Changing Ratios GCSE Maths – Complete Lesson, Worksheet, Video Tutorial and Generator

This Changing Ratios GCSE Maths video explains how to form and solve algebraic equations when ratios change.

This lesson shows students how algebra can be used to model changing ratios—when quantities increase, decrease, or transfer between groups. By introducing an unknown multiplier, students form equations directly from ratio changes and solve them to reveal the original amounts. The accompanying video tutorial walks through each step, from straightforward ticket problems to more challenging situations where values move between categories.

The ratio of full to empty takeaway cups on a counter was 7 : 5.
4 empty cups are filled. The new ratio becomes 3 :1.

How many full and empty cups were there originally?

This GCSE Maths changing ratios example shows how algebra is used to find original values after quantities change.

Changing Ratios Lesson Pack

This complete teaching pack includes everything needed to deliver the topic with confidence: a PowerPoint presentation with solutions, a video tutorial with teacher handout, a student worksheet for practice, and a question generator for unlimited examples. Together, these resources ensure all students are engaged and challenged.

Teacher’s PowerPoint

Download Student Worksheet

Interactive Question Generator

Lesson Download

This Changing Ratios GCSE Maths lesson teaches students how to form equations from ratios that increase, decrease or transfer between groups. It is ideal for GCSE Mathematics, IGCSE Mathematics and advanced ratio problem solving, and is perfect for classroom teaching, revision or homework.

Teachers can download the full resource pack here:

Curriculum Links

United Kingdom (KS3 / KS4)

• Number and Ratio:
  • Use ratio and proportion to solve problems in context
  • Apply algebraic reasoning to relate quantities and manipulate ratios

United States (Common Core / High School Algebra)

• CCSS.MATH.CONTENT.HSA.CED.A.2: Create equations in one variable and use them to solve ratio and proportional reasoning problems
• CCSS.MATH.CONTENT.HSA.REI.B.3: Solve linear equations and interpret solutions in contextual ratio problems

Australia (ACARA – Year 8/9)

• ACMNA203: Solve problems involving ratios, rates, and percentages
• ACMNA205: Use algebra to model relationships and solve ratio problems

Frequently Asked Questions

What are changing ratios in GCSE Maths?

Changing ratios involve situations where quantities increase, decrease or transfer between groups. Algebra is used to form equations and find the original values.

Is this suitable for GCSE students?

Yes. This lesson is designed specifically for GCSE and IGCSE Mathematics students studying ratio and algebra.

Does the lesson include worksheets and PowerPoint?

Yes. The full resource pack includes a teachable PowerPoint, worksheet, video tutorial and question generator.