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National Curriculum: Ratio, proportion and rates of change - KS3 - Exemplification

Created on 15 October 2013 by ncetm_administrator
Updated on 04 June 2014 by ncetm_administrator


Examples of what children should be able to do, in relation to each (boxed) Programme of Study statement

Examples of what children should be able to do, to show a broad grasp of the content of this topic

Example A

Simplify the ratios expressed below in different units.

  • 2m : 50cm
  • 450g : 5kg

Example B

2 parts of blue paint mixed with 3 parts of yellow paint makes green. A boy has 50ml of blue paint and 100ml of yellow.

What is the maximum amount of green he can make?

Example C

The ratios of Lycra to other materials in two stretch fabrics are 2 : 25 and 3 : 40.

Which fabric has the greater proportion of Lycra?

Example D

The cost of 4 kg of apples is £3.36

The total cost of 3 kg of apples and 2.5 kg of pears is £4.12

Work out the cost of 1 kg of pears.

Example E

popcorn cartons

A Large tub of popcorn costs £3.80 and holds 200 g.

A Regular tub of popcorn costs £3.50 and holds 175 g.

Mike says that the 200 g Large tub is the better value for money.

Lucy says that the 175 g Regular tub is the better value for money.

Who is correct?

Explain the reasons for your answer. You must show all your working.

Example F

This is a recipe for fruit squash for six people.


Tracy made fruit squash for ten people.

How many litres of lemonade did she use?

John used 2 litres of orange juice for the same recipe.

How many people was this enough for?

Example G

This map has a scale of 1cm to 6km.


The road from Ridlington to Carborough measured on

the map is 5.2cm long.

What is the length of the road in kilometres

Example H

The length of a coach is 15 metres.

Joe makes a model of the coach.

He uses a scale of 1:24

Work out the length, in centimetres, of the model coach.

coach used under the Attribution-ShareAlike 2.0 Generic CC BY-SA 2.0 licence
Image adapted from photograph by
Glen Wallace some rights reserved

Example I

A truck and van left from Paris in diametrically opposite directions. The truck travelled for 4

hours at 76 mph. The vehicles were 564 miles apart. Find the van's average speed.

Example J


Shapes ABCD and EFGH are mathematically similar.

  • Calculate the length of BC.
  • Calculate the length of EF.

Example K


The graph above shows the relationship between gallons and litres.

Does the graph illustrate direct proportion? How do you know?

  • Change 13 gallons to litres.
  • Change 500 litres to gallons.

Explain how you worked out your answers.


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