This mini-lesson walks you through the whole KS3 Ratio, proportion and rates of change strand: units & scale, ratio notation and sharing in a ratio, direct & inverse proportion, percentage change & simple interest, and compound units like speed and density.
Work through each screen, answer the questions as you go (some are word problems, some are calculations) and collect ⭐ stars. Press Start when you're ready.
Measurements come in different units. To compare or combine amounts you must first put them in the same unit.
Watch out: × when you change to a smaller unit (more of them), ÷ when you change to a bigger unit. 3.5 km = 3.5 × 1000 = 3500 m.
A recipe needs 250 g of flour per person. How much for 4 people, in kg?
250 × 4 = 1000 g = 1 kg
A scale tells you how a drawing or map compares to real life. A scale of 1 : 50 000 means 1 cm on the map = 50 000 cm in real life (which is 500 m).
Tip: the two numbers in a scale are in the same unit. 1 : 50 000 is a length that is 50 000 times bigger, not "50 000 cm".
A ratio compares parts to each other. Orange squash mixed 1 : 4 means 1 part squash for every 4 parts water.
Common mistake: a ratio is not a fraction of the whole. In 1 : 4, the squash is 1 out of 5 (⅕), not ¼. Add the parts to get the whole.
Simplify a ratio like a fraction: divide both sides by the same number (their highest common factor).
You can also write a ratio in the form 1 : n. Divide both parts by the first: 4 : 10 = 1 : 2.5. This is handy for comparing.
Simplify 20 : 35.
HCF of 20 and 35 is 5, so 20 ÷ 5 : 35 ÷ 5 = 4 : 7
To share an amount in a ratio, use the bar model method:
Share £40 in the ratio 3 : 5.
Total parts = 3 + 5 = 8. One part = 40 ÷ 8 = £5.
Shares = 3 × 5 : 5 × 5 = £15 : £25
Check: the shares must add back to the original amount (£15 + £25 = £40). ✔
Two quantities are in direct proportion if, when one doubles, the other doubles too — they go up together at the same rate. The unitary method (find one, then scale) solves these.
5 apples cost £2.00. How much do 8 apples cost?
1 apple = 2.00 ÷ 5 = £0.40. Then 8 × 0.40 = £3.20
Graph clue: direct proportion is a straight line through the origin (0, 0).
Two quantities are in inverse proportion when one increases as the other decreases, so their product stays the same.
3 builders take 8 days to build a wall. How long would 4 builders take (working at the same rate)?
Total work = 3 × 8 = 24 builder-days. Time = 24 ÷ 4 = 6 days
Common mistake: don't treat this like direct proportion. More builders means fewer days, so you divide — you don't scale up.
Tap whether each situation shows direct or inverse proportion.
"Per cent" means "per 100". To find a percentage, turn it into a decimal multiplier and multiply.
Find 20% of £45.
0.20 × 45 = £9
To increase by a percentage, use a multiplier greater than 1; to decrease, use one less than 1.
Common mistake: percentage change is measured from the original value, not the new one. A price rises £20 → £25: change = £5, so 5 ÷ 20 × 100 = 25% (not 5 ÷ 25).
A £80 coat is reduced by 15%. Sale price?
0.85 × 80 = £68
Money in a savings account earns interest. With simple interest, the same amount is added each year, based on the original amount.
£500 is saved at 3% simple interest per year for 4 years.
One year's interest = 0.03 × 500 = £15. Over 4 years: 15 × 4 = £60
With simple interest the yearly amount never changes. (Compound interest, where interest earns interest, comes later at GCSE.)
Speed is a compound unit — it combines distance and time (e.g. m/s or km/h). Use the formula triangle:
A car travels 150 km in 3 hours. What is its average speed?
S = D ÷ T = 150 ÷ 3 = 50 km/h
Density = mass ÷ volume (e.g. g/cm³). Unit pricing compares value for money — find the price for one gram, ml or item.
Shop A: 500 g for £2.00. Shop B: 800 g for £3.04.
A = 200 ÷ 500 = 0.40p/g. B = 304 ÷ 800 = 0.38p/g. Shop B is cheaper per gram.
Tip: to compare "best value", always work out the cost of the same amount (e.g. per 100 g) for each.
Tap a task, then tap the correct box: is it a Ratio share or a Compound-unit rate?
Units & scale: same units first; scale × real length
Ratio: add parts for the whole; a : b is not a/b of the total
Sharing: total parts → one part → each share
Direct proportion: find 1, then scale (line through origin)
Inverse proportion: product stays constant (more → less)
% change: change ÷ original × 100
Simple interest: amount × rate × years
Compound units: speed = D ÷ T; density = m ÷ V; unit price
You've covered the whole KS3 Ratio, proportion and rates of change strand. Press Finish to see your score.
You've worked through Ratio, Proportion & Rates of Change for KS3 Maths. 🎉
Your stars: 0 / 0
Next: test yourself in the Evaluate stage Confidence Quiz, then lock it in with Verify.