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Deep thinking and real fun with vertices, edges, and faces

Other Presenter(s): 
Tracy Manousaridis
Other Presenter(s): 
Michelle Crandell
Meeting: 
NCTM Annual Meeting
Date: 
April 15, 2011
Location: 
Indianapolis

Ever wonder what there is to do with this vocabulary other than know it? Build polyhedra from nets and see how children can have fun deepening their understanding of geometry as they discover and PROVE surprising facts about prisms and pyramids by counting vertices, edges, and faces.

Participants will develop a new image of the fascinating mathematics of prisms and pyramids by building a wide variety of paper models of non-standard polyhedra and discovering and investigating several patterns that are very accessible to children. Participants will also create intriguing exceptions to the patterns they’ve found, getting a glimpse at some deep ideas from topology, and will take home classroom-tested ideas—including all nets—for doing these activities with their students.
From observation and then from reasoning, 4th/5th graders can see that a prism with a n-gon for a base has V = 2n (total vertices = twice the vertices of the base), E = 3n, and F = n + 2. So V − E + F = 2n − 3n + (n + 2) = 2 for all prisms. Similar observation and reasoning shows that V − E + F = 2 for pyramids, as well. Children love the discovery, and the ideas are deep.