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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

# Exemplification

## 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?

#### 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.

#### 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.

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.