We recently proved the Pythagorean theorem in my Geometry class and were working on some related exercises in class today. One of my students asked if since that . “Because you do the same to each”—take the square root of each term, that is. This conversation happened during groupwork—not in front of the whole class.
In response, I wrote the above. “That’s like magic!” he said with a grin. Point made—not to each term, but to each side. We chatted a bit more about it. He’s a kid who loves paradoxes and tricks, so this way of explaining things was right up his alley.
In other news: paper plate tetrahedra and octahedra in Math Art Seminar! They pack space! And can combine to make jumbo copies of each shape!
PS I had a crazy-cool dividing fractions experience with some seventh graders today—blew my mind. Hopefully I can get a good photo of the results tomorrow.