals as an assessment, since students are encouraged to help each other, but I do use them to inform my instruction for upcoming lessons. (09/23/07)

In the 3rd edition, the last cell of each math box page (and sometimes the last two, it will tell you in Part 2 of the lesson) previews the next unit. In the 2nd edition it was the first cell that was the preview or prerequisite. Also, in the last lesson of each unit, the Progress Check lesson, the entire math box page previews the coming unit. Sometimes a cell of a math box page will be designated in the 3rd edition as the RSA (Recognizing Student Achievement) activity for the lesson. When that happens, the teacher's edition will show a red star on the Math Box page in that cell. In that case, that cell is a "Have to D0" and is used for ongoing assessment. Also, in the 3rd edition the math boxes at each grade level are paired. This was true only in grades 4 and 5 of the earlier editions. Now at all grade levels the math boxes are paired. For example, the math boxes for lesson 1.3 and 1.5 may look almost identical...same concepts and skills but different numbers. It will tell you which math boxes are paired in Part 2 of the lesson as well as in the Unit Organizer. (09/24/07)

### Question

I'm a 3rd grade teacher and am interested in hearing how others are using the Math Boxes page. I have tried several different things but still am not happy with what I'm doing. Another area I'd love to explore is writing in mathematics. I've picked up Marilyn Burns' book: Writing In Math Class. This is one of my summer projects. I am interested in hearing how some of you incorporate writing into your day. (06/13/07)

Although not 100% ideal, I use the Math Boxes two-fold. We do them together as a class on occasion. I try to do these with Math Boxes that have Secure Goals in them especially. I then use some of them as a "what do I do when I am done" activity. Whenever students are done with the Student Journal, Study Link, or other assignment in class, they are to work on any of the Math Boxes up to the lesson we are currently on. This is because we don't get to every set of them due to time constraints and other activities. I enjoy this way because they kids aren't just filling time or interrupting the class asking what they should do. As for the writing, I use the Exit Slips a great deal and writing pages that are in our Math Masters (interest inventory, write your own number stories). I teach 5th grade so I'm not sure what the 3rd grade has to offer. I also require that my students keep a Math Notebook. In that they define and put examples of their vocabulary words, add "rules" and formulas, and respond to the books that they read throughout the units. The responses vary depending on the story. I also have my students create their own shape book when we study geometry. Quick version: the student chooses a shape to be the main character (has to be a geometric shape). They write a story about that main character using math as their focus. We do this after reading "The Greedy Triangle". It is one of my favorite activities and the kids have a great time!!!! You can also incorporate writing by using some of the Projects EM offers (again, not sure of 3rd grade ones). (06/13/07)

I'd like to point out some Math Boxes features that are new to the Third Edition of Everyday Mathematics. Much of this information is also available on page 26 of the new grade-level specific Differentiation Handbooks. 1. Now, at every grade level, the Math Boxes page from one lesson is linked with the Math Boxes page in one or two other lessons. "Linked" means that the pages have similar problems. Because linked Math Boxes pages target the same concepts and skills, they may be useful as extra practice tools. 2. The final one or two problems on each Math Boxes page preview content from the coming unit. You can use these problems, identified in the Teacher's Lesson Guide, to assess student performance and to build your differentiation plan. The final Math Boxes page, found in the Progress Check lesson for each unit, summarizes the preview problems throughout the unit just completed. In the second edition of Everyday Mathematics, these preview problems appeared as the first or second problem on the page. As a result of teacher feedback that some students found it discouraging to begin with problems they hadn't recently encountered, the preview problems were moved to the end of the page. 3. Multiple choice problems, in a variety of standardized test formats, now appear on Math Boxes pages. The choices include distractors that represent common errors. You can use the incorrect answers to identify and address students' needs. You also asked about writing within the curriculum. Feedback from the second edition indicated that teachers wanted more writing embedded in the lessons. Below are some new features that can be found in the third edition of the curriculum. 1. Writing/Reasoning prompts, available in the Teacher's Lesson Guides, provide students with opportunities to respond to questions that extend and deepen their mathematical thinking. Using these prompts, students communicate their understanding of concepts and skills and their strategies for solving problems. Each Writing/Reasoning prompt is linked to a specific Math Boxes problem. 2. Each lesson in Everyday Mathematics contains a Recognizing Student Achievement note. These notes highlight specific tasks that you can use for assessment to monitor students' progress toward Grade-Level Goals. Many of these Recognizing Student Achievement notes contain specific ideas for Math Log or Exit Slip prompts. 3. Each Progress Check lesson includes an Open Response task linked to one or more Grade-Level Goals emphasized in the unit. The tasks provide students with the opportunity to become more aware of their problem-solving processes as they communicate their understanding, for example, through words, pictures, or diagrams. In the new grade-level specific Assessment Handbook you will find suggested implementation strategies, a sample task-specific rubric, and annotated student samples demonstrating the expectations described in the rubric. In addition, there are also suggestions for adapting the Open Response task to meet the needs of a diverse group of students. We hope you and your students will find these new features helpful. (06/14/07)

I love the Marilyn Burns' book: Writing in Math Class. I teach fifth grade and have used writing in a variety of 0A ways. The first phase of implementation was to begin a math reflection log. My original goal was for the children to write in it everyday, but realistically that did not 0A happen. I averaged about 4 days a week until the end of tthe year when we began slacking a little bit. I started the year having to model quite a bit. Most of my students had never been asked to write about math before so there was a lot of leg work in the beginning. I treated it just like a writing or reading mini lesson where I modeled my expectations for the first couple of days, then we did shared writing, and finally they began to have independence. Some days I will have them write about something that they learned, connected with, questions they have, or ideas they came up with or anything that they want to share with me about math. Other times, I will give them a specific topic like what is division and write an example of a division story problem and the number sentence. The third type of reflection might be a specific problem like what is 2/3 of 15 and have them solve it and explain how they got their answer. About half way through the year I realized that I needed a rubric so that the kids could self-assess. Linda Dorn has a book called Teaching for Deep Comprehension. It is a literacy book, but she has some very good rubrics in the appendix that she used for her reading reflection logs. Since the students were already using this in reading, I just modified it to meet my needs for math reflections so they didn't need to learn another rubric. One thing that I will add next year that I did not do enough of this year is put a section in the rubric for mechanics and sentence structure. Students did not carryover what they were learning in writing to their math log. I noticed entries with no periods, capital letters in the wrong place, etc. I only gave them about 5-10 minutes to complete the writing each day, so I am not expecting a perfect piece, but they do need to realize that the rules of writing go along with any writing not just the designated writing time. I will give them a minute at the end to go back and reread for quick fix mistakes. A second way that I use writing in my class is through weekly problem solving. These inquiry based activities require the students to use a variety of skills that we have worked on in class to show their understanding. They are usually something that is practical application. Oftentimes, I will use activities provided in the EM lessons or the projects, but I also create some of my own using the National Council of Teachers of Mathematics magazine publication, Teaching Mathematics or the Internet as resources. The students work cooperatively to solve the task and have to then create a written explanation for how they solved the problem and what their answer means. Sometimes they need to give a recommendation for "which" product that they selected if they are looking for the best buy or best fit, etc. They also will share their strategies for solving the problem and their solutions/recommendations with the rest of the class. (06/14/07)

### Question

Does anyone have vocabulary lists for EM that are grade level specific? (11/15/11)

Within the Differentiated Handbook in the Activities and Ideas for Differentiation section, for each unit there is a Vocabulary Development section that has a list of key vocabulary with the lesson the term is defined in. So for example in the Third Grade Differ. HB Unit 2, the list is on page 56. (11/15/11)

### Question

Does anyone have a vocabulary list done for the third grade, 2007 edition? I'd like to start on the words for the Word Wall to get a jump on the year. (07/27/07)

Your differentiation handbook and unit overview will have the vocabulary lists by units. (07/27/07)

In EM3, you can find the vocabulary words for each unit at each grade level in the unit organizers. They are broken down by unit. And the Differentiation Handbook offers effective strategies to support the language development. (07/27/07)

### Question

Is there a list of the books that go with the 3rd grade EM third edition? Is there a web page with the vocabulary words and meanings that can be printed? (09/12/07)

In the Section opener of each unit, they have a sheet called "Language Support" - I have a list of books for the lessons they fit with. This is the Kindergarten edition - but I'm guessing they would be in each one. (09/12/07)

### Question

I am in need of someone to give me tips and information on this program. I feel that it is too abstract for first graders and does not include skill practice. My administrator says it's the best program in the nation so I am committed to learn more and do it justice this year. (06/19/08)

If I can share two things that I have learned over the years (We used editions 2 and 3.) it is to do the calendar everyday, and DO NOT skip the games. Some games seem labor intensive and difficult, but they make a huge difference. This seems like a no brainer, but many teachers skip games when pressed for time. You should make a day for games once a week. I used Fridays. I used to separate doing the calendar and lesson. I found that breaking it up helps. My kids also had "morning work to do every day, and many times if I was pressed for time I let them do the Math Boxes for morning work. In the math journal have children highlight boxes that they cannot do so they can move on and do the rest. You can pull all the children who had difficulty with the same box in a small group to reinforce skills. I also had them keep a Post-It flag on the page of the journal we were working on so I could easily turn to that page to assess, check, or remediate. You won't believe how much time I wasted look for page #__ before I thought of the tags. I hope this helps. (06/19/08)

Please trust the program. I am a second grade teacher who has also taught EM in kindergarten, first grade, and fifth grade. The performance of the students is pretty awesome when the program is followed. You will have to spend time on this. I would suggest reading over each lesson before teaching it. Put materials where you will have easy access to them during the lessons. I use an overhead projector which makes teaching a lesson so much easier. The first thing my students do when they arrive at school is the math boxes from the previous lesson. To me that is an easy wake up assignment that can be done on their own for most children. At the beginning of the year, EM does a great job introducing the routines. Follow them through the year. In the first grade the calendar and number line are important parts of that routine. The lesson will take time to do. I have always set up my schedule so that I have an uninterrupted block of one hour that is always devoted to math. We usually go over that hour. That hour does not include them doing math boxes. We start out the hour correcting the math boxes that were done earlier in the morning. I have students use a colored pencil while we are correcting. I usually don't get worried when the child doesn't get something the first time. They will see it again. When correcting is done, I follow the order of the lesson. Make sure you have them play the games. That is where they will get the most skill practice. Make a running list of games they have learned on a chart. Tell the students that they can play these with a partner when they are done with their work and don't know what to do. I use games and explorations for my math center. You may want to highlight in your manual the children's books you have. I keep all of mine in the same cupboard that my math manipulatives are stored. I will end by saying that I love teaching EM. I have taught using this program for many years and I can't imagine not using it. My students still amaze me with the way they think. (06/20/08)

Just try it...you will be amazed at what your first graders can do at the end of the year! This is our first year using the program and everyone of us again it's the best thing we have done for our first graders in a long time...Don't worry about the skill practice, because of the spiral curriculum they do pick it up. (06/20/08)

### Question

I would like to ask for input on how some schools may have improved parent communication of student EM progress. My concern here is that the student math journal exercises that are found in Parts I and II of the program are spot checked only. As a parent who happened to see my student's work last night replete with errors and no corrections, I would want to continue to see this math journal on a daily basis in order to follow through with my child. I can arrange this because I work at the school, but I am afraid that this is not the regular process at our school. Furthermore, I can see how some parents that are not aware of how the program works in its entirety might be concerned about how and when work is "corrected." Also there may be some questions as far as why work is only spot-checked. I can see how a situation could occur at the end of the first EM unit or, worse yet, at the end of the first marking period if a parent does not receive notice that their student is not making adequate progress and they have not seen any "corrected" class work to date. I am wondering if any schools have worked out a way to communicate their "spot check" policies and/or provided an opportunity for parents to check on their student's class work via the student journal. (08/10/08)

I didn't "correct" a good portion of the journal, and did only "spot-check". But I did this in several ways. When I met with the parents at the beginning of the school year, and reiterated at every parent conference, I told them that I did not go over every journal page entry for several reasons. For one thing, many times they have seeing the work for the very first time and that isn't fair to grade someone when they just learned it. We also work on finding ones own errors as we go through the program. I would write every journal page that we did on the board and keep a running list. On the right hand side of my board I would write the math message at the top, under that was a line and "Journal Pages" was written, every time I said to do a page it would be written there and stay there. Every day I had a period of time for interventions --this was a time students could review with each other, play a math game and work on journal pages from the board. *ANY* pages or problems they didn't understand they were to make a note on the page that said they didn't "get it". That was their way of self-checking and trying after getting additional help. During that period of time I would call students up and ask to see random pages from their books. By the end of the unit I would usually have seen about 8-10 journal pages from each student's book, but a different set from every student. They never knew which ones I would look at and when. If it had a note, I would ask them to tell me what they were doing to get help if they were working with peers, if they wanted time with me, or asking a parent, etc. I wouldn't give them credit for doing the page, but I would offer lunch-and-learn help or recess time if they needed/wanted it. Parents were told that this helps their children help themselves. They were taking responsibility for their learning and being honest with themselves, so I asked the parents NOT to get upset when they saw mistakes or "help" notes in their books. By about 1/2 way through the year, I would have students writing on the board what they needed help with, and if you saw something that you understood you would explain it to me then work with peer students. This way, students were sometimes going back 2 or even 3 units in their books, but they made incredible progress throughout the year. Also, for what it's worth, I usually had about 30 students for math and with some lessons covering 3-4 journal pages plus study links and sometimes tickets out the door. There was no way I could correct 120-150 pages per night per class. (08/11/08)

In response to a question regarding how "spot-checking" or correcting of the student journals was communicated to parents I would like to share what I did while I was teaching 4th grade. I would regularly check and correct the journals at least twice a week. I would send the journals home at the end of each unit with a cover letter to parents regarding how we did the lesson. At that time our district was using the 2nd edition so some lessons were on "beginning" skills. I would also list the pages in the journal that could be redone ( would normally meet with students that appeared to have great difficulty with a student and send home "Skills Links" pages that reinforced the concept of skill). I would also list the Student Reference Book pages that explained and gave examples. This seemed to work well for my class and their parents. With the new edition, assessment of grade level skills is even easier to assess through the "Assessing Student Achievement" piece. This aspect could also be explained to parents at Open House, during parent conferences, or even a class newsletter or weekly announcement. Sally Rochester, NH In response to a question regarding how "spot-checking" or correcting of the student journals was communicated to parents I would like to share what I did while I was teaching 4th grade. I would regularly check and correct the journals at least twice a week. I would send the journals home at the end of each unit with a cover letter to parents regarding how we did the lesson. At that time our district was using the 2nd edition so some lessons were on "beginning" skills. I would also list the pages in the journal that could be redone ( would normally meet with students that appeared to have great difficulty with a student and send home "Skills Links" pages that reinforced the concept of skill). I would also list the SRB pages that explained and gave examples. This seemed to work well for my class and their parents. With the new edition, assessment of grade level skills is even easier to assess through the "Assessing Student Achievement" piece. This aspect could also be explained to parents at Open House, during parent conferences, or even a class newsletter or weekly announcement. (08/11/08)

Each student is a different color and I just rotate through them. So when it is their "day" I correct math journals, reading practice books, etc. What I do is I look through their math journals of pages but don't correct it because I feel that the "lesson" pages are their practice. Because I have to give grades I correct math box pages. Because they are paired 1.1 with 1.3, for example. After the children have completed the first one I go over it on the overhead I then grade the one that is paired with it when we get to it. I also have a homework feedback form I put on the back of every study link for parents to fill out so I know how students did on their homework. This is a way to get parents looking at homework etc. This will be our 7th year with EM and parents now know that the journals come home after the first one is finished and I explain what we do in math and how grades are figured up front. By letting parents know in writing and at conferences they are fine. When parents write on homework about concerns I respond back to them in note form or a phone call home. If it is an overall class concern I just type up a quick note to go home that night. If you are up front with parents it is usually fine but sometimes there are those that need some extra reassurance and notes about what's happening. Remember educating parents is very crucial to them not complaining about the program and you! (08/11/08)

### Question

Could anyone offer suggestions on how they handle criticism from parents about the program not addressing mastery of basic math facts as well as the use of various algorithms? Our district has used the EM for several years and every so often parents question this and I thought with the list serv we could reach out to others who may have had the same issues and perhaps use some of the same strategies. (04/27/08)

Show them your results on state tests. We have used EM for about 10 years now and we have observed a steady upward trend. There is no arguing with the data. We also have annual "Family Math Nights" at every elementary school, which is good PR. We invite kids and their parents to come in and play games. Select the games that address their concerns such as the games that help kids gain quicker recall of their facts. They will enjoy the evening and leave with a more positive feeling about the program. (We sell the math decks if parents are interested (at our cost of course). They have the directions for all games in the Student Reference Books which we let kids take home. We have also shared algorithms (and the reason for use of alternative ones) at PTA meetings. Don't overwhelm them but open the lines of communication and be proactive about the importance of NOT blocking kids thinking with the traditional ones that we all used. Show samples of student work. It tells a story of understanding. (04/27/08)

### Question

Does anyone have any suggestions on what to say to parents as you send home volume 1? I feel the need to explain that not every problem was tackled, not every page is finished, and some pages weren't assigned because we did them together or in another way. (02/20/08)

I came upon 2 letters that I've used in the past years. Maybe one of them would work for you. Dear Parents, Attached is your child's math journal. The journal serves as a source for students to learn concepts from the daily lessons, as well as to practice previously taught skills. There are various ways that we use the journals in class. Often students work together with their peers while a teacher walks around the classroom to help. Sometimes we complete problems as a class and other times students work independently so that we can check their progress. You may keep the math journal at home and use it as means for reviewing skills. Some pages are not complete or corrected. The pages with Math Boxes are the best ones for students if they are looking for some extra practice. You could even make up new problems on a separate sheet of paper based on the ones in the journal. Happy Problem Solving! Dear Parents, Today your child's Everyday Math Journal 1 is coming home. This journal is a portfolio of your child's work over the past several months. The journal shows growth or progress and documents the strengths and weaknesses in your child's mathematical development. You will find some pages completed all the way while others are not. Since this journal is a work in progress to show personal growth in applying strategies and mathematical thinking, many pages or items may not be graded. Your child may want to continue working on some of the incomplete pages or review pages from earlier in the year to see their growth. The journal, with all of your child's work samples, are yours to keep and do not need to be returned to school. Your child's teacher, (02/20/08)

This is the one we just put together for second grade. You're welcome to revise it to your liking. Dear Parents, Attached is your child's math journal. The journal serves as a source for students to learn concepts from the daily lessons, as well as to practice previously taught skills. There are various ways that we use the journals in class. Often students work together with their peers while a teacher walks around the classroom to help. Sometimes we complete problems as a class and other times students work independently so that we can check their progress. You may keep the math journal at home and use it as means for reviewing skills. Some pages are not complete or corrected. The pages with Math Boxes are the best ones for students if they are looking for some extra practice. You could even make up new problems on a separate sheet of paper based on the ones in the journal. Happy problem solving! (02/20/08)

I always send Journal 1 home, and have never had any parent issues. At our open house I explain to parents that the journal will come home in January, and not all pages will be complete. I suggest that the child finish these pages at home over the summer, or if the parent wants to help their child with skills and concepts. As far as other children at home, if one wants to complete problems undone, or begin to peruse what will be learned as they enter into 4th grade, yippee! (02/20/08)

### Question

We have done our best to answer questions and concerns about algorithms, calculators, mastery of facts, and spiraling with as much research and evidence as we can find, but some parents continue to share anecdotes about bad experiences with Everyday Mathematics. They claim there are no positive stories from parents or teachers to be found. Can anyone share links or documents that reflect positive testimonies? (04/14/09)

