Proving Pythagoras’ theorem

This lesson develops the concept of producing and evaluating geometrical proofs. In particular students work on:

• Interpreting diagrams
• Identifying mathematical knowledge relevant to an argument
• Linking visual and algebraic representations
• Producing and evaluating mathematical arguments

The initial activity looks at the ‘tilted square’ approach to proving Pythagoras’ theorem. A diagram is presented with a square tilted so that when it is surrounded by four congruent triangles a larger square is formed. Students begin by writing down all that they can derive from the diagram about the shapes, lengths, angles, and areas. They then go on to derive Pythagoras’ theorem.

A collaborative activity looks at a range of sample work. Students must examine carefully the reasoning that is given in each piece of work and comment on the proofs.

There are pre-lesson and post-lesson formative assessment tasks. Detailed teacher notes give suggestions on questioning and how to use the resources. Full solutions are given for each of the sections.

This is a concept development lesson from the Mathematics Assessment Resource Service, a collaboration between UC Berkeley and the Shell Centre team at the University of Nottingham. Further information on the collection is given here.