So much fun with this project – some great things to notice about geometric shapes, multiple manipulatives to use to help see the geometry, and then an ending that makes a cool connection with algebra. All from . . . this tweet I saw via James Tanton earlier in the week:
Looked like a really fun project and today we sunk our teeth into it.
The first thing was having the kids build the models out from our Zometool set. I was at work when they built the models, and I was happy that they were able to construct the models from the pictures on Twitter. It was interesting to hear what they thought about the shapes:
I wrapped up the first video too soon, unfortunately, because I wanted to ask them some questions that lead into making the shape on Mathematica:
Now we went over to the computer to take a look at the code we used to make the shape. I’ve not talked about this topic with either kid, so this part is more just showing them that you can make this shape rather than teaching them how to do it:
Making the shape on Mathematica allows us to export a version of it to print on our 3D printer. While one of the pyramids was printing I asked each kid to tell me what they noticed about the shape. First my older son:
and then my younger son. I was really excited to hear him say that he noticed that it looked like the shape was being built up out of squares!
Next we went back to the living room to show how the 3D printed shapes fit together. You get a slightly different perspective with the 3D printed shapes compared to the Zometool shapes, and this 2nd perspective was nice. I asked the kids about the volume of the pyramids expecting to hear them say that the volume was 1/3 of the cube. However, they caught on to the idea that the shapes were built up out of squares and that the volume of the pyramids was somehow related to the squares. Fun! Before diving into that, though, we did talk about why each pyramid had a volume equal to 1/3 of the cube.
We finished by talking about how you could sum up squares and get 1/3 of a cube. Mostly because I couldn’t resist, but it was a fun way to end this project, too. My younger son got a little mixed up with the algebra, but we got back on the right track after a minute or two. It is amazing to see how the sum of squares formula produces an answer that is 1/3 of a cube. Super fun way to end this project and a neat way to connect a little algebra with the geometry we just saw.
Mike's Math Page 
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