I have been involved with the Everyday Math Curriculum at every grade level PreK-5th since 2001. I have accumulated an abundance of positive stories in the last eight years, but here is my favorite: In 2001 I was teaching 1st grade in Knoxville, TN. The day's lesson involved writing number stories with the animal cards provided on Activity Pages 7 and 8 in the back of the Student Math Journal 1. A variety of numbers were available for students to access, so the lesson hit students at every level. Some of my first graders did something like, the 7-pound cat weight 1 more pound than the 6-pound rabbit. A student by the name of Jacob shared his number story with the class... that the 120-pound cheetah ate the 56-pound beaver and now weighs 176 pounds. I prodded Jacob to explain to the class how he found the answer (since we certainly weren't adding 3-digit and 2-digit numbers together on an every day basis). Jacob commanded his way to the class number grid, pointed at 20 and explained that he had started there. Before he went further, a student asked why he started at 20 when 20 wasn't in the problem. Jacob explained that he could imagine that the one hundred was in front of each of the numbers on the number grid. He went on to show that he had started at (1) 20 - the cheetah's weight, moved down a row (10), moved down a row (20), moved down a row (30), moved down a row (40), moved down a row (50)... at this point his finger was on the 70. Then he continued on, counting by ones... 1, 2, 3, 4, 5, 6. After a sum move of 56 boxes, he finished with his finger at 176 pounds and stated that 120 + 56 = 176 pounds. In first grade, Jacob would not have been successful using a standard algorithm for this problem (he was barely successful at staying upright in his seat), but the Everyday Mathematics program provided the tools and opportunity for him to accomplish it anyway. The program also provides the deep number sense that our students need to problem solve. (04/14/09)

We used Everyday Math in our elementary school for 12 years. Then a new administration decided to switch to Scott Foresman. In just 2 years we saw a huge difference in the primary grades. The children had little number sense and could no longer decompose and manipulate numbers as they had been doing with EM. When I started using EM one of my students (grade 2) was explaining how he added 7+8. He said "I added the 3 5's. The 5 in the 7 and the 5 in the 8 and there is 5 left over." I also had 2nd graders subtracting using negative numbers. This made sense to them because they were so familiar with the number grid. With EM the children are able to solve problems. Remember we are educating for their future not their past. (04/14/09)

What Works Clearinghouse, run by the US Government currently rates EM as the only program with positive intervention potential. Check out this site. http://ies.ed.gov/ncee/wwc/reports/elementary_math/topic/ (04/14/09)

I looked at the blog from the parent who moved from NJ and complained heavily about the sprialing aspect of the program. It's unfortunate the author did not understand what she was writing about. While it is true that not every concept has to be mastered the first time it is shown, by the end of the program the concepts will be. The corollary to this is that is the author assuming that no other subject sprials? I contend that all other subjects spiral or we would no longer need to teach reading beyond 2nd grade, cursive writing would be the only type of handwriting after grade 3, essays, book reports, and all types of expository writing by the end of 4th. EM, instead, provides a base for higher level math with connections that are usable because the way of solving problems is the same and not a new method. The FOIL method of multiplying binomials (x + 3)(x + 4) is the partial products method. 23 * 45 = (20 + 3)(40 + 5). Yes, many of the algorithms used in EM are not the ones parents were taught. However, I contend that many of the algorithms are ones that parents use! When parents used to work at stores that didn't tell you how much change to give back, I bet they "counted up" to calculate the change. Mental algorithms are not effecient when done on paper; similarly, pen and paper algorithms are difficult in your head (ever see someone trying to multiply with a carry by writing in the air). (04/15/09)

One other thought as to the use of calculators. We are exploring calculating the mean in third grade. The students are not yet able to do the division required for calculating the mean (I believe that is in 4th grade), but they are able to understand the CONCEPT of how and why to calculate the mean because we use calculators to do the division. The calculator allows them to explore the concepts they are able to understand and not be held back by the calculations they are not yet able to do. As for math facts, Everyday Math does include math facts - they are just not in a traditional form. Most of the fact practice is done through math games. My students love to play math games. They even choose to play them during indoor recess instead of other games I have available. The games also motivate my students to learn the facts. One of their favorite games is Top-it. It is basically like War. It can be played with addition, subtraction, or multiplication. Each player draws two cards. They each add (or subtract or multiply, depending on which version they are playing) the two numbers. The player with the highest sum (or difference or product) gets the cards. You can also control how difficult the game is by controlling which number cards they are using. (1-5 only for beginners or 0-20 for advanced, or anything in between.) (04/15/09)

### Question

I am looking for any information people may have about the Mathematically Correct group. (I believe that is the correct name of this organization.) We have a parent who is questioning Everyday Mathematics even though our district has been using EM for over ten years with a great deal of success. This parent keeps referencing this group. Is there any information out there that will be helpful to us as we prepare to meet with these parents? (03/30/10)

Mathematically Correct has been around since the introduction of the "reform curricula" including Everyday Mathematics. Here is a link to their website: http://www.mathematicallycorrect.com/ Program reviews the founders did in 1999: http://www.mathematicallycorrect.com/books.htm Their Wikipedia Site: http://en.wikipedia.org/wiki/Mathematically_Correct Looking at the history of the Wikipedia site you can see others have moderated some of (presumably) Mathematically Correct entries (POV for point of view in the notes - what we teach our kids - just give me the facts!) http://en.wikipedia.org/w/index.php?title=Mathematically_Correct&action="history (03/31/10)

Attached is an article that I received when the You Tube video came out, refuting the Mathematically Correct claims. We knew we would be getting lots of questions regarding EM since it is from our state.
(03/31/10)

attachment.doc

### Question

I attended the Network Communicate Support Motivate conference this week and was fortunate enough to listen to Marilyn Burns give a talk about struggling students and understanding numeracy. She mentioned a video that she saw on YouTube that basically attempted to discredit programs such as Everyday Math and Investigations saying that students should learn traditional methods as opposed to being taught to think and reason through problems. I was curious, so I watched the video today. I am just wondering if there are others who have seen this video and if there are thoughts about it. We have parents who sometimes think this way and a couple of members of our school board. We have been using Everyday Math for about 7 years now and it is still a battle with some to realize the benefits of teaching kids to think and reason through math. Here is the link in case you would like to watch it: http://www.youtube.com/watch?v=3DTr1qee-bTZI (03/23/07)

We had a parent pick up on this video a month or so ago. There are actually two on YouTube (one from a man from UW) and another from a meteorologist (woman). Both are painful to watch. We took a proactive approach. We first showed the video to ALL of our faculty, having them watch it without giving them any context. Afterwards, we asked them what they thought. Of course, the conversation was ripe with passion for how damming and inflammatory such videos are. We also had a good laugh at the video being on YouTube and how this was scholarly. Our message to the teachers: in the absence of hearing from us, this is what parents and board members will listen to. Our decision: ramp up communication about how and why we teach math (including more math nights, etc.). We also hit the board with a presentation. We outlined our EM adoption process, talked about progress and professional development, discredited the term new math by showing them why it is important to teach more than one approach in seeking deeper meaning. We were also transparent about the areas we would like to improve in, such as aligning computation practice and tracking, developing cohesive problem solving expectations, etc. We also made a clear statement that we put NO STOCK in a professor (or anyone else) who turns to YouTube to deliver such a message. We left the board with sense that we have thoroughly investigated the video and its sources and find no reason whatsoever to be alarmed by its message. We were careful in choosing a research-based program that has a proven track record. We threw in some Educational Records Bureau testing scores (which are very high) to placate the number people...Lastly, the administration put out a series of weekly articles about constructivist teaching, EM, etc. that aimed at bringing an awareness of how proud and lucky we are to have such a strong math program. Our approach took two face-to-face meetings and a series of articles and it was a dead issue. Not a peep since...One positive outcome from the video fiasco was that we had a wake-up call. EM is effective if it is taught the correct way. We have been keeping a closer eye on our teachers use of math boxes and computation check-ins. The program is designed to teach kids to be mathematically fluent in facts by certain stages. A fifth grade should have their facts down cold upon entering the grade (or at least a strong awareness of few areas to continue working on). This seems to be improving since we adopted EM, but we are now even more tuned in. (03/24/07)

As someone who has been teaching EM for 6 years now, you can pass along to your parents that the kids have MUCH better number sense after doing it the "new" way. It is hardest for the adults to change, but the kids adapt very quickly. After they have gotten the hang of several algorithms, I let them choose, and you would be surprised how many choose partial sums/ and then partial products for multiplication. More importantly, they have a much better sense of what they are actually doing than when they do it the "old" way. Also, our state math score have skyrocketed since using EM and the kids now find the test mcu easier! (12/18/07)

At the beginning of the year I asked the parents: If you were in the store buying 3 items for $2.95 how much would it come to? I took someone's answer and asked how they figured it out and was told, "I said 3 items at $3.00 is $9.00 then I took off 15 cents." I asked them why they didn't (and I went through the motions in the air) 5 * 3 is 15 put down the 5, carry the 1; 9 * 3 is 27, oh but I have that 1 so that's 28, put down the 8 carry the 2... When told that the other way was easier, I asked where they learned to do it. Wouldn't it make sense if we just showed that you can do this? Partial sums is used in the real world a lot! Many people do it that way in their heads, the written from used in EM is simply a way of putting it on paper. It is far easier to take a mental algorithm and put it on paper than to take a paper/pencil algorithm and do it in your head. 25 + 35 is 50 + 10 is 60. That's a lot easier than 5 + 5 is 10, put down 0 and carry the 1; 1 + 2 + 3 is 6 put that with the 0 so 60. Partial sums is a lot less to hold in your head. (12/18/07)

There is an article in the April 2001 issue of Teaching Children Mathematics (pgs. 480-484) that describes historical origins and relative advantages of many algorithms. In particular, about the partial sums method, it says: "The left-to-right partial sums algorithm was developed in India more than 1000 years ago." (p. 480) It provides a gold mine of a bibliography, too. (12/19/07)

### Question

I teach second grade EM. During our training three years ago, I believe we were shown a map of the world, with countries that teach the partial sums alogoithm identified. In educating parents about the partial sums algorithm, it seems it might help to show them other places in the world that use the algorithm. Perhaps this might help them see that they way they learned is not the only way. Does anyone have information on where this method is routinely taught? (12/18/07)

Wow, what a wonderful idea of making a map. In the meantime, you may wish to compute a list of careers who currently use the partial sums algorithm. A friend of mine in Cave Creek School District in Arizona told me that one of her students brought in a sheet showing how his dad uses the partial sums at his work. He is a pilot with I believe Southwest Airlines and would use partial sums to compute the weight of the plane prior to take off. I have also seen partial sums used in the area of accounting when large columns of numbers need to be added quickly to check to see if the electronic program is working correctly. Lastly, I showed this algorithm and many others at a training I was giving to the Foster Grandparents in our area who volunteer to work in our schools. Many of the foster grandparents told me that this is how they actually learned to do column addition as mental computation when they were young. Another good resource to show how partial sums is a natural way for students to compute addition is the work of Kathy Richardson. She has some amazing videos about Number Talks that show and explain what children do naturally versus what they are taught and how complex it is. She then shows the Number Talks in action with the students explaining their reasoning. This is truly outstanding work. I often feel that when parents see a piece of video, it adds understanding and a 3rd point perspective to the dialog. If anyone else has seen partial sums or any other non-standard algorithm used in the 'real world' please post this experience! (12/19/07)

### Question

Our district has been using Everyday Math for 4 years, and we are seeing positive results. However, Everyday Math and Investigations have both had some bad press recently. My Superintendent wants me to bring her the research behind Everyday Math. I need research from outside sources as well as from the company. (03/29/07)

Here are some links that were given to me by our local consultant. I think they're helpful. Student Achievement Studies: http://www.wrightgroup.com/index.php/home/everydaymathematics/emsecondupdate /stuachievestudies/52- Success Stories: http://www.wrightgroup.com/index.php/home/everydaymathematics/emsecondupdate /emsuccessstories/54- Research and Development articles. Check out the ARC Tri-State Study, the Longitudinal Study and Analysis articles: http://everydaymath.uchicago.edu/educators/references.shtml- One more: http://www.whatworks.ed.gov/Topic.asp?tid=04&ReturnPage=default.asp (03/29/07)

Our school district recently held grade level inservices on Everday Math. Our Assistiant Superintendant began each meeting reading an article from the Education Week Sept. 6, 2006 edition. It has some good information about research and quality of the program. I googled Education Week and then Everyday Math and went right to the article. (03/30/07)

### Question

Please take the time to read the article provided by the link below. This article was posted in the Philadelphia Inquirer on November 9, 2009. http://www.philly.com/inquirer/opinion/20091109_The__reform_math__problem.html The author poses her opinion about Everyday Math and the detrimental effects on Autistic students. (11/11/09)

Curriculum doesn't teach children, teachers do. All of the accommodations and modifications mentioned by this writer can be accomplished in any classroom using the Everyday Mathematics curriculum. I'm no expert, just a teacher who included ALL students in my mathematics instruction successfully...With Everyday Mathematics I think we're looking at a term that is often misunderstood. The National Council of Teachers of Mathematics (NCTM) published a series of standards documents which focused on teaching the standards, not through rote memory and application of specific algorithms, but through exploration and understanding the underlying standards. Basically, these documents (collectively referred to as the NCTM Standards) called for a curriculum to create mathematical thinkers. A program that is 'standards-based' usually refers to that idea. EM is the most popular, so that in itself could lead to a statement that like the one you had. When I present to the parents, such as at our open house, I push that it is presenting math the way that adults often do math -- which is in your head. By that I mean that if you asked a room full of adults how much it would cost if they bought 3 items at $2.95, they would most likely come up with $8.85 but they did that by rounding up to $3.00 multiplying to $9.00 then subtracting the total difference of $0.15. That way can be pretty messy on paper, but the traditional method doesn't work well in your head (I then demonstrate solving it in the air). I tell them that this is what their students are learning to do, and it is sometimes confusing on paper, but they can do it because they (like the adults) understand what is happening. As a small side note: today I was in a classroom that was teaching the 'counting up' method of subtraction. The teacher explained to the students that this was a method she had never heard of or used before. After she demonstrated I mentioned that it reminded me of the old days, when things were all in black and white, and before cash registers said how much change to give back. You saw the lights go on in the teacher's head. She *HAD* seen and used it before, just never seen it on paper. Then she was excited and the students had a very different lesson than they were about to get. Plus, the kids got to subtract by only adding, which they thought was very cool. (11/11/09)

I hope the author is not proposing to "throw the baby out with the bath water". Are we to abandon a proven excellent math programme because it does not suit the learning styles of autistic children, which, according to her article, is only 1% of the population? A good point was made by a respondent: "Curriculum doesn't teach children, teachers do". No programme can possibly fit every learner. That's where good teaching comes in. Sometimes, people forget that teachers are professionals and have extensive training and experience in their field, and that we can adapt our lessons and teaching methods to accommodate our students. (11/12/09)

I disagree with Ms. Beals. I have been teaching EM for 12 years, at various grade levels, and have never left my students unsupervised. When they are playing games or working in small groups, I am always circulating and observing, keeping close tabs on all that is going on in my classroom. As far as taking off points for incorrect oral answers, I don't know who would do that. Even if they did, a good inclusion teacher differentiates and modifies lessons to meet the needs of all students. Most children with autism will eventually need to survive in the world. EM teaches all children to think mathematically, not just perform rote computation (which most people use calculators for in the real world, by the way). Children need to be able to solve number stories, measure and analyze. EM teaches all of this. My autistic children are flourishing with EM. It's all about good teaching!!! (11/12/09)

### Question

We are using some slides from a prepared EM PowerPoint for our Parents' information night next week. One of the slides says that EM is the number one standards-based program in the country. We are expecting 500 parents and I'm sure someone may challenge that. There is no notation about what data supports this statement. Can someone point me to the right reference? Is that based on sales, number of schools using EM, number of children learning with EM, etc.? (09/26/08)

I think we're looking at a term that is often misunderstood. NCTM published a series of standards documents which focused on teaching the standards, not through rote memory and application of specific algorithms, but through exploration and understanding the underlying standards. Basically, these documents (collectively refered to as the NCTM Standards) called for a curriculum to create mathematical thinkers. A program that is 'standards-based' usually refers to that idea. EM is the most popular, so that in itself could lead to a statement that like the one you had. When I present to the parents, such as at our open house, I push that it is presenting math the way that adults often do math -- which is in your head. By that I mean that if you asked a room full of adults how much it would cost if they bought 3 items at $2.95, they would most likely come up with $8.85 but they did that by rounding up to $3.00 multiplying to $9.00 then subtracting the total difference of $0.15. That way can be pretty messy on paper, but the traditional method doesn't work well in your head (I then demonstrate solving it in the air). I tell them that this is what their students are learning to do, and it is sometimes confusing on paper, but they can do it because they (like the adults) understand what is happening. As a small sidenote: today I was in a classroom that was teaching the 'counting up' method of subtraction. The teacher explained to the students that this was a method she had never heard of or used before. After she demonstrated I mentioned that it reminded me of the old days, when things were all in black and white, and before cash registers said how much change to give back. You saw the lights go on in the teacher's head. She *HAD* seen and used it before, just never seen it on paper. Then she was excited and the students had a very different lesson than they were about to get. Plus, the kids got to subtract by only adding, which they thought was very cool. (09/26/08)

### Question

Why does EM start the year with a lesson that is so difficult for the children? In this, my second year teaching EM, I have NO students not even those on grade level, who begin the year able to identify prime and composite numbers. They also do not have the skills necessary to locate these topics in the Student Reference Book. Some questions, like how many cm are in 300mm are not even easily found in the book. These children have no idea what to look up to find those answers. (09/07/08)

I have my students work on this activity with a partner and with permission to ask the pair across from them if they need more help looking something up. I emphasize it is not part of their grade and just practice. If all of your students are having difficulty even looking things up in the Student Reference Book, then I would question whether it is was used at all in 4th grade. Maybe there needs to be more expectation that they look things up there before asking a teacher. (09/07/08)

My students aren't able to solve them. I use it as a way of previewing some of the topics we'll be doing and to basically do a book-walk. It isn't important whether or not they can solve it, it is whether they can find the information to tell them. (08/29/08)

### Question

After using Everyday Mathematics for about five years and recently purchasing the latest edition, our school is wondering if EM still supports a spiraling curriculum. Obviously, since skills are repeated throughout the book, it does, but we also understand that the National Council on Teaching Mathematics standards are now getting away from spiraling within curriculums. Does anyone know about this, have supporting evidence or care to comment? (04/28/08)

I'm thinking that what you might be referring to is "The Final Report of the National Mathematics Advisory Panel" put out by the U.S. Dept. Of Education. I recently was asked the same question you posed at a training I was doing for EM. I was caught off guard because I was unfamiliar with report at that time. So, I downloaded it and will share a few of my thoughts. In the section "Main Findings and Recommendations"...The Panel says that any approach that continually revisits topics year after year without closure is to be avoided. While some people who are unfamiliar with EM may believe that statement to be true, EM users know that there certainly is closure in the form of Secure goals or Grade Level Learning goals, depending on the edition you are using. Many of the findings of the Panel are very much aligned with EM: that by the end of grade 5 or 6, children should have robust number sense; that students need to have fluency with fractions; and that students should have proficiency with particular aspects of geometry and measurement (properties of two-and three-dimensional shapes using formulas to determine perimeter, area, volume and surface area). All of these topics provide the basic foundation for Algebra, which the Panel sees as a central concern and a "demonstrable gateway to later achievement." You can access this report yourself at: www.ed.gov/MathPanel (04/29/08)

### Question

Does anyone have any insight into why grade 4 begins with the geometry unit? Our students struggle with this unit and I'm curious if anyone can explain why UCSMP designed the sequence this way. (10/21/10)

I can't give an official answer, but I found the beauty of teaching that unit first is that you have the whole year to reinforce all the vocabulary and concepts that appear in that unit. (10/22/10)

I believe that the rationale goes like this: By 4th grade, too many students are beginning to view themselves as "not good" in math. Geometry tends to be more accessible to students and, as such, will allow these "struggling" students to feel better about their mathematical abilities. As educators, we need to connect geometric ideas and concepts to the other strands/topics on a regular basis and we need to make these connections explicit. (10/22/10)

