## Subtraction Strategies Through 10

The addition table can be used to find the answers to subtraction facts because addition and subtraction are inverse operations. This leads to families of facts for addition and subtraction. Fact families are useful for finding the differences for subtraction facts by using related addition facts and for finding the sums for addition facts by using related subtraction facts. 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.

4 + 2 = 6
2 + 4 = 6
6 − 4 = 2
6 − 2 = 4

Using variables, the four members of the family can be written as follows.

a + b = c
b + a = c
c − a = b
c − b = a

In first grade, the study of arithmetic is restricted to the whole numbers (0, 1, 2, …). For the set of whole numbers then, it is necessary for a ≥ b and c ≥ a for the facts above to have meaning. It is important to remember that in later grades, when 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 6.5: Fact Families