# 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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## Definitions of Math Properties

Mathematical properties are avenues to higher-level thinking, because they illustrate general cases and lead to mathematical generalizations. The four usual rules of arithmetic for addition are:

1) Commutative Property states that a + b = b + a

2) Associative Property, (a + b) + c = a + (b + c)

3) Identity Property of 0, 0 + a = a (= a + 0)

4) Inverse Property, for every member a, there is - a, such that a + (- a) = 0.

Similar to the addition, the four rules of arithmetic for multiplication rules can be stated as:

1) Commutative Property: ab = ba

2) Associative: (ab)c = a(bc)

3) Identity: 1.a = a (= a.1)

4) Inverse Property, for every a =/= 0, there is (1/a) (or a to the power of -1), such that a (1/a) = 1. It is important to mention that connecting addition and multiplication is the Distributive Rule: a (b t c) = ab + ac. Often rules are consequences of these: for example, a x 0 = 0, because a = a x 1 = a x (1+ 0) x a x1 + a x 0. Now subtract a from both sides to get 0 = 0 + a x 0 = a x 0.