What a number bond is, and how to help your child learn the bonds to 10 and 20

A number bond is a pair of numbers that make a given total: 7 and 3 are a bond to 10, and 12 and 8 are a bond to 20.

Schools in England teach these bonds from Year 1, and children are expected to know the bonds to 20 by the end of Year 2. They look simple, but they carry a lot of later maths: subtraction, mental addition, column methods and, later, bonds to 100 and decimals. Here is what each set contains, why recalling them quickly matters, and how to practise them at home in a few minutes a day, without worksheets.

What a number bond is, starting with the bonds to 10

A bond is a total split into two parts. The bonds to 10 are the eleven pairs of whole numbers that add up to 10, from 0 and 10 to 10 and 0. Each pair gives four facts, two additions and two subtractions: if 7 + 3 = 10, then 3 + 7 = 10, 10 − 7 = 3 and 10 − 3 = 7.

The other five pairs are the same ones swapped round, 6 and 4 up to 10 and 0, so there are really only six facts to learn. A bond can be drawn as a "part-whole" picture: a circle for the total joined to two circles for the parts. The picture helps at the start; the aim is for the answer to come without it.

Bonds to 20, and how the number facts build on each other

The national curriculum for mathematics asks Year 1 pupils to represent and use bonds and the related subtraction facts within 20. Its guidance for Year 1 adds that pupils memorise and reason with bonds to 10 and 20 in several forms, for example 9 + 7 = 16, 16 − 7 = 9 and 7 = 16 − 9. The introduction to key stage 1 says that by the end of Year 2, pupils should know the bonds to 20.

The bonds to 20 come straight from the bonds to 10. If 3 + 7 = 10, then 13 + 7 = 20. And when a sum crosses 10, the bonds to 10 do the work: 8 + 5 is 8 + 2 to make 10, then 3 more, so 13. Writing the same fact in different orders, with the equals sign at the start as well as at the end, is part of the curriculum and helps children read "=" as "is the same as".

Bonds to 100 and the number patterns behind them

In Year 2, the curriculum asks pupils to recall and use addition and subtraction facts to 20 fluently, and to derive and use related facts up to 100. That is where the bonds to 100 come from: they reuse the bonds to 10.

• Multiples of 10: 3 + 7 = 10, so 30 + 70 = 100. The nine pairs from 10 and 90 to 90 and 10 follow directly.
• Any two-digit number: for 64, the ones need a bond to 10 (4 + 6), and the tens need a bond to 9, because the 10 from the ones carries over (6 + 3). So 64 + 36 = 100.

A quick check: in a bond to 100, the ones digits add up to 10 and the tens digits add up to 9, except when the ones are 0, as in 40 + 60. These pairs come back later with money, as in change from £1, and with decimals, since 0.64 + 0.36 = 1. They are also the starting point of many of the shortcuts in our guide to mental maths tricks, such as adding 98 by adding 100 and taking 2 away.

Why addition facts need to be known by heart

Ofsted's research review of mathematics, published in May 2021, explains why quick recall matters. Pupils who cannot recall maths facts quickly and easily struggle with calculations, because their working memory is overloaded. Its example is a child who does not know the bonds and is stuck using various forms of "counting on" for simple addition.

The review also notes that once children recall bonds, sequences and patterns automatically, they no longer need a counting aid such as a simple counting frame. Ofsted's 2023 report on mathematics in schools found less emphasis in some key stage 1 classes on learning addition and subtraction facts by heart, and called it potentially problematic, because pupils need that quick recall to access the mathematics of key stage 2.

Understanding comes first, with objects and pictures, but it is not the end point: the goal is an answer that comes in a second or two, without counting. The same logic applies later to multiplication facts.

Games to practise at home in five minutes

The research review notes that for younger pupils, rehearsal of bonds and sequences can draw on games and songs involving dice, dominoes and counting sequences. A few ideas that need nothing you do not already have:

Keep it short and frequent: five minutes most days does more than half an hour on a Sunday. Start with the pairs your child already knows, add one new one at a time, and go back to objects whenever an answer is a guess.

How to help without turning it into a test

A few habits make practice work better at home.

• Say the whole fact. "Seven and three make ten" sticks better than a bare "three".
• Ask the question in different ways. 6 + ? = 10, 10 − 6 = ?, and "what goes with 6 to make 10?" are the same fact.
• Notice counting on. If your child counts on their fingers for 7 + 3, the fact is not yet stored. Go back to the objects, then ask again later.
• Praise speed only once it is right. Accuracy first, then speed.

If homework becomes a battle, our guide to helping with maths homework without giving the answers has more on keeping the tone positive.

Frequently asked questions

What are number bonds?

Pairs of numbers that add up to a given total. 7 and 3 are a bond to 10; 12 and 8 are a bond to 20.

How many bonds to 10 are there?

Eleven pairs of whole numbers, from 0 and 10 to 10 and 0. Without counting the swapped pairs twice, there are six to learn.

When should children know their bonds to 20?

The national curriculum in England says pupils should know them by the end of Year 2, after working with bonds to 10 and 20 in Year 1.

How do you find a bond to 100 quickly?

Make the ones up to 10 and the tens up to 9: for 64, 4 + 6 = 10 and 6 + 3 = 9, so the bond is 36.

What is the best way to practise bonds at home?

Short daily games with objects, cards, dice or dominoes, five minutes at a time, saying the whole fact out loud.