Number Bonds to 10

What is a number bond?

A number bond is two numbers that join together to make a total. Think of it like two friends holding hands to make one team.

In this lesson our total is always 10. So we are looking for the pairs of numbers that join to make 10. We call these the number bonds to 10.

Here is the big idea, said in a simple way:

A part, plus another part, makes the whole.

When the whole is 10, the two parts must fit together perfectly, like two puzzle pieces.

Use your hands

You always carry the best math tool with you — your two hands. They have 10 fingers in total.

Hold up all 10 fingers. Now fold down some fingers.

• Fold down 4 fingers. How many are still up? 6. So 4 and 6 make 10.
• Fold down 2 fingers. How many are up? 8. So 2 and 8 make 10.
• Fold down 5 fingers. How many are up? 5. So 5 and 5 make 10.

Every time, the fingers you folded and the fingers still up join to make 10. That is a number bond!

All the bonds to 10

There are six special pairs. Let's list them in order so they are easy to remember.

One part	Other part	Bond
0	10	0 + 10 = 10
1	9	1 + 9 = 10
2	8	2 + 8 = 10
3	7	3 + 7 = 10
4	6	4 + 6 = 10
5	5	5 + 5 = 10

Look at the first column. It goes 0, 1, 2, 3, 4, 5 — counting up. Now look at the second column. It goes 10, 9, 8, 7, 6, 5 — counting down! As one part gets bigger, the other gets smaller. That is the pattern, and it helps you remember every bond.

Worked example 1: counting on

You have 3 red blocks. How many blue blocks do you need to make 10?

Start at 3 and count on until you reach 10, lifting one finger each time:

4 (one), 5 (two), 6 (three), 7 (four), 8 (five), 9 (six), 10 (seven).

You said 7 numbers. So you need 7 blue blocks. 3 + 7 = 10.

Worked example 2: finding the missing part

A snail is climbing 10 steps. It has climbed 8 steps. How many steps are left?

Count up from 8: 9 (one), 10 (two). Only 2 steps left.

So 8 and 2 make 10. The missing part is 2.

Worked example 3: the turnaround trick

Here is a happy secret. If 4 + 6 = 10, then 6 + 4 = 10 too! The two parts can swap places and the total stays the same. This is called the turnaround, and it means each bond gives you two facts for the price of one. Learn six pairs and you really know twelve facts.

Why number bonds matter

Ten is a very special number. Our whole way of counting is built on tens — that is why we have tens and ones when we count past 10. You can explore that idea in our lesson on place value with tens and ones.

When you know your bonds to 10 by heart, you do not have to count slowly every time. Your brain just knows that 7 needs 3, and 8 needs 2. This makes adding and taking away much faster, and it helps with bigger sums later, like 17 + 3 or 28 + 2.

Try it yourself

You will need 10 small objects — buttons, coins, dry pasta or toy bricks all work well.

1. Count out exactly 10 objects into a pile. Check by counting one by one.
2. Use both hands to scoop the pile into two groups.
3. Count each group. Say the bond out loud: "3 and 7 make 10!"
4. Mix them up and split again a different way. How many different bonds can you find?
5. Challenge: Cover one group with a cup. Look at the other group. Can you say how many are hidden before you peek?

Do this every day for a week and the bonds will pop into your head like magic.

What's next?

Once you are quick with bonds to 10, you are ready to add and subtract with bigger numbers. Try our friendly lesson on addition and subtraction to keep growing. And if counting itself still feels new, warm up first with counting to 20.