 # 5.01 Relate addition and subtraction

Lesson

## Ideas

We're going to look at how addition and subtraction are related, and number lines can help us with that. Do you recall how to use a  number line to work out subtraction problems  ?

### Examples

#### Example 1

Use the number line to help you find the value of 35-24.

Worked Solution
Create a strategy

Find the bigger number on the number line and count the number of jumps back to the lower number given.

Apply the idea

Here are 35 and 24 on the number line:

There are 11 jumps between 35 and 24. So:35-24=11

Idea summary

To subtract one number from another, count the number of jumps between the numbers on the number line.

We can see how addition and subtraction are related by looking at their fact families, just like in this video.

### Examples

#### Example 2

Use the fact family of 5, 7 and 12.

a

What is 5+7?

Worked Solution
Create a strategy

Count up all the blocks above 7 and 5.

Apply the idea

There are 12 blocks altogether, so:5+7=12

Reflect and check

You could also use the fact family below:

The 5 blocks and 7 blocks in the bottom row make up the 12 blocks in the top row. So:5+7=12

b

What is 12-7?

Worked Solution
Create a strategy

Cross out 7 blocks from the yellow blocks and count the remaining blocks.

Apply the idea

If we cross out 7 of the yellow blocks, we will be left with 5 blocks. So:12-7=5

Reflect and check

You could also use the fact family below:

Both rows have 12 blocks. If we take away the 7 blocks in the second row we are left with 5 blocks. So:12-7=5

c

What is 12-5?

Worked Solution
Create a strategy

Cross out 5 blocks from the yellow blocks and count the remaining blocks.

Apply the idea

If we cross out 5 of the yellow blocks, we will be left with 7 blocks. So:12-5=7

Reflect and check

You could also use the fact family below:

Both rows have 12 blocks. If we take away the 5 blocks in the second row we are left with 7 blocks. So:12-7=5

Idea summary

There are four different number sentences we can make for each fact family, two addition and two subtraction. If we start with the numbers, 12, 13 and 25, we can make the following fact family:

\begin{array}{c} 12+13=25 \\ 13+12=25\\ 25-13=12\\ 25-12=13 \end{array}

### Outcomes

#### MA2-5NA

uses mental and written strategies for addition and subtraction involving two-, three-, four and five-digit numbers