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Beyond Cookies: Understanding Various Division Models

Cindy Jong and Robin Magruder

Build on teachers' and students' understanding of division by emphasizing partitive and measurement models and strategies for writing quality division story problems.

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When the Answer Is the Question

Vanessa M. Battreal, Vanessa Brewster, and Juli K. Dixon

Using donuts to contextualize and enrich mathematical discourse can sweeten students' understanding of how to interpret the remainder in a division problem.

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Firefighters to the rescue

These problems are situated in the context of firefighting to promote problem solving and critical thinking.

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Field day

This department showcases students' in-depth thinking and work on previously published problems. Embedded in the Field Day problem is the big idea of place value. Students explore the scenario of organizing pinnies (scrimmage vests) into bundles of ten, making it easier to distribute them to eight teams participating in a field day.

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Solutions: Firefighters to the rescue

Marie Wright

This department showcases students' in-depth thinking and work on previously published problems. The September 2012 problem scenario helps students build number sense and measurement sense. This problem would make a nice addition to observances Fire Prevention Week (October 6–12).

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Keep on Rollin'

Amanda Sibley and Terri L. Kurz

Here is a simple way to turn an ordinary whiteboard into an interactive tool that allows students to design and build pathways along which a sliding object will flow—within certain constraints—to reach its final destination. Students must reason, conjecture, test, conjecture again, and then retest their design features to determine a solution to the presented investigation.

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A Repeat Look at Repeating Patterns

Kimberly A. Markworth

Working with repeating patterns is important for K–grade 2 students because of the connections they will make in later grades with related mathematical ideas.

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Engaging Teachers in the Powerful Combination of Mathematical Modeling and Social Justice: The Flint Water Task

Julia M. Aguirre, Cynthia O. Anhalt, Ricardo Cortez, Erin E. Turner, and Ksenija Simic-Muller

Two major challenges in mathematics teacher education are developing teacher understanding of (a) culturally responsive, social justice–oriented mathematics pedagogies and (b) mathematical modeling as a content and practice standard of mathematics. Although these challenges may seem disparate, the innovation described in this article is designed to address both challenges in synergistic ways. The innovation focuses on a mathematical modeling task related to the ongoing water crisis in Flint, Michigan. Through qualitative analysis of instructor field notes, teachergenerated mathematical models, and teacher survey responses, we found that teachers who participated in the Flint Water Task (FWT) engaged in mathematical modeling and critical discussions about social and environmental justice. The evidence suggests that integrating these 2 foci–by using mathematical modeling to investigate and analyze important social justice issues–can be a high-leverage practice for mathematics teacher educators committed to equity-based mathematics education. Implications for integrating social justice and mathematical modeling in preservice and in-service mathematics teacher education are discussed.

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The king's really big bowl

Padmanabhan Seshaiyer and Patricia W. Freeman

Each article includes the prompt used to initiate the discussion, a portion of dialogue, student work samples (when applicable) and teacher insights into the mathematical thinking of the students. This month, students are taught the importance of ensuring that their solutions are reasonable. This article describes the creative thinking of a group of students trying to rationalize their unreasonable answer when they meet the Mango problem.

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Halloween treats

This year's solutions to the October 2011 real-life investigation encourage students to apply what they know to a new problem scenario involving how to divide leftover holiday snacks into equal portions. Find the full-size activity sheet at www.nctm.org/tcm, Back Issues.