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Thomas E. Hodges, Terry D. Rose, and April D. Hicks

A series of diagnostic questions helps this teacher better assess and comprehend the misconceptions of third graders who struggle with multiplication.

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Lynn Columba

It is a “read”-letter day when storybooks, thinking strategies, and physical materials can use a splash of whimsy and fun to introduce multiplication facts to third graders.

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Ellen Robinson, Xiaowen Cui, Hiroko K. Warshauer, and Christina Koehne

Collaborative engagement provides an opportunity for students to construct and solidify their own knowledge and understanding of important mathematical ideas. According to Van de Walle, Karp, and Bay-Williams, “learning is enhanced when the learner is engaged with others working on the same idea” (2015, p. 52). In allowing students to work with their peers to practice problems and construct important mathematical connections, the students build on their combined prior knowledge to formulate newfound ideas and conjectures. We recognize that grouping students so that each group will function in a productive manner can often be difficult. Therefore, we have devised this activity that allows students to work together and communicate with ten different students individually. In a usual group setting, the students would get to work with one or two other students, but the format of this activity allows for more forms of mathematics communication and collaboration.

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Sandra Davis Trowell

Edited by Denise Taunton Reid

The Teaching and Learning principle in Principles to Actions: Ensuring Mathematical Success for All (NCTM 2014) states,

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Stephanie Sluyter

This month's problem offers students an opportunity to determine where we find math in the world, interpret it, and engage in mathematical modeling. Each month, elementary school teachers are presented with a problem along with suggested instructional notes and asked to use the problem in their own classrooms and report solutions, strategies, reflections, and misconceptions to the journal audience.

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New Jersey sixth graders who were participating in a school fundraiser to help fight childhood cancer could hardly wait to explore this problem from the September 2011 issue, which invites students to work strategically with combinations of numbers. Afterward, their teacher reflected that so many available activities claim to be authentic learning activities but require little in-depth problem solving. This one does.

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Chrystal Dean

This variation of Simon's (1995) rectangle exploration will have students investigating area in a conceptual manner that goes beyond tiling and formulas. Each month, elementary school teachers are given a problem along with suggested instructional notes; are asked to use the problem in their own classrooms; and are encouraged to report solutions, strategies, reflections, and misconceptions to the journal audience.

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Jennifer R. Brown

Set sail to explore powerful ways to use anchor charts in mathematics teaching and learning.

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The May problem scenario has students explore what happens to the area of a two-dimensional shape as the side dimensions change but the perimeter remains the same. A fourth-grade teacher from North Carolina explored the task and uncovered her students' misconceptions concerning the corner tiles of the rectangle.

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Edited by Colleen D. Foster

Each month this section of the Problem Solvers department features a new challenge for students. Readers are encouraged to submit problems to be considered for future Problem Solvers columns. Receipt of problems will not be acknowledged; however, problems selected for publication will be credited to the author. Find detailed submission guidelines for all departments at