Number bonds to 10, 20 and 100: what they are and how to help

What is a number bond?

A number bond is two numbers that add up to make a total. 6 and 4 are a number bond to 10, because 6 + 4 = 10. 15 and 5 are a number bond to 20.

Schools often show a number bond with a part-whole model. The whole is in the top circle and the two parts are in the circles below it. It is sometimes called a cherry model, because of its shape.

The model shows that the whole can be split into parts, and the parts put back together, without anything being lost. That simple idea is what adding and taking away are built on.

What are the number bonds to 10?

There are 11 number bonds to 10, counting 0 and 10:

Number bond	Turned round
0 + 10 = 10	10 + 0 = 10
1 + 9 = 10	9 + 1 = 10
2 + 8 = 10	8 + 2 = 10
3 + 7 = 10	7 + 3 = 10
4 + 6 = 10	6 + 4 = 10
5 + 5 = 10	5 + 5 = 10

Notice the pattern: as one number goes up by 1, the other goes down by 1. Working through them in order like this is how government guidance suggests children find all the ways to split a number, so they can see there are only so many.

A tens frame is a grid of 10 squares in two rows of 5. Put 7 counters on it, and the 3 empty squares show the other part of the bond straight away.

Before the bonds to 10, children often learn the number bonds to 5 (such as 2 and 3, or 4 and 1). A full row of a tens frame is 5, which helps here too.

Number bonds to 20

The number bonds to 20 come from the bonds to 10. If 7 + 3 = 10, then 17 + 3 = 20, and 7 + 13 = 20. Each bond to 20 is a bond to 10 with an extra ten on one side.

On two tens frames, 13 is one full frame and 3 more. The 7 empty squares show that 13 + 7 = 20.

The national curriculum asks Year 1 to use the number bonds and subtraction facts within 20, and says that by the end of Year 2 children should know the number bonds to 20.

Number bonds to 100

The first number bonds to 100 children meet are multiples of 10. In Year 2, children use 3 + 7 = 10 to work out 30 + 70 = 100: three tens and seven tens make ten tens.

In Year 3, children work out pairs of two-digit numbers that make 100, such as 62 and 38. Government guidance for teachers suggests two steps:

1. Make 10 ones. The ones digits, 2 and 8, make 10.
2. The tens digits make 9, not 10. The 10 ones make one more ten, so 60 needs only 3 more tens.

So 62 + 38 = 100. Children are also expected to just know that 25 and 75 make 100, which helps with money and measures: 1 metre is 100 cm, so cutting 25 cm off a metre leaves 75 cm.

How number bonds link to subtraction

Every number bond gives subtraction facts too. Because 9 + 7 = 16, children also know that 16 − 7 = 9 and 16 − 9 = 7. The curriculum asks Year 1 to use the bonds "in several forms", including missing number questions like 7 = ? − 9 (the answer is 16).

This is why learning the bonds by heart pays off twice. A child who knows 6 + 4 = 10 doesn't need to count back to answer 10 − 4. It also means children see adding and taking away as two sides of the same fact, which the curriculum calls the inverse.

Using number bonds to add across 10 (making 10)

When an addition goes past 10, children use number bonds to "make 10" first. To work out 7 + 5:

1. 7 needs 3 more to make 10.
2. Split the 5 into 3 and 2.
3. 7 + 3 = 10, then 10 + 2 = 12.

So 7 + 5 = 12. This is a Year 2 skill, and it's quicker than counting on in ones.

Subtracting works the same way in reverse. To work out 15 − 9, take away 5 to reach 10, then take away the other 4: 15 − 5 = 10, and 10 − 4 = 6. So 15 − 9 = 6. A number line is a good way to see these jumps, and the same idea of splitting numbers runs through partitioning.

How to teach number bonds to 10 at home

You don't need anything special to teach number bonds. A few minutes at a time works well.

• Hide and guess. Put 10 toys on the table, hide some under a cup and ask how many are hidden. Swap roles so your child hides them.
• Use fingers. Hold up 6 fingers and ask how many are down. Fingers are a ready-made set of 10.
• Make a tens frame. Draw two rows of 5 squares on paper and use pasta or buttons as counters.
• Go in order, then mix them up. Saying 0 and 10, 1 and 9, 2 and 8 shows the pattern. Then ask them in any order until the answer comes without counting.
• Ask the subtraction too. After "what goes with 4 to make 10?", ask "what's 10 take away 4?"
• Move up to 20 and 100. Once the bonds to 10 come quickly, ask "if 4 and 6 make 10, what goes with 14 to make 20?" or "what goes with 40 to make 100?"

Common mistakes to watch for

• Counting on every time. Counting on from 7 to 10 gets the right answer, but slowly. The aim is to know the bond straight away, so keep practising until counting isn't needed.
• Forgetting 0 and 10. 0 + 10 = 10 is a bond too, and it matters later on.
• An extra ten in bonds to 100. A common slip is to say 62 and 48 make 100. Those add up to 110, because the ones make another ten. Remind your child that the tens digits make 9.
• Missing number questions. In ? − 9 = 7, some children take 7 from 9 and write 2. Ask "what number did we start with?", and use the part-whole model: 9 and 7 are the parts, so the whole is 16.

Number bonds questions to try

1. What goes with 4 to make 10?
2. 10 − 7
3. What goes with 12 to make 20?
4. 8 + 6, by making 10 first
5. What goes with 60 to make 100?
6. What goes with 45 to make 100?

Answers

1. 6
2. 3
3. 8
4. 14 (8 + 2 makes 10, then 4 more)
5. 40
6. 55

For the bigger picture of these years, see the KS1 maths guide, and the Year 1 maths and Year 2 maths guides for everything else your child learns alongside the number bonds.