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Maths · Reception and Year 1

Number bonds to 10 and 20: a guide for parents

By Dave Allen · Updated · 6 min read

Drafted and fact-checked with AI help, against the sources below. Not yet reviewed by a teacher. How we write our guides

What it is

Number bond
Two numbers that add together to make a whole. 6 and 4 are a number bond to 10.
Whole and parts
The language schools use for bonds. In 6 = 4 + 2, 6 is the whole, and 4 and 2 are the parts.
Partitioning
Splitting a number into parts, such as splitting 8 into 5 and 3. Putting the parts back together is called composing the number.
Related facts
The other facts that come with a bond. From 7 + 3 = 10 you also get 3 + 7 = 10, 10 − 3 = 7 and 10 − 7 = 3.

A number bond is the same fact whichever way round you look at it. That's why schools teach adding and taking away together: once your child knows a bond, they know a little family of facts.

0 + 10 = 10
1 +  9 = 10
2 +  8 = 10
3 +  7 = 10
4 +  6 = 10
5 +  5 = 10
The number bonds to 10 (each one also works the other way round)

The aim is for your child to just know these facts, rather than count them on fingers each time. That frees up their thinking for bigger sums.

How it's taught at school

In Reception, one of the early learning goals is to recall number bonds up to 5, including the matching take-away facts, and some bonds to 10, including doubles such as 4 + 4. The goal says children should know these automatically, without counting or using rhymes or other aids.

DfE guidance for Reception suggests using a five frame or a ten frame: a row of 5 boxes, or two rows of 5, with counters placed in them. Your child can see at a glance how many spaces are filled and how many are empty, which shows the two parts of 5 or 10.

In Year 1, the national curriculum expects children to represent and use number bonds and related subtraction facts within 20. That means facts like 9 + 7 = 16, not just pairs that make exactly 10 or 20. DfE guidance for teachers adds that children should be able to add and subtract within 10 fluently by the end of Year 1.

9 + 7 = 16
16 − 7 = 9
7 = 16 − 9
One bond within 20 gives a family of facts

Children often learn to work through bonds in order, like the list of bonds to 10 above. As one part goes up by 1, the other part goes down by 1, and the whole stays the same. Spotting this pattern helps your child check they haven't missed any.

By the end of Year 2, the national curriculum expects children to know their number bonds to 20. In Year 2 they also use bonds to 10 to add across 10, a strategy often called making 10.

7 + 5
= 7 + 3 + 2
= 10 + 2
= 12
Making 10: using a bond to 10 to add 7 + 5

Tip
Little and often works best. Two or three minutes of bond games while you wait for the bus or the kettle will do more than a long sit-down session.

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Common mistakes (and how to help)

Counting on in ones every time, for example on fingers
Counting is a fine place to start, so don't stop it. Then help your child use facts they already know: "Double 3 is 6, so 4 + 3 is one more: 7." Over time, the facts start to come without counting.
Missing some of the pairs, or not being sure when they've found them all
Work through them in order together, starting from 0 + 10. Point out the pattern: one number goes up by 1 and the other goes down by 1. When you reach 10 + 0, you've found them all.
Seeing 7 + 3 = 10 and 10 − 7 = 3 as unrelated facts
Use objects. Put 10 pasta pieces down, then hide 7 under a cup. Your child can see that 3 are left, and that 7 and 3 make the 10 you started with.
Forgetting the bonds that use zero
Include 0 + 10 and 10 + 0 in your games. Show 10 pasta pieces with none hidden: "Ten and nothing makes ten." It feels obvious to grown-ups, but it's a fact children need too.

Three quick activities at home

Under the cup

About 5 minutes · You need: A plastic cup and 5 or 10 small things, such as pasta pieces or buttons

  1. Count the objects with your child, so you both know the whole number, such as 5.
  2. While your child looks away, hide some under the cup.
  3. Your child looks at what's left and says how many are hidden. Lift the cup to check together.
  4. When bonds to 5 feel easy, move up to 10.

Fingers to 10

About 3 minutes · You need: Nothing: this works anywhere

  1. Hold up some fingers, such as 6.
  2. Ask your child how many more fingers you need to make 10.
  3. Your child shows the answer on their own fingers. Then swap, so your child asks you.

Pairs to 10

About 10 minutes · You need: A pack of playing cards, using only the aces to 9s (an ace counts as 1)

  1. Lay out 12 cards face up.
  2. Take turns to find two cards that add up to 10, such as a 4 and a 6, and say the bond aloud.
  3. Keep the pair and fill the gaps from the pack.
  4. For a Year 1 challenge, try finding three cards that make 20 together.

Try it with your child

Free Pipkin puzzles on this topic. No sign-up. They open on the children's side of Pipkin.

Questions parents ask

Is it OK for my child to use their fingers?

Yes, while they're learning. Fingers are a helpful way to see the parts of 5 and 10. The longer-term aim is for your child to know the facts without counting, so gently encourage using a known fact first, then checking on fingers.

What's the difference between bonds to 10 and bonds within 10?

Bonds to 10 are the pairs that make exactly 10, such as 4 + 6. Bonds within 10 are all the adding and taking away facts with numbers up to 10, such as 4 + 3 = 7 or 9 − 5 = 4.

My child knows bonds to 10. What comes next?

Bonds to 10 help with bonds to 20. If your child knows 6 + 4 = 10, show them 16 + 4 = 20. After that, try facts within 20 that cross 10, such as 8 + 5.

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Related guides

Sources

  1. Department for Education: Early years foundation stage (EYFS) statutory framework
  2. Department for Education: Development Matters: non-statutory curriculum guidance for the early years foundation stage
  3. Department for Education: National curriculum in England: mathematics programmes of study
  4. Department for Education: Teaching mathematics in primary schools (Mathematics guidance: key stages 1 and 2)
  5. BBC Bitesize: Number bonds to 10 (early years maths)