Math Core

Lesson 1.5 · Addition and Subtraction Within 20

Fact families

Addition and subtraction are connected. Three numbers can make four facts that belong together. We call them a fact family.

One family, four facts

Look at these fish.

🐟🐟🐟 🐠🐠🐠🐠🐠

There are 3 🐟 and 5 🐠. That is 8 fish in all. The numbers 3, 5 and 8 make a family:

  • 3+5=83 + 5 = 8
  • 5+3=85 + 3 = 8
  • 8−3=58 - 3 = 5
  • 8−5=38 - 5 = 3

Definition

Fact family

A fact family is a group of addition and subtraction facts that use the same three numbers.

How a family works

The biggest number is the whole. The two smaller numbers are the parts.

  • Add the two parts to get the whole.
  • Take one part away from the whole to get the other part.

Worked example: Write the family

Write the fact family for 6, 7 and 13.

13 is the whole. 6 and 7 are the parts.

  • 6+7=136 + 7 = 13
  • 7+6=137 + 6 = 13
  • 13−6=713 - 6 = 7
  • 13−7=613 - 7 = 6

Worked example: Use a fact you know

You know 9+4=139 + 4 = 13. What is 13−413 - 4?

9, 4 and 13 are a family. Take the part 4 away from the whole 13. The other part is left.

13−4=913 - 4 = 9.

Worked example: A doubles family

Write the fact family for 4, 4 and 8.

The two parts are the same! So there are only two facts:

  • 4+4=84 + 4 = 8
  • 8−4=48 - 4 = 4

Common mistake

In a subtraction fact, always start with the biggest number. 8−3=58 - 3 = 5 is in the family. 3−83 - 8 is not.

Practice

Practice 1

You know 9+4=139 + 4 = 13. What is 13−413 - 4?

Type a number.

Practice 2

You know 7+8=157 + 8 = 15. What is 15−715 - 7?

Type a number.

Practice 3

The fact family for 6, 8 and 14 has the fact 6+8=146 + 8 = 14. What is 14−814 - 8?

Type a number.

Practice 4

Which fact is not in the fact family for 2, 9 and 11?

Practice 5

Which three numbers make a fact family?

Practice 6

You know 5+7=125 + 7 = 12. What is 12−512 - 5?

Type a number.

Practice 7

The fact family for 5, 10 and 15 has the fact 10+5=1510 + 5 = 15. What is 15−1015 - 10?

Type a number.