Scale factors and scale diagrams
A map that fits in your pocket can still tell you exactly how far it is to the next town — as long as you understand its scale.
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 scale
- • Worked example
- • Scale diagrams
This lesson at a glance
- 24 minutes
- 13 parts to scroll through
- 3 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 13
Watch first
Scale factors and scale diagrams
An English teaching video on this topic from Cognito. Watch it, then scroll down for the lesson.
In a nutshell
Use scale factors, scale diagrams and maps
Learning cycle
Part 2 of 13
Learning cycle 1 of 2
Part 1 · Reading a scale
A short piece of teaching, then a check to make sure it has landed.
Explore the idea
Part 3 of 13
Learn
Reading a scale
A scale of 1:25,000 means 1 cm on the map represents 25,000 cm (250 m) in real life. To find a real distance, measure the map distance and multiply by the scale factor.
Explore the idea
Part 4 of 13
Learn
Worked example
On a map with scale 1:50,000, two towns are 6 cm apart. Real distance = 6 × 50,000 = 300,000 cm = 3,000 m = 3 km.
Quick check
Part 5 of 13
Quick check
On a 1:50,000 map, two towns are 6 cm apart. What is the real distance?
Reset break
Part 6 of 13
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.
Quick check
Part 7 of 13
Quick check
A scale drawing has a scale of 1:20. A wall is drawn 8 cm long. What is the real length?
Learning cycle
Part 8 of 13
Learning cycle 2 of 2
Part 2 · Scale diagrams
A short piece of teaching, then a check to make sure it has landed.
Explore the idea
Part 9 of 13
Learn
Scale diagrams
An architect draws a room at scale 1:20. If the drawn length is 8 cm, the real length is 8 × 20 = 160 cm, or 1.6 m. Scale drawings keep shapes accurate just smaller.
Quick check
Part 10 of 13
Quick check
What does a scale of 1:25,000 mean?
Challenge round
Part 11 of 13
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
Mastery quiz
Part 12 of 13
Marked quiz
End of lesson quiz: Scale factors and scale diagrams
3 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?
Lesson round-up
Part 13 of 13
Lesson round-up
Ready when you are
Quiz score
Not sat
Games
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Points this lesson
0
Best run
0 in a row
Luna: 0 out of 3 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 13 · Watch & discover
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Use scale factors, scale diagrams and maps