Exploring Discrete Mathematics Summary

Monday - Friday, July 16 - 20, 2012

The voting theory group worked on the teacher instructions for the unit along with an instructional PowerPoint. We finalized the student worksheets and project documents. Carl started researching an extension on fair division to add to our unit although he did not finish it.

The group working on discrete dissections for geometry applications, Shaffiq, Aziz, and Carol, continued to work on finishing lesson plans and checked to make sure the dissections worked through doing the dissections physically and researching and thinking about proofs of area and volume. We worked somewhat frenetically to finish our series of 6-7 lessons that can accompany lessons on proof and dissection in the geometry curriculum. Aziz took the lead on the three dimensional shapes, working on rectangular prism dissection of a cube and parts of a triangular prism. Shaffiq worked to develop a student-generated proof of the Pythagorean Theorem, through dissection, and Carol worked to prepare the preliminary lessons on understanding dissection and how it leads to reasoning and proof about how any two two-dimensional shapes with the same area can be dissected into the each other.

The map coloring group worked on the answers to problems in the student worksheets and prepared for the final presentation.

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This material is based upon work supported by the National Science Foundation under DMS-0940733 and DMS-1441467. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.