## Subtraction Facts

Counting back by 1, 2, or 3, using a number line, using the addition table, and using related addition facts are all strategies for finding differences for subtraction facts. The last strategy is the most mathematically powerful strategy since it is based on the inverse relationship between addition and subtraction.

Addition and subtraction are inverse operations. Thus, we have “families of facts” for addition and subtraction. Fact families are useful for finding the answers to subtraction facts by using a related addition fact. Most fact families consist of four related facts.

For example, using the numbers 2, 4, and 6, four facts can be formed to make a family.

6 − 2 = 4

4 + 2 = 6

6 − 4 = 2

2 + 4 = 6

Using variables, the four members of a family can be shown as follows:

a + b = c

b + a = c

c − a = b

c − b = a

In second grade, the study of arithmetic is restricted to the whole numbers (0, 1, 2, … ). For the set of whole numbers then, it is necessary that a > b and c > a for the facts above to have meaning. It is important to remember that in later grades, when children's study of numbers extends to the set of integers, (…, ^{−}2, ^{−}1, 0, 1, 2, …), that the facts above will have meaning even when a < b or c < a.

**Teaching Model 3.4:** Use Addition to Subtract