The National Certificate in

Adult Numeracy

Level 2 Skills for LifeSupport Strategies

Module 5: Measures, ratio and

scale

Aims

To introduce strategies for using common measures, calculating ratios and using scale.

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Outcomes

Participants will be able to:

identify and convert between metric and imperial measures

use ratio and proportion in everyday situations

scale quantities up and down, using direct proportion.

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What do we mean by scale?

When we look at maps, plans and diagrams, they are usually drawn to a specific scale.

This means that every measurement actually represents a greater or lesser ‘real-life’ measurement.

Usually scale drawings are used to represent a far larger ‘real-life’ object or area.

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Scale in everyday life: kitchen design

Scale 1 cm = 1 m

6cm

Length of units = 6 m5

Scale in everyday life: maps

Scale 1 : 1 000 000

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Scale in everyday life: plans

Scale 2 cm = 1 m

pool path

decking

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Here is a plan of a garden.

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On the plan, it measures 10 centimetres long.

10 cm9

The scale is 2 cm = 4 m.

As a ratio, this can be expressed as 2 : 400or simplified to 1 : 200.

10 cm10

To work out the actual length of the garden, divide the drawing into 2 cm strips (2 cm = 4

m).

2 cm 2 cm 2 cm 2 cm 2 cm

10 cm11

Now, write in what each 2cm strip represents (2 cm = 4 m).

2 cm 2 cm 2 cm 2 cm 2 cm

4 m 4 m 4 m 4 m 4 m

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From this, we can see that the actual length of the garden is 20 m (2 cm = 4

m).

2 cm 2 cm 2 cm 2 cm 2 cm

4 m 4 m 4 m 4 m 4 m 20 m

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The width of the garden is 7 cm.The scale is 2 cm = 4 m.

7 cm

14

To work out the actual width of the garden, divide the drawing into 2 cm strips (2 cm =

4 m).

7 cm

2 cm

2 cm

2 cm

15

Now, write in what each 2 cm strip represents (2 cm = 4 m).

7 cm

2 cm

2 cm

2 cm

4 m

4 m

4 m

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What about the remaining part of the plan?

7 cm

2 cm

2 cm

2 cm

4 m

4 m

4 m

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This is 1 cm wide, so must be equivalent to an actual size of 2 m (2

cm = 4 m).

7 cm

2 cm

2 cm

2 cm

4 m

4 m

4 m

1 cm 2 m

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The actual width of the garden is 14 m.

7 cm

2 cm

2 cm

2 cm

4 m

4 m

4 m

1 cm 2 m

14 m

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Now, think about altering the scale.

What if the scale was 2 cm = 1 m?

10 cm

7 cm

20

(2 cm goes into 10 cm five times, therefore length = 5 x 1 m = 5 m) but what about the

width?

10 cm

7 cm

If the scale was 2 cm = 1 m,finding the actual length is straightforward.

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Again, to work out the actual width of the garden, divide the drawing into 2 cm

strips.

7 cm

2 cm

2 cm

2 cm

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Now, write in what each 2 cm strip represents.

7 cm

2 cm

2 cm

2 cm

1 m

1 m

1 m

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What about the remaining part of the plan?

7 cm

2 cm

2 cm

2 cm

1 m

1 m

1 m

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This is 1 cm wide, so must be equivalent to an actual size of ½ m or 50 cm.

7 cm

2 cm

2 cm

2 cm

1 m

1 m

1 m

1 cm ½ m

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The actual width of the garden is3 m 50 cm, or 3.5 m.

7 cm

2 cm

2 cm

2 cm

1 m

1 m

1 m

1 cm ½ m

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Summary: ratio, measures and scale

Use real measuring instruments and real-life contexts where possible.

Use diagrams and pictures to support visual learners, and get learners actually measuring things to exploit kinaesthetic learning styles.

Use ‘non-educational’ web sites such as Ikea, or B and Q for practice with plans and conversion, or visit www.onlineconversion.com.

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