My statistics students were especially restless. We're in the middle of our unit on probability. Monday, we looked at some probability word problems. On Tuesday, I wanted to do something fun and interesting but still related to probability. I did a quick google search of probability activities, and I ran across a net of a cuboctahedron. Isn't that just a fun word? Cuboctahedron. Cuboctahedron. Cuboctahedron. It just makes me smile.
The activity instructed students to assemble their own cuboctahedron. (The net is on page 4 of the linked PDF document. I'm also intrigued by the probability activity on page 5 that involves acting out a Russian fable that predicts who will get married within the next year.) Then, they were to toss the cuboctahedron 100 times and count how many times it landed on a square face and how many times it landed on a triangular face.
|Assembled Cuboctahedron and Net Pattern|
|My Class' Finished Cuboctahedrons|
As a class, they decided that 6/14 of the faces were squares. Therefore, the probability of landing on a square face was approximately 0.43. 8/14 of the faces were triangles. Thus, the probability of landing on a triangular face was approximately 0.57. '
|Our Class Data|
My students were intrigued by this data. I'm not sure what the authors' motivation was in writing this activity. Were we supposed to get these surprising results? We had a discussion of the difference between theoretical and experimental probability. What is the reason behind this discrepancy? Is it related to the differing areas of the faces? Or, is it as one student suggested related to the way that the cuboctahedron lands? It often hits on a corner, and when this happens it almost always favors the square faces for landing.
I liked this activity because it got my students thinking and talking about math on a day when they didn't feel like doing any math. It's a rare thing when I give my students a problem I don't already know the answer to. I need to do this more often! Does anyone know more about this perplexing polyhedron probability problem?