# Number bonds to 100

## Learning focus

Learn about number bonds to 100 using tens and ones (for example 30 + 70 = 100 or 60 + 40 = 100).

This lesson includes:

- one catch-up quiz
- one video
- one learning summary
- one activity

# Quiz

To get started, let's see how well you know this topic already. Take the catch-up quiz below to find out.

# Learn

Can you remember what **number bonds** are? Watch this video from KS1 Maths to remind yourself.

There are different ways to show bonds to 10, for example we can use a bonds to ten rainbow, like this.

We can use 10 frames, like this.

Or we can draw on ‘known number facts’. That means that you’ve done so much work on your number bonds to 10 that you just know them.

1 + 9 = 10

2 + 8 = 10

3 + 7 = 10

4 + 6 = 10

5 + 5 = 10

You can use these number facts to work out new ones.

## Example

Here is the number 2.

Here is 2 made 10 times bigger. How many can you see now?

2 multiplied by 10 equals 20.

Here is the number 8.

Here is 8 made 10 times bigger. How many can you see?

8 multiplied by 10 makes 80.

If I know that 2 + 8 = 10, then I also know that 20 + 80 = 100.

## Example 2

Let's see if this works for other numbers.

We know that 6 + 4 = 10, does that mean 60 + 40 = 100?

Let's look at the 100 square to check.

Can you see how the total is 100? 40 blocks are white and 60 blocks are yellow.

There are 100 blocks altogether.

40 + 60 = 100

Have a look at the number line below to see the same sum.

## Example 3

**What two digit number goes with 55 to make 100?**

Let’s go back to the number line to see how we can solve this.

Here is the number 55 marked on a number line.

If you add 5 to 55, it makes 60.

If you add another 40 to 60, you will reach 100.

You can see that 45 was added to 55 to make 100.

55 + 45 = 100

So we now know that 55 + 45 makes 100. If you adjust the numbers slightly, you can find other pairs that make 100.

Look at these.

51 + 49 = 100

52 + 48 = 100

53 + 47 = 100

54 + 46 = 100

55 + 45 = 100 *(this is the calculation you worked out above)*

56 + 44 = 100

57 + 43 = 100

58 + 42 = 100

59 + 41 = 100

Can you see a pattern in the ones?

## Example 4

**What must I add to 37 to make 100?**

Let’s use a part whole model to show this.

First, let’s make 37 and partition it into tens and ones.

How many do you need to add to 7 to make another multiple of 10?

You need 3, so let’s draw another part-whole model and write in 3.

30 + 7 + 3 makes 40.

What do you need to add to 40 to make 100?

You will need 60.

What number do we write in the top part of the part whole model?

3 + 60 = 63

Now add up all the multiples of 10.

This shows that:

37 + 63 = 100

Another way to solve this would be to subtract 37 from 100.

Look at this 100 square, where 37 has been taken away from 100.

The answer is 63.

100 - 37 = 63

# Practise

## Activity 1

Solve these questions using a number line, hundred square, known facts or a part-whole model.

- 43 + ? = 100
- 28 + ? = 100
- 79 + ? = 100

# Play

Play **Guardians: Defenders of Mathematica** to learn more about this topic and test your skills.