Number bonds game

Number bonds to 10

Pair	Flipped	Subtraction facts
0 + 10 = 10	10 + 0 = 10	10 − 0 = 10, 10 − 10 = 0
1 + 9 = 10	9 + 1 = 10	10 − 1 = 9, 10 − 9 = 1
2 + 8 = 10	8 + 2 = 10	10 − 2 = 8, 10 − 8 = 2
3 + 7 = 10	7 + 3 = 10	10 − 3 = 7, 10 − 7 = 3
4 + 6 = 10	6 + 4 = 10	10 − 4 = 6, 10 − 6 = 4
5 + 5 = 10	5 + 5 = 10	10 − 5 = 5, 10 − 5 = 5

Six pairs, and that's all there is to it. Once a child knows these six cold, bonds to 20 and 100 are mostly the same facts with bigger numbers.

What each year group is expected to know

Year 1 to 3 points come from the national curriculum and the DfE's ready-to-progress criteria.

Why schools spend so long on them

Number bonds are a mental shortcut. A child who knows 8 + 2 = 10 can work out 8 + 5 by "bridging": 8 + 2 makes 10, and 3 more makes 13. Without bonds, the same child has to count on one at a time, which is slow and easy to get wrong.

The Education Endowment Foundation's maths guidance names number bonds among the facts pupils need to recall quickly. Its point is that children who can't retrieve them are likely to struggle with the maths that builds on them later.

The part-whole model

Homework often shows a whole split into two parts. The diagram below is 10 as a whole with parts 6 and 4. Taking one part away leaves the other (10 − 6 = 4). Schools using the NCETM's Mastering Number programme also use a rekenrek (bead frame).

Ten frames

A ten frame is a 2 × 5 grid. Children see 6 as “five and one more” without counting every dot. Point to the empty spaces and ask how many more make 10 — that empty count is the bond partner.

Try both pictures with fingers first, then play bonds to 10 in the game above until the partner appears without counting.

Common mistakes to look out for

• Off by one. Saying 6 + 3 = 10 usually means the child counted on from 6 by saying "6" again. Check by building it on fingers.
• Bonds to 100 that make 110. For 35, children often say 75, because they add 3 + 7 = 10 in the tens and 5 + 5 = 10 in the ones. The right answer is 65: the ones make 10, so the tens only need to make 90.
• Only knowing them one way. A child who knows 4 + 6 but stalls on "10 − 4" knows the fact as a chant, not a bond. Ask it as subtraction and as a missing number: 4 + ? = 10.

Everyday ways to practise

• Fingers: hold up 7 and ask how many are hiding.
• Shopping: "this costs 70p, how much change from £1?"
• Cards: pair up cards that total 10.
• Car journeys: call out a number and your child shouts its partner.

Next step: doubles and halves use the same quick-recall skills.