# 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

Your feedback is important to us!

After viewing our curriculum units, please take a few minutes to help us understand how the units, which were created by public school teachers, may be useful to others.

## Inverse Properties of Addition and Subtraction

Students are told that the order of numbers does not matter in addition, but it does matter for subtraction except when both numbers are identical, for example, 10-10 = 10-10 or 0.

When the two numbers are not the same, such as, 3 and 6, the pair of differences is opposites: one difference is a positive number (e.g., 4) and the other is its negative number (e.g., -4). This can be represented as a-b = c and b-a = -c. If a= b, then a-b = 0 and b- a = 0 = - 0. The pairs of differences sum to zero, such as, +4 + (-4) = 0.

*
Zero Property of Addition
*

The zero property of addition states that the sum of any number and 0 is that number: For example: 2 + 0 = 2, 99 + 0 = 99. The additive Inverse a + (-a) = 0, a-a = 0.

*
Zero Property of Multiplication
*

The zero property of multiplication states that the product of any number and 0 is 0. For Example: 2 x 0 = 0. This can be shown to be a consequence of the zero property of addition and the distributive rule.

*
Multiplicative Identity Property
*

The multiplicative identity property
*
*
states that the product of any number and one is that number, for example 5 x 1 = 5.