Ross MackellUK-qualified primary teacher · 8 min read

Ask your child what 7 + 8 is. If their fingers come out, or you can see them quietly counting on, there is a gap. It isn't a big one, and it's very fixable, but it's one of the most common reasons I see 8, 9 and 10 year olds find column subtraction, mental maths and times tables so much harder than they should be.

That gap is number bonds. Most children meet them in Year 1, and a lot of children never quite make them automatic. They get by with counting, and counting works fine until the numbers get bigger and the questions get faster.

I'm Ross, a UK-qualified primary teacher with over ten years in the classroom. In this guide I'll explain what number bonds are, which ones your child needs to know by heart, the pictures schools use, how bonds to 10 unlock bonds to 100 and 1, the mistakes I see most often, and quick games and practice questions you can use at home.

What number bonds are

A number bond is just a pair of numbers that make a total. 6 and 4 are a number bond to 10. 60 and 40 are a number bond to 100. The word "bond" is there to show that the numbers belong together: one part, another part, and the whole they make.

The real point of number bonds is the next bit: your child should know them so well that they don't have to work them out. Ask "what goes with 7 to make 10?" and the answer 3 should come back as quickly as their own name. That is what teachers mean by recall, and it is very different from being able to count up to find the answer.

In the national curriculum, children learn number bonds and related subtraction facts within 20 in Year 1. In Year 2 they are expected to recall addition and subtraction facts to 20 fluently and use them to work out related facts up to 100. From then on, those facts are quietly assumed in almost every calculation they do.

Number bonds to 10

There are only six pairs to learn. Everything else is built on these.

Six pairs, and each one gives your child up to four facts. That's why it is such a good use of time. In my experience the pairs that cause the most trouble are 3 + 7 and 4 + 6, because the numbers feel close together. Those are the ones worth extra practice.

Once bonds to 10 are secure, do the same with the smaller totals too (bonds to 5, 6, 7, 8 and 9). For example, knowing that 5 and 3 make 8 straight away is what lets your child do 15 + 3 or 48 − 5 in their head.

The pictures schools use

If your child's homework has diagrams instead of sums, these are the three you're most likely to see. They're all ways of showing the same idea: two parts make a whole.

The part-whole model

A big circle with the whole in it (10), joined to two smaller circles with the parts (7 and 3). Your child might be asked to fill in a missing part. It's a picture of "7 and something make 10".

The ten frame

A grid of two rows of five boxes. Put 7 counters in and your child can see straight away that there are 3 empty spaces. This is the most useful picture for home, because it shows why 7 + 3 = 10 instead of just telling them. You can draw one on paper in ten seconds.

The bar model

A long bar labelled 10, split underneath into two shorter bars labelled 7 and 3. Schools use the bar model all the way up to Year 6 for word problems, so it's worth your child getting used to it now. If these pictures are new to you, I explain why schools use them in why is maths taught differently now.

Number bonds to 20

Children don't need to learn a whole new set of facts for 20. They need to spot that bonds to 20 are bonds to 10 with a ten added on.

• If 3 + 7 = 10, then 13 + 7 = 20.
• If 6 + 4 = 10, then 16 + 4 = 20.
• If 8 + 2 = 10, then 18 + 2 = 20.

The other set of facts within 20 that matter just as much are the ones that cross 10, like 7 + 8 or 15 − 9. This is where the bonds to 10 really earn their keep, through a strategy schools call bridging through 10.

Example 1: 7 + 8 by bridging through 10

1. Start with the bigger number, 8. What does 8 need to make 10? 2.
2. Take that 2 from the 7. That leaves 5.
3. 10 + 5 = 15.

Example 2: 15 − 9 by bridging through 10

1. Take away 5 first to get back to 10. 15 − 5 = 10.
2. You needed to take away 9, so there are 4 left to take away.
3. 10 − 4 = 6.

A child who can do this has stopped counting. That's the goal.

Number bonds to 100

Again, it's the same six pairs doing the work.

Multiples of 10

If 3 + 7 = 10, then 30 + 70 = 100. Your child is just counting tens instead of ones. Ask "how many tens in 30?" and "how many more tens to make 10 tens?" and it clicks. This relies on place value being secure.

Example 3: what goes with 64 to make 100?

This is the one that catches children out. Lots of them say 46, because 6 + 4 = 10 and 4 + 6 = 10. But 64 + 46 = 110.

1. Look at the ones first. What goes with 4 to make 10? 6.
2. Now the tens. 64 + 6 = 70. What goes with 70 to make 100? 30.
3. So the answer is 30 + 6 = 36. Check: 64 + 36 = 100.

The shortcut once they understand it: the tens make 9, the ones make 10. In 64 + 36, the tens are 6 and 3 (which make 9) and the ones are 4 and 6 (which make 10).

Bonds to 1 and 1,000

By Year 5 and 6, the same pattern shows up with decimals and bigger numbers. If 3 + 7 = 10, then 0.3 + 0.7 = 1 and 300 + 700 = 1,000. For two decimal places it's the same rule as bonds to 100: 0.64 + 0.36 = 1. This makes adding and subtracting decimals far easier, especially with money: if something costs £3.45, the change from £5 is £1.55.

