The kid jumped in enthusiastically. She started by making one cube, no problem. She added on another cube, then two more to make a four-cube base. She built it up a level, and up a level again.
When she was done, thinking toward my goal of tetrahedrons, I casually mentioned she might try a triangle base. After some experimentation she started making this:
It has an interesting twisting quality to it and is my personal favorite of all her 'marshmallow art' pieces.
By this time, dinner was in the oven and I had time to experiment myself. I made a tetrahedron, then attempted a larger one using four tetrahedral units. It was a pretty strong structure, but only after I figured out that if you're going to connect the tetrahedral unit patterns, you need to share the same marshmallow where the vertices make contact. (An aside: Spell check said that is was 'vertexes' instead of 'vertices'. What do you think?)
She worked on another sculpture and then...lo! The girl created a tetrahedron of her own, then played around and discovered, on her own, how to create an octahedron!
The picture below shows all of today's creations. The 'sculptures' which she created first, are in the back row. The geometric/platonic solids, created at the end, are in the front. What's interesting to me, in terms of my daughter's learning process, is that it is more apparent than ever that she really wants to explore and discover new things on her own first and then, when she's had her fill, she comes more easily and willingly toward 'the point' of the lesson.
Whatever you call this afternoon's explorations it was a fun, full hour of inquiry. It was also the first time, except for origami, that I've willingly pushed us into 3D math. I'm learning right along with her, and it's an amazing journey.