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## Developing Multiplicative Thinking from Additive Reasoning

Using the context of restaurants and ratios to find equivalent fractions can push students' strategies forward.

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## Split It! Unpacking the Equipartitioning Learning Trajectory

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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## Solutions: The pizza party

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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## Moving Math in the Write Direction

Use debate journals as an innovative way to encourage your students to construct mathematical arguments as well as examine and critique others' mathematical thinking.

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## Coaching through Focusing on Student Thinking

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

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## Backing up Moving and Forward in Fractional Understanding

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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## Dessert Dilemma

A good problem can capture students' curiosity and can serve many functions in the elementary school classroom: to introduce specific concepts the teacher can build on once students recognize the need for additional mathematics or to help students see where to apply already-learned concepts. We encourage teachers to use the monthly problem in their own classrooms and report solutions, strategies, reflections, and misconceptions to the journal audience.

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## Dots and Squares

Postscript items are designed as rich “grab and go” resources that teachers can quickly incorporate into their classroom repertoire with little effort and maximum impact. This article adapts the classic Dots and Squares game into fun ways to encourage problem solving and computation. Variations include ways to adapt the game to different levels.

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## Solutions: Dessert Dilemma

This department showcases students' in-depth thinking and work on problems previously published in Teaching Children Mathematics. This article discusses solutions to the Dessert Dilemma problem that ran in the August 2013 issue.

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## A fraction feast

Family time in the kitchen can lead to opportunities to explore fractions in real-life circumstances and tap into children's engagement in the harvest season. You might supplement the October problems by setting up a time for your students to talk with a professional chef or event planner about how they use fractions in their jobs.