Thursday, October 20, 2016

Math Circle Updates

This week: They worked on making hexaflexagons of two types. Students were allowed to choose between a simple easy and a complex lengthy flexagon. This link was provided by our teacher and shows how it is done:

 Last week they worked on two puzzle type problems:

 1) Analyzing a real life situation for fusing five pieces of chains of same length (4 links each) to make a circular chain. They discussed the optimal plan and then figured out how to generalize this to any number of chain pieces. What should be the length of each piece? From that they generalized even further to pieces of variable length and the optimal strategy for that situation.

 2) To encourage students to visualize 3-D polyhedra, they worked on a problem related to fusing faces. They fused two cubes, two (regular) tetrahedron, and then one (regular) square pyramid with one (regular) tetrahedron. After students agreed upon the answers, they looked at 2-D projections of these polyhedra. In the end, they talked about the symmetry of a (regular) tetrahedron and ways to work with a tetrahedron.

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