Rectangles from squares

An investigation, using geometry and algebra, to explain numerical observations when squaring a number, n and when multiplying (n + 1)(n - 1).

Students are asked to try numerical examples and generalise, then to show the problem with diagrams or manipulatives and, finally, using algebra.

The Word document gives an independent investigation with a simple proof extension. The PowerPoint gives an introduction to the concept of algebraic proof for KS3.