Number bonds to 10, 20 and 100

What are number bonds?

A number bond is a pair of numbers that add up to a total: 3 and 7 are a bond to 10, because 3 + 7 = 10. Knowing the bonds to 10 by heart (without counting) is one of the first number facts children learn, and it underpins adding, taking away and later mental maths.

The bonds to 10 are: 0 + 10, 1 + 9, 2 + 8, 3 + 7, 4 + 6, 5 + 5 (and their turn-arounds).

From 10 to 20 and 100

Each bond to 10 gives a bond to 20 and to 100:

Bonds to 100 in fives come next: 35 + 65, 45 + 55. A child who knows 7 + 3 = 10 can see that 70 + 30 = 100 and that 17 + 3 = 20.

Why they matter

Bonds make the jump across ten easy. To work out 8 + 5, a child who knows that 8 + 2 = 10 can split the 5 into 2 and 3: 8 + 2 = 10, then 10 + 3 = 13. Taking away works the same way backwards: 13 − 5 is 13 − 3 = 10, then 10 − 2 = 8. Later, bonds to 100 help with change from a pound or a dollar.

In England, Year 1 pupils learn number bonds and related subtraction facts within 20, and Year 2 pupils use them fluently and work with related facts to 100. In the US, Grade 1 asks for fluency adding and subtracting within 10, and Grade 2 within 20.

Games to practise them

• Hidden fingers. Hold up ten fingers, hide some, and ask how many are hidden.
• Make 10 with cards. Take out the picture cards and turn pairs over: keep any pair that makes 10.
• Ten frames. Draw a box of ten squares, put counters in some, and ask how many more make ten.
• Quick-fire bonds. Say a number, your child says its partner to 10 (or 20, or 100).
• A daily game. Sum Rocket asks bonds like 3 + ? = 10 at the right level for each year group, reads them aloud for younger children, shows a number line after a mistake, and brings back the bonds a child finds hard.