Ratio and Proportion

Some resources for problems on Ratio and Proportion…

Thinking Blocks – Math Playground

Thinking Blocks from Colleen King’s site Math PlayGround – a wonderful way to visualize Ratio and Proportion problems. This works on all devices.

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.

Thinking Blocks Modeling Tool

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

Thinking Blocks Modeling Tool – use for your own problems

AQA Problems - Teacher's Guide
AQA Problems – Teacher’s Guide

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:

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
WolframAlpha – mix 4 white and 1 black

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?!


CIMT Interactive Materials – Year 8

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.


Clumsy Clive on Ratio – Andy Lutwyche

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


Transum Mathematics – Ratio Problems

Further resources include resources from the exam boards; you can also check all these excellent sites for resources.
See, for example:

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.