June 04, 2003
I feel that the Pythagorean theorem is far too important to try to teach as a concept, but a perfect place to use manipulatives and investigate the relationship of squares and their summation. I use one-cm. unit blocks and have the students draw right triangles on paper, then build the squares of their lengths in unit cubes. After several days of building and recording the drawings on graph paper, one bright pair of fifth graders discovered the relationship of the sum to the square of the hypotenuse! At that point I introduced the correct terms for vocabulary. I can be absolutely certain that at least those two students (if not the other 27 who said, oh, yeah, I get it!) will understand the theorem, and can use their practical manipulation to understand the more complex uses of geometrical theorems.