Addition & Subtraction Fact Families

Instructor: Mark Boster
The focus of this lesson is learning all about fact families that are addition and subtraction. By the end of the lesson, you will be able to figure out all the number sentences for addition and subtraction that belong to the fact family.

Families Are Awesome

Dad likes to go out into the garden and pull weeds in his swimsuit. Mom likes to mow the grass in a dress, and brother Tom likes to turn the television upside down when he plays video games. What a family that is! The truth is that families belong together. The same is true with numbers. Number families like to stick together.

Number Families

Pick any two numbers and add them together. You now have three numbers that are a family. A fact family is three numbers that when added or subtracted, gets another number in the same family. Maybe you pick 2 and 3. When you add them together, you get 5. So, 2, 3 and 5 are a family. With each family, you can make four true math sentences, two addition and two subtraction. For our 2, 3, 5 fact family, here are the four true math sentences you can make:


2 + 3 = 5

3 + 2 = 5


5 - 3 = 2

5 - 2 = 3

Wait...what about 3 + 5 = 8 or 3 - 2 = 1 ? Oh, that isn't right because there is no 8 or 1 in this family. That must be other families.

Who Is in the Family?

If you draw a triangle and put the three numbers of a fact family in it, one at each corner, sometimes it is easier to figure out all four sentences.


This fact family triangle lets you easily see how the family works. Only the numbers in the triangle can be used. Here you can see there is a 3, a 5, and an 8. There are two addition and two subtraction problems using only these numbers. As you can see, only the numbers in the family were used to make the equations.


3 + 5 = 8

5 + 3 = 8


8 - 5 = 3

8 - 3 = 5

How about another one for practice?


Okay, one more. This time, the numbers are given to you in the triangle and you have to figure out the correct facts for that family. OK, here you go:


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