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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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## 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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## Flying High with the Bird Tetrahedron

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

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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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## 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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## Technology Tips: Exploring Three-Dimensional Worlds Using Google SketchUp

Google SketchUp is free, powerful and widely used Computer Aided Design (CAD) software that can have a transformative impact on the teaching of geometry. This article introduces Google SketchUp to readers through lessons that can be integrated into geometry classrooms and also provides additional resources for readers interested in learning more.

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## Activities for Students: Error Tolerance Formulas Related to Classical Algebra and Geometry

When the diameter of a basketball must be within a certain tolerance, what are the implications for the surface area and volume of the basketball?