# 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 I

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.

Performance Standard 1.3

Student will be familiar with characteristic of operation and numbers and properties of rational numbers. Students will recognize applications of commutativity and associativity.

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Objective 1: To have students rewrite the following problems by using the commutative or associative properties

Use the Any Which Way Rule for addition or multiplication to do these calculations mentally.

For example, 2 + 57 + 28 = 57 + 30 = 87.

2 + 57 + 28, 23 + 9 + 7 + 41

422 + 36 + 24 = 38(50 (47) (2)

97 x 125 x 8 (25) (41) (4) (2)

Strategies:

1. Have students use an example to explain why the order of adding or multiplying two numbers does not change the result.

2. Use an example to explain why grouping numbers in different ways does not change the result of addition or multiplication.

3. Give justification of the commutative Rule of Multiplication using the array model

4. Have students explain why the Commutative Property does not apply to subtraction or division.

Objective 2: Explain and define which property is illustrated.

6+5 = 5+ 6

9 + (4 + x) = (9 + 4) + x

(7 x 2) x 6 = 7 x (2 x 6)