Number bonds within 20

What it is

Number bonds within 20 are the pairs that make a given total up to 20: 13 and 7 make 20, 8 and 9 make 17, 15 and 2 make 17 as well. There are far more of these than a child could sensibly learn one at a time, and they are not meant to be learned that way. Each one is worked out from a pair that is already known.

The pairs that make 10 are what they are worked out from. If 3 and 7 make 10, then 13 and 7 make 20: the same pair with a ten added to one part. If 8 and 2 make 10, then 8 and 9 make 17, because 9 is 2 and 7 more. The skill is that step, done quickly enough that it feels to the child like remembering rather than working out.

It is worth getting solid because the next things lean on it. Year 2 uses these facts to derive related ones up to 100, so a child who knows 3 and 7 make 10 can see that 30 and 70 make 100, and the same pairs come back in every mental subtraction across a ten.

When children learn it

Year 1 is where these bonds start: the requirement is to represent and use number bonds and related subtraction facts within 20. Year 2 asks for recall of addition and subtraction facts to 20 fluently, and for related facts up to 100 to be derived from them. The key stage 1 introduction states the expectation directly: by the end of Year 2, children should know the number bonds to 20.

Reception sits underneath that, where the early learning goal asks for recall of the bonds up to 5 and some of the bonds to 10. More of this work falls in Year 1 in one school and in Year 2 in another.

What it looks like when it goes wrong

These patterns come up again and again in children's answers on this skill. Each one points at a specific missing idea, not carelessness.

• The pair to ten is not used. Asked what goes with 13 to make 20, they count up from 13 in ones. The answer often comes out right, and slowly. The pair sitting inside it, 3 and 7, has not been noticed, so every bond within 20 is being built from nothing rather than derived from a pair they already know. This is the error to look for first, because a child can hide it for a long time behind answers that are correct.
• Every counter counted from one. Shown a full ten frame and four counters on a second frame, they count all fourteen from the beginning rather than reading ten and four. The gap here is behind the bonds rather than in them. Seeing how many are there without counting them, which the early years framework calls subitising, is what a bond is derived from, and a child who counts a full ten frame every time has nothing to derive with.
• Counting across ten instead of using the bond. 8 + 6 answered as 13 or 15. They count on past ten in ones and the count slips, usually at ten itself. Crossing a ten is its own skill, bridging through 10, and it rests on the same fact: knowing that 8 needs 2 is what turns 8 + 6 into 10 and then 4 more.

How to help at home

• Ask for the pair to ten first. If "8 and what makes 10" does not come back straight away, that is the thing to work on, because the pairs to 10 are what every bond within 20 is derived from.
• Say the pair to 20 next to the pair to 10: 3 and 7 make 10, so 13 and 7 make 20. Heard together, the second one is a step from the first rather than another fact to store.
• Use two ten frames, or two rows of ten counters, and fill the first row completely before anything goes in the second. What you want them reading off is ten and four, not fourteen separate things.
• Ask the subtraction as well: 8 and 9 make 17, so 17 take away 9 is 8. Year 1 asks for the subtraction facts alongside the bonds, and children often have one half of a pair without the other.

Other guides

• Number bonds to 10The pairs that make 10, why instant recall matters, and how to practise them.
• Bridging through 10Crossing a ten by stopping at it: 8 + 5 worked as 8 + 2 and 3, and why fingers persist.