Number bonds to 10 and 20, explained for parents

01

What is a number bond?

A number bond is a pair of numbers that join to make another number. 7 and 3 make 10, so 7 and 3 are a number bond to 10. So are 6 and 4, and 10 and 0.

The idea underneath is simple and powerful: a number can be split into parts, and the parts can be put back together. Your child is learning that 10 is not just the word after 9. It is also 7 and 3, and 5 and 5, and 9 and 1, all at once.

Schools often show this with a part-whole model. The whole goes in the top circle and the two parts go in the circles below. Read it either way: the parts make the whole, or the whole splits into the parts. Older children meet the same idea as a bar model, where a long bar is split into two shorter ones.

The same picture holds four facts. If 7 and 3 make 10, then 3 and 7 make 10, 10 take away 3 leaves 7, and 10 take away 7 leaves 3. That link between adding and taking away is one of the main reasons number bonds are taught so early. You can see where they sit in the bigger picture on our maths overview.

02

Number bonds to 10, on a ten-frame

There are eleven number bonds to 10 if you count both orders. Children are usually taught them as a set, in order, because the pattern helps: as one number goes up by 1, the other goes down by 1.

• 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

• 1111number bonds to 10, counting both orders
• 66pairs to learn, once you know order doesn't matter
• 2121number bonds to 20, counting both orders

A ten-frame makes these pairs easy to see. It is a box of ten spaces in two rows of five. Put 7 counters in, and the empty spaces show the 3 that are missing. Your child doesn't need to count them one by one for long: soon they see 7 and simply know 3 more fill it.

Try it below. The darker counters are the part you start with; the lighter ones are the part your child adds. The words and the part-whole model change as they go, and the numbers are said aloud.

03

Why number bonds to 10 matter so much

Our numbers are built in tens. Once your child knows the pairs that make 10 without having to count, a lot of later maths gets easier, because they can use 10 as a stepping stone.

Take 7 + 5. Counting on from 7 works, but it is slow and easy to slip. A child who knows that 7 and 3 make 10 can split the 5 into 3 and 2, hop to 10, then add the 2 that is left: 7 + 5 = 10 + 2 = 12. Teachers call this bridging through 10, and it only works smoothly when the bond is known by heart.

The same bonds help with taking away (13 − 5: take 3 to get to 10, then 2 more), with adding bigger numbers and, later, with money. That is why schools talk about fluency: not just getting the answer, but knowing it quickly enough that the thinking can go on the harder part of the problem.

04

From number bonds to 10, to 20 and to 100

Here is the good news for your child: number bonds to 20 are not a whole new list to learn. They are the bonds to 10 with a ten added. If 3 and 7 make 10, then 13 and 7 make 20. One full ten-frame, plus the same 3 and 7 on a second frame.

Bonds to 20 also include pairs that cross over the ten, like 12 and 8 or 9 and 11. Children work these out from the same facts: 12 is 10 and 2, and 2 needs 8 to make the next 10.

In Year 2 the pattern grows again. Swap every counter for a ten, and 3 and 7 make 10 becomes 30 and 70 make 100. Seeing the three rows together helps your child notice that one fact they already know opens up two more. That habit of spotting a known fact inside a new problem is worth more than any single answer.

05

Which number bonds should my child know in each school year?

In England, the expectations come from the Early Years Foundation Stage for Reception and the national curriculum for Years 1 and 2. In short: bonds to 5 and some bonds to 10 by the end of Reception, bonds within 20 in Year 1, and quick recall to 20 with the step up to 100 in Year 2.

These are end-of-year goals, not starting points. Children get there at different speeds, and plenty of them find bonds to 10 shaky at the start of Year 1. That is normal, and a few minutes of play a week makes a real difference.

06

How to teach number bonds at home, step by step

You don't need worksheets or flashcards. Most children learn number bonds best by handling real things, then seeing pictures, then working with the numbers alone. Schools often follow the same order.

1. Start with 5. Use one hand. Hold up 3 fingers and ask how many are folded down. Bonds to 5 are the stepping stone to bonds to 10.
2. Make it real. Split 10 buttons, pasta shapes or toy cars into two groups, in as many ways as you can. Say each one out loud: "6 and 4 make 10."
3. Show it in a frame. An egg box with two eggs cut off makes a fine ten-frame. Seeing the empty spaces builds the picture your child will later hold in their head.
4. Hide one part. Show the whole, cover one part, and ask what is hiding. This is the step that turns knowing into recall.
5. Little and often. Two or three minutes in the car or at tea time beats a long session. Stop while it is still fun.

When your child knows the bonds to 10, the same steps work for 20. If they are also learning to read, our phonics guides follow the same little and often approach.

07

Number bonds games to play at home

Games beat drills because your child gets to say and see the bond many times without it feeling like a test. Here are four that need almost nothing.

For more ideas by age, see Reception maths and the full list of games in the app.