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Connecting Parabolas and Quadratic Functions

In this 3-part activity, students use paper-folding and an interactive computer sketch to develop the equation of a parabola given the focus and directrix.

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How High Is the High?

When visitors enter the High Museum in Atlanta, one of the first pieces of art they encounter is Physic Garden, by Molly Hatch (details in photographs 1 and 2). Physic Garden consists of 456 handpainted dinner plates arranged to form a rectangle with 24 horizontal rows and 19 vertical columns and extends from the floor to the ceiling of the first floor. The design of the “plate painting” was inspired by two mid-18th-century English ceramic plates from the museum's collection (photograph 3).

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The Joy of Paper Folding

A paper-folding problem is easy to understand and model, yet its solution involves rich mathematical thinking in the areas of geometry and algebra.

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Formative Assessment at Work in the Classroom

Assessment tools–a rubric, exit slips–inform instruction, clarify expectations, and support learning.

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Delving Deeper: What's So Special about 3?

A few years ago, I encountered two different problems in which the number 3 played surprising roles. I found myself wondering, “Why 3? What's so special about 3?” Further investigation led to continuous extensions involving exponents, logarithms, a parametric equation, maxmin problems, and some history of mathematics. As you read, pause to try the problems and play with the applets (the article's title is a big hint!)

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Calendar and Solutions – May 2014

A set of problems of many types.

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Technology-Enhanced Discovery

Exploration, innovation, proof: For students, teachers, and others who are curious, keeping your mind open and ready to investigate unusual or unexpected properties will always lead to learning something new. Technology can further this process, allowing various behaviors to be analyzed that were previously memorized or poorly understood. This article shares the adventure of one such discovery of exploration, innovation, and proof that was uncovered when a teacher tried to find a smoother way to model conic sections using dynamic technology. When an unexpected pattern regarding the locus of an ellipse's or hyperbola's foci emerged, he pitched the problem to a ninth grader as a challenge, resulting in a marvelous adventure for both teacher and student. Beginning with the evolution of the ideas that led to the discovery of the focal locus and ending with the significant student-written proof and conclusion, we hope to inspire further classroom use of technology to enhance student learning and discovery.

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Calendar and Solutions – April 2014

A set of problems of many types.

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March 2014 Calendar and Solutions

A set of problems of many types.

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February 2014 Calendar and Solutions

A set of problems of many types.