Scale factors, drawings and maps
Scale lets a whole city fit on a page and a microscopic cell fill a screen. The mathematics is proportion, and the discipline is unit conversion.
Part of your national curriculum
- Ratio, proportion and rates of change: Use scale factors, scale diagrams and maps
Lesson overview
What you'll learn in this lesson
Use scale factors, scale diagrams and maps
Key learning points
- • Reading a map scale
- • Scale drawings
- • Enlargement and its effect
- • Similar shapes
This lesson at a glance
- 28 minutes
- 17 parts to scroll through
- 4 quick checks
- Marked quiz at the end
- Gentle pace: short sittings with pauses
Words to know
Scroll down — the lesson carries on below
Watch & discover
Part 1 of 17
Watch first
Scale factors, drawings and maps
An English teaching video on this topic from The Organic Chemistry Tutor. Watch it, then scroll down for the lesson.
In a nutshell
Use scale factors, scale diagrams and maps
Learning cycle
Part 2 of 17
Learning cycle 1 of 2
Part 1 · Reading a map scale
A short piece of teaching, then a check to make sure it has landed.
Explore the idea
Part 3 of 17
Learn
Reading a map scale
A scale of 1 : 25 000 means 1 cm on the map represents 25 000 cm on the ground, which is 250 m, so 4 cm represents 1 km. Converting the ground distance into sensible units immediately is what makes later calculations easy.
Explore the idea
Part 4 of 17
Learn
Scale drawings
A room drawn at 1 : 50 shows a 4 m wall as 8 cm. Scale drawings must state the scale, keep every measurement to the same scale, and use a ruler and protractor accurately; bearings on the drawing must match bearings in reality.
Quick check
Part 5 of 17
Quick check
On a 1 : 25 000 map, 4 cm represents
Quick check
Part 6 of 17
Quick check
A 4 m wall drawn at 1 : 50 measures
Learning cycle
Part 7 of 17
Learning cycle 2 of 2
Part 2 · Enlargement and its effect
A short piece of teaching, then a check to make sure it has landed.
Reset break
Part 8 of 17
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.
Explore the idea
Part 9 of 17
Learn
Enlargement and its effect
Enlarging a shape by scale factor k multiplies every length by k, the area by k² and the volume by k³. A shape of area 8 cm² enlarged by factor 3 has area 72 cm². Forgetting to square the factor for area is the most heavily penalised error here.
Explore the idea
Part 10 of 17
Learn
Similar shapes
Two shapes are similar when corresponding angles are equal and corresponding sides are in the same ratio. Finding a missing side means identifying the pair of corresponding sides that are both known, calculating the scale factor, then applying it to the unknown side.
Quick check
Part 11 of 17
Quick check
A shape of area 8 cm² enlarged by scale factor 3 has area
Quick check
Part 12 of 17
Quick check
Similar shapes have
Explore the idea
Part 13 of 17
Worked example
Worked answer: two similar triangles have bases 6 cm and 15 cm. The smaller has area 20 cm². Find the larger area (3 marks)
The length scale factor is 15 ÷ 6 = 2.5 (1). Area scales by the square of the length factor, 2.5² = 6.25 (1). The larger area is 20 × 6.25 = 125 cm² (1). Multiplying 20 by 2.5 to get 50 cm² treats area as if it scaled like length.
Challenge round
Part 14 of 17
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
Challenge round
Part 15 of 17
Game · Fill the gaps
Finish the sentences
Choose the word that belongs in each gap.
Scale ____ must state the scale, keep every measurement to the same scale, and use a ruler and protractor accurately; bearings on the drawing must match bearings in reality.
Mastery quiz
Part 16 of 17
Marked quiz
End of lesson quiz: Scale factors, drawings and maps
4 questions, marked with the reasoning shown. No timer.
1. On a 1 : 25 000 map, 4 cm represents
2. A 4 m wall drawn at 1 : 50 measures
3. A shape of area 8 cm² enlarged by scale factor 3 has area
4. Similar shapes have
Lesson round-up
Part 17 of 17
Lesson round-up
Ready when you are
Quiz score
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Games
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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 LunaDo 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.
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
- Work out the total cost of the trip if 50 pupils go.
- Show why the price per pupil falls when more pupils go, using numbers.
- At £20 each, how many pupils must go before the trip makes money? Show your working.
Working out
Working outDo 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
WritingCopy one question out and write underneath, in words, why each step works.
1 question, 4–5 sentences
Problem in words
Working outWrite your own real-life problem that uses today's method, then solve it.
1 problem + solution
Saved as you type.
Part 1 of 17 · Watch & discover
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Use scale factors, scale diagrams and maps