Key Stage 3: Ratio Scheme of Work

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This Key Stage 3 Ratio scheme of work brings together lessons on simplifying ratios, sharing in a given ratio, equivalent proportions with fractions and percentages, and best-buy problems.

Use this page to sequence the lessons below, keep ratio notation distinct from fraction and percentage forms, and connect sharing problems to real contexts before students compare offers using unit ratios.

Last updated: May 2026

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How to use this scheme

Read the prerequisite and key-concept cards first so fractions, decimals and percentages are secure. Teach the lessons in the order listed unless your timetable requires otherwise — keep simplifying ratios before sharing, teach Ratio and Equivalent Proportions before Best Buys, and link best-buy work to unit cost and proportional reasoning.

Mr Mathematics membership

Presentations, worksheets, question generators and video tutorials for the lessons in this unit are available to members. Explore Mr Mathematics membership if you need full access to the library and schemes of work.

If you are comparing options for a department, the membership page sets out exactly what is included so you can align this unit with your wider Key Stage 3 number and proportion plan.

Prerequisite knowledge

Students should be secure with the following before this unit.

Understanding the equivalence between fractions, decimals, and percentages

Converting between fractions, decimals, and percentages (e.g., 1/2 = 0.5 = 50%)
Recognising that percentages are fractions out of 100 (e.g., 75% = 75/100)

Writing a proportion as a fraction or percentage

Expressing a part-to-whole relationship as a fraction (e.g., “3 out of 5 students” as 3/5)
Converting a fraction to a percentage by multiplying by 100 (e.g., 3/5 × 100 = 60%)

Understanding equivalent fractions

Recognising equivalent fractions (e.g., 2/4 = 1/2)
Simplifying fractions by dividing numerator and denominator by common factors

Key concepts

Ideas to keep explicit while students work with ratio and proportion.

How to write and simplify a ratio: Express the ratio in its simplest form by dividing all terms by their highest common factor (e.g., 12:16 simplifies to 3:4 by dividing both terms by 4).
How to convert a ratio to a fraction or percentage: A ratio can be expressed as a fraction by writing each part over the total (e.g., in a 3:5 ratio, the first part is 3/(3+5) = 3/8, which as a percentage is (3/8) × 100 = 37.5%).
How to share an amount in a given ratio: Divide the total amount by the sum of the ratio parts to find the value of one part, then multiply by each ratio term (e.g., sharing £80 in a 3:5 ratio: total parts = 3+5=8, so one part is £80 ÷ 8 = £10, meaning the shares are £30 and £50).

Subject content (Ratio and proportion)

Use ratio notation, including reduction to simplest form
Divide a given quantity into two parts in a given part:part or part:whole ratio; express the division of a quantity into two parts as a ratio
Understand that a multiplicative relationship between two quantities can be expressed as a ratio or a fraction

Working mathematically

How this unit supports fluency, reasoning and problem solving in Key Stage 3.

Develop fluency
- Simplify numerical expressions, including those involving ratios, by using the highest common factor.
- Convert between different units, fractions, decimals, and percentages, including expressing parts of a whole in ratio format.
- Use efficient numerical and algebraic methods to divide quantities in a given ratio.
Reason mathematically
- Recognise and use proportional relationships to compare and simplify ratios effectively.
- Use proportional reasoning to relate ratios, fractions, and percentages in real-world and abstract contexts.
Solve problems
- Apply ratio and proportion calculations to real-life problems, including financial mathematics.

Common misconceptions

Typical slips to address during teaching and marking.

Simplifying only one part of a ratio, or subtracting terms instead of dividing by a common factor.
Writing a ratio part as a fraction of another part rather than of the whole when converting to a fraction or percentage.
Sharing an amount by dividing by one ratio term instead of by the sum of all parts.
Comparing best buys using total cost rather than cost per unit.

Frequently asked questions

How do I use this scheme page in practice?

Use it to sequence teaching, align vocabulary and spot likely errors before they become habits. Then use the lessons below as the delivery route for the unit.

What should students already know before this unit?

They need secure equivalence between fractions, decimals and percentages, and confidence simplifying fractions so new work focuses on ratio notation, sharing and proportional reasoning rather than basic conversion.

Where are the lesson presentations and worksheets?

Each lesson listed below has its own page with downloadable resources and, where available, online tasks. Access depends on your membership level.

Can I change the order of the lessons?

Yes if your timetable requires it — keep Writing Ratios in their Simplest Form before Sharing in a Given Ratio, teach Ratio and Equivalent Proportions before Best Buys, and ensure students can simplify and share before comparing value-for-money offers.

Where can I find revision resources for this topic?

Additional revision lessons, exam-style questions and topic-based practice are available on the GCSE Maths Revision Hub. This is useful for consolidating learning after teaching the unit or for Year 11 exam preparation.