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Calculating
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# 1. How confident are you that you can use an empty number line to model the mental calculations:

## Example

Mental addition and subtraction can be developed with a number of strategies, such as the following.

Counting on

• Put the larger number first and count on: 4 + 27 = 27 + 4; count on from 27
• Count on from the smallest number: 25 – 17; count on from 17 to 20 and 20 to 25
• Count on in tens: 45 + 26 = 45, 55, 65 + 6
• Count on in ones and tens: 72 – 48 = 48 to 50, 60, 70 to 72

Partitioning

28 + 15 = 28 + 2 + 13 = 30 + 13
76 – 33 = 76 – 30 – 3 = 46 – 3

Using near numbers

39 + 42 = 40 + 40 – 1 + 2

Breaking numbers into tens and units

36 + 42 = 30 + 40 + 6 + 2 = 70 + 8

Combinations of these strategies may also be used.

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

48 + 36 = 84 or: Doubling near numbers:

40+38= 40+ 40 - 2= 80 - 2=78

## What this might look like in the classroom

Question:
Use an empty number line to work out the answer to 48 + 36 using three different ways.
Possibility 1 Possibility 2 Possibility 3- ## Taking this mathematics further

The history of the use of the empty number line is explained in the document in the following link.

## Making connections

To be able to develop mental calculation strategies for addition, children first need to be able to:
• count on and back in ones and tens,
• know or calculate number pairs to ten, understand the place value of numbers and partition them into tens and ones,
• understand the concept of addition and its inverse operation of subtraction.
Children need to be able to apply the concept of addition to real−life applications, for example the total cost of two items costing 48p and 36p. They may then need to be able to convert their answer into the appropriate units.

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