Geometry is an important mathematical strand. It is crucial for our understanding of how the real world fits together. Geometry is related to the visual arts, architecture, engineering, mapmaking, astronomy, and other activities that require spatial thinking or involve creating material objects. Teaching geometry first is a way to start the year on an 'even playing field.' You don't necessarily need to be successful with typical elementary computation topics to succeed with geometry topics. Geometry is a natural and deeply intuitive part of mathematics for students. All students have an opportunity to get off to a good start. Opening the year with geometry enables a relatively relaxed beginning of the school year and allows teachers and students to get acquainted and establish yearlong routines. Students who have used Everyday Mathematics since kindergarten have had many experiences with geometry, and much of the content of the first unit of Grade 4 will be familiar to them. It's possible that some of the students who are struggling are new to EM and could benefit from the Readiness activities in Part 3 of the lessons. (10/22/10)

### Question

First off, I really don't care for this latest "standards-based" fad. Sure, it seems nice on the surface level, but for people who have actually read and tried to teach a standard - yikes. I mean, vague much? I love EM, and of course I am teaching it in order. Well, at a recent meeting, we got this district-generated document telling us to when to teach what skills. They aligned the document with EM, so it looks something like this: Teach lesson 12.2, then 5.4, then 2.3, then... Our city has spent a TON of money on EM, and yet jumping around in this way, in my view, totally negates the value of the program. What do you think? Should I abandon unit 3 and follow their document, or keep doing what I'm doing? (Note: I really don't mind getting in trouble as long as I am doing what is best for the kids.) (11/14/07)

Our district wanted us to do something like that the first year, but they listened when we complained. It messes up the whole spiral with the math boxes. We suggested they insert lessons to cover the concepts we needed to have taught before the state assessments in April. It worked for us. (11/15/07)

The EM fifth grade lessons do NOT hit all of the indicators that are tested on our state assessment, so you might want to double-check your requirements. I still like the program, but I do still have to supplement. (11/16/07)

There is a great article in the August 2007 issue of Teaching Children Mathematics, Grade-Level Learning Expectations: A New Challenge for Elementary Mathematics Teachers. The authors looked at many state standards for many states and compared them. Their conclusion was that there is not a true match from state to state. The article also discusses how a textbook can not meet every state standard for every state according to the state's scope and sequence schedule. As an elementary math teacher the challenge then becomes meeting the state standards even when a text may not hit each one when it is needed for state testing. We have had great success by using the philosophy of EM and the format of the 3 part lesson plan whenever we have to make adjustments to meet our state standards. Since EM suggests 3 to 4 lessons a week we use the other day to plan a lesson based on our needs. We use a lesson study format to develop a 3 part lesson, including the EM components our students are familiar with, for what we call a Power Day. This has given us a comfortable way to use the EM program to benefit our students and still meet the challenge of meeting those state standards. It also gives us a great way to provide differentiation for our students. (11/16/07)

### Question

Hi, I am seeking any current information or research supporting the use of EM in grades 3-6. My school system is thinking of only using EM K-2 (where we are currently using it), and then using something else for grades 3-6. I am vey upset by this as they are citing that the spiral is not proving effective and don't feel students will be ready for algebra. Please help I don't think I can go back to teaching from a basic text! (05/02/08)

I challenge your district to find a program that will better prepare students for pre algebra! (05/02/08)

My school district has implemented EM for a number of years with great results! Normally, we have some students begin algebra in eighth grade. Last year, we had over a hundred students begin Algebra I (not pre-algebra) in seventh grade. These students started EM in kindergarten. (05/03/08)

In our district, years back, we had (literally) a different company in each of our grade levels. Our Math scores were AWFUL!! About 2-3 years ago, we switched completely to EM and we've seen good results. It's only a couple years into it, but it is seems as though the test scores are on the rise... I know that isn't any "hard data" but take it from me - being consistent with a program is what ALL districts need!! I know that doesn't help you much but it's just the best for the kids... (05/02/08)

Much of the rhetoric from the feds focuses on research-based materials as the means for improving achievement. While I am not endorsing the What Works Clearinghouse (WWC), they did a review of hundreds of research articles related to elementary math materials, and Everyday Math was the only program rated as having "potentially positive effects." Another way to say that is that every program WWC examined other than EM was found to have no discernible effect on student mathematics achievement. http://ies.ed.gov/ncee/wwc/reports/elementary_math/topic/ So I would take the argument to the research base. Keep asking the question, where is the research base for these new proposed materials, and does it match up for the research base we have to support the effectiveness of EM? On that vein, where is the evidence that students are unprepared for Algebra? What data was used to make this determination? Have students actually matriculated from the full sequence of K-6 EM into Algebra I courses, and if so, what have we used to make a determination that those students are less prepared than previous cohorts of students? Does that measure align to the actual content of the Algebra I course? Be wary that this whole thing isn't being driven by an Algebra teacher at the high school who can't be bothered learning the partial products method of multiplication. Finally, "the spiral isn't working," isn't a logically sound indictment of EM when you can find numerous places where the spiral is working just fine. If "the spiral isn't working," this is far more likely that the problems are due to program implementation and fidelity within your district. It's fair to ask that if your district believes itself incapable of implementing EM effectively the way it is written, what aspects of the proposed materials make it confident that it will be able to effectively implement those? Professional development around the topic of effective implementation and supervision of spiral curricula may prove far less expensive than new books. We too often don't call people on ambiguous straw-man arguments like "the spiral isn't effective." Time for you to go on the offensive. Your district is about to invest a lot of money in new materials and there is a substantial research base that indicates there's nothing wrong with the old ones. Somebody that lives in your district will have a problem with that. Make sure they know what's happening. (05/05/08)

Starting in early elementary, students use function machines (in/out boxes, also called "What's My Rule" tables) to solve problems and find patterns. These are definitely an early introduction to algebra. [Note that in fifth grade they use variables at the top of some of the "What's My Rule" tables.] Also in early elementary, students use Parts and Total diagrams, which are an introduction to missing variables in an equation. In third grade, students begin learning to use parentheses to make a number sentence true. They continue to use parentheses throughout fourth, fifth and sixth grade in EM. Pan balance problems (grades 4-6) are an excellent tool for teaching algebra. (I had a high school teacher who attended a parent night in my school district who was going to take the idea back to his classroom so his kids would understand algebra better.) Some of the games used in EM that practice algebra include Name That Number, Algebra Election, Broken Calculator, First to 100, Credits/Debits, Spreadsheet Scramble, Getting to One and Multiplication Wrestling. If your school deems it necessary, perhaps they could be more intentional in some of the teaching of algebraic concepts. For example, they could encourage teachers to model how to write a number sentence for each problem in a "What's My Rule" table so they can "see" the variable. Personally, I think that when students see these tables written as an equation it helps them to solve them more effectively, as they look more like "math" to the students, rather than a table with missing numbers that makes little sense to them. Your teachers could also use the terms "variable", "constant", "function", "equation", etc. more often in fifth and/or sixth grade to call some of the algebra vocabulary to mind in a more intentional manner. You might suggest that your administrators read the part of the Teacher's Reference Manual that relates to algebra and show them some examples of the activities in which students engage (including some of the games listed above). If they want to see the algebra connection it is there. My students got more algebra in EM than they ever had in any other program, and they were well prepared for their algebra classes in middle school. (05/11/08)

If you look at the articulation of EM, it flows nicely into the University of Chicago School Mathematics Project middle/high school programs. Students can go into the Transition (pre-algebra) or sometimes right into Algebra from 6th grade EM, but if students need an extra year there is also a Pre-transition Math that fits in nicely either as a 6th grade course in the middle school program, or as an additional year of significant mathematics for students who need an extra year of math development before studying pre-algebra. (05/11/08)

### Question

I have been teaching EM for several years now, at different grade levels. This is my first time looping from fourth to fifth grade with my students. Last year, many of them struggled with partial quotients. Many of my parents fought me about teaching this algorithm. This year, the algorithm was reintroduced (love spiraling!). My children did amazing with it the second time around. Their accuracy and enthusiasm for long division is unbelievable. The few children whose parents encouraged them to stick with the old way, are still not able to divide. The rest of my class is now proficient (including decimals). It is so exciting to see the spiral work!!!!!! I guess my message is that we must all trust the spiral and even though I have been preaching it for years, I now have proof! (12/19/07)

I recall the first year that I taught partial quotients...the students were so excited to do "long division" that they asked if they could stay inside at recess time to do the partial quotients method. I went to my principal and asked him what could possibly be "wrong" with these kids. I had been teaching at various levels and had NEVER had this response to division. When parents question the method I invite them in for a short tutoring session and find that soon they are in total agreement with the method. (12/19/07)

### Question

Our district timelines do not match up with the order of Everyday Math. They want us to complete the book out of order to fit the curriculum timeline. Has anyone had to face this issue? I can't imagine the program would work since there is so much spiraling. (07/06/09)

I don't think that is a good idea. Our system has changed their timeline to fit the EM curriculum. The program works, but the spiraling is well thought out and I don't think it should be tampered with...I have taught all of the versions. (07/06/09)

Our state test demands that certain things need to be completed before the end of April. This requires some creative planning to finish all the lessons, while finishing all lessons relating to the state test by the end of April. It can be done. (07/06/09)

If you are doing multiage classrooms, then you may have to do lessons out of order anyway. I am teaching a split 4-5 Everyday Math class next year. EM advises to start the 4th graders with Unit 1 and the 5th graders with Unit 3 as that would put both groups in Geometry. But I do not know how that affects the Math Boxes, or whether a link (maintaining similar strands in the split class) can be achieved throughout the school year. (07/07/09)

Is it at all possible to make this shift throughout all grades using EM by shifting the books by 1/2 a year? In other words, start the first book (typically used for grade 1) to start mid way through K, so that they finish the 1st book by the time you need things aligned? Then you wouldn't be rearranging the spiral, you would just be shifting it a little. (07/16/09)

If you pace yourselves to finish the program by the end of the year, what difference does it make? You will end up in good shape. The only problem might be covering material for a state test by the time it is given if it is given in March or April. In which case you need to look ahead to see if you need to move something up. I certainly hope this is not your first year! Teaching a new curriculum is difficult enough without having to teach it out of order and with no prior years knowledge to fall back on. Your math boxes will not work for you if you are teaching out of order. You will have two journals going at the same time if you teach out of order. We put out pacing charts for each grade for each year based on the school calendar. If you were to cover a lesson a day in most grades you would have between 40 and 55 free days a year. We try to schedule four lessons a week - especially on the weeks you are giving a unit assessment. I understand a district mandating what must be covered at each grade by the end of the year but I have never heard of mandating when exactly it must be covered. We have some schools piloting performance based reporting. For those schools we have suggested skills and concepts to be covered each quarter based on their arrangement in EM. Best of luck in convincing the powers that be that covering the curriculum according to the EM map is best for all. (07/06/09)

I do not think the program will be effective if you teach the lessons/units out of order. The program is based upon spiraling concepts. The daily Math Boxes and Study Links (Home Links) have previous concepts included in order to spiral the concepts throughout the year. If lessons are not taught in order, students will continually come across questions that they cannot answer. Our district adapted the program to our state curriculum by following the program sequence and adding supplementary lessons where needed. The supplemental lessons ensure that our teachers are covering all material required by the state. This requires teaching more topics, but seems to be the only way to solve this problem. (07/06/09)

### Question

We have just started using the EM program this year in our 5th grade classrooms. We teach in a very highly competitive district. Parents are very upset with what they see as a lack of homework and how easy the program appears to be. We also have parents upset that we are not taking the time to stop and reteach each concept that their kids do not benchmark the first time they see it on the assessment. We have explained the spiral part of the program until we are blue in the face, but the complaints continue. Also, does anyone have a letter that they send home with the chapter assessments that explains how the programs works with regards to spiraling back to hit the concepts again? Parents don't understand that this is not a test in the traditional test but an assessment of their students knowledge. (10/09/07)

We had the same experience during our first year of EM. We are now in our 3rd year and parents are now singing it praises. I'm not sure that our parents saw the program as easy, but they were very frustrated with students having to learn the different algorithms. I send home the Individual Profile of Progress with each graded assessment and specify which items were to be secure. It is also helpful to explain to parents that many of the items that are taught in each unit are in the 6th grade standards for Ohio. For example, prime factorization doesn't have to be secure until 6th grade according to the standards. Would it help to share the alignment of EM with the standards to parents who are concerned about reaching the benchmark? Do you have that alignment? (10/09/08)

Standards alignment for Ohio can be found at ohedresources.com (10/09/07)

### Question

After 3 years of implementation, grade one students are still not able to count coin combinations (pennies and nickels) accurately. We have looked for activities in Minute Math, and we have highlighted the coin counting games to reinforce this skill. However, this does not appear to be having much impact on student success. I realize students do not use coins (or see parents using coins) as much as I did when I was a child so this is less of a "real life" skill for them than in the past. Does anyone have any suggestions to help these teachers/students? (11/22/08)

This has been a problem with many students as well at my school. I was recently introduced to "touch math" where they have some materials on coins and it has helped tremendously! Basically, each coin has touchpoints. penny=line under and they slide their fingers for one nickel=dot in the middle equals 5 dime=two dots (5+5=10) quarter=5 dots (like on a die...5+5+5+5+5=25 I hope that helps! After a bit, my students have internalized this and don't use the touchpoints anymore. (11/23/08)

The best way is to make it meaningful. One way is to set up a store and have the children spend coins that they have earned throughout the week. It is surprising how much a child will save to buy a special object in your "store" In Kindergarten, I did an economics unit where the children planned how coins could be earned doing certain things, such as jobs. The children have some great thoughts on this. We even discussed and then voted on whether children should have paid holidays and if a child should be paid if sick, or on a vacation. Of course their can be fines for certain things. . . if the children vote on it. You then have "paydays" once a week and discuss any needs in the community that arise and set aside some time for the children to spend their money OR save it to buy that something special (they love buying privileges like a lunch party). It takes some time to plan. . but the rewards are HUGE!! (11/23/08)

We use a money chart as part of our calendar routine. The children make coin combinations (with real coins which have velcro to attach them to the chart) to match the number of the date. (Ex. Coin combinations for 26 on November 26th) This gives them daily practice in counting coin combinations and we also work on exchanges using the money chart. With some of my kids who are struggling I'm also going to try using a number grid and placing the coins on the numbers. (A dime would go on 10, a second dime on 20, nickel on 25, penny on 26 etc.) This also could be done with the number grid pocket charts. (11/24/08)

### Question

My students had a great deal of difficulty with Study Link 9.7 (fourth grade). Lesson 9.7 is about working with population data and ranking it. It is somewhat tedious but not very challenging. The class enjoyed doing it as busy work. However, Study Link 9.7 is about ratio and percent and is very challenging. I don't see the correlation between what we did in class and with the Study Link. My students were very puzzled. (04/02/08)

Good question. One of the Key Concepts and Skills cited in Lesson 9-7 is "Order data reported as percents." I would agree that this aspect of the lesson wasn't the most challenging. Another of the Key Concepts and Skills cited is "Interpret 'percent-of' data." This gets at the concept behind the data that the students have been asked to order. For example, in the Math Message, students discuss what is meant by a statistic such as "21% of the population in the United States is 14 or younger." Later in the lesson students discuss what is meant by statistics such as a 2.0% growth rate for Haiti in one year or a -0.1% growth rate for Italy. All of this work with percents ties into the focus of Unit 9 - links among fraction, decimal, and percent names for numbers, with a special emphasis on percents. Unit 9 follows up on the work students did with fractions in Unit 7 - work such as finding the fractional parts of sets and regions. So now we move to Study Link 9-7. Students are asked to use population data from the 10 least-populated countries in the world to estimate answers to problems. Here are some thoughts as to how students might approach the problems given that the focus of the unit is on the link between fraction decimals and percents. 1. The population of Liechtenstein is about __% of the population of Dominica. >From the table students know that the population of Liechtenstein is about 33,000 and the population of Dominica is about 69,000. Think about it in terms of a fraction and then make the conversion from a fraction to a percent. 33,000 is about 1/2 of 69,000. 1/2 is equivalent to 50%. If the numbers seem too large for some students to work with, consider the Study Link 9-7 Follow-Up which states, "Some students may note that when working with populations rounded to the nearest ten thousand, they only have to consider the first two digits." 2. What country's population is about 33% of Liechtenstein's population? Students know the population of Liechtenstein - 33,000. They know that 33% is about 1/3. What's 1/3 of 33,000? Find a country in the table with a population close to 11,000. 3. The population of Vatican City is about __% of the population of Palau. Consider the strategy used to solve the Writing/Reasoning problem on page 761 of the Teacher's Lesson Guide. 4. The population of the 10 countries listed is 314,900. What 3 country populations together equal about 50% of that total? 50% is equivalent to 1/2. 1/2 of 314,900 is about 155,000. Find three numbers in the table whose sum is about 155,000. 5. The population of St. Kitts and Nevis is about __% of Nauru's population. >From the table students know that the population of St. Kitts and Nevis is about 39,000 and the population of Nauru is about 13,000. The population of St. Kitts and Nevis is about 3 times that of Nauru. Students can think about this problem in a similar way as they thought about the yearly growth rate in Haiti. (The Teacher's Lesson Guide referenced Student Reference Book, page 300 as a model for thinking about this problem.) Keep in mind that many of the Math Boxes problems in this unit focus on problems such as the ones in the Study Link. For example, Problem 1 on Math Boxes 9-7 offered the following: 10% of 50 = __ 5% of 80 = __ 20% of 40 = __ __% of 16 = 12 __% of 24 = 6 Last thought - I just finished reading "Open and Closed Mathematics: Student Experiences and Understandings" by Jo Boaler (Journal for Research in Mathematics Education, 1998, Vol. 29, No. 1, 41-62). Part of the study includes a discussion on student performance on contextualized questions. I thought about the study immediately as I compared the Math Boxes problems to the ones that were posed on Study Link 9-7. It might be worth a quick read. (04/08/08)

### Question

Can anyone explain to me the mathematical importance of tessellations? I am not sure I understand how they relate to other mathematical concepts. (01/09/08)

Tessellations are patterns formed by repeated use of polygons or other figures to cover a surface without gaps or overlaps. They can be mathematical models of real-life patterns such as honeycombs or chessboards, or simply patterns in the imaginations of artists like M.C. Escher, the decorators of centuries-old buildings, or students of Everyday Mathematics. Tessellations have wonderful connections to the EM strands of patterns, geometry, measurement, and even algebra. For example, in a regular tessellation, several of the same regular polygon meet snugly at each vertex in the pattern, such as the four squares that meet at each vertex on a chessboard. For a regular polygon to be able to tessellate the plane, the measure of its interior angle must divide evenly into the 360 degrees around a vertex. In the chessboard, the four 90-degree interior angles of the four squares evenly fill the 360 degrees around the vertex and so the squares tessellate the board. This can be generalized. The interior angle of a regular n-gon is (n - 2) * 180 / n degrees. If this degree measure evenly divides 360 degrees, the n-gon will tessellate the plane. Studying regular tessellations connects to all the mathematical strands mentioned above. But simply drawing or examining any tessellation allows students to use their spatial reasoning and pattern-recognition skillsskills that are important in many areas of everyday life, not the least of which is the pleasure we find looking at beautiful art. And because all tessellations can be described in terms of one or more transformations such as reflections (flips), rotations (turns), and translations (slides), they help students understand these important concepts of transformational geometry. For more detail about regular tessellations and much more information about many kinds of tessellations and their mathematical connections, see the Geometry chapter of the Grades 3-6 Everyday Mathematics Teacher's Reference Manual. (01/10/08)

### Question

Can someone give me a real world application of mean, median, and mode for a 2nd or 3rd grader? I try to begin new concepts with reasons why a concept is taught. I can think of all kinds of reasons for adults for this one, but none for children. (12/20/07)

For mean I used to use a big bag of M&Ms (nurses/dieticians-read no further:-). Give students different amounts, group them, then tell them to share. I had a bowl to dump them all back into (record the addition) then distribute (division) with the remainders going to the teacher. :-) I have used this set up in different grade levels, just adjusting the number of candies given out to allow or exclude remainders and to limit the totals for the computations. (12/21/07)

