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The Asked & Answered department shares excerpts from discussion threads on the online MyNCTM community. In this issue, featured threads highlight responses to members' questions related to mathematical depth in preschool, spiral review in the upper elementary grades, ideas for differentiation in middle school, and projects for high school algebra.

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The Asked & Answered department shares excerpts from discussion threads on the online MyNCTM community. In this issue, featured threads highlight responses to members' questions regarding 1st grade number sense, multiplication and division of fractions, issues of definition and precision related to circles, and the value of rationalizing denominators.

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Stefanie D. Livers, Kristin E. Harbour, and Lindsey Fowler

In our attempts to make a concept easier, we may hinder student learning.

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Annie Perkins and Christy Pettis

Students are given a problem to break down rectangles.

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Students use a super-hero theme to compare the imperial system to the metric system.

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Stephen Phelps

Edited by Anna F. DeJarnette

A monthly set of problems targets a variety of ability levels.

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Lingguo Bu

The rise of dynamic modeling and 3-D design technologies provides appealing opportunities for mathematics teachers to reconsider a host of pedagogical issues in mathematics education, ranging from motivation to application and from visualization to physical manipulation. This article reports on a classroom teaching experiment about cube spinning, integrating traditional tools, GeoGebra (www.geogebra.org), and 3-D design and printing technologies. It highlights the rich interplay between worthwhile mathematical tasks and the strategic use of diverse technologies in sustaining sense making and problem solving with a group of prospective teachers.

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P. Reneé Hill-Cunningham

Hundreds of species of animals around the world are losing their habitats and food supplies, are facing extinction, or have been hunted or otherwise negatively influenced by humans. Students learn about some of these animals and explore multiple solution strategies as they solve this month's problems. Math by the Month features collections of short activities focused on a monthly theme. These articles aim for an inquiry or problem-solving orientation that includes four activities each for grade bands K–2, 3–4, and 5–6.

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Sarah A. Roller, Elizabeth P. Cunningham, and Katherine Ariemma Marin

Use photographs as a formative assessment tool.