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.
Development:
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.