A **number line** can help pupils to record their steps forwards and backwards when trying to find the result of different addition and subtractions questions. If pupils are using the number line with smaller numbers they are more likely to show their calculations with single steps:

7 + 3 = 10

Or 20 – 6 = 14

When pupils are familiar with number lines they may also use them to record their thinking when doing more difficult calculations, with larger numbers.

An **empty number line** helps to record the steps to calculating a total. Here are two possible ways to do 48 + 36. There are others.

48 + 36 = 84

or:

Pupils are most likely to use different approaches when doing larger subtraction questions:

For example 83 – 25 could be calculated as

83 – 3 – 20 – 2

**Additional User Example**

Children will have different ways of counting up, so it is important for them to put their own ideas forward about how they will be counting up. It is also important to that children know that addition questions can be done forwards or backwards.

Here are some more examples of doing this same question:

48 + 36

is the same as 36 + 48

so we can do 36 + 4 to make 40

Then 40 + 40 to make 80

Then 80 + 4 to make 84

or

48 + 36 is the same as 36 + 48

so we can do 36 + 24 to make 60 and then

60 + 24 to make 84.

It is sometimes better to start with the bigger number.

Some children will confidently be using the skill of doubling and halving numbers.

It is a good idea for children to look at the numbers and see how they fit together before deciding on an approach.

**Question 1:**

Use a number line.

Choose a starting number (for example 3) and a number to repeatedly add on to the previous number (for example + 4). What results do you get?

**Answer 1:**

**Question 2:**

Use a number line

Choose a starting number (for example 63 and a number to repeatedly subtract from the previous number (for example – 7). What results do you get?

**Answer 2:**

**Question 3:**

Use the same process in questions 1 and 2 to explore additions and subtractions with larger numbers. For example start at 89 and subtract 22.

For example start at 12 and add 35

**Answer 3:**

- Consider the use of ‘time lines’ to solve problems involving addition of time.