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Thirteen formulas or one idea? Area, volume, dissections, and proof

Paul Goldenberg
Other Presenter(s): 
Cindy Carter
Other Presenter(s): 
Keith Civin
NCTM Annual Meeting
April 15, 2011

Unify all familiar area and volume formulas, 2- and 3-D, as one versatile idea: scale factor x base x height. Engage in interactive whiteboard and hands-on activities that make this idea intuitive to students. See how these compelling activities can also deceive the eye and mind, motivating proof, through ideas that are accessible in middle school.

Just what is area, anyway? Participants will learn unifying and accessible ideas about measure that introduce middle schoolers to the elegance and interconnectedness of mathematics. They will see how students use dissections and constructions to derive a bucket-load of formulas from one underlying idea that aids understanding of the geometry, bridges and unifies seemingly distinct topics in middle school math, and provides a natural, accessible, and compelling entry into proof for middle school.
Participants dissect plane figures, construct solids from nets, and develop proofs. They also interact with dynamic models using geometry software. Dynamic images on interactive whiteboard give a sense of continuous change, and the way such change affects the various measures (angle, perimeter, area, volume...) applied to a geometric object.