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Ron Lancaster

Students analyze items from the media to answer mathematical questions related to the article.

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R. Alan Russell

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.

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Doug Wilcock

“Mathematical Lens” uses photographs as a springboard for mathematical inquiry and appears in every issue of the 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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Laurie H. Rubel, Haiwen Chu, and Lauren Shookhoff

Maps at four levels of scale—global, national, regional, and local—provide a context for mathematical investigations that help teachers learn about their students.

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Doug Wilcock

Students analyze a photograph to solve mathematical questions related to the images captured in the photograph. This month, two differently shaped soda containers are compared. Volumes, including volumes of revolution, are computed.

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Gloriana González and Anna F. DeJarnette

An open-ended problem about a circle illustrates how problem-based instruction can enable students to develop reasoning and sense-making skills.

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Michael J. Bossé and Kwaku Adu-Gyamfi

A geometry course for teachers—easily adaptable to a high school geometry class—integrates technology, reasoning, communication, collaboration, reading, writing, and multiple representations.

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Zhonghong Jiang and George E. O'Brien

Using technology to explore the Three Altitudes of a Triangle problem, students devise many proofs for their conjectures.

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A set of problems of many types

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Irina Lyublinskaya and Dan Funsch

Symbolic geometry software, such as Geometry Expressions, can guide students as they develop strategies for proofs.