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Sandra J. Miles

This lesson uses the pH scale to build students’ understanding of the additive identity and inverse. It also gives suggestions for how to extend the lesson to multiplication.

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George J. Roy, Kristin E. Harbour, Christie Martin, and Matthew Cunningham

Using this strategy, a teacher facilitates a short conversation during which students verbally explain and justify reasoning. We have found that a coordinated series of number talks supports students’ reasoning when comparing fractions.

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Josephine Derrick, Joe Champion, and Ramey Uriarte

A new classroom-tested lesson was designed to engage students in the joy of mathematical inquiry through a game, while building number sense, understanding of uncertainty, statistical reasoning, and discourse skills.

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Katherine N. Vela, Michelle Parslow, Rita Hagevik, and Kathy Cabe Trundle

A real-world integrated activity allows middle school students to design a scale drawing for a garden at their school.

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Paula Beardell Krieg

An artist uses graphic tools and circles to illuminate the illusive concept of the golden ratio.

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Blake E. Peterson, Shari L. Stockero, Keith R. Leatham, and Laura R. Van Zoest

Do your students ever share ideas that are only peripherally related to the discussion you are having? We discuss ways to minimize and deal with such contributions.

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Marina Basu, Karen Koellner, Jennifer K. Jacobs, and Nanette Seago

This set of tasks progressively engages students in geometric proportional reasoning.

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Nasim Chenari

This article describes how fortuitous mathematical moments should be noticed, encouraged, embraced, and capitalized upon.

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Katherine Baker, Scott A. Morrison, and Mirella F. Cisneros Perez

Integrating mathematics and nature offers students benefits for physical and mental health and enriches their learning.

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Catherine A. Little, Sherryl Hauser, Jeffrey Corbishley, and Introduction by: Denise M. Walston

From the Archives highlights articles from NCTM’s legacy journals, as chosen by leaders in mathematics education.