Day 92: The Same To Each

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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!

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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.

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