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## Fractions: Thinking Beyond the Lines

The implementation of CCSSM helped this teacher think about how to use different representations to help fourth-grade students increase their conceptual understanding of fractions.

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## S'more Fraction Fun

This article presents solutions to the April 2017 problem scenario, which offers students the opportunity to explore many ways to partition a square. Students can generate ideas about halves, thirds, and fourths through the exploration of squares and rectangles. Students can also recognize that equal shares do not necessarily have to be congruent. 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.

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## Common Core confusion about modeling

Share news about happenings in the field of elementary school mathematics education, views on matters pertaining to teaching and learning mathematics in the early childhood or elementary school years, and reactions to previously published opinion pieces or articles. Find detailed department submission guidelines at http://www.nctm.org/WriteForTCM.

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## Techniques for small-group discourse

Different types of instructional facilitation influence students' thinking and reasoning; reflecting on your own practices can help you determine your role as an instructor and increase your competence.

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## When pictures just will not do

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## An Appetite for Fractions

Using candy bars as models gives students a taste for learning to represent fractions whose denominators are factors of twelve.

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## Reflecting on Standards When Lesson Planning

Share news about happenings in the field of elementary school mathematics education, views on matters pertaining to teaching and learning mathematics in the early childhood or elementary school years, and reactions to previously published opinion pieces or articles. Find detailed department submission guidelines at http://www.nctm.org/WriteForTCM.

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## The Unusual Baker

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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## How to Leverage the Potential of Mathematical Errors

Incorporating a focus on students' mistakes into your instruction can advance their understanding.