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March 2012, Volume 105, Issue 7

 FEATURES Tapering Timbers: Finding the Volume of Conical FrustumsDustin L. Jones and Max ColemanMany 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 PolyhedraS. Louise GouldPop-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 TheoremMatt B. RoscoeHaving prospective teachers find the inscribed angle theorem for themselves can foster mathematical reasoning. Exploring Conics: Why Does B squared – 4AC Matter?Marlena HermanAn 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 GeometryBarbara M. KinachMore emphasis on spatial reasoning is a way to increase meaning when students study geometry.

 Departments Reader ReflectionsReader Reflections - March 2012 Sound Off!Sound Off!: Learning from Finland: Formative Assessment Media ClipsMedia Clips: Election Campaign Expenses // 100 Percent—Not! Mathematical LensMathematical Lens: Linear Reasoning about Circles Calendar ProblemsCalendar and Solutions - April 2012 Activities (for students)Activities for Students: Filling Bottles with Water Delving DeeperDelving Deeper: Fermat’s Method of Finding Areas under Graphs For Your Information/Products/PublicationsFor Your Information - March 2012 The Backpage: My Favorite LessonThe Back Page: My Favorite Lesson - The Purple Milk Problem

 Second Look - Paper Folding for Learning Paper Folding and Conic SectionsHow the conic sections can be approximated by paper-folding activities and proves why they work. Sharing Teaching Ideas: Angle Limit - A Paper Folding InvestigationStudents 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 RegionsStudents 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 12Instructional programs from prekindergarten through grade 12 should enable all students to—  create and use representations to organize, record, and communicate mathematical ideas; select, apply, and translate among mathematical representations to solve problems; use representations to model and interpret physical, social, and mathematical phenomena.