# The Craft of Word Problems

## CONTENTS OF CURRICULUM UNIT 04.05.07

- Introduction
- Definitions of Math Properties
- Commutative Properties of Addition and Multiplication
- Inverse Properties of Addition and Subtraction
- Associative Properties
- Distributive Property
- Reviewing Properties
- Rules for Properties of the Real Numbers
- Lesson Plan I
- Lesson Plan II
- Lesson Plan III
- Appendix A: Using Basic Properties To Solve Problems In Math
- Appendix B Glossary of Math Terms for Basic Properties
- Reading List
- Teacher Resources
- Bibliography

### Unit Guide

## Using Basic Properties to Solve Problems in Math

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## Lesson Plan II

Content Standard 1.0 Number Concepts, Arithmetic, and Operation Concepts: Students will work comfortably and confidently within the real number system and its operations. They will make comparisons, recognize patterns, and use multiple representations of the same number.

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Learning Multiplication Facts

Content Standard 5.0: Problem Solving and Mathematics Reasoning: Problem solving concepts and strategies lie at their heart of mathematics. Students will use them in the formulation of problems. They will appropriately test problem conclusions against conditions. They will reason mathematically.

Performance Standard 5.3: Problem Implementation

Students will invoke problem solving strategies, such as illustrating with sense-making sketches to clarify situations or organizing information in a table. Students will integrate concepts and techniques from different areas of mathematics and will justify logical statements.

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Understanding the relation between addition and multiplication makes it possible for students to relate the learning of multiplication facts to their knowledge of addition.

Objective 1: To engage students in a discussion of the relation between 3 and 4. The following examples of true or false number sentences can be used to engage students in a discussion about their relation.

3 x 7 = 7 + 7 + 7

3 x 7 = 14 + 7

4 x 6 = 12 + 12

Is it true that 4,287 + 3, 156 = 4, 285 + 3, 158?

Objective 2: To engage students in learning number facts and to learn patterns that makes the number facts easier. Have students to solve the following problems by carrying out the calculations on each side of the equal sign.

3 x 8 = 2 x 8 + 8

6 x 7 = 5 x 7 + 7

8 x 6 = 8 x 5 + 6

7 x 6 = 7 x 5 + 7

9 x 7 = 10 x 7 -7

- - Denotes a false number sentence. The above source of information is taken from: Thomas Carpenter, Megan Loef Franke and Linda Levi, Thinking Mathematically Integrating Arithmetic & Algebra in Elementary School, Heinemann, Portmouth, NH, 2003, p 39.