#MathArtChallenge 91: 3D Cube Cut-Outs

The Challenge: Find some materials that will allow you to create one of those beautiful 3D 3-letter (or shape? Follow your heart) cut-outs. I used a potato.

Materials Needed: Something you can cut up. Potatoes, crafting foam, apples… food, I think would work well here.
Math concepts you could explore with this challenge: angles, geometry, perspective, polyhedra, symmetry

This one was suggested by Sam Shah (although for the life of me I can’t find the tweet suggesting it), and while there are no obvious historical or mathematician connections, I really love how challenging it was to find a way to do this. I thought about legos (don’t have enough at home), did actually try it by cutting foam, but it was suuuuper messy and difficult to see the shadows, and considered cheese to precious (the potato made for good hash browns, I assure you I wasn’t wasteful).

Reflection questions & Math Practices Used:

• The tool I used was a pumpkin carver – what else may work?
• How might your students interpret this activity?
  • What might they do besides just their initials? I used mine: AKP (Anne Kristine Perkins), but what shapes might work?
• Is there anything that wouldn’t work here? Something that’s impossible to carve on the 3 sides/perspectives/orthogonal axes (?) of a cube?

Depending on how you use this activity, you may engage with different mathematical standards. I’ve listed possible connected math content above. Here are a few suggestions for how you might integrate the 8 mathematical practices. Feel free to add your own suggestions in the comments! 

1.) Make sense of problems and persevere in solving them. To get the shadows correctly, I needed to play with 3-D space and engage in how the letter shapes would and would not impact each other.

5.) Use appropriate tools strategically. I’ve been sitting on this math challenge for a while as I perused all the resources I had – it wasn’t until I remembered the pumpkin carving tools (bought probably 6 years ago) sitting in my basement that I was satisfied with what I was able to create. Scissors in foam just didn’t work effectively enough and foam itself was too difficult to carve appropriately.

6.) Attend to precision. To make the letters visible, I needed to design them appropriately so they’d be recognizable after being carved in potato, and so their interactions with each other wouldn’t warp the shapes too much.

7.) Look for and make use of structure. Both in selecting potato and in recognizing the sides of the cube I needed to carve and then in how to twist the carved potato to get the requisite shadows in the correct order.