We had a nice emergence today in class. We were practicing the habit of pattern sniffing. Everybody has been assigned a 3D shape and they are trying to become experts in that shape. Today, they started to count the vertices, edges and faces. When we got around to the cone, a disagreement arose.
How many faces does a cone have?
Some students said 1, others said 2. Same problem with a sphere. How can something have no faces? It must have one, right? We switched courses and started to conjecture. A conjecture is a theory that you have before it has been tested. It is like a hunch, it hasn't been proven. We wrote three statements on the board and each child filled out their responses.
1) I think a sphere has _ faces because....
- 1 face because I feel something, so there must be a face
- 0 faces because faces are flat
- 0 faces because it rolls, and things with faces cannot roll
- 0 because a 2D circle has a face, but a 3D circle is not made out of 2D shapes
- 1 face because there can't be nothing
2) I think a cylinder has _ edges because...
- 2 edges because it is not smooth
- 2 edges because a circle needs an edge
- 0 because I can't see any points
3) I think a cone has _ vertices because...
- 1, because I can touch the sharp part
- 1, because there is only one pointy part
- 0, because there are no straight lines, and vertices are only on straight lines
- 6, because there are shapes inside that make the cone round
- 1, because a vertex is a point and it can't be round
Great conjectures. We need to investigate further. Where should we go next? I was thinking of consulting an expert....