Key Stage 3: Proportional Reasoning Scheme of Work

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This Key Stage 3 Proportional Reasoning scheme of work is designed for Year 8 work on direct proportion, exchange rates, inverse proportion and modelling proportional relationships with y = kx.

Use this page to sequence the lessons below, keep ratio notation and scale factors secure, and connect tables and graphs to algebraic models before students tackle problems that mix direct and inverse proportion.

Last updated: May 2026

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Curriculum Hub

For more schemes and topic routes across KS3, GCSE and A-Level, browse the Mr Mathematics Curriculum Hub.

How to use this scheme

Read the prerequisite and key-concept cards first so fractions, decimals and basic ratio work are secure. Teach the lessons in the order listed unless your timetable requires otherwise — keep Direct Proportion and Exchange Rates before Inverse Proportion where possible, and place Direct Proportion once students can identify proportional relationships from tables and contexts.

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 ratio and proportion plan.

Prerequisite knowledge

Students should be secure with the following before this unit.

Basic fractions and decimal equivalences.
Simple ratio concepts (sharing in ratios, simplifying ratios).

Key concepts

Ideas to keep explicit while students work with proportional reasoning.

Using tables and graphs effectively to represent proportional relationships.
Understanding and applying scale factors.
Expressing ratios clearly and simplifying them to the simplest integer ratio.
Identifying direct proportion relationships algebraically, represented as y = kx.
Solving problems using proportional reasoning in various real-life contexts.

Subject content (Ratio and proportion)

Understand the concepts of direct proportion and constant of proportionality.
Solve problems involving direct proportional relationships, including graphical representation.
Relate ratios to fractions and algebraic equations.

Common misconceptions

Typical slips to address during teaching and marking.

Misunderstand ratios as fractions, applying fraction rules incorrectly.
Fail to recognise that the multiplicative scale factor must remain consistent when dealing with proportions.
Incorrectly cross-multiply without understanding the proportional relationship.

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 fraction and decimal equivalences and basic ratio skills, including sharing and simplifying ratios, so new work focuses on direct and inverse proportion, exchange rates and y = kx.

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 exchange-rate and ratio scaling work before inverse proportion where possible, and teach Direct Proportion once students can read proportional relationships from tables and simple contexts.

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.