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
- 21 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 21
Visual introductionPicture this
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.
In a nutshell
Use scale factors, scale diagrams and maps
Learning cycle
Part 2 of 21
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 21
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.
Reset break
Part 4 of 21
Pause
That's sitting 1 of 5 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 5 of 21
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 6 of 21
Quick check
Part 7 of 21
Reset break
Part 8 of 21
Pause
That's sitting 2 of 5 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.
Learning cycle
Part 9 of 21
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.
Explore the idea
Part 10 of 21
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 11 of 21
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.
Reset break
Part 12 of 21
Pause
That's sitting 3 of 5 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.
Quick check
Part 13 of 21
Quick check
Part 14 of 21
Explore the idea
Part 15 of 21
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.
Reset break
Part 16 of 21
Pause
That's sitting 4 of 5 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.
Challenge round
Part 17 of 21
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 18 of 21
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.
Challenge round
Part 19 of 21
Game · Recall cards
On a 1:50,000 map, two towns are 6 cm apart. What is the real distance?
Card 1 of 4
Mastery quiz
Part 20 of 21
Marked quiz
End of lesson quiz: Scale factors, drawings and maps
4 questions, marked with the reasoning shown. No timer.
1. On a 1:50,000 map, two towns are 6 cm apart. What is the real distance?
2. A scale drawing has a scale of 1:20. A wall is drawn 8 cm long. What is the real length?
3. What does a scale of 1:25,000 mean?
4. On a 1 : 25 000 map, 4 cm represents
Lesson round-up
Part 21 of 21
Lesson round-up
Ready when you are
Quiz score
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Points this lesson
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Best run
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Luna: 0 out of 4 on the practice checks. Only if you feel up to it — one more?
Ask LunaPart 1 of 21 · Watch & discover
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Use scale factors, scale diagrams and maps