Scale drawings/maps | Year 9

01 / LEARN

The idea, step by step

Read both sides in the same unit

A scale of $1 : 50 000$ means one unit on the map represents 50,000 of the same units in real life. Thus 1 cm represents 50,000 cm, which is 500 m or 0.5 km.

Multiply a map distance by the scale denominator to get the real distance in the same unit. Convert after multiplying. For a drawing distance, first put the real distance in the drawing unit, then divide by the denominator.

Follow the route that is asked for

A route distance follows the specified path; a straight-line distance joins the start and finish directly. These are not interchangeable. Count each grid interval, rather than grid lines.

Scales are valid only at the intended print size. Resizing a map changes a written ratio scale, while a scale bar printed with the map resizes with it. Check a known measurement before using a photocopied drawing.

A common trap

A scale of $1 : 500$ means 1 cm represents 500 m.

Instead: Both numbers refer to the same unit: 1 cm represents 500 cm, which is 5 m.

02 / WORKED EXAMPLES

See the thinking

Example 1

Map to real distance

On a $1 : 25 000$ map, a path is 7.2 cm long. Find its real length in kilometres.

$7.2 \times 25 000 = 180 000$ cm.
Divide by $100 000$ cm/km: $180 000 / 100 000 = 1.8$ .

1.8 km

Example 2

Choose the route

Using the map, find the length of the route A–B–C.

A–B is six 1 cm squares; B–C is four squares.
Map route length is $6 + 4 = 10$ cm.
Each centimetre represents 0.5 km, so the route is $10 \times 0.5 = 5$ km.

5 km

Check your understanding

A 9 m room is drawn using scale $1 : 100$ . How long is it on the drawing?

Show answer

9 cm

$9$ m $= 900$ cm and $900 \div 100 = 9$ cm.

03 / WORKSHEET

Your turn

6 questions · 13 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

State what 1 cm represents on a $1 : 20 000$ map, in metres.
2 marks
A distance is 4.8 cm on a $1 : 50 000$ map. Find its actual length.
2 marks
Drawn at $1 : 200$ , what length represents a 14 m wall?
2 marks
A model is 18 cm long and represents a 9 m vehicle. Find the scale.
2 marks
On the supplied map, find only the actual distance A–B.
2 marks
A plan marked $1 : 100$ is enlarged so every printed length doubles. What is its new scale?
3 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

State what 1 cm represents on a $1 : 20 000$ map, in metres.
2 marks
$20 000$ cm $= 200$ m.
200 m
A distance is 4.8 cm on a $1 : 50 000$ map. Find its actual length.
2 marks
$4.8 \times 50 000 = 240 000$ cm $= 2.4$ km.
2.4 km
Drawn at $1 : 200$ , what length represents a 14 m wall?
2 marks
$14$ m $= 1 400$ cm.
$1 400 \div 200 = 7$ cm.
7 cm
A model is 18 cm long and represents a 9 m vehicle. Find the scale.
2 marks
$9$ m $= 900$ cm.
Scale $18 : 900 = 1 : 50$ .
$1 : 50$
On the supplied map, find only the actual distance A–B.
2 marks
A–B is six 1 cm squares.
$6 \times 0.5 = 3$ km.
3 km
A plan marked $1 : 100$ is enlarged so every printed length doubles. What is its new scale?
3 marks
An original 1 cm now becomes 2 cm but still represents 100 cm.
New scale $2 : 100 = 1 : 50$ .
$1 : 50$

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Curriculum reference & lesson scope

Australian Curriculum v9 and SA Curriculum Mathematics

Year 9 proportional modelling, rates, scale, similarity and enlargement. Assumptions, interpretation and model limitations are taught alongside calculation.

Official curriculum source ↗

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