## A Square Puzzle

Compare the areas of the square and rectangle. This is expected to trigger the discussion about difference between a^2 and (a+b)(a-b). It may not be obvious to the students at the beginning that the square is always greater than the rectangle. Present the algebraic expression in this context of an area model and a puzzle to solve may encourage meaningful examination of the expressions and their equivalence.

The video below shows how the applet is made. One key step is identifying the centre of rotation for the rectangular piece on the right and defining arc and angle that allow the piece to be dragged back and forth via its

Drag the green dot to vary the rectangle.
24 December 2012, Created with GeoGebra |

Check this construction below.

For more geometric models for this identity, check the GeoGebraTube: