There are several ideas that we are trying to build when we introduce students to fact families. Here are some of them:
- Notice that 3+7 and 7+3=10, thus the first two equations
illustrate that if we add two numbers in any order, we get the same answer.
- Notice that 3+7 and 7+3=10, so subtraction and addition are
related. Similarly 10-3=7 or 10-7=3.
So, informally, you can think of a fact family as consisting of three numbers, two of which add up to the third.
If you are given two numbers, there are two possible fact families you can build. For example, if we are given 5 and 7, we can build the family 5,7, and 12 as above, or the family 2,5, and 7 since