Discovering the Pythagorean theorem

This lesson develops the concept of Pythagoras’ theorem. In particular students will:

• Use the area of right triangles to deduce the areas of other shapes
• Use dissection methods for finding areas
• Organise an investigation to systematically collect data
• Deduce a generalizable method for finding lengths and areas (The Pythagorean Theorem)

The first activity looks a ‘tilted squares’ drawn on dotted paper. In this context a ‘3 by 5’ square is one that has one vertex at (3, 0) joined to a second vertex at (0, 5). A square is then constructed from this side. Students must calculate the area of the square. They then go on to look at a 3 by 7 square, and generalise to a 3 by y square.

The activity is then developed using a collaborative approach to work on 25 squares from 0 by 0 up to 4 by 4. Students look for patterns in their results as an introduction to the Pythagorean theorem. There then follows an algebraic derivation of the result using a similar approach to that taken in the numerical examples.

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.