Common Core Standards: Math
4. Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.
If your students think they're too old for Play-Doh, they should think again. It's colorful fun for ages 2 to 102! If cheeky students give you any lip, just ask them if they'd rather be doing proofs. Works every time.
Have them make 3D solids with the Play-Doh. Start by having them make cubes, pyramids, cones, spheres, and cylinders. To look at cross-sections of these solids, have them cut these Play-Doh solids in different ways and see what kinds of 2D shapes they form. (If rulers aren't sharp enough, borrow some clean scalpels from the biology teacher. You don't want frog guts all over your classroom.)
This interactive activity helps students visualize what happens when we intersect a plane with a solid. The cross-sections we get can be squares, rectangles, triangles, or circles, and students should be able to link these 2D and 3D shapes to each other. (Now might also be a good time to tell them about conic sections, too.) They can then examine cross-sections of whatever amorphous, amoeba-shaped solids their imaginative little minds can come up with.
While spinning Play-Doh is more trouble than it's worth, you can get some construction paper or index cards to relate the two-dimensional back the three-dimensional. The key is to get students to identify the 3D shape formed when a polygon or circle is rotated along an axis.
If students can visualize these rotations and cross-sections, you've done your job. You might be left with a bit of Play-Doh and paper to clean up, but it's nothing compared to those gutted frogs left for that biology teacher.
Here is a basic video about the 3D Geometry to help refresh your memories.