# Week 34: Kirigami

I love paper cutting, so last week I did kirigami with some of my classes. What was so fun about this activity is the amount of play and discovery that happened with two simple supplies (paper and scissors).

Below are the videos I recorded for my classes to be able to go back and work at their own pace. These videos are just a starting place. There are so many methods for folding, cutting, and scoring that can be discovered and explored. My son made dioramas of forests and landscapes that fold with his creations. If you like pop-up books, this is a great place to start.

# Flipping Origami Class Video

After teaching this a few times this week, I created a video for those that missed it or want to go back. We made two different origami toys that have some flipping fun. Feel free to contact me if you have any questions.

# Week 11: Soma Cubes

I love Martin Gardner’s work and books that brought math to so many people in a fun and engaging way. One of the topics he covered was Soma Cubes. This week learners can create and play with this wonderful seven piece puzzle that was invented by Mr. Piet Hein during a lecture on physics. I love this puzzle because there are so many questions to ask and ways to solve it. There are a few options for creating your own:

Option 1: Wooden cubes

I ordered wooden cubes and found they aren’t perfect, but do the job with students. You can get them at craft stores or amazon (affiliated link).

Option 2: Sonobe Origami

You can make a Soma cube with a lot of folding. I would recommend doing this with teams and older students (or as an adult). The folds need to be exact. That being said I have seen 9 and 10 year olds do beautiful origami Soma cubes. The best tutorial that I was able to find is on the Luck Paper Scissors Blog here.

Here are some questions/exercises:

• How many unique ways can you solve it? Is there a systematic way to track your solutions?
• Are there combinations that will never have solutions (ex: starting with one or two pieces in a particular way)
• What other symmetric constructions can you create?

One of the coolest links to all of the solutions I have found is here on GeoGebra by Michael Borcherds.

Another unique page devoted to Soma is here.

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# Week 4: Polyhedra Study

Leonardo da Vinci was an amazing mathematician, inventor and artist. His sketches in The Divine Proportion are a wonderful collection to study. Spacial awareness and being able to draw what we see is a skill that can be mastered through practice.

This week, I encourage learners to sketch polyhedra from cubes to tetrahedrons to dodecahedrons. Use charcoal, pencils or watercolors to create works of art. You can model with clay, paper, glue and sticks, or building toys and then sketch. Play with various forms of lighting and shading. Move beyond the numbers this week and look for math in the objects/polyhedra around you.

You can combine this study with history and architecture. Go out and look for polyhedra around you. Can you make a pyramid scene? What is a soccer ball? What is the shading like at different times of day for a favorite building? Are there planes of symmetry for your sketch? How many vertices are there?

# Week 3: Sonobe Octahedron

Octahedrons are such a fun shape. This week we are going to learn an important fold in origami that can be used to make so many mathematical shapes, puzzles and works of art. We are going to learn Sonobe. Below is a video of how to create the basic fold and then assemble the octahedron. You will need 12 sheets of origami paper. I have done this project with 7yrs and up. My high school students have folded in teams to make larger polyhedra. In future weeks we will be making other structures and sonobe will be an option.

The best resource for Sonobe I have found is here: https://www.amherst.edu/media/view/290032/original/oragami.pdf