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March 2012, Volume 105, Issue 7

FEATURES

Tapering Timbers: Finding the Volume of Conical Frustums
Dustin L. Jones and Max Coleman
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?

Ponderings on Pocket-sized Polyhedra
S. Louise Gould
Pop-up polyhedra—three-dimensional models that can be stored for future reference—are easily constructed using The Geometer’s Sketchpad and give students experience in using transformations in the plane.
Second Look:
Paper Folding for Learning

Discovering the Inscribed Angle Theorem
Matt B. Roscoe
Having prospective teachers find the inscribed angle theorem for themselves can foster mathematical reasoning.

Exploring Conics: Why Does B squared – 4AC Matter?
Marlena Herman
An introduction to definitions and equations of conic sections can be extended to explain the significance of the discriminant.

Exploring Conics: Appendix and Websites

Fostering Spatial vs. Metric Understanding in Geometry
Barbara M. Kinach
More emphasis on spatial reasoning is a way to increase meaning when students study geometry.

Second Look - Paper Folding for Learning

Paper Folding and Conic Sections
How the conic sections can be approximated by paper-folding activities and proves why they work.

Sharing Teaching Ideas: Angle Limit - A Paper Folding Investigation
Students repeatedly fold a sheet of paper in a prescribed manner and discover that the measure of bisected supplementary angles formed by successive folds approaches 60 degrees, regardless of the initial angle chosen.

Is There a “Best” Rectangle?
In trying to find the ideal dimensions of rectangular paper for folding origami, students explore various paper sizes, encountering basic number theory, geometry, and algebra along the way.

Illuminations Lesson: Dividing a Town into Pizza Delivery Regions

Students will construct perpendicular bisectors, find circumcenters, calculate area, and use proportions to explore the following problem:

You are the owner of five pizzerias in the town of Squaresville. To ensure minimal delivery times, you devise a system in which customers call a central phone number and get transferred to the pizzeria that is closest to them. How should you divide the town into five regions so that every house receives delivery from the closest pizzeria? Also, how many people should staff each location based on coverage area?

Representation Standard - Pre-K through Grade 12

Instructional programs from prekindergarten through grade 12 should enable all students to—