3D Printing Paula Beardell Krieg’s dissected cube shapes

I’ve been thinking about exposing the boys to math through 3d printing lately. Today I decided to explore making Paula Beardell Krieg’s cube shapes with them. Here’s the exploration the boys did back in March when we first got them:

Even though we’ve played a bit with these shapes before I still thought that thinking through these yellow and pink shapes would be a fun challenge. The project turned out to be a tiny bit harder than I thought it would be, but it still was a nice conversation.

We started by first looking at the three pyramids that can come together to make a cube and continued by looking at what happens when you slice those shapes in half.

In the last video the boys were thinking about trying to describe these shapes by describing the lines that formed the edges. At the beginning of this video I told them that this particular approach was going to be tough since they didn’t know how to write equations of lines in 3 dimensions.

So, I had them continue to search for properties of the shapes that they could describe.

The boys were still struggling to find some ideas about the shape that went beyond the lines on the boundary, but we kept looking.

My older son hit on the idea that the shape was made from “stacking squares on top of each other.” We spent the rest of the video exploring that idea.

Now that we had the idea about stacking squares we went to Mathematica to try to create the shape. It took a few steps to move from the ideas about the squares to generating the code for the shape. We didn’t get all the way there during this video, but we did figure out how to make a cube.

Unfortunately I had to end the video since the camera was about to run out of memory.

While I was getting the videos off the camera the boys worked on how to change the cube shape to the pyramid shape. It was a good challenge for them and they got it. We talked about that shape for a bit and then moved on to the challenge of creating the “pink” and “yellow” shapes that Paula Beardell Krieg created from paper.

We had a little bit of extra time today and it was fun to walk through this challenging problem. I think creating shapes to 3d print is a really fun way to motivate math with kids. Can’t wait to use the printed shapes in a project tomorrow!