Maths GCSE: Ratio and Proportion

Over the course of this short film, mathematician and comedian Matt Parker explains different approaches to ratio and proportion questions for students who are struggling to gain a passing mark on their maths GCSE.

Traditional ratio questions and proportional reasoning questions are solved using a unitary method, finding a multiplier and also with a graphical aide demonstrating simple uses of the Singapore Bar Method. Finally, he shows how the concepts of ratio and proportion can be helpfully applied to other topics such as pie charts.

This short film could also be used in a more piecemeal approach to introduce a topic, as such this could be used for an earlier Key Stage.

This short film is from the BBC series, The Maths Show.

Teacher Notes

During watching

This video can be paused in many places to ask students to attempt the question that Matt will explore.

When the bar method is explored, pause the video to elicit different representations from students. Students often struggle drawing their own diagrams. In this case, you can draw different diagrams and ask students which suitably represent the problem and which don’t work - include diagrams split in to the wrong proportions.

After watching

Explore the many areas of the exam papers that uses ratio and proportion, building up from simple ratio questions to the triple ratio questions that are common on exam papers where students are asked to combine two different ratios. Repeatedly refer to the video, asking students how the different (but not necessarily more complex) example relates to the examples shown in the video.

Next steps after gaining confidence in the method would include looking at scale drawings, converting between metric units or metric and imperial units and looking at similar shapes.

Curriculum Notes

Suitable for teaching maths at GCSE in England, Wales and Northern Ireland and National 4/5 or Higher in Scotland.

More from The Maths Show

Fractions, Decimals and Percentages
Algebra and Negative Numbers
Algebra - Formulae and Graphs
Exam Techniques for GCSE Maths