GCSE Maths: Ratio & Proportion — Topic Revision Workbook

Inside GCSE Maths: Ratio & Proportion — Topic Revision Workbook

simplify ratios and share amounts in a given ratio, link ratio and fractions, solve direct and inverse proportion with the unitary method and compare best buys, work with scale factors, maps and scale drawings, calculate percentage change and compound growth and decay, then use compound measures — speed, density and pressure — and convert units. About 30 minutes.

Learning objectives

• simplifying ratios to lowest terms, sharing an amount in a given ratio, and linking ratio to fractions of a whole;
• direct and inverse proportion using the unitary method, and comparing best buys by unit cost;
• scale factors, maps and scale drawings, converting between drawing and real-life lengths;
• percentage change, percentage increase and decrease, and compound growth and decay such as interest and depreciation;
• compound measures — speed, density and pressure — and converting between units of length.

Activities in this book

1. Task 1 — Simplifying & Sharing Ratios

   to simplify a ratio, divide every part by the same number (the highest common factor). To share an amount in a ratio, add the parts to find how many equal shares there are, work out one share, then multiply. The first part of the ratio a:b is the fraction a/(a+b) of the whole.

2. Task 2 — Direct & Inverse Proportion, Best Buys

   use the unitary method: find the value of ONE item first, then scale up or down. In direct proportion, if one amount doubles the other doubles too. In inverse proportion (like workers and time), more of one means less of the other — multiply to find the fixed total first. For best buys, compare the cost of one unit.

3. Task 3 — Scale, Percentage Change & Growth

   a map or scale-drawing ratio like 1:50000 means every 1 unit on paper is 50000 units in real life. For percentage change, work out the actual change, divide by the ORIGINAL amount, then multiply by 100. For compound growth or decay, multiply by the same decimal multiplier once for each year (1.05 grows by 5%, 0.9 falls by 10%).

4. Task 4 — Compound Measures & Unit Conversion

   compound measures combine two quantities: speed = distance ÷ time, density = mass ÷ volume, and pressure = force ÷ area. Rearrange the formula for what you need (distance = speed × time). Always check the units match, and convert first if they do not (1 km = 1000 m).

5. Task 5 — Ratio & Proportion in Real Life

   exam questions love a real context — a recipe, a car journey, a shopping bill. Practise spotting which tool you need (ratio, proportion, percentage or a compound measure), and always show your working so an examiner can follow your method.

Suggestions for teaching

• Unitary method first. Model finding the value of one item before scaling — it works for cost, ingredients and best buys alike.
• Ratio bar models. Draw the parts of a ratio as equal bars so sharing becomes “find one part, then multiply”.
• Original amount for percentages. Stress that percentage change is always divided by the original, not the new, amount.
• Formula triangles. Teach the speed, density and pressure triangles and how to rearrange each to find the missing quantity.
• Check the units. Insist on converting to matching units (km to m, hours to minutes) before substituting into a formula.