Bringing Joy – President’s Message December 2022

When was the last time you planned a classroom activity to promote the joy and beauty of mathematics? I have always loved origami. It brings creativity and artistic expression to mathematics. This month, I am going to share my favorite activity with you. This activity is inspired by the work of Tomoko Fuse (his book “Unit Origami: Multidimensional Transformations” is phenomenal).

This activity builds an example of modular origami using sonobe units. One version of directions for folding a basic unit is here: bit.ly/3V08BmE. There are alternate versions that add extra folds for design embellishment.

To build a solid, you need to start with squares of paper and fold each one as precisely as possible following the unit directions. Origami paper is great, but this works well with squares cut from colorful copy paper (I get neons and bold colors). With younger students, 5.5” squares are probably best. I tend to use 4.25” squares with my high school students. You can get the paper laser cut at an office supply store (probably more accurate than the 30-year old paper cutter in your workroom).As you fold each piece, make crisp folds and creases.  Once all the pieces are made, you are ready to assemble your solid.

The simplest version of a completed solid uses 6 units and builds a cube. My favorite is a stellated octahedron which uses 12 units. Either 4 colors (3 pieces each) or 3 colors (4 pieces each) make nice patterns. If you are feeling ambitious, 30 units builds a stellated icosahedron.

To assemble your solid, points from one unit gets tucked into the cross of another unit. The best way to learn is to watch a YouTube of the process, so you can pause and rewind. There are dozens of good videos available.

This is typically a two-day activity for my classes. Folding on Day 1 and assembling on Day 2. Once a few students have their solid assembled, they can help others. In geometry classes, I use this project at the end of the unit on solids. Follow up questions that you can ask: How many faces, edges and vertices are in the completed solid? What is the surface area of the solid? What is the volume of the solid? I have it planned for December 21-22 this year.

And speaking of bringing joy, Spring Conference registration is open! See the article in MathBits for the live link.

Karen Hyers
MCTM President