I think teaching mean, median and mode to our students is designed to give real world vocabulary to observations that children have been making since Kindergarten. If EM is taught with fidelity, then even pre-kindergarten students start to collect and look at data in a visual way. With the collection of temperature data over time (a kindergarten routine) children make observations about the number of cold days versus warm days, or red days vs. blue days (for example). They keep tally marks for attendance data in first grade (a routine introduced in Unit 1) to determine how many times there was 1 student absent, 2 students absent and so on. I've observed children expressing what they see verbally---for example, a kindergarten student says "if we have 1 more red day, we'll have the same number of red days as orange days" on the temperature graph. I've observed first graders taking the attendance data and forming a bar graph at the end of the month, so to make generalizations about the data collected. "We had 5 days with only 1 student absent this month". I think giving students the opportunity to learn the real names for this data information at an early age gives meaning to observations some have already made. When you consider the amount of informational text and non-fiction reading that students are exposed to these days (and required to comprehend) I think it just follows that we need to give them the tools with which to understand the graphics they will encounter in the informational material. (12/22/07)

### Question

Does anyone have ideas on how I could show students the reason two negatives become a positive when you multiply them together? Same with division... When in real life are students going to need to multiply two negative numbers together or divide two negative numbers together? I would like to give them a few real-life examples... (03/23/09)

You can show the pattern: 4 x 4 = 16 4 x 3 = 12 4 x 2 = 8 4 x 1 = 4 4 x 0 = 0 The first factor stays the same. The second factor decreases by 1, therefore the product decreases by 4. Hence: 4 x -1 = -4 and so on.... Then: -4 x 3 = -12 -4 x 2 = -8 -4 x 1 = -4 -4 x 0 = 0 1st factor remains the same. 2nd factor decreases by 1, the product INCREASES by 4. Hence: -4 x -1 = 4 and so on... (03/23/09)

I have a graph in the form of a wave, such as temperatures. If it is 70 degrees and it went down 2, what happened? 70 - 2. If it went down twice as much the next day, what happened? -2 * 2. Use a salary system. If they deduct x in taxes each week -- but one week you work twice as much, how much is deducted? How much did you earn? Watch the stock market or national debt. When the debt grows it is a negative * a positive. When it goes down it is a negative * a negative. (03/24/09)

I did a GOOGLE search for "REAL LIFE EXAMPLES FOR MULTIPLYING TWO NEGATIVE NUMBERS" and found a couple of interesting things. Math Central gives the example of the motion of an object along a line or even the motion of an object in 3Dspace. It also references a book that you and your students might find interesting: Barry Mazur's Imagining Numbers (particularly the square root of minus fifteen). Go to http://mathcentral.uregina.ca/QQ/database/QQ.09.08/h/stephanie4.html to see the full explanation. Ask Dr. Math gives instances of calculations using variables that can take positive or negative values, such as rates or positions in space. We might define the flow rate through a pipe in gallons per minute, with a positive rate meaning the flow is into a tank, and a negative rate being flow out of the tank. Then a process control computer (which is what I design) might calculate the time it will take to fill the tank by dividing the volume remaining in the tank (its capacity minus the amount of liquid now in it) by the rate. If the resulting time is negative, it means that the tank is emptying and WAS full some time ago. Go to http://mathforum.org/library/drmath/view/65645.html to see the full explanation. I liked the example of paying bills as well: 1. Let's say you get five bills in the mail for seven dollars each. You'd have 5 x -7 dollars, or -35 more dollars, i.e. 35 fewer dollars. But what if you had sent out five bills instead of getting them? Then, in a sense, you'd have gotten negative five bills, so you'd have -5 x -7 = 35 more dollars than you started with. Go to http://mathforum.org/dr.math/faq/faq.negxneg.html to see more examples. I'm wondering if the Credit/Debit game might be used somehow for this type of explanation. And then I think this explanation from Dr. Peterson to a question much like yours at Ask Dr. Math is also helpful... Date: 03/04/2004 at 09:32:50 From: Doctor Peterson Subject: Re: Thank you (dividing by a negative number) Hi, S.Y. Since you didn't specify the age of the child involved, I chose not to try to give an age-appropriate example. And I suspect that there are none to give! Negative numbers probably don't arise in ordinary daily lives except in very basic ways. After all, the world got along without them for a very long time. I like introducing the concept of negative numbers to young children using a concrete example (usually a thermometer); but there is no need to introduce multiplication and division by negative numbers at that point, because they don't arise in a child's experience--you don't need to divide by a negative temperature. Only when ideas like coordinates and rates are introduced is it really necessary to raise the question of division. That's not to say that children won't think to ask "if negative numbers are numbers, how do you multiply them?"; but perhaps if they ask that, they are ready for less concrete answers! - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ ; When you read his comment you can almost see the strand trace with negative numbers in Everyday Math. The mention of coordinates reminds me of the activities with coordinates in 5th grade where students are doubling and halving the size of objects (sailboats) they construct on a grid by changing the points they plot. (03/25/09)

We must be careful about falling into a trap where we have to explain everything we teach in terms of "When will we use this in real life?" The fact is, not everything a child learns will be used in "real life." What is so much more important than the application of any given concept is developing the ability to THINK abstractly and conceptually. We are trying to prepare kids for the 21st century, where many of the jobs we are preparing them for don't even exist yet. How do we prepare them for jobs that don't yet exist? The answer is by teaching them the thinking skills necessary to apply concepts, think creatively, abstractly and problem solve. So, while I respect your effort to find a real life application, and we should certainly try to do so whenever possible, I also think students need to understand that we are teaching thinking skills along with application of knowledge. Heaven forbid we only teach, and they only learn, what has direct application. How ill-prepared kids will be for life. Students need to understand that. (03/25/09)

tp://www.mathsisfun.com/multiplying-negatives.html Having students model the direction along the number line is especially helpful as an introductory, concrete model. (03/25/09)

We discuss this in the G4-6 TRM, (pp. 101-102), where we essentially agree with the fact that, yes, it's hard to model multiplication (or division) of two negative numbers. But then we give a couple of suggestions anyway: one looking at patterns and the other using properties. Here's a bit more. The real problem is why (-1)*(-1) = 1 (since (-a)*(-b) = (-1)*a*(-1)*b = (-1)*(-1)*a*b). Here's a proof of (-1)*(-1) = 1, not suitable for kids but important for teachers to understand. Start with the fact that every number times zero is 0. So, in particular, (-1) times zero is 0: (-1) * 0 = 0 Then note that (-1) + 1 = 0 and substitute into the left hand side of the equation above: (-1) * (-1 + 1) = 0 Apply the distributive law: (-1)*(-1) + (-1)*(1) = 0 which is the same as (-1)*(-1) + (-1) = 0 (because 1 times any number, including -1, is that number). Add 1 to both sides to get (-1)*(-1) = 1 The Ask Dr. Math page at the Math Forum has some models for multiplying two negative numbers: http://mathforum.org/dr.math/faq/faq.negxneg.html (03/25/09)

### Question

On Journal p. 37 fourth-graders are asked to convert 413 feet to yards and inches. My students understand they need to divide 413 by 3, but I don't think they have any previous work with division. I think they are introduced to it next Unit. Are we supposed to tell them to use their calculator on these problems? (09/27/07)

You're lucky that your students understand that they can solve conversion problems by dividing! This is my first year in Everyday Math and my kids can't even do that with a calculator. I would probably let them use a calculator, since they understand how to solve the problem but not how to divide yet. Since converting unit of measure is a standard in my state (NH) and my students have no concept of division, as a center activity we created conversion charts. The students worked in small groups and made charts that showed if 1 foot = 12 inches, then 2 feet = 24 inches, and so on. Students learned to count by ones for the feet and by 12s for the inches. They enjoyed making the charts together and I was able to differentiate by having adept students do harder conversions (such as 16 oz. = 1 lb.) and less adept students do easier conversions (1 yard = 3 feet). Once we were done, I copied enough conversion charts for each student to keep. (09/28/07)

### Question

I am a parent of twin 5th graders. They are learning about factorization, and their teacher insists on them using calculators when factoring numbers. When I learned it many years ago, we were not allowed to use calculators. Because of this, I learned my multiplication, division, etc. very well. I just have a problem with the whole calculator issue. Also, I was surprised to hear that students were allowed to use calculators on their state assessments. Any input from 5th grade teachers on this matter will be greatly appreciated. (08/24/07)

I teach 5th grade, and personally I don't let the students use calculators when we are factoring "smaller" numbers because that is one more way for them to practice their multiplication facts. I do, however, sometimes let them work with partners so they can work out some of the multiplication or division together. This lessens their frustration level and leads to more accuracy. That is not to say that your children's teacher should not be letting the students use calculators. She may want the students to be focusing on the process of finding factors rather than on the process AND the multiplication facts. I agree with you that children should memorize their multiplication facts. There is not enough time in the school day, however, to have students do that. A lot of it must be done at home. I hope you are one of the few parents who insist upon helping their children learn their facts at home. Unfortunately, too many parents don't help with or monitor their children's learning. If you work with them on their facts (or monitor their working together) several evenings a week, they will learn them and the idea that their teacher lets them use the calculator for factoring will not be an issue. They will probably be able to factor smaller numbers faster than their peers who are using the calculators! EM has wonderful cardstock fact triangles in the back of Journal 1. If your students are using them at school, you might ask the teacher if she would copy an extra set that you could cut out and use at home. As far as the use of calculators on the state assessments, in Kansas they can use calculators, but not on the parts where calculators would do them any good! The calculations part of the assessment is to be done without a calculator. Students can use calculators for parts of the geometry and measurement sections, for example, but what good will a calculator do them when they are to say how long a segment is? My opinion about calculators is that they are to be used when the focus is on the process, not on the calculations. I think students should know how to use calculators because we all use them in life, but we can't let students depend on them totally because we all also need to use mental math and paper/pencil math in life. (08/25/07)

I am a third grade teacher, but here are my thoughts on using calculators in math class. 1. In Everyday Math, many skills are introduced at a much younger age than traditional math programs. For example, my third graders learn to calculate the mean of a set of numbers. (I'm pretty sure I didn't learn that until junior high.) It would be way too complex for them to calculate it by hand, so we use calculators. The point of the lesson is for them to understand the concept of HOW to calculate a mean. This may be what's going on with your fifth graders. 2. EM puts a HUGE emphasis on estimating answers before calculating. In real life, if I need to do any calculating, I grab a calculator. An example would be balancing my checkbook. I am perfectly capable of doing it with pencil and paper, but it's much faster and more accurate with a calculator. Of course, as I work, I'm constantly estimating and making sure the answer on the calculator makes sense. EM teaches kids to do this. Hopefully a fifth grade teacher can address your specific concern about factorization, but I hope this gives you an idea of why EM uses calculators. (08/25/07)

### Question

The school district I work with uses the Houghton Mifflin Science series. Unit 4 in 5th grade asks the students to compare data from two line graphs drawn on the same axes. For example, they investigate and compare the month-by-month average precipitation for two different cities. The students need to answer questions such as "Describe the precipitation patterns in both places. Which place receives more precipitation? Is precipitation constant throughout the year?" I cannot find any examples in the 5th grade Everyday Math materials to develop and/or reinforce this concept. Is there some reason why this skill was not developed in Grade 5? Are the students developmentally ready to understand this analysis? Has anyone found a good resource to teach, "comparing two line graphs'? (01/03/08)

Third Grade EM has a yearlong activity where students create a line graph comparing the high and low temperatures around the U.S. It can be a weekly activity, where the students graph the high/low temperature for that day of the week, and then find the difference between the two temperatures. I coordinated it with a map of the U.S. and we would plot the cities each week as well. If you keep it to the contiguous states, it can vary from week to week where you find the high/low temperature and it becomes an integrated geography lesson as well. If students are unable to develop their own line graphs, the activity can be done as a whole class lesson on one big graph, where the students make their observations and use their journals to record the data, not make the line graph. (01/03/08)

### Question

Why does each lesson jump around from one idea to another in one given unit? The children seem to understand, or at least start to understand, the first idea and then we move on to another idea in the same lesson. Why is this? (09/17/07)

I'm wondering if this question is coming from a 1_3rd grade teacher who is on Unit 1. In Grades 1__3 Unit 1 is designed for assessment and review and establishment of program routines. It's like a K-W-L (What I Know, What I Want to Know, What I Learned) for mathematics. You "jump around" from lesson to lesson to get a feel for the mathematical knowledge your students have. If that's the case, you might recommend having the teacher read the Introduction and Mathematical Background section in the Unit Organizer for Unit 1. It might help her/him see the rationale behind this format. (09/18/07)

I personally do not teach math and am only a pre-service teaching candidate who won't be teaching until next fall after graduation (hopefullY!!!)...but I have had some exposure with EDM in my undergraduate placements (hence my subscription to this group!)? With that being said, it is my understanding that many topics seem to "jump around" because certain concepts are introduced?but are not intended to be learned at a mastery level right after one lesson.? Rather, the curriculum spirals 'round and 'round continually revisiting "old" lessons, where the students then look deeper into a topic when developmentally ready.? For example, multiplication is taught one digit times another, then bumped up to two place holders, and so on...when it reaches the point where decimals are introduced, it's essentially the same multiplication, but with a "." thrown in to deal with...And that example is ignoring how multiplication is just repeated addition...which?is itself another?example?of revisiting prior concepts to learn new ones.? ? One of?the instructors at my college said that it might not make sense on the surface, but the research indicates that we should "trust the spiral!"? I have no first hand experiences in seeing the results, but this is just my two cents based on my education...I am very interested in hearing?what other "real teachers" have to say though...along with anyone affiliated with the EDM program itself...ESPECIALLY if I am way off base!? :-)? I am here to learn! (09/18/07)

### Question

The second grade team at my school has a concern about math box #3 in lesson 10.10 of the 2004 edition. The problem, $3.74-$0.27, instructs to solve using partial sums. When you get to adding the partial sums you have .90 + .10 which makes for a carrying situation of $1.00. Can anyone help explain how you explain this to the kids? (06/05/08)

There are a few things you can do. The first is to encourage kids to add those lower partial sums mentally. So 90 cents + 10 cents would be $1. That really is mental math. I think it is really important to get kids away from following the steps of the algorithm and get them really THINKING about the numbers. The second way is to use the same type of carrying they use in the column addition method. They carry the one over to the next column. I think by far the most valuable lesson would be to have the student problem solve and figure out what to do themselves. I would be more than willing to bet that at least one student will come up with mental math to solve the problem. (06/05/08)

It's my understanding that Partial sums is for adding, not subtracting, so they must mean adding up from 27 to 74, so from 27 to 30 is 3 and then from 30 to 70 is 40 and 70 to 74 is 4 - that's a total of 47 cents; then $3.00 minus 0 is $3.00 - so the answer is $3.47. I don't have the 2004 edition and looked at the reference book for the last edition. When they tell students to use partial sums, they want them to add from the lowest to the highest number, by getting to the base-10s. If that makes any sense!! That's one of the ways I try to teach my students - there are so many ways, but when they are subracting to find change, they are counting from the lowest to the highest. (06/05/08)

### Question

I have a question regarding the Extra Practice section on a Grade 5 Home Link in Unit 1. It is a division problem (for example 29/4) and instead of the equal sign it has an arrow. Is it standard math notation that the arrow means estimate or round or what? (09/29/09)

Take a look in your Teachers Reference Manual for grades 4-6 in the Algorithm section (in my edition it is on page 133) for one explanation of the use of the arrow instead of an equal sign...I know there are other notes in the teachers materials as well but this one explains the arrow is used because the answer includes a remainder (which is not a proper number sentence)...To use the equal sign they explain the answer would be given with the remainder written as a fraction. (09/29/09)

I had a question the first time I saw this as well. If you look in your teacher reference manual in the essay about algorithms, under division (it is on page 121 of mine--2nd edition) there is a good explanation in the note section on the right side of the page. It has to do with when there is a reminder in division it is not actually a proper number sentence because of the R we use for remainder. So the arrow is used. If the remainder is expressed as a fraction or a decimal, then the = sign can be used. Sarah Meadows (09/29/09)

### Question

I received this question from a fifth grade teacher and I could use some assistance in compiling a response. A lot of the information on remainders is presented in fourth grade and I have referred him to those lessons. However, I am unsure how to respond to his last statement. I also said that If there is a remainder, it should be used to round the quotient to the nearest whole number before placing the decimal point. Here is his question: "Today I was teaching the students how to divide decimals by whole numbers and I was wondering if you could explain something. In the book it instructs us to tell them to divide the decimals as if they were whole numbers after they have done a magnitude estimate. The division is fine but what happens when the divisor does not go into the dividend evenly and there is a remainder? The book and program doesn't address it in the section I am teaching. This concerns me because on the Pennsylvania State School Assessment, the students could see division problems where they may have to extend the problem with 0's like we did using the old long division algorithms." (01/06/10)

I teach 6th grade and run into this often. Many times, the divisor is a number that when the remainder is written as a fraction, students know the decimal equivalent. I use this to help students. For example: .13 / 4 = .03 and 1/4 = 0.25. The student can then convert the remainder of 1/4 to the decimal equivalent, getting .0325. I have shown some students the way to "add zeros" with partial quotients division. If they finish dividing and need to insert a zero, a zero is added to the left hand side of all numbers in the division problem and quotients. 4 | 13 | 8 | 2 ______________ 5 | 4 | 1 ______________ 1 | Becomes...(if adding two place values). 4 | 1300 | 800 | 200 ______________ 500 | 400 | 100 ______________ 100 | Then they can continue dividing (01/08/10)

### Question

I'm currently teaching 5th grade, and we are on Unit 9. The past few days have been spent on using the rectangular method for finding area of triangles and parallelograms. Today, I was planning on them finding the formula for the area of triangles and parallelograms, but they couldn't even get through the rectangular method. Does anyone have any suggestions on how to teach this method? My students have a very limited math background. They may not have been taught anything about area last year. Thoughts on brushing over the rectangular method, and moving on to finding the formula for the area? (02/28/07)

I ABSOLUTELY would not skip this lesson. Students need the background knowledge of what area means before they are given the formula. Instead, use easier problems even if you have to start with a regular rectangle and subdivide it into two triangles. There are some problems that are easier. Students also need to know how area is used. So maybe in the context of a word problem or a situation in where they will have to use area students can grasp how to find area better. (02/28/07)

I'm not sure you can as the formula is based on half the area of a rectangle with the same base and height as the triangle. However you can concentrate only on drawing two perpendiculars (the height of the triangle up from the ends of the base. Connect them at the top. Cut down through the triangle from its apex and show the inside and outside of the triangle are the same. This is shown on page 692 of your TLG. (02/28/07)

You may be right and your students might not have much background with area...they may need some concrete experience with area to help them "see" the relationships involved in area. I have used things as simple as construction paper rectangles (different sizes) to just cut in half on the diagonal to show the basic idea that a right trianlge is half of a rectangle. Students can repeat this activity with a sheet of looseleaf paper. You can do a similar activity by recreating various triangles and parallelograms surrounded by rectangle(s) (for example from Journal page 316 ) and then "cutting" out the rectangles used in the rectangle method. Some students benefit from working from the whole to the parts.... Students can use geoboards and rubberbands to create triangles (and parallelograms) and the surrounding rectangles. I have used inch tiles to cover the rectangle to show a concrete model of area. They can record their work on dot paper or grid paper and note the area, base, height, and base * height. (In lesson 9.6 they could recreate the shapes from journal pages 318-319 on a geoboard, trace the rectangles onto the journal page and then cut out the rectangles, * I NOTICED ON MY JOURNAL PAGE 319 THE AREA OF PARALLELOGRAM G IS WRONG...IT SAYS 3SQ. CM WITH BASE * HEIGHT= 6 sq.cm ..THAT WILL REALLY CONFUSE THE STUDENTS TRYING TO FIGURE OUT THE PATTERN FOR AREA * I have also had the students create a "What's My Rule" table for the area and base* height information from journal page 319. * A great online geoboard is found at http://nlvm.usu.edu/en/nav/frames_asid_282_g_3_t_3.html?open=activities What I love about this link is the geoboard can be manipulated and will give the measures (area and perimeter). Try making a right triangle of base 2 and height 5...show the measures. Students can explore moving the vertex at the "top" or the triangle right and left (maintaining the same base and height) and showing how the area stays the same and exploring how the rectangle(s) they make to surround the triangle changes. * I have also used tangrams with area...one activity is found at http://mathforum.org/trscavo/tangrams/area-answers.html#parallelogram I think it helps students explore the relationships between the areas of the shapes. Hopefully the concrete explorations will help students really 'get it' when working with the rectangle method so that when they 'discover' the formula it will make sense!! (03/01/07)

