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How to partition a number

Part of MathsPlace valueYear 3

Partitioning

Partitioning is a useful way of breaking numbers up into smaller parts, making them easier to work with.

It is helpful for when you want to add or subtract larger numbers.

There are many different ways to partition numbers.

For example, take the number 5, it can be partitioned in all these different ways:

There are several equations on the screen, 4 + 1, 4 + 2 + 1, 1 + 1 + 1 + 1 + 1, 2 + 1 + 1 + 1, 3 + 1 + 1, 3 + 2
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Activity: Partitioning numbers

Complete this interactive activity to find out how to partition numbers. Then put your knowledge to the test.

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What is partitioning?

Partitioning in maths means splitting a number up into smaller parts.

It helps you to understand what numbers are made up of and makes it easier to add and subtract.

There are multiple ways to partition a number.

You can use a part-whole model to partition a number. In this model, 276 has been partitioned in different ways:

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  1. Part whole model showing 200 + 70 + 6 = 276

Part-whole models are just one of the tools you can use to help you partition.

In this, 100 grid, 100 has been partitioned into 55 and 45.

A 100 grid has been partitioned into 55 and 45.
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Example 1

A part-whole model. In the top circle is 150. In a circle below is 100. Next to that circle is another circle containing a question mark. Both of the bottom circles are connected to the top circle by a line.

What number is missing from this part-whole model?

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Example 2

A 100 grid which has been partitioned into shaded sections of 30, 5 and 65.

How has 100 been partitioned in this grid?

to count in tens when you can.

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Example 3

On the left there are 7 stacks made out of 10 blocks, with 5 individual blocks next to that. There is a + sign in the middle. On the right there are 5 stacks made of of 10 blocks with 3 individual blocks next to that. Above, text reads 75+53=

Use your partitioning skills to work out the answer to 75 + 53.

You may need a pen and paper, or you could try to work it out in your head.

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Use your times tables and more maths skills to defeat monsters and reclaim the Kingdom of Mathematica

Play our fun maths game Guardians: Defenders of Mathematica
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More on Place value

Find out more by working through a topic