Connecting with Mathematics

What is Mathematical Investigation?
Dissections and Area
Linearity and Proportional Reasoning
Pythagoras and Cousins
Pascal's Revenge: Combinatorial Algebra
Games and Number Theory

Dissections and Area

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The Dissections and Area module provides a new approach to learning and teaching area, perimeter, and volume. Participant teachers rethink the concept of area through hands-on activities that involve the dissection and rearrangement of various geometrical figures. Using dissections, they see various proofs of the Pythagorean theorem and refine their concepts of similarity, congruence, recursive thinking, elements of number theory, and fractals. This module illustrates connections between graphs, vectors, coordinate geometry, and geometrical transformations. Interesting applications, such as tesselations of the plane, origami as a dissection, tangrams, jigsaw puzzles, and triangulations of the earth are discussed.

This module also includes an opportunity for teachers to investigate student thinking via a discussion of student work on problems from new standards-based curricula.

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