Number Bonds Explained (and How to Teach Them)

If your child has come home talking about number bonds, you may not have heard the term at school yourself. In the US, the same idea is often called "making ten", "combinations of ten", "decomposing numbers" or part of "fact families". Whatever the name, it is one of the most useful ideas in early math.

What is a number bond?

A number bond shows how a number can be split into two parts. Take 7. It can be split into 5 and 2, or 4 and 3, or 6 and 1. Each of those pairs is a number bond for 7. Children often see this drawn as a "part-whole" diagram: one circle for the whole (7) joined to two circles for the parts (5 and 2).

The key insight is that one bond holds four facts. If 5 and 2 make 7, then 5 + 2 = 7, 2 + 5 = 7, 7 − 2 = 5 and 7 − 5 = 2. Learning bonds is learning addition and subtraction at the same time.

All the number bonds to 10

That is only six pairs to learn. Once your child knows them, the bonds to 20 follow the same pattern: 3 + 7 = 10, so 13 + 7 = 20. And later, the same pattern works for tens: 30 + 70 = 100.

Why number bonds matter so much

The make-10 strategy

Ten is the most useful number in our number system. If a child can quickly see how far a number is from 10, they can add without counting on their fingers. For 8 + 5: 8 needs 2 more to make 10, so split the 5 into 2 and 3. Now it is 10 + 3 = 13. For 9 + 6: 9 needs 1 to make 10, leaving 5 from the 6, so the answer is 15. For 7 + 6: 7 needs 3, leaving 3, so the answer is 13.

Faster subtraction

Bonds work backwards too. For 13 − 5, take away 3 to get to 10, then take away the other 2 to get 8. Children who know their bonds see subtraction as "what is missing" rather than a long count back.

What schools expect

• England, Reception (age 4–5): children work towards recalling number bonds up to 5, and some bonds to 10, including doubles.
• England, Year 1 (age 5–6): number bonds and related subtraction facts within 20.
• England, Year 2 (age 6–7): addition and subtraction facts to 20 fluently, and using them for related facts up to 100.
• US, kindergarten (age 5–6): for any number from 1 to 9, find the number that makes 10, and break numbers up to 10 into pairs in more than one way.
• US, 1st and 2nd grade: fluent addition and subtraction within 10 by the end of 1st grade, and within 20 using mental strategies in 2nd grade.

How to teach number bonds at home

1. Start with real objects. Put 5 buttons on the table. Hide some under a cup. "How many are hiding?" Lift the cup to check. Repeat with different amounts.
2. Use fingers. Ten fingers are a built-in bonds-to-10 tool. Hold up 7. How many fingers are down? That is the bond: 3.
3. Use a ten frame. Draw a 2 by 5 grid (or cut an egg box down to 10 cups). Fill some spaces with counters. The empty spaces show the partner number.
4. Draw a rainbow. Write 0 to 10 in a row and draw arcs joining the pairs: 0 to 10, 1 to 9, 2 to 8 and so on, up to 5 and 5 in the middle.
5. Practise little and often. A few minutes a day, out loud, in the car or at bath time. "I have 6, how many more to make 10?"

Number bond games

• Treetop Fair: our free addition and subtraction game practises sums within 10 and 20, so you can start small and step up.
• Shake and spill: put 10 beans, painted on one side, in a cup. Shake, spill and say the bond: "6 painted and 4 plain makes 10."
• Make-10 snap: using playing cards from ace (1) to 9, turn over two cards. Shout "ten!" if they make 10.
• Go fish for 10: like Go Fish, but you ask for the partner card. "Do you have a 3?" if you are holding a 7.

Common sticking points

• Counting every time: that is fine at first. Keep practising until the answer "pops" without counting. Quick, regular practice gets there.
• Mixing up 4 and 6 or 3 and 7: practise those pairs on their own with fingers. Put up 4 fingers on one hand, then 6 across both hands, and compare.
• Forgetting the zero pair: 10 + 0 seems too easy to count, but it helps children see the full pattern.

Number bonds rest on solid counting. If your child is still building that, start with our counting activities for preschoolers, then come back to bonds when counting to 10 feels easy.