While I was at NCTM I left my Math 2 classes with this three-dimensional figures task. When I returned, I was greeted with a messy classroom full of ants (marshmallow bag left open : / ) , but also this:
It’s pretty clear that these are mathematical shapes, but I could never get past the fact that Platonic solids, particularly stellated ones, are aesthetically pleasing. But I did some research and came up with a not totally visual task for my students to work on. Since I wasn’t going to be there, everything is extremely spelled out – on a non-sub day I may leave some things more open.
This task first has them construct three out of cardboard. I had printed a bunch of nets, but I guess they couldn’t find them because nobody used them. I kind of like it without the nets better anyway, because that’s a nicer, richer visualization task. Then they were supposed to re-create two of them with toothpicks and marshmallows or with straws. Only a couple actually attempted straws. I made all of the shapes with straws just to try it out, and I’m still struggling with the icosahedron. I’m really excited to try to make a stellated one.
The question I wanted them to answer is why there are only a limited number of Platonic solids. I’ll admit the task only gets them most of the way there, but I think it’s a good start.
The coolest thing about this whole thing is that I gave nets for the stellated shapes to my advisee group, and now I’m seeing kids just folding un-assigned 3D figures. I’d say that’s an engaging task! I definitely want to continue in this vein of highly visual mathematics with rigorous tasks aside from just “see how cool math looks.”
Although it does look pretty cool!