# Day 92: The Same To Each

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 $a^2+b^2=c^2$ that $a+b=c$. “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.