Number bonds to 10
Every pair of numbers that makes 10, drawn on a ten frame, and why knowing them by heart makes adding faster.
The answer
The number bonds to 10 are 0 + 10, 1 + 9, 2 + 8, 3 + 7, 4 + 6 and 5 + 5, and the same pairs turned round.
Every number bond to 10
| Bond | On a ten frame |
|---|---|
| 0 + 10 = 10 | |
| 1 + 9 = 10 | |
| 2 + 8 = 10 | |
| 3 + 7 = 10 | |
| 4 + 6 = 10 | |
| 5 + 5 = 10 | |
| 6 + 4 = 10 | |
| 7 + 3 = 10 | |
| 8 + 2 = 10 | |
| 9 + 1 = 10 | |
| 10 + 0 = 10 |
Try it on a ten frame
3 + 7 = 10
Each time one part goes up, the other goes down by the same amount, so the total stays 10.
The pattern
Read the list from the top. The first number goes up 0, 1, 2, 3 while the second comes down 10, 9, 8, 7. Halfway, at 5 + 5, the pairs start again turned round: 6 + 4 is 4 + 6.
So there are really only six facts to learn: 0 + 10, 1 + 9, 2 + 8, 3 + 7, 4 + 6 and 5 + 5. On the ten frame, the filled counters show one part and the outlined places show the missing part: 3 filled leaves 7 outlined.
Using the bonds
A bond with two different numbers gives four facts. Knowing 3 + 7 = 10 also gives 7 + 3 = 10, 10 − 3 = 7 and 10 − 7 = 3. A double such as 5 + 5 gives only two: 5 + 5 = 10 and 10 − 5 = 5.
Bonds to 10 make adding across a ten easier. For 8 + 5, 8 needs 2 more to make 10, which leaves 3 of the 5, so 8 + 5 = 13. Children in England meet number bonds within 20 in Year 1.
More number bonds and mental maths
Questions parents ask
What is 10 take away 4?
6, because 4 + 6 = 10. Every bond with two different numbers gives two take-away facts like this: 10 − 6 = 4 as well.
How many number bonds to 10 are there?
There are 11 if you count every order, from 0 + 10 up to 10 + 0. If 3 + 7 and 7 + 3 count as the same bond, there are 6.
How do number bonds to 10 help with adding 7 + 6?
Make 10 first. 7 needs 3 more to make 10, which leaves 3 of the 6, so 7 + 6 = 13. The same trick works for any sum that crosses 10.
When do children learn number bonds to 10?
In Year 1. The national curriculum asks children to represent and use number bonds and related subtraction facts within 20, and bonds to 10 are the first step.
Quick mental maths starts with number bonds
11+ maths is timed, and number bonds are behind fast adding, subtracting and working out change. The free diagnostic checks maths, English and both kinds of reasoning, and shows what to practise next. No card is required.