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The National Certificate in Adult Numeracy Level 2 Skills for Life Support Strategies Module 5: Measures, ratio and scale

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Aims To introduce strategies for using common measures, calculating ratios and using scale. 2

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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. 3

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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. 4

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Scale in everyday life: kitchen design Scale 1 cm = 1 m 6cm Length of units = 6 m 5

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Scale in everyday life: maps Scale 1 :

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Scale in everyday life: plans Scale 2 cm = 1 m pool path decking 7

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Here is a plan of a garden. 8

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On the plan, it measures 10 centimetres long. 10 cm 9

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The scale is 2 cm = 4 m. As a ratio, this can be expressed as 2 : 400 or simplified to 1 : cm 10

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To work out the actual length of the garden, divide the drawing into 2 cm strips (2 cm = 4 m). 2 cm 10 cm 11

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Now, write in what each 2cm strip represents (2 cm = 4 m). 2 cm 4 m 12

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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 4 m 20 m 13

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The width of the garden is 7 cm. The scale is 2 cm = 4 m. 7 cm 14

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To work out the actual width of the garden, divide the drawing into 2 cm strips (2 cm = 4 m). 7 cm 2 cm 15

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Now, write in what each 2 cm strip represents (2 cm = 4 m). 7 cm 2 cm 4 m 16

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What about the remaining part of the plan? 7 cm 2 cm 4 m 17

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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 4 m 1 cm2 m 18

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The actual width of the garden is 14 m. 7 cm 2 cm 4 m 1 cm2 m 14 m 19

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Now, think about altering the scale. What if the scale was 2 cm = 1 m? 10 cm 7 cm 20

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(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

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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 22

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Now, write in what each 2 cm strip represents. 7 cm 2 cm 1 m 23

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What about the remaining part of the plan? 7 cm 2 cm 1 m 24

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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 1 m 1 cm½ m 25

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The actual width of the garden is 3 m 50 cm, or 3.5 m. 7 cm 2 cm 1 m 1 cm½ m 26

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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 27

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