Addition and subtraction fact families

An addition and subtraction fact family is a set of two addition facts and two subtraction facts that use the same three numbers: two parts and one whole. For the parts 6 and 8 and the whole 14, the family is 6 + 8 = 14, 8 + 6 = 14, 14 − 6 = 8 and 14 − 8 = 6.

What is an addition and subtraction fact family?

Think of a whole that is split into two parts. The whole is the total, and the parts are the two smaller numbers that add up to it. Adding puts the parts together. Subtracting takes one part away from the whole and leaves the other part. Because the same three numbers appear in every fact, the four facts are a family.

You may also hear this called a family of facts, an addition family, or a part-part-whole relationship. Teachers draw it as a number bond, a triangle or a house.

Addition and subtraction fact family examples

Look at the first card. The parts are 1 and 9 and the whole is 10, so 1 + 9 = 10, 9 + 1 = 10, 10 − 1 = 9 and 10 − 9 = 1. More worked cases are on the fact family examples page.

Build your own addition and subtraction family

Use fact families to subtract

Subtraction feels harder than addition for many children. A fact family gives them a way in. To solve 14 − 6, think of the addition fact that goes with it.

1. Write the subtraction problem: 14 − 6 = ?
2. Turn it into a missing addend problem: 6 + ? = 14.
3. Use a fact you know. 6 + 8 = 14, so the missing number is 8.
4. Check with the family: 14 − 6 = 8 and 14 − 8 = 6 both use 6, 8 and 14.

How many addition fact families are there?

If both parts must be at least 1, there are 25 different addition and subtraction fact families with a whole of 10 or less, and 100 with a whole of 20 or less. We list every one of them:

• Addition fact families to 10
• Addition fact families to 20

Common mistakes to watch for

• Picking the wrong whole. The whole is always the biggest number. In 6, 8 and 14 the whole is 14, never 6.
• Subtracting the whole from a part. 6 − 14 is not part of the family. Every subtraction fact starts with the whole.
• Forgetting the swap. Children often write 6 + 8 = 14 but not 8 + 6 = 14. Remind them the order of addition does not change the total.
• Using numbers that do not match. 6, 8 and 15 is not a family, because 6 + 8 is 14.

Ideas for practice at home or in class

• Use two colors of counters. Put a whole group of 10 in a part-part-whole mat and slide counters between the two parts.
• Draw a fact family house and write the four facts in the rooms.
• Print addition and subtraction fact family worksheets with an answer key.
• Play a round on the fact family games page.

Frequently asked questions

What is the fact family for 5, 6 and 11?

5 + 6 = 11, 6 + 5 = 11, 11 − 5 = 6 and 11 − 6 = 5.

Do all addition fact families have four facts?

No. If the two parts are equal, like 7, 7 and 14, there are only two different facts: 7 + 7 = 14 and 14 − 7 = 7.

What grade learns addition and subtraction fact families?

Mostly first and second grade, usually with numbers up to 20. See the 1st grade and 2nd grade pages.