### Question

The grade 3_5 elementary school I work at has been meeting to decide whether to include the lattice multiplication algorithm when we do multidigit multiplication later this year. I think it would be a terrible mistake not to include lattice along with partial products. Although I have quoted from the assessment handbook and the Everyday Mathematics website for including lattice, the decision is still up in the air. Concerns cited include that students use lattice as a crutch and that they can and do use lattice without understanding what is happening. With that as a background, do you know of any research I could cite about the value of lattice, or do you have any advice for me? (09/30/07)

I'm thinking that as part of "building algorithms" and "owning" information/knowledge, removing lattice would be a mistake. Yes, some of the children do latch onto it, but in some sense, so what? If it provides them with a method that they know will work, it will allow them to move onto more advanced things that require multiplication. Eventually they will stop doing it as they start to know their facts and use easier methods. I've had children in 5th grade that use repeated addition to solve problems, and they do get tired of it and find that they need to learn their facts for themselves and not because a book, teacher, or parent is trying to make them. At the beginning of the year I have many children who are using lattice, but as we play the games and they get more comfortable with partial products they stop using lattice. I would estimate that I had about 20 out of my 27 students using lattice at the beginning of the year and only about 4 or 5 by the end of the year. (09/30/07)

Last year was our first year using EM, so my fifth graders had not had any exposure to lattice multiplication. All of my students tried the method, and my 2 students who were least adept at multiplying kept using lattice. When the other students saw how fast and accurate these 2 previously-poor students were when they used lattice, a few of them starting using it all the time, too. I was amazed how proficient they were at it. We had races using lattice vs traditional or partial products. The lattice won more than either of the other two methods. This year, all of my students who were here last year use lattice. I have 2 new students. One of them is switching over, and the other one is continuing to use the traditional method. I don't think any of them know or care "what is happening," but it works for them. As far as partial products, they use it when the series says they have to, but they are much less accurate, and I still don't think it soaks in to most of them what they are really doing. I don't understand the crutch argument at all. It is a valid algorithm. I can't see anything wrong with using it. I think you would be cheating your students not to introduce it to them and let them use it if they so desire. Those two students my first year with EM sold me! (09/30/07)

The lattice method is mathematically sound - it's not just a gimmick that works. How many studnets using the traditional algorithm genuinely understand the math behind it? Many have just learned a process that works to get the answer. (10/01/07)

I would make every effort to reserve lattice for multi-digit problems. (3-4 digits x 3-4 digits) It is actually quite efficient when dealing with large numbers. I would, however, discourage MOST students from using it as a substitute for partial products. I have seen kids rely too heavily on lattice at the expense of ever developing the number sense and math concepts that come with proficiency in partial products. Once proficient, portions of partial products can be done mentally. Not true for lattice,. (10/01/07)

### Question

I am gathering data from parents regarding their questions/concerns about Everyday Math. The most common complaint I am receiving is that the do not understand the point of teaching the lattice method. Many called it "stupid" and said since the students aren't allowed to use that method in middle school, they shouldn't learn it. I would love to hear any and all information that might help us explain this to parents. I teach first grade, so although I am familiar with the lattice method, I am not sure how it is taught in relation to other algorithms or what research supports this method. (05/14/07)

My first concern would be why the lattice method isn't allowed in middle school???? Why would a district teach something for 3-4 years and then not allow students to utilize it? I think I would start there. (05/14/07)

Here is my personal opinion on the lattice method. If you need to multiply multiple-digit numbers, then this algorithm is by far the most efficient. Try multiplying something like 1,248 X 276 using the traditional method. It is extremely cumbersome and provides a lot of room for error. Now try it using the lattice. You will find it to be much easier. When I teach my remedial students I do not let them use lattice for smaller numbers such as 2 digit x 2 digit. I require them to use partial products. The reason being...I want them to become so proficient with partial products that, in time, they will be able to perform all, if not most of it mentally. They will never reach this level of proficiency if they rely on lattice. So lattice is great for large numbers, but smaller numbers should be performed using partial products. (05/14/07)

Frank Hatcher, a teacher in our district, showed this to me. Label under each lattice column - ones, tens, hundreds, thousands Do problem 27 * 34. Turn box 90 degrees to the left so columns are vertical. Do the same problem using partial products next to it . Numbers in lattice diagonals correspond to numbers in partial products. Each has 8 ones, 8, 2 and 1 ten, 6 and 2 hundreds Lattice is just another way of organizing the partial products. Look up history of John Napier and his "bones"--I think that is where lattice originated. I cut out strips corresponding to represent his "bones," laminate them and sometimes carry in my pocket when introducing lattice. (05/14/07)

n the 2007 4-6 reference book, it explains the reasons for introducing multiple algorithms. There are many ways to do computations. The lattice method was included for fun, historical interest, and practice with multiplication facts. It became the favorite of many students. It corresponds to place-value columns and has been used since A.D.1100 in India. (05/14/07)

Here is a perspective from a 24 year veteran high school mathematics teacher. Students do not need the traditional algorithms for algebra. In fact, the approach of EM is a much better preparation for algebra (unless the algebra teacher teaches algebra as a bunch of isolated rules and procedures). The algorithm for multiplying polynomials IS the partial products algorithm. For example: (x + 1)(x - 3) = (x*x - 3x + 1x - 3) = (x^2 - 2x - 3) -- Multiply each part of one polynomial by each part of the other polynomial, then add. Now dividing polynomials is a little different. Here is what the algebra polynomial division algorithm would look like using numbers only (forgive me if this turns out not to be readable when you receive it. I tried!) Divide 236 by 4. You divide each part of the dividend by the divisor and add: ____ 4)236 _____________ 4)200 + 30 + 6 50 _____________ 4)200 + 30 + 6 200 -------- 30 50 + 7 _____________ 4)200 + 30 + 6 200 -------- 30 28 ------ 2 + 6 50 + 7 + 2 = 59 _____________ 4)200 + 30 + 6 200 -------- 30 + 6 28 ------ 8 The polynomial algorithm is similar enough to either division algorithm that you will not be hurt by learning one or the other. (05/15/07)

Do your middle school teachers use algebra tile when teaching students multiplication and division of polynomials? Multiplying "polys" using traditional algorithm really involves partial products and the distributive property. The algebra tile is a very hands on visualization of the algorithm. The student can learn the concept and then relate it to a traditional algorithm - better yet development the algorithm themselves. We have students that may struggle with the traditional algorithm for multiplication of whole numbers but can learn the multiplication of polynomials using algebra tiles. Conversely, I have worked with students who can multiply using traditional algorithm yet struggle with the multiplication of polynomials. One does not insure the other. This doesn't relate specifically to lattice vs not lattice, but as is often the case in math, we want students to development a richness for multiple ways of approaching math. I think for students to become mathematical rather than just arithmetical, this "richness" is essential. The lattice method is rooted in partial products and from what I have found, can afford students success rather than frustration. Success breeds success - too much frustration can lead to "giving up". The algebra tile can be used to "visualize" partial products of whole numbers as well. Perhaps that would be a good background for students. And, as I mentioned before help students see the relationship of lattice to partical products to traditional algorithm. (05/15/07)

### Question

A 5th grade teacher and his students are troubled by the Study Link question #4 from lesson 7_5. The question is this: 115 _ 10_ + 3 * 5 =________. Some of the students solved and got zero for an answer and the rest got 30. The answer key says 30. Can someone explain why the answer of zero is incorrect? Has anyone else had this problem? (04/22/09)

You would square 10 first so the problem becomes 115 - 100 + 3 * 5. Then multiply, so you get 115 - 100 + 15 = 30. (04/22/09)

I think I might be able to help. If you follow the order of operations: 115 - 10^2 + 3 * 5 = 115 - 100 + 3 * 5 = 115 - 100 + 15 = 15 + 15 = 30 Exponent, then multiply, then either subtraction or addition. I think you are getting 0 because of the following: 115 - 100 +15 = 115 - 115 = 0 Technically, this is really 115 + (-100) +15= 115 + (-85) = 30 Any order is fine, as long as you watch the negative. For example: -100 + 115 + 15 = 30 15 - 100 +115 = 30 115 + 15 - 100 = 30 (04/22/09)

It is a subtle issue. Remember that addition is commutative and multiplication is commutative while subtraction and division are not. So to use the commutative properties as you describe, you are really changing the problem to all addition or all multiplication. I know it is a subtle issue especially at this level but the conceptual distinction between 7 _ 4 and 7 + -4 are important in algebra and beyond. So I would not want to rotely teach kids to always make that change without thought. So treating as an operation, 7 _ 4 + 5 needs to be done from left to right. Treating it as adding the additive inverse, 7 + -4 + 5, order does not matter. Same thing with division. Treating / (or your favorite division symbol) as an operation, 12/3*4, needs to be done L to R. Treating it as multiplying by the multiplicative inverse, 12*(1/3)*4, order does not matter. If you use your example of 100*40/2, you need to be careful about what you imply to your students. Order does not matter in this case regardless of how you think about it. But, consider the following example. Would your students think order does not matter? 12/3*4 L to R: 12/3*4 = 4*4 = 16 R to L: 12/3*4 = 12/12 = 1 Now, changing to multiplication only: 12*(1/3)*4 = 16 regardless of order. (04/23/09)

115 - 102 + 3 *5= 115 - 100 + 3 * 5= First do the exponent 115 - 100 + 15 = Second do the multiplication 15 + 15 = Third, subtract 30 Finally add The most common mistake is that kids assume addition always comes before subtraction in order of operations, as opposed to being equal order operations (so they are done from left to right). This is a great example of how that assumption can really change the value of an expression. This concept is very important as the kids move on to negative numbers, then adding like terms in algebra. It's worth emphasizing. It's also worth comparing a problem with parentheses like (6 - 2) + 4 with 6 - 2 + 4. The parentheses do not have any effect in this case. (04/22/09)

### Question

A question was brought up about what to do when using partial sums. Say the problem was 285 + 115 = ? Using partial sums, the students would either be forced to carry the partial sums or would have to go through the process again to avoid carrying. We are wondering how to teach students about this issue. (04/07/09)

The University of Chicago has updated the EM website with some excellent new FAQs and materials for teachers. Here's one that includes an explanation of Partial Sums in the Parent section under the heading: What are the Algorithms? Why are these part of the Everyday Mathematics curriculum? http://everydaymath.uchicago.edu/parents/faq In the Educators' Section, there's also a video of Partial Sums that may give you some ideas: http://everydaymath.uchicago.edu/educators/computation/add_partial_sums One thing that recently occurred to me about doing partial sums from left to right is that this much like the way we might count money from a garage or bake sale. In counting the proceeds, I would start by counting the biggest bills first and then continue counting up from there. (04/07/09)

If the problem is 285+115, students can use partial sums to get to 300+90+10. If they understand that addends can be added in any order, they can recognize that 90+10=100. This can easily be added to 300. I think that we want students to use their understanding of counting by tens along with their emerging understanding of the associative property of addition in this particular situation. All of the counting practice and all of the mental math work should help students compute efficiently. They should not be forced to start again, but should choose to use the number sense we are working so hard to help them acquire. (04/07/09)

I have found that a great way to record student thinking with partial sums (especially at first) is to record each step horizontally. This helps others understand their thinking and helps the student keep the value of the numbers clear. 285 + 115 _________ 200 + 100 = 300 80 + 10 = 90 5 + 5 = 10 _______________________ 300 + 90 = 390 390 + 10 = 400 If the students are used to using the whole numbers and mental math, regrouping is not an issue. Another option is to use an open number line to count up or to represent the partial sums that work well. The student starts by putting 285 at the beginning of the number line he/she is using. Then adds the 115 in pieces that make sense (ie the given place value OR get to the next ten, get to the next hundred, then add the rest). I model it with arrows above the line with how much is being added and label the number on the number line where that brings you below the line. +100 +10 +5 I_____________I_______I______I 285 385 395 400 Once again, by using the value of the numbers and mental math, regrouping is not an issue. I am hoping the visuals work on the computer. (04/07/09)

### Question

Can someone prove that the partial products multiplication and partial quotients method for division can be used for multiplying and dividing polynomials? That would go a long way in ending the alternative vs. traditional algorithm debate in our district. Is there a reason the traditional algorithms are needed for algebra? (05/24/11)

The partial products can definitely be used to multiply polynomials. Look at the following problems: In the problem 23 x 45, if you break 23 apart into 20 + 3 and 45 into 40 + 5, you can then multiply in the following manner (which is the same as the partial products method): 40 5 20 800 100 3 120 15 Then adding the partial products, you get the product of 1035. Now look at the problem (x + 2)(x - 3): x 2 x x^2 2x -3 -3x -6 Then adding the partial products, you get the product of x^2 - x -6. The partial quotient method is so important to understanding what division is all about. Think about the traditional algorithm. Where in the algorithm does it get across any understanding of what division is all about? If you divide 829 by 3 using the traditional method, students ask themselves how many threes are in 8 but they aren't pushed to understand that they are actually finding how to split 800 into 3 equal groups. The partial division algorithm helps students understand division. Taking the same problem, have your students start with 829 in base ten blocks. Ask them to share the blocks evenly between three people. They have 8 flats and give two flats to each person. They passed out 200 to each of three people so they passed out a total of 600. That is why we are placing 200 in the partial solution column and subtracting 600 because we have "spent" or taken out 600. That leaves 229. Now they can't pass out any more flats evenly, so they trade the flats for longs. They can pass out 7 longs to each person. This means 70 is a partial quotient (part of what the students will end up with) and they have "spent" 210 leaving 19. They can't pass out any more longs evenly, so they trade for units. They now have 19 units to split among 3 people and each one gets 6. Six is also part of the quotient, so that also goes into the partial quotient column. Each person got 200 + 70 + 6 = 276 and there was one left over. This method helps students understand what division means. The other method is only good for students who can follow and memorize a process. That leaves out students who learn in other modalities. Shouldn't we focus on educating ALL students and not just the ones who learn easily with memorized processes? Think about how often students struggle with identifying what operation to use in a story problem. I believe this is because of the traditional way we have often taught division. Students don't recognize division in story problems because they don't understand what division is all about. Stick to your guns on these methods...they work AND they help students understand what is actually happening. (05/25/11)

Keep multiplication wrestling horizontal forever. There you have your multiplication of polynomials! There is an advanced calculus teacher here in the district who uses the term "wrestling," as FOIL works for only binomials and wrestling works for any number of terms. Our middle school teachers love it when our students come to them wrestling and keeping the operation horizontal as the game does when it is introduced. (05/24/11)

Partial Products is what is used in Algebra to multiply polynomials. It just is not called that. Many high school teachers will teach an acronym called FOIL (First, Outer, Inner, Last). If you break partial products down as follows: 34 x 56 (30 + 4) x (50 + 6) You would do 30 x 50, 30 x 6, 4 x 50, and 4 x 6 which is FOIL for algebra. You can do Partial Quotients for polynomials, but it would be difficult to type in an email to show you. I have done it before with high school teachers to show them. (05/25/11)

Partial products multiplication IS multiplying polynomials. There is no carrying/regrouping in polynomial multiplication. Like terms are collected after the fact. Partial quotients division is important for helping students understand division. The traditional division algorithm is simply a scheme that makes partial quotients most efficient and productive (you could see it as a kind of culmination of the partial quotients algorithm). The traditional algorithm, unfortunately, loses much of its connection conceptually to what is going on and can confuse number sense (something you would not want to happen when initially learning about division). (For example, to divide 13567 by 18, you have to first divide 135 by 18. Well, how is 135 connected to 13567? A kid has to have significant number sense to make sense of this.) Now you have the issue of whether you WANT kids to be able to divide 13567 by 18 to multiple decimal places of accuracy without a calculator. Is estimation enough? Is calculator usage enough? That is where you will likely run into an unresolvable debate. With partial quotients, you can do this, but really need to know how many decimal places you want to carry it out before you start. I would not want to do this with partial quotients. The hard part in these debates is that you are admitting that there are objectives you no longer see as important, but that your opponents value. FOR ALGEBRA, if students know partial products and the algebra teacher realizes this, the teacher can make a nice analogy/connection to introduce polynomial multiplication. Great! Polynomial long division is similar but different from both partial quotients and the traditional division algorithm. If you have had experience with either, your work with polynomial division will be supported. Since the terms are separated in a polynomial, there is natural meaning related to dividing 18x^6 by 3x^2 when you really want to divide 18x^6 + 6x^4 - 3x^3 + 1 by 3x^2- 6. It is a natural meaning that is not there for dividing 135 by 18 when you really want 13567 by 18. Polynomial long division would be like dividing 10000 + 3000 + 500 + 60 +7 by 10 + 8 (but don't try this using polynomial division unless you are a real math nerd and like to see funky things happen with numbers and then like to figure out what is going on). PRACTICALLY SPEAKING, even in a rigorous traditional algebra course, your leading coefficients in a polynomial division problem are almost certain to be like 18 and 6 and NOT 13567 and 18. Thus, partial quotients would suffice for algebra (and Calculus, for that matter). Now, you cannot argue that high school curricula is changing and students don't need polynomial division any more--students who eventually take 2 semesters of Calculus or AP Calculus BC will need basic polynomial long division and the teacher/professor will assume they know how to do it (ask me if you need examples). (05/25/11)

### Question

Could any author tell us why Trade First was moved from Unit 11 to Unit 6 and then it is revisited in Grade 3 Lesson 2.9? This appears to be a disconnect. Is anyone moving it back to unit 6? (09/26/07)

My name is Cheryl Moran. I am one of the authors of the 2nd grade curriculum. We moved the trade-first algorithm to unit 11 because we felt that children needed more hands-on experience with the subtraction concept prior to being introduced to formal paper-and-pencil algorithms. To balance the move of the introduction of the trades-first algorithm to unit 11, we added more 2-digit subtraction practice using the Number-Grid and base-10 blocks in units prior to unit 11. (09/27/07)

My name is Ellen Dairyko. I'm one of the authors of Third Grade Everyday Mathematics. Cheryl Moran and I had many discussions throughout the 3rd edition writing process about the treatment of algorithms in the 2nd and 3rd grades. After using base-10 blocks and the number grid to solve problems involving subtraction in 2nd grade, it is expected that most children will be comfortable using manipulatives to solve problems involving subtraction early in 3rd grade. Note that in the Lesson 2-8 Recognizing Student Achievement suggestion (see TLG page 144), children are being assessed on their ability to solve 2-digit addition and subtraction problems with or without the use of manipulatives. Throughout the year, children will have the opportunity to learn and practice a variety of strategies for solving problems involving subtraction including paper-and pencil algorithms so that by the end of 3rd grade, they will meet the Grade-Level Goal that addresses addition and subtraction procedures in 3rd grade: Use manipulatives, mental arithmetic, paper-and-pencil algorithms, and calculators to solve problems involving the addition and subtraction of whole number and decimals in a money context; describe the strategies used and explain how they work. (09/28/07)

### Question

Do districts allow students to use Lattice as their multiplication algorithm of choice or require partial products? What happens when they do the division algorithm (EM way)? There is still subtraction and multiplication to do. What if a student is using the adding up strategy to do subtraction and lattice as multiplication? What happens when students go to middle school and teachers want them to use the traditional methods? What happens when algebra teachers say they have to have traditional methods to multiply and divide polynomials? What are districts doing? I asked Marilyn Burns these questions last week in Atlanta. She said Lattice is nice for enrichment. Let the middle and high school teach the traditional if they think they need them. Elementary should continue teaching for what makes sense. (03/27/07)

