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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.
2
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.
3
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.
4
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
16
What about the remaining part of the plan?
7 cm
2 cm
2 cm
2 cm
4 m
4 m
4 m
17
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
18
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.
21
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
22
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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