Why do scales matter?
In Chapter 1, William has located his school. He wants to
learn more about locations of Sheung Shui, the Hong Kong
Special Administrative Region (SAR) and China. Can you
help him?
(a) Scale:
1:200 000
Map series
HM200CL
Fujian
N
Xiamen
Guangxi
Guangdong
Shantou
Guangzhou
Xi Jiang
Shenzhen
Hong Kong SAR
Macau
KEY
City
(b) Scale:
1:11 800 000
KEY
National boundary
Provincial boundary
(c) Scale:
1:250 000 000
Figure 2.1
9
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Part one
1
Refer to Figure 2.1.
(a) Which map should William use if he wants to find the following locations?
(i)
Sheung Shui
(ii)
Hong Kong SAR
(iii)
China
(b) Can he use one map to find all the locations? Explain your answers.
2
(a) Which map shows the largest area? What is its scale?
(b) Which map shows the smallest area? What is its scale?
*3
Do you know what is the relationship between scale and the size of the area shown?
What is a scale?
Every map needs a scale. It tells you the ratio between the distance on a map and the actual
distance on the ground. There are three ways to show the scale of a map.
A statement scale shows the scale by words.
This example means that 1 cm on the map
represents 1 km on the ground.
1 cm to 1 km
0
5
0
5
10
15
20 km
10
15
20
km
or 1:1 000
10
A linear scale shows the scale by a line
divided into equal parts. These examples
mean that 1 cm on the map represents 5 km
on the ground.
A representative fraction (R.F.) shows the
scale by a fraction or a ratio. This example
means that 1 cm on the map represents
1 000 cm (or 10 m) on the ground.
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Chapter 2
Skills
How to change from one type of scale to another
We can change from one type of scale to another by following the steps below.
R.F.
Statement scale
Statement scale
=
R.F.
=
=
Linear scale
e.g. 1 cm to 1 km
Change the unit to cm.
i.e. 1 cm to 100 000 cm
(⬗ 1 km = 1 000 m = 100 000 cm)
e.g. 1 cm to 1 km
Draw a line of 5 cm.
Divide the line into equal parts of
1 cm each.
Delete the units, and change ‘to’ into ‘:’.
i.e. 1:100 000
Put the numbers 0, 1, 2, 3, 4, 5 on
the top of the marks.
R.F.
Write the unit (km) on the right
hand side.
Statement scale
e.g. 1:20 000
Add cm to both sides.
i.e. 1 cm:20 000 cm
Change ‘:’ into ‘to’.
i.e. 1 cm to 20 000 cm
= 1 cm to 200 m
(⬗ 100 cm = 1 m)
e.g. 1:10 000
Change the R.F. to a statement scale.
i.e. 1 cm to 100 m
Statement scale
Follow the steps we have mentioned
Linear scale
to draw the linear scale.
R.F.
0
e.g.
0
50
100
150
200
0
cm
1
2
3
4
100
200
300
400
500 m
250 m
Do the following exercises.
5
1
Change 1 cm to 5 km into a R.F. and a
linear scale.
2
Change 1:100 000 into a statement
scale and a linear scale.
3
Change
Measure each part of the linear
scale with a ruler, which is 1 cm in
the example.
Write it in the form of a statement
scale.
i.e. 1 cm to 50 m
into a statement scale and a R.F.
Change it into R.F.
i.e. 1 cm to 5 000 cm
= 1:5 000
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Part one
How can we measure distance?
Skills
What is the distance between two points?
We can measure the straightline distance between two
points by following these
steps.
C
Step 1
Draw a straight line between
Points A and B.
A
B
Step 2
r
Rive
Use a paper strip to mark
the distance between
Points A and B.
Step 3
Put the paper strip onto the
linear scale. We can see that
the straight-line distance
between Points A and B on
the ground is 800 km.
Figure 2.2
We can also measure
the length of a curve
such as a railway or a
river. The following steps
show how we measure
the length of the river
between Points A and B.
12
Step 1
Step 2
Place a paper strip along
the first straight portion
of the river. Mark the
starting point, A.
Mark the length of the
first straight portion
onto the paper strip.
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Chapter 2
N
Railway
Try to do the following exercise after
you have learnt the skills. Refer to
Figure 2.2.
1
Find the straight-line distance
between:
(a) Points A and C
(b) Points B and C
Island
A
Sea
2
Find the length of:
(a) the railway
(b) the coastline of Island A
0
200 400 600 800
km
Step 3
Step 4
The scale of the map is
1 cm to 200 km.
The actual length of
the river between
Points A and B:
Turn the paper strip along
the second straight portion.
Mark the length again.
Repeat this step until you
reach the end point, B.
Measure the length of
the river between Points
A and B with a ruler. It
is 4.5 cm on the map.
4.5 ⫻ 200 km
= 900 km
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Part one
Large-scale and small-scale maps
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Figure 2.4 A small-scale map
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Chapter 2
*Activ
ity
Measuring distances
Refer to your atlas. Measure the following actual distances / length on the ground. Write
your answers in Figure 2.5.
Distance / length (km)
From the Hong Kong SAR to Shanghai
From the Hong Kong SAR to Beijing
The Xi Jiang
The coastline of Hainan Dao
Figure 2.5
Key words
scale (
representative fraction (R.F.) ( )
statement scale ( !"# )
large-scale map (
linear scale ( !" )
small-scale map ( !" )
!")
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Key points
1
Scale is the ratio between the distance on a map and the actual distance on the ground.
2
There are three ways to show the scale of a map.
(a) Statement scale
(b) Linear scale
(c) Representative fraction (R.F.)
3
A large-scale map covers a small area, but can give detailed information.
4
A small-scale map covers a large area, but the information is less detailed.
5
The scale helps us calculate the actual distance between two points on a map.
Xi Jiang Hainan Dao 15
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