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

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)

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)

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)

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)

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)

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)

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)

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)

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)

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

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

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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

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)

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)

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)

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

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)

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)

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)

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)

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)

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)

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)

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)

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)

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

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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 &ndash; 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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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

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)

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)

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)

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)

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)

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)

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)

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)

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

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

You can read an interesting explanation of lattice multiplication and its role in classrooms here: http://rationalmathed.blogspot.com Also, look at Dr. Math&#8217;s archives for an explanation of its history and the place value connections. (09/30/07)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

There is an old saying that refers to something about getting off a dead horse. Trying to memorize 100 individual, unrelated facts is the dead horse! I started teaching over 45 years ago. 42 years ago I realized that memorizing facts didn't work for me or Einstein and it didn't work for most children as well. Early in his life, Einstein thought he was not good at mathematics because he couldn't recite his math facts fast enough. Those students for whom memorizing works seem to have a bit of photographic memory that many children do not have, myself included. If memorizing is going to work for a child it will work soon. If after a few weeks, memorizing isn't working , it is not going to work! Oh, maybe if you keep at it, it will appear to work but chances are the facts will not be there after summer vacation. First of all, all the research I can find states that 5 minutes is the minimum time a child should be given to recall 100 facts - 3 seconds a fact. If you are asking students to complete the 100 fact is 3 minutes under the guise of higher standards for students, you are building in negative self esteem and creating a dislike for mathematics in many children. Nor do you need a 100 fact test on the 3's to see if a student knows his three's. 20 facts are enough to get in the facts and turn-around facts. So if memorizing does not work what does? Strategies work! One strategy for each set of facts. This approach strengthens number sense and creates brain tattoos that stick from year to year. First of all give their brains a picture of what multiplication is. 2*3 is 2 sets of 3. The "of" is extremely important as the student moves on to fractions and decimals. 2/3 * 12 is no where near as easily understood as 2/3 of 12. Use bags of marbles, rectangular arrays, etc. to demonstrate the process and picture of multiplication. 0's and 1's are fine. Show students that in most cases they know all their 2 facts because their doubles in addition are 2 sets of.. If they are having trouble with their doubles in addition it is usually only 6+6 - 9+9. Give them pictures and fact cards for these 4 facts. They never have to learn their 4 facts because they are double the 2 facts. Each finger except the thumb has 3 knuckles. Write the 3 tables on fingernails with a black visa-vie marker. Have them count by 3's and then have them tap finger 4 and tell you 3x4 etc. Clean off the fingernails and the brain still has the picture for life. No need to memorize the 6's they are double the threes. 5's are half of tens or use the move the decimal to the ri