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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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## 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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## 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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## Problem: Sharing a Birthday Cake

This month, students are presented with a scenario in which two friends must decide how to cut a cake so they each get the same amount. Students will use transformations and their spatial reasoning to determine various ways to cut the cake. Each month, elementary school teachers receive a problem along with suggested instructional notes and are asked to use the problem in their own classrooms and submit solutions, strategies, and reflections to the journal.

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## Solutions: Family Vacation

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 October 2014 problem scenario offers students an opportunity to divide whole chocolate bars into fractional amounts to gain understanding of the partitioning of a whole into different fractional amounts, on comparing these amounts, and on the ability to develop and defend their thinking.

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## Evidence-Centered Assessment

Comparing two fractions gives a context for exploring students' flexibility with and understanding of mathematical ideas.

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## Line 'em up!

Post Script items are designed as rich “grab and go” resources that any teacher can quickly incorporate into their classroom repertoire with little effort and maximum impact. This article shares ideas for using a clothesline number line to build understanding of number relationships across the elementary grades.

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## Problem: Jesse's Train

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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## Using Math Stations for Commonsense Inclusiveness

To meet diverse student needs, use an approach that is situated in understanding fractions.

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## The Power of Problem Choice

Fourth- and fifth-grade learners can use differentiated number sets within CGI problem structures to add and subtract fractions with unlike denominators.