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LouAnn H. Lovin

Moving beyond memorization of probability rules, the area model can be useful in making some significant ideas in probability more apparent to students. In particular, area models can help students understand when and why they multiply probabilities and when and why they add probabilities.

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Tracy E. Dobie and Miriam Gamoran Sherin

Language is key to how we understand and describe mathematics teaching and learning. Learning new terms can help us reflect on our practice and grow as teachers, yet may require us to be intentional about where and how we look for opportunities to expand our lexicons.

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Christopher Harrow and Nurfatimah Merchant

Transferring fundamental concepts across contexts is difficult, even when deep similarities exist. This article leverages Desmos-enhanced visualizations to unify conceptual understanding of the behavior of sinusoidal function graphs through envelope curve analogies across Cartesian and polar coordinate systems.

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Alyson E. Lischka and D. Christopher Stephens

The area model for multiplication can be used as a tool to help learners make connections between mathematical concepts that are included in mathematics curriculum across grade levels. We present ways the area model might be used in teaching about various concepts and explain how those ideas are connected.

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S. Asli Özgün-Koca and Matt Enlow

In this month's Growing Problem Solvers, we focused on supporting students' understanding of congruence and similarity through rigid motions and transformations. Initial understandings of congruence and similarity begin in first grade as students work with shapes in different perspectives and orientations and reflect on similarities and differences.

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Alyson E. Lischka, Kyle M. Prince and Samuel D. Reed

Encouraging students to persevere in problem solving can be accomplished using extended tasks where students solve a problem over an extended time. This article presents a structure for use of extended tasks and examples of student thinking that can emerge through such tasks. Considerations for implementation are provided.

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Steve Ingrassia and Molly Rawding

Problems to Ponder provides 28 varied, classroom-ready mathematics problems that span grades PK-12, arranged in order of grade band. Links to the problem answers are available in this department.