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Ann McCoy, Joann Barnett, and Tammy Stine

Try an activity that was designed to help third graders organize their thinking about rational number notation by connecting to well-established, whole-number routines.

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Edited by Drew Polly

Students' in-depth thinking and work on problems previously published in Teaching Children Mathematics are showcased. The December 2011 problem scenario explores area models and fractions but intentionally avoids using a circular shape, which is the scenario most often drawn on to develop students' fractional understanding. Instead, students cut square “cakes” into fractional pieces.

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Jennifer Suh, Sara Birkhead, Rachelle Romero Farmer, Terrie Galanti, Alexandrea Nietert, Tyler Bauer, and Padmanabhan Seshaiyer

Working with a mathematics coach and university researchers in a K-4 lesson study, teachers increase their understanding of student abilities in a fair-share sandwich problem.

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Each month, this section of the Problem Solvers department showcases students' in-depth thinking and discusses the classroom results of using problems presented in previous issues of Teaching Children Mathematics. The March 2015 problem challenges students to determine how many pizzas they need to order for a class party. During this investigation, students have the opportunity to explore the meaning of division and to examine, compare, and connect additive and multiplicative strategies that may be used to solve this division problem.

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Corey Webel, Erin Krupa, and Jason McManus

Contextual tasks such as the Milk problem and the Cupcake problem can illuminate operations with fractions, but not all visual models align with the standards.

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Lynsey K. Gibbons, Melinda C. Knapp, and Teresa Lind

Why is it so crucial that coaches and teachers concentrate their interactions on students' mathematical reasoning?

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Angela T. Barlow, Alyson E. Lischka, James C. Willingham, and Kristin S. Hartland

A well-crafted opening problem can provide preassessment of students' fraction knowledge and assist teachers in determining next steps for instruction.

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Julie James and Alice Steimle

Each month, elementary school teachers are given a problem along with suggested instructional notes. They are asked to use the problem in their own classrooms and report solutions, strategies, reflections, and misconceptions to the journal audience. This task allows students the opportunity to explore the magnitude of fractions in comparison to different sizes of wholes.

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A cartoon involving whole milk and half and half is coupled with a full-page activity sheet.

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Hagit Sela, Nicole Davis, and Jennifer Hulse

Teachers reflect on how three dialogue protocols can promote meaningful and efficient communication and learning through social interactions.