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## Constructed-response problems

This department publishes brief news articles, announcements, and guest editorials on current mathematics education issues that stimulate the interest of TCM readers and cause them to think about an issue or consider a specific viewpoint about some aspect of mathematics education.

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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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## Flipped Learning: Embedding Questions in Videos

Use math videos and different types of inquiries to increase students' intellectual engagement.

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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.

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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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## Can Kindergartners Do Fractions?

Do prekindergarten students describing and illustrating their attempts at fair-sharing tasks exhibit a spontaneous understanding of fractions prior to formal instruction? This researcher shares her findings.

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## Solutions: Fall Festival Fun

The problem scenario from October 2012 engages students in simple permutations along with finding the probability of an event. Two sixth-grade teachers report on the seasonal, open-ended, authentic learning that their students experienced with a scarecrow-dressing contest.

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## Paper Plate Fractions: The Counting Connection

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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## 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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## 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.