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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

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.

scroll

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.

map

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

diagrams

Shapes ABCD and EFGH are mathematically similar.

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

Example K

graph

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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