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The first part of the All About Ratio activity from Underground Mathematics is classed as a ‘many ways’ problem, and can be viewed below.

So, how many ways can you find to tackle it? Are any approaches A level only? Are any also accessible to GCSE? Is there a method that is more efficient than the others?

Here are some ways that you can use this problem:

  • with your A level pupils – to refresh GCSE skills and make links between them and new topics, or to introduce a new topic
  • with your Higher GCSE pupils – to consolidate or to problem solve or reason, or as an inquiry when introducing similar triangles, for example
  • with your colleagues – as a basis for discussion of alternative approaches to maths, to consider teaching approaches, or to introduce the website.


Find the sum of the angles α, β and γ in this diagram.

Does the work done above exploring the ratios help or hinder finding the angle sum?

Please download this document for further ideas, including:

  • links to all of the ‘many ways’ problems from Underground Maths
  • hints for three different approaches to All About Ratio
  • ideas for modelling problem solving using ‘many ways’ problems
  • hint cards.

By Christine Watson

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