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Fact Families: Three Numbers, Four Facts
A fact family is three numbers that belong together. Learning them as a family is what connects addition and subtraction.
A fact family is a set of related addition and subtraction facts that use the same three numbers. 6, 9 and 15 give 6 + 9 = 15, 9 + 6 = 15, 15 − 6 = 9 and 15 − 9 = 6. A child who knows one of them is most of the way to the other three.
The triangle
The whole goes at the top and the parts at the bottom. Cover a corner to make a question.
Why they matter
Subtraction feels hard when it's a separate set of things to remember. Fact families show that there's only one set. If a child knows 8 + 5 = 13, they already know 13 − 5 and 13 − 8. It also gives them a way to check: add back and see if you get the number you started with.
Doubles are the exception. 7, 7 and 14 only make two facts, 7 + 7 = 14 and 14 − 7 = 7, because swapping two 7s changes nothing. That's a nice thing for children to spot for themselves.
How to teach them
- Use real things. Line up 6 red blocks and 9 blue blocks. Count them all: 15. Take the red ones away: 9 left. Put them back and take the blue ones away: 6 left.
- Draw the triangle with the whole at the top. Cover one number and ask what's hiding.
- Write all four facts together, in the same order each time, and read them aloud.
- Play Family House in the game, and print fact family sheets for practice on paper.
Every family to 20
Families of numbers from 1 to 10, grouped by their total.
| Total | Families |
|---|---|
| 2 | 1, 1, 2 |
| 3 | 1, 2, 3 |
| 4 | 1, 3, 4 · 2, 2, 4 |
| 5 | 1, 4, 5 · 2, 3, 5 |
| 6 | 1, 5, 6 · 2, 4, 6 · 3, 3, 6 |
| 7 | 1, 6, 7 · 2, 5, 7 · 3, 4, 7 |
| 8 | 1, 7, 8 · 2, 6, 8 · 3, 5, 8 · 4, 4, 8 |
| 9 | 1, 8, 9 · 2, 7, 9 · 3, 6, 9 · 4, 5, 9 |
| 10 | 1, 9, 10 · 2, 8, 10 · 3, 7, 10 · 4, 6, 10 · 5, 5, 10 |
| 11 | 1, 10, 11 · 2, 9, 11 · 3, 8, 11 · 4, 7, 11 · 5, 6, 11 |
| 12 | 2, 10, 12 · 3, 9, 12 · 4, 8, 12 · 5, 7, 12 · 6, 6, 12 |
| 13 | 3, 10, 13 · 4, 9, 13 · 5, 8, 13 · 6, 7, 13 |
| 14 | 4, 10, 14 · 5, 9, 14 · 6, 8, 14 · 7, 7, 14 |
| 15 | 5, 10, 15 · 6, 9, 15 · 7, 8, 15 |
| 16 | 6, 10, 16 · 7, 9, 16 · 8, 8, 16 |
| 17 | 7, 10, 17 · 8, 9, 17 |
| 18 | 8, 10, 18 · 9, 9, 18 |
| 19 | 9, 10, 19 |
| 20 | 10, 10, 20 |
Quick quiz: does it belong?
Questions people ask
How many facts are in a fact family?
Usually four: two additions and two subtractions. Families made from a double have two.
What is the fact family for 3, 4 and 7?
3 + 4 = 7, 4 + 3 = 7, 7 − 3 = 4 and 7 − 4 = 3. See it here.
Are fact families the same as number bonds?
They use the same three numbers. A number bond is the picture and the fact family is the four written facts.
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