Why they matter so much

It's tempting to think number bonds are a Reception or Year 1 thing that older children have moved past. In the classroom, it's often the opposite. When a Year 4 or Year 5 child is slow and inaccurate with written methods, number bonds are one of the first things I check. Here's where they turn up:

• Column addition and subtraction. Every column is a number fact. A child who has to count on for each one is slow, and every count is a chance to slip.
• Times tables. Children often work out a times table fact from one they know, like 6 × 7 = 35 + 7. That only works if the adding is instant.
• Mental maths. 46 + 7, 83 − 5, 300 − 160: all of these are number bonds in disguise.
• Money and time. Change from £1, minutes to the hour, and so on.
• Rounding and estimating. Knowing how far a number is from the next 10 or 100.

Every time a child has to stop and count, they use up working memory that should be going on the method. That's why a gap here can look like a problem with something much bigger. If you suspect gaps like this are building up, is your child behind in maths? explains why they grow and what to do about it.

5 common mistakes and how to fix them

Mistake 1: Counting on fingers instead of recalling

Your child gets the right answer to 7 + 3, but it takes five seconds and you can see them counting.

The fix: don't ban fingers, because that just moves the counting into their head. Instead, practise the six bonds to 10 every day for a couple of minutes with a ten frame until the answers come without counting. Speed comes from familiarity, not pressure.

Mistake 2: Making the ones add to 10 in bonds to 100

Your child says 64 + 46 = 100.

The fix: ask them to check by adding. 64 + 46 is 110, which shows them straight away that they've gone too far. Then teach "the tens make 9, the ones make 10".

Mistake 3: Forgetting the zero bonds

Your child lists the bonds to 10 and leaves out 0 + 10 and 10 + 0.

The fix: it's a small thing, but schools will ask for all of them. Put 10 counters on a ten frame and ask "how many empty spaces?" Zero is an answer.

Mistake 4: Not linking addition and subtraction

Your child knows 3 + 7 = 10 but has to count back for 10 − 7.

The fix: every time you practise a bond, ask for its family. "3 + 7 = 10. So what's 10 − 7? And 10 − 3?" One fact becomes four.

Mistake 5: Thinking bonds to 20 are new facts

Your child knows 4 + 6 = 10 but has no idea what goes with 14 to make 20.

The fix: write them side by side. 4 + 6 = 10, 14 + 6 = 20. Ask "what's the same and what's changed?" Once they see the pattern, they've learned ten new facts in a minute.

Games and practice questions

Same three steps I use for every skill: watch, copy, practise. Do the first one out loud yourself, then let your child have a go at a similar one before they try the rest on their own.

Three quick games for home

• Ten frame flash. Draw a ten frame. Put in some coins or pasta and cover it for two seconds. "How many? How many more to make 10?"
• Number bond snap. Use playing cards from ace (1) to 9. Turn two over at a time: if they add up to 10, the first person to say "bond" keeps them.
• Car journey ping-pong. You say a number, they say its bond to 10. Then move to 100 in tens (you say 30, they say 70), then any number to 100 (you say 64, they say 36).

Practice questions

Cover the last column and ask your child to fill in the gaps.

Bonus question: I bought a drink for 65p and paid with a £1 coin. How much change did I get? (Answer: 35p.)

Two or three minutes a day is better than twenty minutes once a week. Only move on when they're answering instantly, not just correctly.

Frequently asked questions

What are number bonds?

Number bonds are pairs of numbers that add together to make a total. For example, 7 and 3 are a number bond to 10, and 70 and 30 are a number bond to 100. Children learn them so they can recall the answer instantly instead of counting.

What are the number bonds to 10?

The number bonds to 10 are 0 + 10, 1 + 9, 2 + 8, 3 + 7, 4 + 6 and 5 + 5, plus the same pairs the other way round (10 + 0, 9 + 1, 8 + 2, 7 + 3 and 6 + 4). That makes 11 number sentences in total.

How many number bonds to 20 are there?

There are 21 number sentences that make 20, from 0 + 20 up to 20 + 0, or 11 different pairs if you don't count the turned-around versions. Children don't need to learn them separately: each one comes from a bond to 10, so 3 + 7 = 10 gives 13 + 7 = 20.

What year do children learn number bonds?

In England, children start number bonds in Reception and learn number bonds within 20 in Year 1. By the end of Year 2 they should recall facts to 20 fluently and use them for related facts up to 100, such as 30 + 70 = 100.

My child is 9 and still counts on their fingers. Should I worry?

It isn't a reason to panic, but it is worth fixing. Counting gets them the right answer, but it's slow and uses up working memory that they need for written methods. A few minutes a day on bonds to 10 with a ten frame usually makes a noticeable difference within a few weeks.

Sources and further reading

• Department for Education, National curriculum in England: mathematics programmes of study (addition and subtraction, Years 1 and 2)
• Department for Education, Mathematics guidance: key stages 1 and 2 (number facts and bridging through 10)
• Ross Mackell, Teacher's Perspective on YouTube