# 3D Figures

I remember in college we had this super big “unit plan” project where we had to write out lesson plans for every day of a unit about a particular topic. Some classmates felt this was unrealistic because nobody would create an entire unit from scratch. I hoped that it was unrealistic because I wanted to create all of my units from scratch, which I kind of am now, and I didn’t really think it was possible to devote all of this attention to every detail of everything. Our professors gave us some really good advice, that if you focus on making one unit each year really good, then you can save that, and the next year you can focus on making another one really good, and then eventually you can teach everything to the best of your abilities.

This is not to say that I have created a really good 3D figures unit, just that I’ve been improving it steadily. I had planned on revamping the similar figures stuff, but I ended up only slightly tweaking that. 3D figures definitely have so much potential.

I have 2 sections of this class, and each is focusing on something slightly different: one on the visual aspects, and one on the algebraic aspects. This is giving me a great chance to experiment. I have this exciting exploration with marshmallows and toothpicks that I’ve had kids do in the past. It’s designed to have them discover the Euler Characteristic, V – E + F = 2, for vertices, edges, and faces.

Cool Platonic solids, right? I had to look this up, but Platonic solids are polyhedra with regular shapes as faces. Because of reasons I’m having them investigate next week while I’m at the NCTM conference, there are only 5 of these. Making an icosahedron out of toothpicks and marshmallows is extremely difficult, FYI.

We’ve also been working on volume and surface area. We found the volume of this little house in our school’s back yard by measuring everything and splitting it into a rectangular prism and a triangular prism.

When I was looking for non-terrible proof stuff I came across this and needed us to do it.

See, the surface area of a sphere is 4 times the area of the great circle! I love this so much. We proved the surface area of a cone using party hats and sector area – some great review, and great fashion statements! This is going to allow us to compare the surface area of a cylindrical cup and a conical cup with the same volume.

There are so many more things we can cover in the 2 weeks (!!!) that I have left for content this year. Stay tuned for another post!