- National Curriculum Tool
- KS3 - Ratio and Proportion and Rates of Change
KS3 - Ratio and Proportion and Rates of Change
New Curriculum
Pupils should be taught to:
- change freely between related standard units (for example time, length, area, volume/capacity, mass)
- use scale factors, scale diagrams and maps
- express one quantity as a fraction of another, where the fraction is less than 1 and greater than 1
- use ratio notation, including reduction to simplest form
- divide a given quantity into two parts in a given part:part or part:whole ratio; express the division of a quantity into two parts as a ratio
- understand that a multiplicative relationship between two quantities can be expressed as a ratio or a fraction
- relate the language of ratios and the associated calculations to arithmetic of fractions and to linear functions
- solve problems involving percentage change, including: percentage increase, decrease and the original value problems and simple interest in financial mathematics
- solve problems involving direct and inverse proportion, including graphical and algebraic representations
- use compound units such as speed, unit pricing and density to solve problems
Non-Statutory Guidance
Links and Resources
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
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.
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.
