Some resources for problems on Ratio and Proportion…

From AQA Maths, check their excellent GCSE Maths Focus on success modular Teacher Training packs. Looking at the pack on Ratio for example you will find activities and discussion prompts on switching representations, combining ratios, problem-solving with ratio and dividing quantities in a given ratio.

From Andy Lutwyche, many excellent Ratio resources, including these from some of my favourite series:

• Building Blocks – Ratio
• What Was The Question? – Ratio and Proportion Special
• Clumsy Clive On Ratio
• Non-Examples – Ratio and Proportion – Reasoning Tasks
• Ratio Spider
• Andy’s SSDD Questions – Daytime TV Edition
• Spot The Mistakes – Proportion

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• Transum Mathematics on Ratio, the above problem is part of this set of self-marking exercises.
• Dr Austin Maths – Number
• Jess Prior’s Minimally Different Problems on Ratio and Proportion
• Ratio Knowledge Organisers See for example Nicola Whiston’s White Rose Year 10 Knowlege Organiser on Ratio and Fractions
• Further resources include resources from the exam boards; you can also check all these excellent sites for resources.

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Thinking Blocks from Colleen King’s site Math PlayGround – a wonderful way to visualize Ratio and Proportion problems. This works on all devices. See this post on bar modelling which includes more details on using bar models to solve problems.

Models like this really help students to visualise problems. Note the numerous videos showing how to model problems (scroll down the page). You can use the Thinking Blocks Tool to model your own problems; watching the videos will help you learn to use the tool. There is a very clear help section also.

I have used the tool to model a problem from Andy Lutwyche’s Clumsy Clive on Ratio resource – see below for Andy’s resources.

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Part of the Rich Tasks collection, from AQA

From AQA comes an outstanding resource, GCSE Mathematics: 90 maths problem  solving questions. Em  @EJmaths has a brilliant PowerPoint with all the questions and answers – see it here.

The guide includes indices by topic and also by strategy. I have used many of the problems successfully in the classroom with a variety of ages, they really do make students think. Checking the content index, there are several problems involving ratio:

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Nrich of course, a search on Ratio returns this selection of problems. Nrich problems always include teacher’s notes and solutions.

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The GCSE specification includes: “relate ratios to fractions and to linear functions”.

Grey paint is made by mixing white paint with black paint in the ratio 4:1. Represent this information by drawing a straight line graph. (AQA GCSE Exemplification)

We can use the excellent Desmos graphing calculator to demonstrate examples; taking the above exemplification question from AQA I created a Desmos page to illustrate the problem. And did you know that you can mix colours on WolframAlpha?!

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Just as one can always find something on Nrich, the same is true of CIMT. From the Centre for Innovation in Mathematics Teaching, we have Ratio and Proportion from the Year 8 book (UK age 12-13) and Variation from the GCSE course (UK age 14-16). The Year 8 Interactive material includes lots of practice questions where the answers are checked for students.

Unit 7(Ratio and Proportion)
7.1 Equivalent Ratios
7.2 Direct Proportion
7.3 Proportional Division

As well as the Year 8 text, further resources are available such as Activities and Extra Exercises. Most CIMT resources require no password – a few like Teachers’ notes and answers do. An educational institution can obtain the password.

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These sorts of problems must be on everybody’s Mathematics specifications all over the world! In the UK there is an increased emphasis on Ratio and Proportion in the latest GCSE specifications; a link to these resources has been included on the GCSE Content page.