How to teach fact families
Grade 2 to Grade 4
A fact family is the set of related number facts you can make from the same three numbers. From 2, 3 and 5 you get 2 + 3 = 5, 3 + 2 = 5, 5 - 3 = 2 and 5 - 2 = 3. Fact families make addition and subtraction (and later multiplication and division) two sides of the same coin, so learning one fact gives you three more for free.
How to teach it
- Use a part-part-whole frame or a triangle with the three numbers so the whole and its two parts are visible.
- Write all four facts from one family together, pointing out how the numbers stay the same and only the operation and order change.
- Show that addition and subtraction are inverses: the whole minus one part gives the other part.
- Move to multiplication and division families once times tables begin (3, 4 and 12 give 3 x 4, 4 x 3, 12 / 3, 12 / 4).
- Give students two numbers and ask for the whole family, then a missing number to find using the family.
Worked example
The family for 3, 4 and 12: 3 x 4 = 12 4 x 3 = 12 12 / 3 = 4 12 / 4 = 3
Common mistakes
- Writing only one or two facts instead of the whole family.
- Muddling which number is the whole and which are the parts.
- Not seeing subtraction as the inverse of addition (or division as the inverse of multiplication).
Frequently asked questions
What is a fact family?
A fact family is the set of related number facts made from the same three numbers. From 2, 3 and 5 you get 2 plus 3 equals 5, 3 plus 2 equals 5, 5 minus 3 equals 2 and 5 minus 2 equals 3. Learning one fact gives the other three for free.
What age or grade are fact families taught?
Fact families are usually taught from Grade 2 to Grade 4. Addition and subtraction families come first, and multiplication and division families follow once the times tables begin, reinforcing that the operations in each pair are inverses.
How do fact families help children learn?
They show that addition and subtraction, and later multiplication and division, are two sides of the same coin. Because the same three numbers make four facts, learning one fact gives three more, which builds recall efficiently and reinforces that each operation has an inverse.
What is an example of a multiplication fact family?
From 3, 4 and 12 you get 3 times 4 equals 12, 4 times 3 equals 12, 12 divided by 3 equals 4, and 12 divided by 4 equals 3. The numbers stay the same while only the operation and order change, showing multiplication and division as inverses.
How do you teach fact families?
Use a part-part-whole frame or a triangle holding the three numbers so the whole and its two parts are visible. Write all four facts from one family together, then give students two numbers and ask for the full family, or a missing number to find using it.
How do fact families relate to number bonds?
A number bond gives the whole and its two parts, and a fact family writes out all four number facts from that bond. So the bond 6 and 4 to 10 produces the family 6 plus 4, 4 plus 6, 10 minus 6 and 10 minus 4. Bonds and fact families reinforce each other.
Why does my child only write two facts instead of four?
A common slip is stopping at the two facts that feel obvious and forgetting the inverse pair, or muddling which number is the whole and which are the parts. A triangle or part-part-whole frame keeps all three numbers and their four facts in view.
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