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

1. Use a part-part-whole frame or a triangle with the three numbers so the whole and its two parts are visible.
2. Write all four facts from one family together, pointing out how the numbers stay the same and only the operation and order change.
3. Show that addition and subtraction are inverses: the whole minus one part gives the other part.
4. 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).
5. 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).