Ratio & Proportion Problems
This topic covers 5 learning steps, guiding your child from the basics through to confident problem-solving. Each step includes a worked example and adaptive practice questions.
What Your Child Will Learn
- Simplify ratios
Reduce ratios to simplest form - Share in a ratio
Divide an amount in a given ratio - Direct proportion
If one doubles, the other doubles - Inverse proportion
If one doubles, the other halves - Compound measures
Speed, density, pressure problems
Before This Topic
Your child should be comfortable with:
- Ratios (Year 6)
- Percentage Increase & Decrease (Year 6)
Common Mistakes
- Adding the ratio parts incorrectly when sharing an amount (e.g. sharing £40 in the ratio 3:5 and giving £3 and £5 instead of £15 and £25)
First add the ratio parts: 3 + 5 = 8 parts total. Then divide the amount by the total parts: £40 ÷ 8 = £5 per part. Finally multiply: 3 × £5 = £15 and 5 × £5 = £25. Check: £15 + £25 = £40. - Confusing direct and inverse proportion (e.g. thinking that if 4 workers take 6 hours, 8 workers take 12 hours)
In direct proportion, more of one means more of the other (more items cost more money). In inverse proportion, more of one means less of the other (more workers means less time). 4 workers in 6 hours = 8 workers in 3 hours, not 12.
Tips for Parents
- Use recipes: "This recipe serves 4 people but we need to serve 6. The recipe uses 200g of flour — how much do we need?" Scale up by multiplying by 6/4.
- Practise sharing in a ratio with real objects: "Share 20 sweets between you and your friend in the ratio 3:2. How many does each person get?" (12 and 8).
- Explain direct proportion with shopping: "If 3 apples cost £1.20, how much do 5 apples cost?" Find the cost of 1 apple first (£0.40), then multiply.
- Use speed to illustrate compound measures: "You walked 6 km in 2 hours. What was your speed?" Speed = distance ÷ time = 3 km/h.
Key Words
- Ratio — A way to compare amounts — a ratio of 3:2 means for every 3 of one thing, there are 2 of another.
- Direct proportion — When two quantities increase together at the same rate — if you buy twice as many, you pay twice as much.
- Inverse proportion — When one quantity increases as the other decreases — twice as many workers means half the time.
- Unitary method — Finding the value of one unit first, then scaling up — find the cost of 1 apple, then multiply by how many you want.
- Compound measure — A measure combining two units — speed (km/h), density (g/cm³), and pressure (N/m²) are all compound measures.
Where This Fits
Before this topic: Children should understand simplifying ratios, basic proportional reasoning, and be confident with multiplication and division of decimals.
After this topic: Ratio and proportion lead to direct and inverse proportion graphs, similar shapes and scale factors, and algebraic proportion at GCSE.
How MathCraft Teaches This
In MathCraft, Ratio & Proportion Problems is taught through the Money, Data & Measure adventure track. Your child follows guided lessons with friendly characters, works through examples step by step, then practises with questions that adapt to their level.
The adaptive engine tracks mastery across all 5 steps, revisiting concepts your child finds tricky and advancing when they're ready. Parents can see detailed progress in the Parent Dashboard.
Practise Ratio & Proportion Problems with MathCraft
Step-by-step lessons, worked examples, and adaptive practice — all wrapped in an adventure game your child will love.
Try MathCraft Free No credit card required