Same Math › Grades 1–3 › Fact families
What is a fact family?
A fact family is a set of three numbers and the four facts they make. 3, 7 and 10 give you 3 + 7, 7 + 3, 10 − 3 and 10 − 7. Learn one fact, and you get the other three.
- The top number is the total (or, for multiplication, the product).
- The bottom numbers are the parts (or factors).
- 3 + 7 = 10, 7 + 3 = 10, 10 − 3 = 7, 10 − 7 = 3
Why schools teach it
Subtraction and division come free
First graders learn subtraction as a missing-number problem: 10 − 3 is "what plus 3 makes 10?" (1.OA.B.4). A child who knows the family doesn't have to memorize subtraction as a separate list.
The same thing happens in 3rd grade with multiplication. 24 ÷ 6 is taught as "what times 6 is 24?" (3.OA.B.6), so a solid 6 × 4 gives you the division fact for free.
At the kitchen table
What to say, and what to skip
Say this
Which number is the biggest? Where does it go?
If 3 + 7 = 10, what is 10 − 7?
Let them use the family instead of counting back.Can you make a take-away fact from these three numbers?
What times 6 makes 24?
Asking division this way is exactly how 3rd grade teaches it.
Skip this
- Drilling subtraction facts as their own list.The family does that work. Practise the families instead.
Subtraction is a totally different thing.
Showing it as the opposite of adding is the whole point.- Mixing numbers from two families.3, 7 and 11 don't make a family. Check the top number is really the total.
See it in action
Building the family for 6, 8 and 14
Find the biggest number. That's the total.
14Write the two adding facts
6 + 8 = 14, 8 + 6 = 14Write the two take-away facts
14 − 6 = 8, 14 − 8 = 6
When a child answers 14 − 6 quickly because they "know 6 + 8," the family is working.
Free practice sheet
Make a fact family sheet
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Parents also ask
Why do doubles only have two facts?
With 5, 5 and 10, the two adding facts are the same (5 + 5) and so are the take-away facts (10 − 5). Most worksheets skip doubles for this reason.
Is a fact family the same as a number bond?
They're cousins. A number bond is the picture of the whole and its parts. A fact family is the four equations that picture gives you.
Does it work for multiplication?
Yes. 4, 6 and 24 give 4 × 6, 6 × 4, 24 ÷ 4 and 24 ÷ 6.
Some worksheets use a house instead of a triangle. Does it matter?
No. Triangle, house or circles, the idea is the same three numbers.