I have a real problem with the general population of kids using the lattice method. I love it for multiplying long, multi digit numbers, and for those kids who REALLY struggle with partial products, but I am increasingly concerned with the number of teachers who are allowing kids to use lattice instead of partial products. One of the greatest benefits to using partial products is that, once mastered, it can easily be performed mentally. It does wonders for developing number sense and mental math. The problem is that kids find the "tricks" of traditional and lattice to be easier (because it doesn't require them to think as much) and therefore do not use partial products enough to get to that level of proficiency with it. If I were a classroom teacher, I would insist that the general population of my students use partial products, and other methods such as traditional and lattice could be used as a method of differentiation. As for division...yes, it may mean that high school teachers may have to teach the long division algorithm in order to divide polynomials. However, what a small price to pay for the tremendous amount of number sense that kids will develop by using partial quotients. Kids really have to develop a deep understanding of estimation, place value, etc. in order to even perform partial quotients. What do they learn from long division???? ...besides how to memorize a set procedure that makes no sense, but somehow arrives at the correct answer???? Do your high school teachers know that partial products is the distributive property, that it is the FOIL method? Here is the bottom line...the ONLY thing that kids learn by performing traditional algorithms is how to divide or multiply 2 numbers. That's it. However, by practicing the EM algorithms over time, and becoming completely proficient with them, they will develop incredible number sense, estimation, mental computation and a much deeper mathematical understanding. Surely that is well worth the high school teachers having to spend a little extra time teaching a simple procedure for dividing polynomials. Besides, EM kids are so used to learning several methods of computation, I suspect teaching them long division with polynomials will be a piece of cake. Middle and high school teachers should be fully trained in the methods of EM, and the philosophy behind it should be fully understood by them. I see no reason for middle school teachers to force kids to use traditional methods. This may mean an intervention by your administration. We have only used EM for 3 years, and our middle school teachers are already telling us that they can see a difference in the number sense the kids are coming to them with. (03/27/07)

I have been teaching EDM for 4 years and still do not understand why some educators do not feel as though lattice multiplication is a valid algorithm. Just because it is not what has been done in the U.S. for the past 200 years does not lessen its validity. If middle and high school teachers are not allowing this algorithm I would be very upset. As long as a student has an algorithm that works for them they should be allowed to use it. I have a friend who teaches high school math and loves when students come in knowing how to do lattice because if they are having troubles with algabraic equations using the FOIL method she can show them how to set the problem up with a lattice grid and they immediately know how to solve the problem. (03/27/07)

I find that for Individualized Education Program and below level students lattice seems to work best and enables them to compute more difficult problems. Most students will tire of this method and will find partial products to work more efficiently. I encourage students that know their multiplication facts to move on to using the partial products. Our Middle School does not permit the lattice method, therefore getting students to move on is highly encouraged. (03/27/07)

I have never had a middle school teacher who had a problem with lattice as long as the children could get the correct answer. I have been teaching lattice for nine years now, along with several other methods and a high percentage of my students choose to use the lattice method whenever they can! (03/27/07)

### Question

Does anyone have any information on these traditional division algorithms? As you will see from the link, they are prototypes. It says the other algorithms will follow...Our district wants to remain true to the Everyday Mathematics series, while still addressing the need to have our students finishing 6th grade with proficiency in the traditional algorithms. These seem like a great tool to help accomplish this, but I'd love to see the multiplication versionespecially to see EM's recommended time frame (i.e. suggested timing for using the Projects). Does anyone have any more information on this? https://www.wrightgroup.com/everydaymath/support.html?PHPSESSID=a97ac32564c596a35d174635256d272d&gid=207 (01/28/09)

They are accessible online via your teacher/administrator account at everydaymathonline.com. If, however, your district did not purchase access to Everyday Math Online with your curriculum, you probably have to order the algorithm resource in book form from the Wright group. If you have an account, scroll down to the bottom of your home page and you will see the link. (01/28/09)

Even without the account they are available as a free resource from Wright Group. Go to the Wright Group website at www.wrightgroup.com and click on Math and then Everyday math and then Third Edition Everyday Math and then Support for Teachers. There are a lot of new tools on this updated webpage that you might find useful. (01/29/09)

Wright Group/McGraw-Hill, the publisher of Everyday Mathematics, is pleased to announce that online animations of Everyday Mathematics focus algorithms, as well as U.S. traditional algorithms, are available on www.EverydayMathOnline.com. The online algorithms are free to all EM users by logging in and clicking on "Free Resources". There you will find animations for partial-quotients division, column division, and U.S. Traditional Long Division. Additional practice and projects for both Everyday Mathematics focus algorithms and U.S. traditional algorithms are also available in the Algorithms Handbook. This is available to all Everyday Mathematics customers by logging in at EverdayMathOnline.com or may be purchased here: https://www.wrightgroup.com/everydaymath/buynow.html?PHPSESSID=ae87ed0fb53e0eb51f68fd4c1fadb2aa&gid=207 Please check it out as this should help meet your needs (and more)! Please let me know if you have any additional questions. (01/29/09)

### Question

How do other grade 4 and grade 5 schools handle teaching the Partial-Quotients Algorithm and traditional long division? Our grade 6 and 7 teachers are finding it difficult to transition students to long division when they do not use Everyday Math. (02/05/09)

Our district solved the issue of partial quotients division by a decimal by teaching the "column division" algorithm at the beginning of 6th grade. This has proved to be a great alternative to "traditional division". They seem to pick it up very quickly!! (02/05/09)

We also have started to use the column division algorithm as early as 4th grade in our district. Partial quotients is great, but when the students need to take their answer out to a decimal instead of just interpreting a remainder it falls short. This does not do that. It can be found in the new algorithm book (perhaps online?) and your teacher reference manual in the algorithm section (02/06/09)

We just used 90 minutes of an in-service day to bring in a consultant to work through the algorithms for third through eighth grade math teachers together. They each received the new algorithm book, although I see that much of it is also online now. That way everyone could see how the progression of the algorithms works and the number sense that is developed along the way. Elementary teachers can also teach the traditional algorithm after the concepts are built through the focus algorithms, but our Middle School teachers will also see that there is more than one right way to arrive at the answer and be willing to accept multiple algorithms. Everyone still has their own biases, but they've all had the opportunity to learn about the processes their students experience and expand their understanding of acceptable algorithms as they enter Middle School. (02/05/09)

As a math coach, I came to the realization that for children to truly be able to use and understand multiple algorithms, they must first understand the math thinking that goes behind each one. I was in a fourth grade class watching students use the partial quotient algorithm to solve a problem concerning jelly beans. Here is the prompt: Divide 143 jellybeans among 8 kids. In the space below, show two strategies (algorithms) you used to explain your thinking. I asked one student to explain why he chose to take 80 out of 143...(part of the process for partial quotient...) He answered because that's what I am supposed to do. I asked what does that 80 represent......He couldnt answer. That was when a light went off with me and and the teacher. From that point on, we asked the students to be able to identify each number on the algorithm within the context of the problem. It this case it was "Jellybean" talk. Within minutes, we had everyone able to indentify every number they wrote on their paper using partial quotient algorithm. This made it much clearer when the student came to the end of the algorithm and had a remainder of 7. Instantly they knew that the 7 represented jelly beans left over which was not enough to give each kid a whole bean. As we learned different algorithms, we were able to identify each step and number used as it relates to the context of the problem. Needless to say, as teachers we need to be giving children lots of opportunities to use these different algorithms within a context of problem solving situation. (02/05/09)

What concerned me most is that many of our high school honors students are using partial quotients and it is deterring from their learning. The students are writing out pages of work and frequently coming to the wrong answer. The students are asking for additional time to finish quizzes because the partial quotient work is taking so long. There is a fine balance between preserving the integrity of the program and assessing the needs of the students as they arise. This year our district added a unit on traditional long division for 6th grade. Students must demonstrate that they are able to use this method, but not required to use it throughout the school year. Because students have a good understanding of long division through partial quotients, it is not nearly as tedious to teach as in years past. It seems appropriate to introduce students to as many methods as possible, which would include both partial quotients and traditional long division. (02/05/09)

My question is about how the students instructed in how to CHOOSE numbers when using partial quotients. If they are not taught where to begin- like a number in the 100s- use 50s, 25s (like quarters) and then go to tens- they may not be very efficient with the process. However, I have not found a kid yet that can't use partial quotients efficiently when they are taught this process. This also gives them an understanding of the meaning of division- rather than just a process by which they arrive at an answer. (02/05/09)

### Question

The grade 3_5 elementary school I work at has been meeting to decide whether to include the lattice multiplication algorithm when we do multidigit multiplication later this year. I think it would be a terrible mistake not to include lattice along with partial products. Although I have quoted from the assessment handbook and the EM website for including lattice, the decision is still up in the air. Concerns cited include that students use lattice as a crutch and that they can and do use lattice without understanding what is happening. With that as a background, do you know of any research I could cite about the value of lattice, or do you have any advice for me? (09/30/07)

I don't know any research, but I think that one point you could make is that it is yet another strategy for students to successfully find an answer. Some children have a very difficult time, so if they can do it with lattice, then isn't that what counts? NO Child left behind. HEEEE. Although I understand their concern, it doesn't make sense not to give students every chance to get it right. (09/30/07)

You can read an interesting explanation of lattice multiplication and its role in classrooms here: http://rationalmathed.blogspot.com Also, look at Dr. Math’s archives for an explanation of its history and the place value connections. (09/30/07)

### Question

I have two second grade students who have great difficulty in math. They struggle with number sense and applying concepts. We are at the point in the program where the Partial-Sums Algorithm will be introduced. I spoke with our special education teacher who recommended that I teach the standard algorithm for double-digit addition rather than Partial Sums. As the "math coach" for our building I am having a hard time and feeling guilty about veering away from the program on this. I am looking for advice on teaching Partial Sums successfully to students with number sense difficulties. (11/16/09)

You should keep in mind that the standard algorithms were not chosen by educators or mathematicians; they were chosen by publishers because they take up the least amount of space on a page. The shortest possible shortcut is not the best way to learn a process, especially for students who are already struggling. Why are they struggling? Do they need more time with base 10 blocks, number grid activities, and trading games? The strengths of the Algorithms lie in making place value explicit and only doing one step at a time. For students struggling with number sense, making the place value more explicit would be highly desirable. I encourage you to let the program work. (11/16/09)

I also teach second grade , and have been using EM for 6 years. Our SPED teacher has also found that many of our Math students who struggle do a better job using the regular algorithm( Carrying) when learning this concept. (11/16/09)

I certainly would not revert back to teaching the standard algorithm. The partial sums algorithm helps the students maintain place value. It makes much more sense to teach it. I find it very helpful to use the base ten blocks when teaching this algorithm. That way, the students see first hand how adding the tens and ones together works. Are you certain that the special education teacher you spoke of knows the partial sums algorithm. I really can't imagine that she would prefer to teach the traditional algorithm that makes very little sense to kids except for its roteness over parital sums. Try it! I think you'll be surprised at how quickly they catch on. (11/16/09)

Being the focus algorithm I would strongly reccommend staying the course with the partial sums addition. They will see it again and again going up through the grades. Also, it is how multiplication will be taught, using partial products. I would much rather see students understanding how to use partial sums than how to use the procedure of the standard algorithm. If the students are struggling with this concept, it could be that they have not had enough experience with the base ten materials, which starts as early as kindergarten. For some of our struggling learners, we have them create the number using arrow cards and then pull the number apart in order to see the tens and ones. Then create the number using base ten materials and put combine the ones and tens. The students then create the partial sums using the arrow cards and then combine the patial sums to get the total sum. I have put arrow cards online to download at: http://www.suscom-maine.net/~greeley/enmath (There's an activity there as well that explains how to use them. It's my stuff. Feel free to copy them and use them. That's what they are there for.) Another good resource is the National Library of Virtual Manipulatives. In particular, the base 10 addition activity. http://nlvm.usu.edu/en/nav/frames_asid_154_g_2_t_1.html Once students have played around with base ten materials enough to know ten units makes one ten...ten tens makes one hundred and so on, this site is great for seeing how to put these pieces together. (11/16/09)

### Question

I am having trouble explaining to my second-graders that equations can be written with the answer first or last. Ex. 7 _ 3 = 4 or 4 = 7 _ 3. We have even noticed that in lesson 2.12, the Recognizing Student Achievement for this lesson has one of those kinds of problems. My students, with the exception of one or two, all got this wrong because they had trouble with the equal sign being first. All of them would have gotten it right if it was written in the more traditional way. I understand that students need to get used to seeing equations written both ways, but is it fair to assess them on it, especially second graders? (10/27/08)

Please remember that = means "the same as" -- 4 is the same as 7 minus 3 or 7 minus 3 is the same as 4. This is really important, especially as your students progress as mathematicians -- critical concept in algebra. (10/27/08)

I too have a tough time explaining that math box to the kids... most of them get it wrong. I explain that the turn around numbers in the equations are very different and that the subtraction ones always start with the 'higher " number. I created a cut and paste activity that separates all of the different equational parts and then I have them place them in the correct equation.( even ones with the equal sign switched. ) I also stress that they have to read the equation just like they read a regular sentence. ( kids always want to read them backwards) (10/27/08)

It is not a good idea to teach students "rules" that only work for a while. When they move a little farther along with subtraction concepts and the"larger" number is subtracted from the "smaller" number (which gives negative numbers), it is very confusing for them and leads to some misconceptions that also carry on into Algebra. (10/28/08)

I think it is an important mathematics concept for children to understand, that the equal sign is not just a sign in an algorithm, but a concept of equality or balance. This helps children understand the concept of equal much better as they get older and helps with their understanding of algebra. I would use a balance to demonstrate this with the equal sign being in the middle and using blocks to balance this out. For example: Start with 7 blocks on the left side and 4 on the other and how many do we need to take away to make it balance or make it equal. Do a number of examples using the "answer" on both sides. (10/29/08)

The way I address it is have the kids cover up the _____ = if it comes first. That way they can read the number sentence. When they come up with the answer, they uncover the _____ and put it on the line. I also start showing them that number sentences can be written in the opposite direction from the beginning of the year. This helps some. (10/29/08)

### Question

I have a parent who feels that Partial-Product and Partial-Quotient Algorithm methods are "stupid and a waste of time". Are there any research articles that talk about the benefits of learning these methods? (02/22/07)

Just keep your equation horizontal and send it home right along with an algebra problem solved with the (foil method). I have had no parent complaints when they see how it eases right into algebra. (02/22/07)

I am not sure you will find any "research," but sitting down and talking with these people may be your best bet. Parents need to be reminded that we live in a global society. They do not use the same algorithms around the world that we do. Ours may be standard in the US, but not around the world. Are we so arrogant to think that ours are the best when our kids are ranking middle of the pack according to the TIMSS report? It occurred to me the other day that when we teach reading, we teach kids to read the words, and to comprehend the entire passage, yet we have not been doing the same with math. We have been teaching kids computation, but not "math comprehension." We have not been teaching kids to understand math the way we want them to understand text in reading. Partial sums and partial products does just that - teaches math comprehension. Standards algorithms are tricks and shortcuts. While they may seem more efficient to calculate, they do nothing to develop understanding. Once kids become proficient with EM algorithms, they will perform them mentally. The same cannot be said for traditional algorithms. (02/23/07)

There is an explanation on the parent's page of the Everyday Math website found at http://everydaymath.uchicago.edu/parents/faqs.shtml. (02/22/07)

Question: What connections may be made to increase students' understanding of calculation procedures? Our Answer: Examining the partial products is more likely to place an emphasis on the value of the digits in a problem and may extend an understanding of place value. It may also increase students' understanding of the steps that are involved in the standard multiplication algorithm, in particular, noticing that two partial products involve a quantity of tens in two-digit problems. This leads to a better foundation for later work when multiplying algebraic expressions. For example, this can be connected to procedures for multiplying expressions, such as (x + 2)(3x - 1). Having read (somewhere) that students in the United States are behind many countries in the understanding of place value, I would think any additional exposure would be healthy. I almost forgot. I obtained a copy of a math book that dates back to the 1800s, early 1900s. In it they present various ways to add/multiply. Among them were partial sums and partial products, though they were not called such. This is not new. (02/22/07)

In the February 2003 edition of Teaching Children Mathematics, there was an article entitled, "Toward Computation Fluency in Multidigit Multiplication and Division", that compares traditional algorithms to what they call more accessible methods ( which are actually the partial products and partial quotients methods). l always share this article with doubting parents because I explain that this article was in a monthly magazine published by the National Council of Teachers of Mathematics who has no direct ties with Everyday Math, rather they recognize best practices. (02/22/07)

### Question

I have a student who is having difficulty with the Partial Quotients Algorithm method. If we talk about division the student understands the concept of division. He can split up money equally. He loves the lattice method and is very proficient at his number facts for multiplication. He has viewed the power point that Rina Iati created and enjoys it but is having difficulty transferring the information that he is seeing to pencil and paper problems. The student has a hard time putting the numbers in the proper place. For example, instead of putting the groups of 10 on the right side of the problem he will put the 10 under the quotient. Does anyone out there have a graphic organizer or a strategy that they use with similar students? (01/04/07)

I don't know if this will help him visually, but I always tell students to extend the horizontal line through the vertical so there is a place to put his "guess." For example, ____ 6)153! 120! 20 ---!---- 33! 30! 5 ---!---- 3! Answer: 25 R3 The horizontal line acts as a space that must have a number on it. It is also helpful because if a student "guesses" 10, then 10, instead of 20 the first time, there is a place for both 10's. I have seen some students put the first 10, then guess 10 again, but not write it because there was already a 10 there...does that make sense? (01/05/07)

### Question

I have a teacher who is having difficulty dividing by decimals using the Partial-Quotient Algorithm. She can get the answer using column division, but not when she uses partial quotients. This is the problem: 85.6/5. The answer should be 17.12. Could someone please explain how to get this answer using partial quotients? (02/18/09)

Everyday Math wants the students to estimate what the answer should be before solving the problem. After they do that they use that estimate to determine where the decimal should go. Ex. About how many 5's are in 85? About 15. So the decimal once you solve using partial quotients will go after a number that will be in the tens. When they solve using partial quotients they need to ignore the decimal in the quotient. The fifth grade book explains it better. Basically they have to estimate where the decimal point goes. (02/18/09)

85.6 divided by 5 would start with taking out a friendly number of 5s. It this case, 10 fives or 50. Subtract 50 from the 85.6 leaves 35.6. Then think that there are seven 5s in 35, so that means you remove 7x5 or 35 from the remainder of 35.6. That leaves .6. So the next move is to think of how many 5s can I get out of .6? Well, its got to be less than one whole five.....in fact, it would be about 1/10th of a 5 or .5. (.10 of 5= .5) So remove .5 from the remaining amount of .6. This leaves .1. So now think of how many whole 5s can come out of .1 or it could be represented as .10? Its got to be way less than one, or even less than 1/10th. Think of 1/100 of 5 or .05 but then 2/100 of 5 or .02 of five is equal to .10. So you remove .10 leaving 0. Now you add up all of the "fives" you took out: 10 fives equaling 50 7 fives equaling 35 .1 five equaling .5 and .02 fives equaling .01 17.12 total...and we are finished! -------------------------------------------------------------------------------- (02/18/09)

I am all for estimating the placement of the decimal both in multiplication and division. However, I admit that sometimes (when both numbers are decimals) it is difficult because it cannot easily be envisioned by the student. I believe there is a great deal to be said for explaining the traditional form of moving the decimals. As a student myself I wondered how one could move the decimals, thus changing the entire problem, solve the new problem and still get the answer to the original problem. Exploring this phenomenon is a great math activity. First on a hundreds grid I pose the problem 0.2 / 0.04 and have students color in sets of 4 hundredths in different colors within the 2 tenths. This way it is clear that there are 5 sets of 4 hundredths in 2 tenths. From here we color how many sets of 4 tenths are in 2 wholes. You can do the same thing to see how many sets of 4 are in 20--also 5 sets. You see, I have no problem with moving the decimal to make the problem easier to solve once students have conceptual understanding of why the process works. The key to using partial product division is the understanding of the nature of division. It is always about repeated subtraction or divvying out. It is never about "Guzinta." (02/18/09)

Try column division, it is an algorithm as part of EM, sixth grade I think, in the Teacher's Reference Manual for all upper grades and a great bridge if secondary math programs do not use a similar math concept. (02/19/09)

