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## Flying High with the Bird Tetrahedron

An origami activity can lead to rich tasks in several branches of mathematics.

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## Thinking outside the Cube

Mathematical Lens uses photographs as a springboard for mathematical inquiry and appears in every issue of Mathematics Teacher. all submissions should be sent to the department editors. For more background information on Mathematical Lens and guidelines for submitting a photograph and questions, please visit http://www.nctm.org/publications/content.aspx?id=10440#lens.

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## Convex Polyhedra Are Assembled of Pyramids

Volumes of convex polyhedra are determined from constituent pyramids.

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## School's Out–Gone Fishing!

Rational functions and inverse variation underlie questions about fish tanks.

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## Mathematical Lens: Math of Steel for Supermath

The sculpture Synergism, by William Severson and Saunders Schultz, is a stainless-steel structure exhibited in St. Louis (see photographs 1, 2, and 3). It is a series of three nested cubes in which the corresponding faces are parallel. The outer cube is punctured by three overlapping square-based prisms. The vertices of the square base of each prism are located at midpoints of the edges of the outer cube. A second cube attaches within the remaining structure and is similarly punctured, and a third cube attaches within the second and is punctured in the same manner. The outer cube measures approximately 4 meters on each edge. For the purposes of the following problems, we will use 4 m as the edge of the cube.

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## Geometry and the Design of Product Packaging

Simulating a real-world marketing situation, students examine the mathematical calculations that play an integral part in product design.

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## Tapering Timbers: Finding the Volume of Conical Frustums

Many everyday objects–paper cups, muffins, and flowerpots–are examples of conical frustums. Shouldn't the volume of such figures have a central place in the geometry curriculum?

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## A River Runs through Math Class

Let's go wading! Students connect fundamental mathematics concepts in this real-world, problem-solving field experience.

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## Using Disks as Models for Proofs of Series

Students use balls and disks to prove the general formulas for sums of squares and cubes.

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## Reader Reflections – October 2012

Readers comment on published articles or offer their own ideas.