KS3 Maths · Year 7 · Chapter 11: Shape and ratio · Lesson 3

Map scales

Year 7About 75 minutesNo calculator45 marks

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Date

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Quick questions to start.

A1
Needed today
How many centimetres are there in $3$ km?
[1 mark]
Answer
A2
Needed today
Write $6 : 42$ in the form $1 : n$ .
[1 mark]
Answer
A3
Last lesson
A shape is enlarged by a scale factor of $\frac{1}{4}$ . One side of the shape is $20$ cm. How long is this side on the image?
[1 mark]
Answer
A4
From chapter 8
Work out $4.6 \times 1 0^{4}$ .
[1 mark]
Answer

Example, then your turn

Year 7

Your teacher works through each example with you. Then try the one beside it.

Example 1

The scale of this map is $1$ cm to $6$ km. (a) Work out the actual distance from Fenmoor to Holt. (b) Holt and Wick are $21$ km apart. How far apart are they on the map?

Not drawn accurately

Hint Each centimetre on the map is

6

km. Going back, divide by

6

B1
A map has a scale of $1$ cm to $8$ km. (a) Two villages are $2.5$ cm apart on the map. How far apart are they? (b) Two lakes are $52$ km apart. How far apart are they on the map?
[2 marks]
Answer

Example 2

Write each map scale as a map ratio. (a) $1$ cm to $3$ km (b) $2$ cm to $7$ km

Hint A ratio has the same unit on both sides.

1

= 1000

= 100000

cm.

B2
Write each map scale as a map ratio. (a) $1$ cm to $4$ km (b) $4$ cm to $18$ km
[2 marks]
Answer

Example 3

A map has a map ratio of $1 : 40000$ . (a) A canal is $6.5$ cm long on the map. How long is it, in km? (b) A footpath is $3.4$ km long. How long is it on the map?

Hint

1

cm on the map is

40000

cm on the ground. Divide by

100

for metres, then by

1000

for km.

B3
A map has a map ratio of $1 : 60000$ . (a) A river is $7.5$ cm long on the map. How long is it, in km? (b) A road is $2.4$ km long. How long is it on the map?
[2 marks]
Answer

Example 4

On a map, $8$ cm represents $12$ km. Write the map ratio.

Hint Change the km into cm, then make the map side

1

B4
On a map, $5$ cm represents $4$ km. Write the map ratio.
[2 marks]
Answer

Practice

Year 7

C1
This is the scale bar on a map. Each section of the bar is $2$ cm long. A lake is $7$ cm long on the map. How long is the real lake, in km?
[2 marks]
Not drawn accurately
Answer $\dots\dots$ km
C2
A plan of a classroom is drawn with a scale of $1 : 50$ . On the plan the room is $18$ cm long and $14$ cm wide. Work out the area of the real room, in m².
[3 marks]
Answer $\dots\dots$ m²

C3
Two towns are $45$ km apart. How far apart are they on a map with a map ratio of $1 : 250000$ ?
[2 marks]
Answer $\dots\dots$ cm
C4
A path is $9$ cm long on map $A$ , which has a map ratio of $1 : 20000$ . How long is the same path on map $B$ , which has a map ratio of $1 : 30000$ ?
[3 marks]
Answer $\dots\dots$ cm
C5
A bus goes from $A$ to $B$ to $C$ to $D$ along the roads shown on a map. The map ratio is $1 : 200000$ . How far does the bus travel, in km?
[2 marks]
Not drawn accurately
Answer $\dots\dots$ km

Exam-style questions

GCSE Foundation

D1
Nia says, "A map ratio of $1 : 70000$ means that $1$ cm on the map is $70000$ km on the ground."
Nia is wrong. Work out what $1$ cm on the map represents, in km, and say what Nia has done wrong.
[3 marks]
Answer $1$ cm represents $\dots\dots$ km

D2
The map shows the paths between a camp, a farm and a village. The map ratio is $1 : 15000$ .
Not drawn accurately
(a)
Leah walks from the camp to the farm, then to the village, then straight back to the camp. How far does she walk, in km?
[2 marks]
Answer $\dots\dots$ km
(b)
Leah walks at $4$ km per hour. How many minutes does the walk take?
[2 marks]
Answer $\dots\dots$ minutes
(c)
How many metres shorter is the straight path from the camp to the village than the path through the farm?
[2 marks]
Answer $\dots\dots$ m
Total for D2: 6 marks
D3
A model railway is built to a scale of $1 : 76$ .
(a)
A real carriage is $19$ m long. How long is the model carriage, in cm?
[2 marks]
Answer $\dots\dots$ cm
(b)
A model platform is $2.5$ m long. How long is the real platform, in metres?
[2 marks]
Answer $\dots\dots$ m
Total for D3: 4 marks
D4
On a map with a map ratio of $1 : 5000$ , a rectangular field is $4$ cm long and $3$ cm wide. Work out the actual area of the field, in m².
[3 marks]
Answer $\dots\dots$ m²

Extension

Stretch

No route is given. The hints are at the end of the sheet. Use one at a time.

E1
On map $A$ , which has a map ratio of $1 : 120000$ , two lighthouses are $7.5$ cm apart. On map $B$ the same two lighthouses are $4.5$ cm apart. Work out the map ratio of map $B$ .
[5 marks]
Hint 1 · What to try
Work out the actual distance between the lighthouses first.
Hint 2 · The first line
$7.5 \times 120000 = 900000$ cm, which is $9$ km.
Hint 3 · The full method
On map $B$ , $4.5$ cm represents $900000$ cm. Make the map side $1$ .
Answer $1 : \dots\dots$

How did it go?

Colour one circle on each line.

	Not yet	Nearly	Yes
I can use a map scale to change a map distance into an actual distance, and back.
I can write a map scale as a map ratio.
I can use a map ratio, changing centimetres into metres and kilometres.
I can find the map ratio from a map distance and an actual distance.

Answers and mark scheme

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