Try multiplying the numerator and denominator of a fraction by a power of 10. If you can get your students to rewrite any division problem as a fraction, this algorithm we learned in school is very useful and "meaningful" as EM prefers. 41.52 divided by 4 becomes the improper fraction 41.52/4 Now we multiply by 100/100 to get 4152 / 400 If we teach this algorithm, then students can also handle decimals in the devisor/denominator. 12 / 3.2 multiplied by 10/10 = 120/32. Students can also benefit from simplifying this fraction first before dividing. My students really understand this concept and benefit from the continued discussion of representing division as a fraction. (02/19/09)

### Question

We are having some discussions around the Trade First Algorithm. Some of us are teaching Trade First from left to right to be consistent with the addition and also because of the ease with the 0s. Our problem is that the reference books have it going from right to left. We are looking for direction on what way it is supposed to be. (10/22/08)

According to the Teacher's Reference Manual (Gr1_3, p105), " . . . the trades can be done in any order. Working left to right is perhaps more natural, as with partial-sums addition; but working right to left is a bit more efficient." In my opinion, it is most important to teach students to recognize when trading is necessary and how that is done. Allowing students the choice of subtracting from left to right or right to left builds their flexibility with numbers. I would think a consistent message from your teachers would help facilitate this flexibility. (10/22/08)

We use the computer program called Fastt math- it is by Tom Sawyer Productions. It is a researched based program- that uses drill sandwich technique and game play to reinforce basic fact recall. It addresses addition, subtraction, multiplication, and division (in isolation). It works great for our second graders. I personally would caution using it with all first graders- as they are still building an understanding of why addition and subtraction works- and rote memorization may be counterproductive to their foundation building. (10/03/08)

### Question

I am responsible for sharing the algorithms with our middle and high school teachers. In the 6th grade edition, the Everyday Mathematics material suggests that when you divide a decimal by a decimal, you ignore the decimal places, divide as normal, then estimate to find the location of the decimals. Sounds simple enough. However, when I tried it myself, I was fine as long as I was allowed a remainder. If a teacher, however, wants students to divide until they get to a certain place value, that's when things get ugly. Take for example 23.5 divided by 4.38. By ignoring the decimals it becomes 2354 by 438. The answer is 5 with a remainder of 164. Now, if I am asked to divide to the 3rd place value...I can add a zero to 164 to get 1640. This is where it gets ugly. If the kid is good enough, he will know that 1640 by 438 is 3. Then he can just tack the 3 on to the end to get 5.3. However, if he estimates 2 and subtracts 876, he gets 5.2 with 766 left over. He then can take another 438 out. The thing is, he has to know to ADD the .2 and the .1 together to get 5.3. Instead of tacking it on to the end to get 5.21. If you are confused, well wouldn't a student be also? (03/09/07)

I agree that the partial quotients method becomes confusing when working with decimals and their remainders. The estimation rule applies easily when dividing by tenths and hundredths. However, I believe that in most upper level math classes, especially when calculating with decimals to the third place, students are "allowed" to use their calculators, which by the way are most likely required for the class. (03/09/07)

In 6th grade we are now teaching the "column division" method for this very reason. It takes care of decimal division and most kids seem ready for it. (03/09/07)

Decimal long division is something the EM authors have thought about quite a bit. Here are some comments. First, we should keep in mind that complicated division with decimals is not something that should normally be done with paper and pencil. In today's technological world, kids do still need to know how to divide with paper and pencil, including simple decimal cases, but we should be paying less attention to paper-and-pencil methods for complicated decimal long division. This is what the National Council of Teacher's of Mathematics Standardssaid in 1989, which the EM authors agree with. Second, the partial quotients method works fine when the number of decimal places desired is specified in advance. In the case below, the original problem was 23.5/4.38. The solution given started by considering 2354 / 438. (What was meant, I think, was 2340/438.) A solution, 5 R 164, was obtained -- and then a decision was made to get three decimal places in the quotient. Then things got more complicated than they had to. The best way to make partial quotients work in such situations is to decide before you carry out the algorithm how many decimal places you want in the quotient. This is discussed, for example, on pages 86-87 of the second edition fifth grade SRB. In the case at hand, since three decimal places are desired in the quotient and the divisor has two decimal places, the dividend should be padded with 0s to the fifth decimal place, so the problem to be solved would be 23.50000/4.38. This can be solved by ignoring the decimal points and applying the partial quotients algorithm to 2,350,000/438 --> 5365 R130. [Since the divisor has three digits, it's a good idea to make a table of multiples of the divisor to help in carrying out the partial quotients method.] Finally, before you place the decimal point, use the remainder to round the quotient to the nearest whole number: Since 130/438 < 1/2, the quotient rounds to 5365. Since 23/4 is about 5, this means 23.5 / 4.38 = 5.365 (to the nearest thousandth.) Problems as difficult as this one, 23.5/4.38 with the quotient to be computed to the nearest thousandth, are not worth spending lots of time on. Three place divisors are not all that common in paper-and- pencil division work and answers to more decimal places than either of the numbers in the original problem are equally rare (and probably unjustifiable in most problem situations). Another option to solving such problems is to use the column division algorithm, which doesn't require the number of decimal places to be fixed in advance. Using column division with decimals is discussed in both the fifth and the sixth grade SRBs. (03/09/07)

The subject of "traditional column" division and partial quotients division has come up a few times at grade level discussions. We only use Everyday Math up tp 5th grade. It is my understanding that students will be using column division at that point. Do you have any experience in this transition and is there anything we can do now in the lower grades to help with this transition? (05/12/07)

### Question

I remember seeing an eloquent explanation of how the Partial Quotients algorithms can be used with decimals and I thought I saved it but I can't seem to find it. (02/06/08)

When we talk about when you use fractions and what they are, it comes up that it is a division problem. It also usually comes up that it is a ratio. 4:5 is 4/5 or "4 out of 5". An equivalent fraction maintains the ratio. I just write the problem on the board and have them see it as a fraction then find an equivalent fraction: 9 divided by 4.5 would be 9 / 4.5 which would become 90 / 45, then solve it like they had been doing all along. (02/11/08)

Decimal long division is something the EM authors have thought about quite a bit. Here are some comments. First, we should keep in mind that complicated division with decimals is not something that should normally be done with paper and pencil. In today's technological world, kids do still need to know how to divide with paper and pencil, including simple decimal cases, but we should be paying less attention to paper-and-pencil methods for complicated decimal long division. This is what the NCTM Standards said in 1989 and something the EM authors agree with. Second, the partial quotients method works fine when the number of decimal places desired is specified in advance. In the case below, the original problem was 23.5/4.38. The solution given started by considering 2354 / 438. (What was meant, I think, was 2340/438.) A solution, 5 R 164, was obtained -- and then a decision was made to get three decimal places in the quotient. Then things got more complicated than they had to. The best way to make partial quotients work in such situations is to decide before you carry out the algorithm how many decimal places you want in the quotient. This is discussed, for example, on pages 86-87 of the second edition fifth grade SRB. In the case at hand, since three decimal places are desired in the quotient and the divisor has two decimal places, the dividend should be padded with 0s to the fifth decimal place, so the problem to be solved would be 23.50000/4.38. This can be solved by ignoring the decimal points and applying the partial quotients algorithm to 2,350,000/438 --> 5365 R130. [Since the divisor has three digits, it's a good idea to make a table of multiples of the divisor to help in carrying out the partial quotients method.] Finally, before you place the decimal point, use the remainder to round the quotient to the nearest whole number: Since 130/438 < 1/2, the quotient rounds to 5365. Since 23/4 is about 5, this means 23.5 / 4.38 = 5.365 (to the nearest thousandth.) Problems as difficult as this one, 23.5/4.38 with the quotient to be computed to the nearest thousandth, are not worth spending lots of time on. Three place divisors are not all that common in paper-and- pencil division work and answers to more decimal places than either of the numbers in the original problem are equally rare (and probably unjustifiable in most problem situations). Another option to solving such problems is to use the column division algorithm, which doesn't require the number of decimal places to be fixed in advance. Using column division with decimals is discussed in both the fifth and the sixth grade SRBs. (02/06/08)

### Question

I have begun to really believe that long division is a good algorithm for students to learn, not stand alone, but as another way to do things. The reason I tack this idea onto math facts is this: long division emphasizes the repetition of the 1_9 math facts. My kids come in with understanding the Partial-Quotient division algorithm and it helps them to a point, but as we begin to explore division with decimals which requires them to divide much larger numbers (because we ignore the decimal point, and then place it at the end), they seem most comfortable using the divisor in multiples of 2, 10, 100, etc. I know the Partial-Quotient Algorithm helps many students, but some students end up doing 9 or more subtraction problems because they cannot identify more appropriate multiples. Each time they subtract, it is another opportunity for them to make an error. Even if they can solve the problem correctly, this process takes a tremendous amount of time and space. These problems are much shorter when using long division. The beauty of long division when introduced at the elementary level is that it allows for repetition of math facts. Please do not argue that "students dont understand why the old algorithm works" because I would have to counter that they do not understand the new algorithms any better (lattice for example). (11/04/08)

I would suggest you look at the Column Division Algorithm in the EM Operations handbook. It is a nice balance between the traditional algorithm and understanding. It works well for decimals and you can model it with base-10 blocks. (11/04/08)

I could not disagree with you more about the long division algorithm. I understand that some of your sixth graders may have some difficulty with partial quotients, but in the long run, you are doing them a huge disservice by abandoning it for long division. Yes, they will learn nothing from long division, as they do with lattice (which is why I didn't let my students rely on lattice either. I required them to use partial products as the focus algorithm and reserved lattice for those IEP kids who struggled). We need to stop taking the easy way out. If you would continue to plug away at partial quotients, eventually they will be able to identify more appropriate multiples. You just need to give them more time, patience, and support. I would make the same argument for abandoning partial products for lattice. Certainly there may be a select few who are truly falling behind, in which case long division may be most appropriate for them. But the justification that it emphasizes basic facts is a weak argument when you are sacrificing so much number sense and mental math by switching to long division. If allowed the opportunity to become proficient with partial quotients, the mental math skills and number sense they stand to gain are well worth the time and effort. Those who you allow to resort to long division will be disserved. (11/04/08)

I completely agree that using the partial products helps kids with number sense. I have had to explain to parents that we are preparing their minds to be able to do much of this in their heads. After they are solid in their number sense, I teach the "short cut". (11/07/08)

### Question

I would be really interested in hearing others' opinion of the lattice method of multiplication. There are so many teachers that allow their kids to rely on this method because it is easy. My concern is that even if students know the Partial-Products Algorithm, if they don't use it consistently, they will not develop the level of proficiency that we want: high enough that they can do all (or large portions) of it mentally. If kids use Partial Products almost exclusively, over a few years time they WILL be able to multiply numbers mentally. They will not develop this using lattice. The only thing accomplished by using lattice is that they learn how to multiply on paper. My middle and high school teachers are completely on board with Partial Products because they see the value of it in developing number sense. What is the value of lattice other than it works great for kids who struggle, and for very long numbers? (03/28/07)

I agree that the lattice method is just a "tool" that allows young students to multiply large numbers. It does not support developing number sense. When my students choose to use lattice, they must first show an estimated product for me. We just started teaching partial products to third graders in the last few weeks. I was thrilled to see some of my remedial students be able to find the product mentally. (03/28/07)

### Question

In a couple of weeks I am going to be helping with a workshop for our middle school teachers. We use EM 3rd ed. K_5, and then go to a more traditional program beyond that. To say that it is a bumpy transition is an understatement. Anyway, I was looking for a way to demonstrate how to solve polynomial division with algorithms similar to EM. Is anyone who is using the secondary program able to explain this to me? The reason we want to have the teachers have an understanding is our students are using the Partial-Quotients algorithm quite effectively, so much so that many students are abandoning the traditional algorithm, when they get into a traditional math class, where the teacher is not very flexible they have a hard time adjusting and relearning the traditional algorithm. By the way, the Column-Division Algorithm is great, and may be a great bridge between EM and more traditional programs. (11/20/09)

I guess I am confused as to what difference it makes which algorithm is used to solve polynomials. That statement has me somewhat perplexed. This looks long, but please take a moment to go through the example. Look at the partial products method of multiplication for 2 2-digit numbers, hopefully this will line up for you. 12 *34 --- 8 (2 * 4) 40 (10 * 4) 60 (2 * 30) 300 (10 * 30) --- Now, let's take a look at that same EXACT same problem written out in expanded notation horizontally. (10 + 2) * (30 + 4) Or, if you prefer: (10 + 2)(30 + 4) Now to solve it I still have to multiply all the place values by one-another: 300 (10 * 30) 40 (10 * 4) 60 (2 * 30) 8 (2 * 4) Whoops...did I just use the FOIL method to solve this as a polynomial? Ok, technically I didn't because there are no variables and a polynomial has variables, and whole numbers. So, let's substitute x for 10 and do it again. (x + 2)(3x + 4) 3x^2 (x * 3x) First term * First term 4x (x * 4) Outer term * Outer term 6x (2 * 3x) Inner term * Inner term 8 (2 * 4) Last term * Last term Now, to put that into an expanded polynomial form: 3x^2 + 4x + 6x + 8 = 3x^2 + 10x + 8 Yup, I can see EXACTLY why students NEED to know the traditional algorithm. What could I possibly have been thinking!!!! What's my point? It is difficult for ANY grade-level teacher to teach math without knowledge of what was taught earlier. We cannot exist in a box. To be a successful math problem solver or thinker, you must draw on past knowledge and experiences. 6th grade will have a harder time teaching what an algebraic equation is without using an in-out function machine or a whats-my-rule table to make the connection that this isn't something new, it is merely a new way of writing it. An algebra teacher will have a hard time teaching how to solve polynomials if they cannot draw on past references. Most importantly, a student will have a harder time learning if their tour guide can't help them form connections. (11/20/08)

In the 5th grade EM program, Projects 12, 13, and 14 all teach the standard division algorithm. You could decide, as a school or district, that teachers do these projects so that students have the opportunity to learn standard division. (11/21/08)

I became curious myself, and determined that you could build the simple lattice you'd use to multiply the poynomials, write the divisor on the side, and create as many boxes as you'd need to reach the highest power of exponents.? Fill in the highest exponent in the interior box (as the product of the two factors), the whole number in the lower corner box and determine the factors that would make those work.?Then you could work backwards, with the numbers you had, almost like a Sudoko puzzle, filling in the spots.? Works really well!? It was actually kind of fun!? But, then I love math puzzles! (11/21/08)

### Question

In a problem subtracting one 3-digit number from another requiring trading in two places, should the first trade be 100s to 10s or 10s to 1s? The third grade Teachers Lesson Guide on page 144 models trading one of the 100s first with base-10 blocks, though the written version below trades a ten first. The animated algorithms in the family resources show trading a ten first. It doesnt matter as long as all the trading occurs before the subtracting. What are any thoughts on this? (10/06/10)

Either way is fine. I teach left to right because of problems with 0s such as 900-782. They don't have to jump 2 places to trade, as they would if they worked right to left. When they work left to right I find children get less confused. (10/06/09)

We, too, were frustrated with the inconsistent modeling of trading in the second edition. The third grade Student Reference Book clearly showed trade first from the left. We found that we needed to be consistent in our modeling of the trade first subtraction algorithm as students practice this skill in many settings including regular classroom, intervention classes, after school homework groups, and of course at home. We agreed to always start with the greatest place value (left most) and use the same "script" in talking through the steps. This approach completely eliminates the middle zero challenge as well. It is critical that the students understand trading through the use of manipulatives before they can become fluent with the abstract algorithm. Then for them to become fluent and accurate with the algorithm, it is helpful to always start at the same place. The third edition now states that the authors recommend trading starting from the right, but we have continued to model and practice from the left as we have found it to be more successful with our students. (10/07/08)

I have found the animation on the National Library of Virtual Manipulatives to be a great tool with Trades First Subtraction... Go to http://nlvm.usu.edu/en/nav/vm1_asid_155.html for subtraction (10/08/10)

There are two phases to the trade-first algorithm, the trading phase and the subtraction phase. In the trading phase, it may be easier to do the trades left to right: with this approach, one never has to look beyond the adjacent place to see if a trade is needed or not. For example, in 7008 - 4619, with right-to-left trading you first need to trade to increase the value of 8 -- and the 10s place doesn't help, nor does the 100s place, so you must move to the 1000s place, and then trade back one place at a time. But with left-to-right trading, it's a sequence of easier adjacent-place trades from start to finish. Once the trades are all done, then the subtraction can proceed column- by-column from either the right or the left or, indeed, in any order starting anywhere. In some algorithms, such as partial sums or partial products, it makes a good bit of sense to start at the leftmost column(s) because that yields a quick approximation of the final answer. That rationale is less compelling with trade-first because one is working on single digits (or numbers 10-18 minus single digits) in each column, so the results are not approximations of the final answer. Starting at the rightmost column follows the U.S. traditional subtraction algorithm, which trade-first closely resembles, so that's an argument for starting at the right. On the other hand, if students are used to starting from the left (from their experience with other algorithms or from their experience making trades in this algorithm from left to right), that's OK too. This is why we don't specify starting the subtraction phase either at the right or the left. We'd like to make two other important points about Algorithms: (1) Different algorithms are appropriate for different problems and (2) different people like different algorithms for their own reasons. If anyone feels like an algorithm is tougher than another on a given problem, then that person should feel free to use the easier one. There is no underlying mathematical or pedagogical reason why one algorithm should be the best one all the time (which is not to say, of course, that an algorithm shouldn't work for all occasions -- it must). As for the algorithm animations, we'll make a note that perhaps it might be helpful to include one (or more) involving 0s in the minuend. We have, as usual with EM, a number of improvements and changes we'd like to make when the animations are revised or expanded. (10/08/09)

### Question

In Unit 9 students are asked to compute the area of a polygon in decimals. Nowhere in the unit did we study how to place the decimal point. It just showed up in the Journal and on homework. In class, we used the calculator. Students without calculators at home were quite frustrated as were several parents who felt they had to teach where to place the decimal. I don't understand why children would be taught to use a calculator without understanding first. How do I respond to parents who ask my method of teaching multiplication with decimals? They have finally gotten used to the fact that EM teaches different techniques and were concerned that they might be teaching their children something different than what might be taught at school. Needless to say, I was a bit embarrassed to say I had not taught any method other than how to plug the numbers into the calculator. Has anyone else felt this frustration? Did I miss something in the previous lessons? I obviously need to rethink this next year. (03/24/07)

We, too, have found this to be a very challenging part of the fourth grade curriculum. Most of my kids do lattice for the multiplying and then use their understanding of numbers to find where the decimal point goes. (If the resulting answer is 1567, they need to think if 156.7 is more reasonable, 15.67, 1.567, etc.) There also is a "trick" with the lattice to know where the decimal point goes, but I like my kids to have to reason through it a bit. I have tackled this in class and have chosen to not send those few study links home; instead, we do them in pairs in class. Have you looked back at the Teachers Reference Manual? I believe it does tackle the issue of multiplying decimals. (03/25/07)

I have run across the same problem and posted it a couple of years ago. Most responses indicated that multiplication of decimals is not that difficult of a task and needs to be taught at this time. I tried it and disagree. The students were unable to grasp the idea. I feel this is one of the few flaws in EM. I ended up whiting out the decimals on the homework sheet and subsequent homework sheets and replaced them with double digit dimensions since they need the extra practice. When it comes to the math boxes I go ahead and show the students how to multiply decimals but explain that they will be expected to master it later. (03/25/07)

When teaching 4th grade, I always previewed the homework. Anything (such as this - multiplication of decimals) I marked as a bonus question. I had 2 students who intuitively could "see" decimals and were able to do it. At my open house at the beginning of school I warned parents that there may be some problems on their child's math homework which have not worked with yet and would be marked as bonus and left to the student to try if they wanted to, but which were not required. If those problems were not completed credit would not be taken off. In addition, any student who tried the problem and did not get the correct answer would also not have points taken off for having tried. (03/26/07)

