Good Learning Co.
SavannahYear 8
← Maths
MathsRatio, proportion and rates30 min★★★ difficulty

Scale drawings, maps and scale factors

A map is a ratio you can walk through. Scale lets you turn centimetres on paper into kilometres on the ground and back again.

Lesson overview

What you'll learn in this lesson

Use scale factors, scale diagrams and maps

Key learning points

  • • What a scale means
  • • Both directions
  • • Scale drawings and plans
  • • Bearings and journeys

This lesson at a glance

  • 30 minutes
  • 19 parts to scroll through
  • 4 quick checks
  • Marked quiz at the end
  • Gentle pace: short sittings with pauses

Words to know

factorsdiagramsdirectionsdrawingsbearings

Scroll down — the lesson carries on below

Part 1 of 19 · Discover5%
1

Watch & discover

Part 1 of 19

Watch first

Scale drawings, maps and scale factors

An English teaching video on this topic from mathantics. Watch it, then scroll down for the lesson.

In a nutshell

Use scale factors, scale diagrams and maps

2

What you already know

Part 2 of 19

Before we start

What you already know

You can simplify ratios and convert between mm, cm, m and km.

Recap: Sharing in a ratio
3

Key words

Part 3 of 19

Key words

Words you'll need today

scale
The ratio of a length on a drawing to the real length.
scale factor
The number you multiply lengths by.
bearing
A direction measured clockwise from north, written with three figures.
4

Learning cycle

Part 4 of 19

Learning cycle 1 of 2

Part 1 — Reading a scale

A short piece of teaching, then a check to make sure it has landed.

5

Explore the idea

Part 5 of 19

Learn

What a scale means

A scale of 1:50,000 means 1 cm on the map is 50,000 cm on the ground — that is 500 m, or 0.5 km. Convert the big number into sensible units straight away: 1:25,000 means 1 cm to 250 m. Written scales like '1 cm to 2 km' say the same thing more plainly.

6

Explore the idea

Part 6 of 19

Learn

Both directions

Map to real: multiply. Real to map: divide. On a 1:50,000 map, 6.5 cm represents 3.25 km. Going the other way, a 9 km walk needs 18 cm of map. Always write which direction you are going before you touch the calculator.

7

Quick check

Part 7 of 19

Quick check

On a 1:50,000 map, 1 cm represents...

8

Quick check

Part 8 of 19

Quick check

Scale 1:25,000. How far is 8 cm?

9

Reset break

Part 9 of 19

Pause

That's sitting 1 of 2 done

Stretch, get a drink, look out of the window. There is no timer and nothing is counting down — your place is saved, so you can come back in five minutes or tomorrow.

Stop here for now
10

Learning cycle

Part 10 of 19

Learning cycle 2 of 2

Part 2 — Using scale in real problems

A short piece of teaching, then a check to make sure it has landed.

11

Explore the idea

Part 11 of 19

Learn

Scale drawings and plans

A room 4.5 m long drawn at 1:100 is 4.5 cm on the plan. Scale drawings must keep every length in proportion, or the shape distorts. Angles do not change under scaling — only lengths do, which is why a scale drawing is still the right shape.

12

Explore the idea

Part 12 of 19

Learn

Bearings and journeys

Bearings are measured clockwise from north with three figures: due east is 090°, south-west is 225°. Combined with a scale, a bearing and a distance fix a position exactly, which is how a walker uses a map and compass. To find a real distance, measure the straight line in cm, then apply the scale.

13

Quick check

Part 13 of 19

Quick check

A 6 m wall at 1:100 is drawn as...

14

Quick check

Part 14 of 19

Quick check

The bearing of due west is...

15

Common mix-ups

Part 15 of 19

Common mix-ups

Things people often get wrong

  • Leaving 50,000 cm as centimetres instead of converting to 0.5 km.
  • Multiplying when going from real life to the map.
  • Writing a bearing as 90° instead of 090°.
16

Challenge round

Part 16 of 19

Game · Sort it

Which of these are true?

Drag each card into the right column. Tap a card first if dragging is fiddly.

True

Not true

17

Challenge round

Part 17 of 19

Game · Fill the gaps

Finish the sentences

Choose the word that belongs in each gap.

Scale ____ must keep every length in proportion, or the shape distorts.

____ are measured clockwise from north with three figures: due east is 090°, south-west is 225°.

18

Mastery quiz

Part 18 of 19

Marked quiz

End of lesson quiz: Scale drawings, maps and scale factors

6 questions, marked with the reasoning shown. No timer.

  1. 1. Scale 1 cm to 2 km. A 7 km path measures...

  2. 2. On a 1:200 plan, 4.5 cm represents...

  3. 3. Real to map means...

  4. 4. Under enlargement, angles...

  5. 5. A bearing must be written with...

  6. 6. Scale 1:50,000. A 15 cm route is...

19

Lesson round-up

Part 19 of 19

Lesson round-up

Ready when you are

Quiz score

Not sat

Games

Not played

Points this lesson

0

Best run

0 in a row

Luna: 0 out of 4 on the practice checks. Only if you feel up to it — one more?

Ask Luna

Do the work

Your written work for this lesson

This is the part you'd do in your book at school. Pick the pieces below, write here or on paper, and photograph anything you draw or work out.

Article

The cost of a school trip

A school is planning a trip to a wildlife park. The coach costs £480 however many people go. Entry costs £9.50 for each pupil and each adult goes free. The school says every pupil must pay the same amount, and the trip must not lose money.

If 60 pupils go, the coach works out at £8 each, so the total for each pupil is £17.50. If only 40 pupils go, the coach works out at £12 each, so the price rises to £21.50. The teacher explains that the coach is a fixed cost and the entry is a cost per person — which is why the price per pupil changes when the number changes.

The school decides to charge £20 and to use anything left over for a second trip later in the year.

Written for Good Learning Co.

Reading questions

  1. Work out the total cost of the trip if 50 pupils go.
  2. Show why the price per pupil falls when more pupils go, using numbers.
  3. At £20 each, how many pupils must go before the trip makes money? Show your working.

  • Working out

    Working out

    Do the practice questions on paper, showing every step — not just the answer. Mark them yourself and circle anything you got wrong.

    10–15 questions

  • Worked example, explained

    Writing

    Copy one question out and write underneath, in words, why each step works.

    1 question, 4–5 sentences

  • Problem in words

    Working out

    Write your own real-life problem that uses today's method, then solve it.

    1 problem + solution

Saved as you type.

Part 1 of 19 · Watch & discover

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