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What is scale factor?

What is a scale factor?
Children learn about scale factor in Year 6 maths. Find out how to reinforce their understanding at home with our parents' guide to scale factor.

What is a scale factor?

We use scale factor when we talk about increasing the size of a 2D shape. The size by which we make the shape larger is described by its scale factor.

For example, this rectangle has the measurements 5cm and 2cm (not shown to scale):

If we increase this rectangle by a scale factor of 2, we double both the sides:

If we increase the original rectangle by a scale factor of 3, then we multiply each measurements by 3 to end up with this shape:


When do children learn about scale factor in primary school?

Children learn about scale factor in Year 6 maths. They may be given a shape and then asked to increase it by a certain scale factor, or they may be given a question like the following:

Look at square B. What scale factor has square A been increased by?
Your child would need to think about what 2cm has been multiplied by to make 8cm and use their knowledge of times tables to work out that the square had been increased by a scale factor of 4.

Scale factor can be used with various different shapes.

The irregular pentagon A, on the left, has been increased in size to make B, which has all the same angles as A, but sides that have all been increased by the same scale factor. Can you work out what the scale factor is?
Answer: 2

Your child may be asked to solve a problem where they are only given part of the information and have to 'work backwards', for example:

A triangle was increased by a scale factor of 3 resulting in this new shape:

What were the measurements of the original triangle?

Answer: 3cm by 5cm by 6cm

Learning about scale factor at home

The concept of scale factor is closely linked to ratio, proportion and percentages, where various amounts must be multiplied or divided by the same number to increase or decrease a quantity. Your child will need to understand the relationship between these concepts. 

Here are some example of activities they may have to carry out at school, related to scale factor; a lot of them are very useful in the everyday maths we depend on at home, too!

  • Increasing all the ingredients in a recipe by multiplying each one by the same number in order to feed a larger group of people
  • Increasing amounts by a certain percentage, or finding a percentage of an amount.
  • Working out ratios and proportions of different groups, using their knowledge of times tables.
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