The authors of Everyday Mathematics have always recognized the importance of feedback from classroom teachers. joejames219@wowway.com noted, 'I have run across the same problem and posted it a couple of years ago.' Please note that due to numerous comments from teachers regarding this issue, in the third edition of Everyday Mathematics all of the problems in Study Link 8-6 and Study Link 8-7 now involve multiplication with whole numbers only. The problems involving decimals have been replaced. You might consider the following if you are using these Study Links from the second edition. 1. In May 2003, Rachel Hanson, a fourth grade teacher from Georgia, noted: 'I've handled this a couple of different ways. With the kids that I knew could handle it, we had a quick mini-lesson on multiplying decimals. With the kids that could not, I had them round the numbers to the nearest whole numbers and multiply them. I think really in Unit 8, we were trying to get the children to find area successfully, so I didn't feel uncomfortable about rounding the numbers. By the time we got to Unit 9 to multiply decimals, many students already knew how and were good helpers as well.' 2. Send the Study Links home, but save the decimal problems for class. Then embrace the problems. Students are correct to state, 'We haven't learned how to multiply decimals yet.' Ask them to think about what they do know how to do that might help them solve the problems. For example, take Problem 4 on Study Link 8.6. Students are asked to find the area of a parallelogram with one side that measures 6.5 meters and another side that measures 7.2 meters. In Unit 4 students practiced converting between metric measures. Can students find equivalent names for 6.5 meters and 7.2 meters that will make the problem easier to solve? 6.5 m = 65 cm and 7.2 m = 72 cm. 65 cm * 72 cm = 4,680 square centimeters. 4,680 square centimeters = 46.8 square meters. Please note that decimal multiplication is introduced in Unit 9 in Lesson 9.8 "Multiplication of Decimals." (03/28/07)

Our school has been doing EM for 4 years for grades K-6. Most of the issues with algorithms involve decimals or larger number computation. I know in the EM Teacher's Reference Manual it explains that the purpose of the computation should be considered when choosing a method. The purpose ranges on a continuum from efficiency to meaningfulness. Obviously, the most efficient method is to use a calculator. Partial products is very meaning-directed method, but may be cumbersome and not efficient. In grade 6, some of the math boxes contain problems that have 3-digit times 3-digit factors. Partial products takes up an enormous amount of space and it is cumbersome to do several problems with this method. When students use lattice, they can do them accurately and efficiently. I always use this as an opportunity to talk to the students about the different methods and which makes the most sense to use for a certain task. The great thing about EM is that it empowers students to make choices that make sense to them. I always use partial products when I am teaching because it is the focus algorithm for EM, but I usually use the traditional method I learned first when I am checking a problem on my own. From my experience, partial products is best for 1-digit or 2-digit factors. This method should be emphasized because of the meaning it gives to computation and number sense. Lattice is not as number-sense friendly, but it can be taught so that the values of the diagonal places are emphasized. Also, we meet with our high school teachers several times a year to discuss these issues and they have been great about learning the Algorithms. Each year we learn a little more, both as teachers and as students. (03/28/07)

I have supported the continued or extended use of lattice with two populations....those needing enforced organization, and those needing more competence with their multiplication facts. Some students have trouble tracking visually, so the required slots offer place holder support. Some students need to refocus on the facts before they can take on the bigger picture. When the lattice is filled in, the student should view the array as columns, either by physically turning the paper or by changing perspective. Once done the enforced organization of place value columns becomes more clear and can be deliberately noted by the teacher. This is a great segue into the partial products for these students. Children should not be using it as the 'easier method' but instead as the one that works for them for now. (As soon as I see this method being a crutch I offer a few problems with lots of zeros and demonstrate the efficiency of partial products. Usually students begin to use both, and have a much better understanding in the higher levels of math using FOIL, matrices, and other general solving patterns. (03/28/07)

### Question

My 1st grade teachers always dread Unit 3 when they introduce frames and arrows. They tell me it's their least favorite thing in Everyday Math to teach. I have to say that the teachers in the older grades feel like their kids do really well with this skill, so the 1st grade is certainly doing something right. Is there anything special that anyone does that would help these folks? I would like to lower their frustration levels a bit! (11/12/07)

My students have portable number grids that seem to help a lot. (11/12/07)

I always look at them as the natural extension of the skip counting and number line/grid work we've done prior to the frames and arrows. Once I help my first graders make that connection, they seem to really take off. (11/12/07)

In the Differentiation Handbook, page 36 in the 5th grade, EM discusses Frames and Arrows as providing opportunities for students to practice basic and and extended addition, subtraction, and multiplication facts. One way that I use Frames and Arrows with first graders is writing the number models below the frames and arrows as a way to connect number sentences to frames and arrows. There is also a template in the differentiation handbook for extra practice for frames and arrows. (11/12/07)

In second grade, we teach our lessons with powerpoints we made ourselves. Frames and Arrows look really cool when you can click and they just appear and answers fill! In the past we have also played a revised game of "what's my rule", where we fill in the frames and ask kids to guess what the number is for the next frame (using the rule they think in their head without saying it.) We keep asking for answers to frames until about 10 are filled in. Usually by about ten frames, everyone has figured out the rule and can answer. (11/13/07)

I have presented a lesson that may be helpful to your teachers...the objective of the lesson is to help students see that Frames and Arrows are like a number line....except that instead of every number appearing on the number line the only numbers that appear in the 'frames' are the numbers you would say for 'skip counting'. The Arrows tell what 'the rule' is for skip counting. I actually create a class number line of blank frames and arrows and laminate it. I then have the students help me complete the number line by counting by 1s...I have purposely made the number line with 20 frames (or however many students are in the class) and give them a problem such as, let's count how many feet are in the class, or how many fingers...a number that will obviously be greater than 20 and won't fit on my number line. We discuss how this number line just isn't big enough to show all the numbers and then discuss that since each person has 2 feet (or 5 fingers) maybe it would be easier to count by 2s (or 5s). I dramatically erase the numbers from the frames and arrows number line and then have the students line up under the 'frames' (one student under each frame) and count their feet (or fingers) by counting by 2s (or by 5s). I have had a great deal of success using the Reeses Pieces Count by Fives book by Jerry Pallotta with this lesson/concept as well. We discuss the idea that the arrows are there to make sure we remember this is a 'skip counting' number line and we may not be counting by 1s. It's a simple, beginning lesson but it seems to help 1st graders see the purpose of 'frames and arrows'. (11/13/07)

### Question

My question is directed to any districts that have successfully convinced teachers to simply use the Partial-Quotients Algorithm and not confuse students by additionally teaching the traditional algorithm. It is NOT a part of the program but they still teach it. I am not questioning the reasoning of the authors. I LOVE the Partial-Quotients Algorithm, as I believe it gives kids a much better understanding that division is repeated subtraction. EVERY ONE of my students can use it efficiently after a few sessions with me. I am just curious about HOW to convince the teachers that I work with (who are a well-intentioned group of dedicated professionals) to STOP teaching the traditional algorithm. (11/25/08)

I'm not sure I'm clear on why the partial quotients is taking so much longer. If you have students that are doing the traditional, I would expect that they could transition to the partial quotients fairly easily. If not, and don't take this the wrong way, it sounds as though they don't understand what the traditional is doing, which is more evident in the partial quotients. For instance, if they have 543 / 21 and they're saying "how many times does 21 go into 54, oh 2" then couldn't they just take that to ask "how many times 21 goes into 540?" The lattice is great at working on single-digit multiplication facts, but it does take extra time to draw the lattice itself. How are these students at using partial products? I also have students in 5th and 6th grade and often hear that they don't do the partial quotients well. When I sit and watch them do it, it is because they are stuck trying to do the traditional. However, they often make mistakes with the traditional because they don't understand it either _ its just that their parents do traditional, so they want to too. Understanding how the algorithms work and what they are doing comes with time, and may not be realized until much later on. However, many of the algorithms used in standards-based programs are the same ones that are used in algebra they are just written differently. It's also important to see that the traditional algorithms work great on paper, but not in your head. Things like partial quotients and partial products work closer to the way you do mental math and aren't as efficient on paper. (11/25/08)

### Question

Our kindergarten teachers are feeling frustrated (this is our first year of the program) because the EM materials do not "label" patterns in the traditional way (ABAB, AABAAB, ABCABC, etc.) Can anyone tell me (a) if the labeling is introduced in later grades or (b) if there is a reason that the teachers cannot continue to refer to patterns in this way, even if the EM materials do not do so? (12/20/07)

We have been talking about patterns in our school as well...one interesting 'note' is found in the Kindergarten Teacher's Guide to Activities on page 19, Activity 4.5, where it says that "It is not necessaryand is potentially distractingfor the teacher or children to label patterns... at this point." Refer to Chapter 15 in the Early Childhood Teacher's Reference Manual for some great information about patterns. We have had some good discussions across grade levels about patterns and the idea that they are not all repeating...some are growing and some are diminishing, some are visual and some are number patterns. In kindergarten many patterns are repeating patterns and children will also explore odd and even patterns. (12/20/07)

I follow the EM program in my Kindergarten and still refer to the patterns as in the standard way-->ABAB, AABB and so on. I'm not sure why EM does not include this but I have not found any reason why I can't add in the labeling of patterns with letters after a time of exploration and observation. It helps the kids have a common language, and to demonstrate understanding. (12/20/07)

Seems to me that the important concept here is the ability to detect a pattern. That is an algebraic concept...to be able to detect, repeat, and use patterns. I have an early childhood degree, and was taught in undergrad how "important" patterning was, but in practice, I fail to see how identifying whether the pattern is AAB, ABA, or whatever is important. If they can identify the pattern, great. If the pattern is rhombus, triangle, rhombus, triangle, and they identified it, and can continue it, what purpose does it serve to call it an ABAB pattern? (12/21/07)

I find it helpful to have the common language that ABAB, AABB etc. allows for. Additionally, it allows for some measure of pattern complexity, while providing for specific assessment, rather than random patterns when asking a child to demonstrate understanding. The children become fluent in their understanding of this method of identification to delineate patterns. I think the original question was born of a need in the areas of communication (common language) and identification. (12/21/07)

The evidence that a student "understands" a pattern is in being able to predict what comes next or what comes before or what comes in between. The labeling does not necessarily capture this generalization: that patterns are predictable and can be continued in both directions. Watching kids acting on patterns gives you all the evidence of understanding you need. (12/21/07)

### Question

Our school has adopted Everyday Math through the 4th grade. Our 5th and 6th grade teachers are accepting of the students using alternate algorithms, but feel the Partial- Quotients method poses some challenges when moving into decimals. Beyond estimating/using magnitude estimates, any suggestions on how to adapt the Partial- Quotients method for use with decimals? (11/03/09)

I teach 6th grade. I apologize for the length, but I really like this topic. There are some great responses in the archives, so check those out too. EM takes an approach to division with decimals like this (3 choices when dividing): 1) the answer will be expressed as a fractional remainder 2) the place you are dividing to will be specified or 3) youll be using a calculator if the decimal continues for an unknown amount of places. The most important step for my students, especially those that struggle with division, is to take time to organize some "mental facts." (I'm not sure what EM calls this). If I am dividing 548 by 23, to the side, I come up with some facts to help myself. 23 * 10 = 230 23 * 20 = 460 (multiply 230 by 2) Sometimes we'll do 2, then double to 4, then double to 8 or add 2 and 4 to get times 6. The issue I have with partial quotients is often that students are not identifying large enough facts to subtract. This causes them to subtract and subtract and subtract, allowing regrouping errors to happen. This is why they MUST take time to organize themselves to the side. A big idea to take away from this is it should take about the same number of steps (give or take 2) as long division to this place value. 2-8 is division of decimals. I teach it differently than the EM strategy of estimation. I treat it much like multiplication. Ignore the decimal points and divide. Replace the decimal point in your answer, moving it the same number of places to the left that you ignored originally. If told to divide to the hundredths, I teach students to add zeros to the hundredths. This is a strategy that is used for long division as well!! 184.98 divided by 8. Round to the nearest thousand. In division house: 184.980 divided by 8. Ignore the decimal point and divide. 184,980 by 8. Use mental facts, to the side: 8 * 1,000 = 8,000 8 * 10,000 = 80,000 8 * 20,000 = 160,000 (double 10,000) 8 * 3,000 = 24,000 (triple 8,000) 8 * 500 = 4,000 (half 1,000) 8 * 250 = 2,000 (half 500) Answer 23.122 and 4/8 students examine 4/8 to determine if they should round or not. Answer 23.123 I found it almost impossible to get them to remember to add an extra zero from the specified place value, which is why I teach them to use the remainder to round at the end. Every time you see division, show it both ways (partial quotients and long division). The repetition of seeing it both ways really helps most students. I tell them they should be able to do it both ways because then they can help their friends. (11/04/09)

### Question

Regarding second grade in the third edition, I know there was some conversation here about the Trade-First Algorithm being moved from Unit 6 to unit 11. We are now starting Unit 6. To those of you who may be ahead of us in units for second grade, how are you finding the amount of hands-on practice to be from Unit 6 on, insofar as building up the children's number sense so that they will more quickly grasp the algorithm in Unit 11 when it is introduced? Some of us on my grade level team are feeling a little nervous about this change, feeling that this is a hard concept and maybe we should start teaching the written algorithm sooner, as when we do get to it in Unit 11, it will be just about the end of the year for us. I have already looked back in the listserv, found the previous discussions, and will share them with my teammates. (01/22/08)

I found that having a similar discussion with third grade was also very important. At the beginning of the year this year (we used EM3 last year) our third grade teachers discussed how and why the change occurred the previous year and looked at how much practice students realistically had with the trade first algorithm. Knowing this, they were able to provide the support necessary for those students who needed it. As the year has progressed our third graders are showing good progress with subtraction and we feel it has been a successful transition. Also, our second grade teachers are reporting they feel the pacing is much more kid friendly and appropriate for second grade. (01/22/08)

I usually use the Place Value blocks for a good long time before I get to the written algorithm. I also use money... it also helps with this concept, and the kids have already traded in the beginning of the year. I am glad that it has been moved to Unit 11. It takes a while for second graders to fully understand this concept. We make up little tunes to remember "ten more.. one less" (01/22/08)

### Question

We currently have quite a debate going on traditional vs. EM strategies. There are some students who have already learned traditional methods of carrying, multiplying, etc. The teachers are teaching the EM strategies. Some teachers are allowing students to use traditional methods as long as the understanding is there, not just the process. Other teachers are saying they have to stick with the EM strategies and can't use any traditional methods. I'm sure this has come up in other schools so I'm curious as to what your solutions were. (12/06/07)

The most important thing in my mind is...how well do the algorithms translate into mental math, and what do they reveal about underlying math concepts. There is nothing inherently evil about traditional algorithms. However, they are very difficult to perform mentally (something we want all kids to be able to do) and they tend to be a series of steps (a procedure) that mysteriously arrives at the correct answer with little understanding of how they really work. If the students are proficient with the traditional algorithm, AND the teacher claims they have mastered the underlying concepts, then they should have no trouble with using the EM algorithms. I would argue that if there are only proficient with traditional, then chances are the understanding is NOT there. They are just following a procedure. If I were a classroom teacher, I would strongly recommend using the EM algorithms, with the ultimate goal that parts, if not all, will eventually be done mentally. Very few students will ever be able to add or multiply 2 digit numbers mentally with ease using traditional, but many will using partial sums and partial products. Partial quotients, once proficient, will be a far more efficient algorithm than long division, and helps kids learn how to divide mentally. Long division will never do that. Seems like a no brainer to me...give kids ample time to become proficient with EM algorithms, and you will be teaching them way more than just the algorithm. (12/06/07)

### Question

I was wondering if anyone could tell me where I could find a list of the basic fact strategies that EM uses to teach basic facts? (Ex. +0, +1, doubles, make a ten). I would like to find a list for each operation. (11/20/07)

There is some information in essay 2 in the Teachers Reference Manual and more in the second grade Teachers Lesson Guide in the unit organizer of unit 2. However, it seems as if you have a general idea. I have always followed the following strategies pretty much in order. Anything plus zero; anything plus 1; ten plus anything; nine plus anything; addends of ten; doubles; one off a double; sharing numbers (5 + 7 the seven gives one to the five and they are both sixes - back to doubles) Additions of two can easily be counted ant you are just about done. (11/26/08)

Getting in the extra time to practice facts sometimes seems very difficult! Something I'm trying this year - I created a basket with many different types of fact manipulatives. After student have completed their morning job/routine, they are to practice facts alone or with a partner until we are ready to start reviewing the morning math routine (calendar, weather, etc.). There are also some times in the afternoon when I find a few minutes between lessons and I tell them to pick something out of the basket to practice math facts. Here are a few of the manipulatives I have in the basket: - Addition and subtraction fact cards from the dollar store - lower level and higher level (or you could make from index cards or Microsoft Word) - Fact triangles on a ring - I copied the fact triangles from the workbook onto cardstock, had them laminated, cut them out and put them on a ring. The students take a ring and practice alone or with a partner. - I also made large fact triangles - on construction paper - and laminated them. The students take a triangle and practice writing their own fact families. (12/02/07)

The latest thing that I'm going to try, and it is still partially in the planning stages now, is to build this into the projects. I plan on having my kids start working on a multiplication project (I think it is project 3, grade 5, EM 2007) which has a study of different methods. However, as part of the project, I'm going to use the assessment CD to generate some problems that will use the basic skill they'll be using for the project. I'll also use the blank masters and some some of the activities from earlier assignments. The plan is that they will have a total of about 10 different sheets to choose from, each one being worth a different amount of points (5-10 points each). They need to earn between 50 and 65 points in order to continue on. For those who have used a layered curriculum approach, this is the C layer. The project itself is 4 pages, with the 4th page also asking for an analysis. They will all need to complete the first 2 pages, with each section being worth a certain number of points. They must earn enough points to continue on to the next layer, etc. At any point, they only have one worksheet at a time, they receive a new one when they turn in one, so they do not have the entire thing to do as they please. The idea is that they have to get through and show a level of proficiency. This is a knowledge level, it is not a matter of "getting it right" but showing that they have the right level of understanding. The next layer would be application and the final one would move into reflection and analysis. If they only get into the C layer, they only get a 75. If they make it to the B layer, they get an 85 and if they get to the A layer they receive a 95. A 100 is possible if they do the final question, which is taking it beyond the basic project. (12/02/07)

### Question

Can any of you offer your thoughts, or ideas for supplemental programs to help with automaticity of math fact or ideas to help support the ideas within EM? (07/14/10)

I don't have a program but we had a consultant that came in that gave us the break down of facts and after so many things like 5s 10s, 2s, etc. it only leaves like 12 facts that the students have to memorize, and then she gave us chants to go with them but the kids were happy to make their own. It went to the tune of we will, we will rock you, they liked banging on their desk also, which only lasted the first few days. We had a fact for a few days then added it to our song that we chanted everyday. The students really loved it. If they would forget a fact I would just say, for example, 6 and 8 went out to skate and they would reply and came back as 48. At the end of the year all of my students could get at least 40 facts on the 3-minute time test, including special education students. I don't have the paper here at home so I can't give too much more than this for now. We were chanting fools and it worked!! (07/14/10)

FasttMath by Scholastic is an excellent program. Go to http://www.tomsnyder.com/fasttmath/index.html to get a look at it. (07/15/10)

We use the Book of Facts and Box of Facts by Origo to supplement our fact work. The program focuses on strategies and has worked well. I also went to one of the author's presentations at the National Council of Teacher's of Mathematics conference last fall. (07/14/10)

You bet I can. Google "ten frames." There are lots of resources out there that use the ten frame to develop number sense by anchoring numbers to 5 and ten. I have experienced incredible success with this. I was introduced to the concept of ten frames through the work of John Van de Walle. It is well worth the time to research it. (07/15/10)

We use Math Facts in a Flash which is an Accelerated Math product. We also participate in World Maths Day , a world wide computation competition, and the American Math Challenge. This summer we are requiring students to spend some time on basic + and - facts on Encyclopedia Brittanica's Smartmath program. This is new for us so we will look at our results when school resumes. (07/15/10)

My students love World Maths Day (http://www.worldmathsday.com/2010/Default.aspx? And Multiplication.com http://multiplication.com/index.htm)! Our district has also purchased subscriptions to Compass Learning (in conjunction with students' Measure of Academic Progress scores) http://www.compasslearningodyssey.com/ and Everyday Math Online Games https://www.everydaymathonline.com/ Both are popular with our students and are an expectation for students to use over the summer (first time for that). (07/15/10)