Ratio and Proportion

Some resources for problems on Ratio and Proportion…

Thinking Blocks from Colleen King’s site Math PlayGround – a wonderful way to visualize Ratio and Proportion problems. With the full screen option, this will display well. An example is illustrated in the following slides:

I believe that drawing great diagrams to illustrate problems really helps understanding – something I intend to work more on this year.


AQA Problems - Teacher's Guide

AQA Problems – Teacher’s Guide

Part of the Rich Tasks collection, from AQA comes an outstanding resource, ‘Problem Solving Questions‘ and accompanying Teacher’s Guide which 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:

AQA Problems on Ratio

AQA Problems on Ratio

AQA Problem Solving Guide

AQA Problem Solving Guide – Inside Circle


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

Nrich - Mixing Lemonade

Nrich – Mixing Lemonade


Ratio problem illustration

Ratio problem illustration

The new GCSE specification includes: “relate ratios to fractions and to linear functions”. Use the excellent Desmos graphing calculator to demonstrate examples; taking an exemplification question from AQA I created a Desmos page to illustrate the problem.


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 GCSE course (UK age 14-16). 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.


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 new GCSE specifications; a link to these resources has been included on the GCSE New Content page.

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