Friday, January 6, 2012

Marshmallow Math: Solids & Sculpture

Given my daughter's resistance to formal lessons, it really was the perfect storm.  A supervised math activity of new concepts thinly disguised as 'something to do while mama makes dinner'?  Yes, please!

It came about as a sort of semi-premeditated accident: It was time to get dinner ready and there was a lot of prep work to it.  I had the mini-marshmallows and toothpicks at the ready, as well as buy-in from the kid who had seen this post of the amazing, huge, Serpinski-esqe giant tetrahedron built by the kids at Almost Unschoolers the day before.

I laid out some newspapers on the kitchen floor and poured the marshmallows into one bowl, the toothpicks into another.  Completely off the cuff I said, "Here's how you can make a square base, and then build up from there."  I built about one half of a cube and then said, "I really want to make tetrahedrons, but I don't have time now.  See what you can do."

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. 

"I'm an artist!  I'm making a sculpture!  Let's put these piece under glass, like in a museum. It's marshmallow art."  Despite this enthusiastic chatter she was actually a little worried that the kids at Almost Unschoolers would be mad at her for copying their work. This led to some conversation about copying vs. learning the basics so you have the skills to express your own personal vision, and then, thankfully, our attention was diverted. 

The tower/sculpture of cube units started to lean. 

These marshmallows are tricky!  The kids at Almost Unschoolers made it look easy, but it's not!  There are all sorts of structural problem solving challenges to overcome. I suggested turning her 'sculpture' on its side (pictured below) so it would be a little more sturdy.  We counted how many cube units made the structure.

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.


  1. Very, very cool! Please assure your daughter she has complete permission from the kids at Almost Unschoolers to copy away, anytime :)

  2. (Vertices it is. Bad spell-checker.)

    Sounds like a great time. If I buy those mini-marshmallows, my son will eat them before he's done much construction. But I might still have to do it now... (When next I make it to a conventional grocery store...)

  3. Hey Sue!

    Thanks for checking! Re: marshmallows, two things:

    1. I got mine at our co-op. They were still full of sugar, but somehow I felt better about it, lol! And, miraculously I was able to keep the kid from eating more than 10 or so

    2. You can also use little clay balls, but not playdoh, for the same purpose. Color!!

    One thing I didn't mention was that I had an epic failure of my own. I had the bright idea to try a solid with a pentagon which, as you know, can turn into a dodecahedron. The marshmallows were not strong enough, and hilarity ensued! I think I'll try again with clay balls.

  4. I just love this Malke. You know I recently started homeschooling and my son has been somewhat resistant to math because all they did in p.s. was worksheets. I'm using Math-U-See to give him a variety of input and that is helping. But I came to see what inspiration you could give me to help him. And I love this!!

  5. I'm so glad my stories are helpful to you, Julie! I've received a lot of inspiration myself from the math sites,, the Living Math Yahoo forum,,, and Enjoy your journey!

  6. Malke, the funniest thing happened. I dragged my son with me to a math and social justice workshop yesterday. As we left the high school classroom it was held in, he saw a mini-marshmallow structure in the garbage can. I asked if we should do that. He said "No, I'd eat them."


Thanks for reading. I would love to hear your thoughts and comments!


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