Teach GCSE Maths

Scales and Scales and MapsMaps

Teach GCSE Maths

Scales and Scales and MapsMaps

© Christine Crisp© Christine Crisp

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You will need squared paper to do the exercise.

A scale drawing would be used by a builder fitting kitchen cupboards.

To find the measurements of the kitchen, we must multiply each 1 cm on the plan by 20.

Length = 21 20 = 420 cm

= 4 m 20

cmWidth = 15 20

= 300 cm= 3 m

This is a copy of 1 cm squared paper.

Scale: 1 cm represents 20

cm

21 cm

15 cm

Measurements of kitchen:

This is a copy of 1 cm squared paper.

A scale drawing would be used by a builder fitting kitchen cupboards.

Decide with your partner how wide the doorway is.

Ans: There are 4 1 cm squares, so it is 4 20 = 80

cm

The scale 1 cm represents 20 cm can be written as 1 : 20

Scale: 1 cm represents 20

cm

21 cm

15 cm

EXERCISE

This is a scale drawing of a study on 1 cm squared paper.

2 cm represents 1 m

1.

(a)How wide is the study on the plan?

(b)How wide is the real study?(c) How wide is the doorway?

desk

(d)How wide is the large window?(e)What are the length and width of the desk?

window

EXERCISE

(a)On the plan the study is 6

cm wide.(b)6 ÷ 2 = 3. The study is 3 m

wide.(c) The doorway is 1 m wide.

desk

(d) The large window is 1·5 m wide.(e)The desk is 1·5 m long and 1 m wide.

window

Answers:

This is a scale drawing of a study on 1 cm squared paper.

2 cm represents 1 m

1.

Street maps use a variety of scales.I found a local map booklet which had: Map 1. Scale: 3 Miles to 1

inchMap 2. Scale: 7 inches to 1 Mile

How large would map 2 need to be to show both A and B?

How far apart are places A and B that are shown as 2 inches apart on Map 1?

x

x

A

B

2 inches

3 2 = 6 miles

Ans: 7 6 = 42 inches

There are about 39 inches in 1 metre so the map would be more than a metre across !

Ans:

Ans: 1 000

Ans: 100

An Ordnance Survey map used by walkers might have a scale given as 1 : 50 000

Can you work out what this means?

Ans: 1 cm on the map represents 50 000

cmBut we don’t measure an afternoon’s walk in cms !

How many centimetres are there in 1 metre?

How many metres are there in 1 kilometre?

So, 50 000 cm is

50 000100 1 000 =

510 =

12 k

m2

1

So, a map with a scale of 1 : 50 000

means that 1 cm represents 50 000 cm or ½ km.

How far is a walk that covers 16 cm on the map?

Ans: 16 ½ =8 km

SUMMARY

Scale drawings and maps show scales in many ways:e.g. 1. If 1 cm represents 20

cm,

e.g. 2. If scale is 1 : 50 000

0 5 km

e.g. 3.

10 cm on the plan represents

10 cm on the plan represents

1 division represents 1 km, so 10 divisions on the map represents

10 1 = 10

km

10 20 = 200

cm

10 50 000 = 500 000 cm = 5

km