This idea can be used as an activity or as a demonstration by the teacher. If done as a demo, the teacher can have the "pieces" pre-cut to save time. The demo works nicely on an overhead projector. Colored acetate is helpful, but not mandatory.
large grid graph paper,
1. on large grid graph paper, draw a right triangle with legs of 3 units and 4 units. This triangle should be positioned as to allow for a square to be drawn on each leg.
2. cut a 3 by 3 square and a 4 by 4 square apart into individual (1 x 1) squares cutting along the lines of the graph paper.
3. arrange these small squares into a large square along the third side of the triangle. What do you think the length of the hypotenuse will be?
4. repeat for a triangle with legs of 5 and 12.
5. Do you see a pattern developing between the squares you have used for each of the triangles? If students are familiar with the Pythagorean Theorem, ask if they can describe how the theorem is being applied in this activity.