FAQs
(Frequently Asked Questions)

1. How does Everyday Mathematics address basic facts? When should students be expected to know their facts?
2. How does Everyday Mathematics address computation?
3. What are alternative algorithms, and why are these part of the Everyday Mathematics curriculum?
4. How and why does Everyday Mathematics encourage the use of calculators?
5. How does Everyday Mathematics meet the needs of students at various levels of ability?
6. How can I help my child?
   

How does Everyday Mathematics address basic facts? When should students be expected to know their facts?

Helping children learn the basic facts is an important goal in the Everyday Mathematics Curriculum. Most children should have developed an automatic recall of the basic addition and subtraction facts by the end of the second grade. They should also know most of their 1, 2, 5, and 10 multiplication facts by this time. By the end of the fourth grade most students should have an automatic recall of all the basic multiplication facts and be familiar with the basic division facts. Multiplication and division facts are reinforced at the beginning of fifth grade.

The Everyday Mathematics curriculum employs a variety of techniques to help children develop their "fact power", or basic number-fact reflexes. These include:

Practice Through Games
The curriculum has a wide variety of fact practice games. Because children find these games much more engaging than standard drill exercises, they are willing and eager to spend more time practicing their basic facts.

For more information and instructions for playing sample games click here.

Fact Triangles and Fact Families
Fact Triangles are Everyday Mathematics' flash cards with a difference. The difference is fact triangles help children learn fact families rather than isolated facts. Partner practice with addition and subtraction fact triangles begins in first grade. Multiplication and division fact triangles are introduced in second grade. Practice with Fact Triangles is often suggested in the Home Links homework assignments.

50-Facts Multiplication Tests
Beginning in fourth grade, students take timed tests on multiplication facts. These are recommended at least once every three weeks. Students calculate their percentage correct and track their progress with line graphs.

Choral Drills and Mental Math Exercises
Beginning in first grade, short oral drills are suggested for fact review. These drills can become a routine during transitional times of the day. In 4th through 6th grade, basic fact power is reinforced in routine mental math exercises. For more information on mental math activities click here.

Math Boxes
Math Boxes, which are sets of practice and review problems, are included with almost every lesson.

Fact Extension Practice
Fact extensions are calculations with larger numbers by using knowledge of basic facts. If children know that 3 + 4 = 7, then they also know that 30 + 40 = 70, and 300 + 400 = 700. Children are introduced to fact extensions in first grade and are encouraged to practice them throughout the program. For more information on mental math practice click here.

Frames and Arrows Diagrams

These diagrams are visual representations of rule-based sequences of numbers. Variations of these diagrams are used routinely from kindergarten through third grade. The challenge of solving these number puzzles by filling in the blank frames involves lots of practice with basic facts.

What's My Rule? Function Machines
Variations of these function machines are used routinely through third grade, and provide another avenue for basic fact practice.

Home Links
Home Link homework assignments are included with every lesson and have many opportunities for basic fact practice built-into the suggested activities.

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How does Everyday Mathematics address computation?

Everyday Mathematics recognizes that, even in the computer age, it is important to teach children how to compute "by hand". The curriculum is designed to provide all students with a variety of dependable and understandable methods of computation. These methods include traditional algorithms, as well as alternative algorithms that many students find easier to learn and use with greater accuracy. Throughout the program an emphasis is placed on developing computational skills through application-based problem solving.

Instead of requiring all students to learn the same computation procedure, by rote, at the same time, Everyday Mathematics aims to make students active participants in the development of algorithms. This process begins by developing students' background skills and knowledge in three areas: basic fact skills, place value skills, and their understanding of the meanings of operations. Once these background skills are in place, and before students are taught standard algorithms, they are encouraged to invent and share their own ways for doing operations.

Giving students the opportunity to invent and share their own operational procedures has the following benefits:

• Children are more motivated to solve problems when they have to come up with their own strategy instead of just following a rote procedure.
• Children with different learning styles are given problem solving options. They may choose to use manipulatives, drawings, oral and written words or symbols to represent and solve problems.
• Children become adept at changing problems into easy-to-solve equivalent problems. For example, 30-17 is equivalent to 30-10-7.
• When children explain and discuss their own algorithms with other children, they internalize what the operations mean and learn from each other. Children's discussions also provide valuable information that can help teachers assess the development of their numerical thinking.

After children have had opportunities to experiment with their own operation procedures, they are introduced to standard algorithms and a number of alternative algorithms. Multi-digit addition and subtraction algorithms are formally introduced in second grade, and most children should be proficient in the use of at least one algorithm for each operation by the beginning of fourth grade. Division algorithms are introduced in fourth grade, with proficiency expected in fifth grade.

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What are the alternative algorithms? Why are these part of the Everyday Mathematics curriculum?

For decades, all American school children have been taught one standard procedure for each of the four basic operations of arithmetic. These "standard" algorithms, like the regrouping ("borrowing") algorithm for multi-digit subtraction and the long division algorithm, are not the only way to perform these operations. There are many alternative algorithms taught in other countries. Compared to the standard U.S. algorithms, many of these alternative algorithms are more efficient and easier to learn.

Research has shown that teaching the standard U.S. algorithms fails with large numbers of children, and that alternative algorithms are often easier for children to understand and learn. For this reason, Everyday Mathematics introduces children to a variety of alternative procedures in addition to the customary algorithms. Examples of some of the most popular alternative algorithms follow:

Partial-Sums Algorithm	2 6 8 + 4 8 3 ________ 6 0 0 1 4 0 1 1 ________ 7 5 1
Add 100s Add 10s Add 1s Add partial sums

Partial Product Algorithm
	67
	x 53
	_______
50 x 60	3000
50 x 7	350
3 x 60	180
3 x 7	21
	_______
	3551

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How and why does Everyday Mathematics encourage the use of calculators?

Based on research that has shown calculator use can enhance cognitive gains in the areas of number sense, conceptual development and visualization, the National Council of Teachers of Mathematics recommends the integration of calculators into mathematics programs for all grade levels. Everyday Mathematics offers appropriate applications for the calculator at each grade level.

In the Everyday Mathematics program, emphasis is placed on using the calculator as a tool for learning mathematics. In kindergarten, for example, calculators add a visual dimension to oral counting routines as children count forwards and backwards by 1s, 2s, 5s, and 10s. Seeing the numbers on the calculator display as they count also helps children learn written number sequences.

In first and later grades, students play a calculator game called Beat the Calculator. This game challenges students to develop an automatic recall of the basic facts, and demonstrates why it is better to develop quick mental math skills instead of always relying on a calculator. The program also includes a number of calculator games that are designed to provide practice with place value and problem-solving skills.

To see other sample calculator activities, click here.

The student materials also include exercises for which it would be inappropriate to use calculators. These are clearly marked with "no calculator" signs.

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How does Everyday Mathematics meet the needs of students at various levels of ability?

Simply stated, the primary goal of Everyday Mathematics is to help more children learn more mathematics. The curriculum expects higher levels of accomplishment at every grade level, but also incorporates features that help make mathematics accessible to all students. It does this by:

• Connecting the study of mathematics to real world, age-appropriate contexts
• Providing multiple avenues for representing and solving problems including the use of manipulatives, tools, spoken and written words, pictures, diagrams, and symbols.
• Incorporating individual, partner, and small group activities that make it possible for teachers to provide individualized feedback and assistance
• Encouraging risk-taking by establishing a learning environment that respects multiple problem solving strategies
• Building in multiple exposures to concepts and skills and providing frequent opportunities for review and practice
• Providing engaging open-ended activities that can easily be customized to meet the needs of students with a range of abilities

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How can I help my child?

The authors of Everyday Mathematics believe it is very important to help parents become actively involved in their child's mathematical education, and they have worked hard to provide opportunities for this to happen. Here are just a few suggestions about how you can learn about the mathematics your child is studying in school, and how you can help reinforce their math learning at home.

• A Home Link or Study Link homework assignment is included with almost every lesson in the program. Periodically these homework assignments include a letter to parents (2002 edition 2004 edition) explaining various aspects of the program. Be sure to read these letters and discuss what's going on in math class with your child. Whenever possible work with your child on their Home and Study Links. If there is something unfamiliar to you in these assignments encourage your child to "teach" you about what they are working on in class. If an assignment is confusing or difficult for you or your child, jot a note explaining your difficulties on the Home or Study Link paper and return it to your child's teacher.
  
  
• Encourage your child to teach you the math games she is learning in school, and play these games whenever you have an opportunity. You might even enjoy inventing some of your own math games together! (If you'd like to share your inventions, send us instructions for playing via our Suggestion Box). Wright Group/McGraw-Hill offers Family Games Kits for purchase. You can find out about them at
  http://www.wrightgroup.com/index.php/programsummary?isbn=0076020347&longCopy=Y.
  
  
• If your child needs additional basic fact practice ask his teacher to send home a set of fact triangles and spend a little time each day practicing fact families.
  
  
• Many Everyday Mathematics teachers set aside special days for math activities like Explorations, Games Days, and Projects. If possible, volunteer to help in the classroom on these days.
  
  
• Whenever you find yourself using math in your daily lives point out this fact and discuss math's usefulness in real-life situations. Encourage your child to experiment with and use everyday "math tools" like rulers, tape measures, measuring cups and spoons, clocks and calculators.
  
  
• For more information and suggestions visit these Web Sites:

Helping Your Child Learn Math

The Math Forum

Math Resource suggestions from Kankakee, IL

Math Opens Doors...and it's Fun Too!

Doing Mathematics With Your Child

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