A cutting and sticking exercise which leads pupils towards the discovery of pythagoras’ theorem. Beyond introducing the aim of the lesson, this requires very little whole class input from the teacher.
I’ve used this with higher-attaining pupils and it’s worked very well. I’m not sure whether more structure in the questions would be needed for others – I don’t have too many ideas how to break it down further: each individual question is relatively simple so at least the first two numerical examples should be achievable by most.
At Highgate, we then spent a lesson or two in which pupils found missing sides in a triangle by drawing both diagrams out each time – quite a substantial use of time, but it meant that they were very comfortable with the ‘proof’ when we came to generalise it.
I now tend to dive straight into the algebraic generalisation (either individually, in small groups or as a class, depending on how the class are finding it) before proceeding with more traditional applications of Pythagoras.
A follow up to show the pupils which demonstrates the idea in a subtlety different way was tweeted by @solvemymaths. This would make a nice follow up to show pupils.
Suggested improvements please!