Ratio, proportion and compound measures
Proportional reasoning runs through the whole specification: recipes, currency, speed, density, growth and scale drawings are all the same idea in different clothing.
Lesson overview
What you'll learn in this lesson
Use proportional reasoning, probability and statistics to interpret and solve problems.
Key learning points
- • Ratio problems
- • Direct and inverse proportion
- • Compound measures and growth
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
Scroll down — the lesson carries on below
Watch & discover
Part 1 of 19
Visual introductionPicture this
Ratio, proportion and compound measures
Proportional reasoning runs through the whole specification: recipes, currency, speed, density, growth and scale drawings are all the same idea in different clothing.
In a nutshell
Use proportional reasoning, probability and statistics to interpret and solve problems.
Learning cycle
Part 2 of 19
Learning cycle 1 of 2
Part 1 · Ratio problems
A short piece of teaching, then a check to make sure it has landed.
Explore the idea
Part 3 of 19
Learn
Ratio problems
For sharing, add the parts, divide the total by that number and multiply back. When a question gives the difference between shares rather than the total, that difference corresponds to the difference in parts — a distinction that decides whether the answer is right.
Reset break
Part 4 of 19
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 19
Learn
Direct and inverse proportion
In direct proportion y = kx, so doubling x doubles y and the graph is a straight line through the origin. In inverse proportion y = k ÷ x, so doubling x halves y and the graph is a curve. Find k from the given pair, then use it for the unknown.
Quick check
Part 6 of 19
Quick check
Part 7 of 19
Reset break
Part 8 of 19
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 19
Learning cycle 2 of 2
Part 2 · Compound measures and growth
A short piece of teaching, then a check to make sure it has landed.
Explore the idea
Part 10 of 19
Learn
Compound measures and growth
Speed = distance ÷ time, density = mass ÷ volume, pressure = force ÷ area. For repeated percentage change, use a multiplier: a 4% annual rise over 3 years is × 1.04³. Reverse percentage questions divide by the multiplier, since the stated figure is the result, not the original.
Quick check
Part 11 of 19
Reset break
Part 12 of 19
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 19
Explore the idea
Part 14 of 19
Worked example
Worked answer: after a 20% discount a coat costs £68. Find the original price (3 marks)
Paying 80% of the original gives a multiplier of 0.8 (1). The original price is therefore 68 ÷ 0.8 (1) = £85 (1). Adding 20% to £68 gives £81.60, which is wrong, because 20% of the larger original is more than 20% of the reduced price. Checking: 20% of £85 is £17, and £85 − £17 = £68.
Challenge round
Part 15 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
Reset break
Part 16 of 19
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 19
Game · Recall cards
£120 shared in the ratio 2 : 3 gives the larger share as
Card 1 of 4
Mastery quiz
Part 18 of 19
Marked quiz
End of lesson quiz: Ratio, proportion and compound measures
4 questions, marked with the reasoning shown. No timer.
1. £120 shared in the ratio 2 : 3 gives the larger share as
2. In inverse proportion, doubling x
3. A 5% annual increase over 4 years uses the multiplier
4. Density is
Lesson round-up
Part 19 of 19
Lesson round-up
Ready when you are
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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 19 · Watch & discover