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## Exploratory Writing to Support Mathematical Sense Making

A teacher implements this type of personal prose in the classroom to help students make sense of fractions and communicate ideas.

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Each month Asked & Answered highlights selected threads from the MyNCTM community. MyNCTM is an online community where NCTM members can ask questions, start and join discussions, and interact with education experts. We encourage you to join the conversation at https://my.nctm.org.

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The Asked & Answered department shares excerpts from discussion threads on the online MyNCTM community. In this issue, featured threads highlight responses to members' questions related to mathematical depth in preschool, spiral review in the upper elementary grades, ideas for differentiation in middle school, and projects for high school algebra.

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## Modeling a Bouncing Ball with Exponential Functions and Infinite Series

We modify a traditional bouncing ball activity for introducing exponential functions by modeling the time between bounces instead of the bounce heights. As a consequence, we can also model the total time of bouncing using an infinite geometric series.

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The Asked & Answered department shares excerpts from discussion threads on the online MyNCTM community. In this issue, featured threads highlight responses to members' questions regarding 1st grade number sense, multiplication and division of fractions, issues of definition and precision related to circles, and the value of rationalizing denominators.

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## Creating Joy in PK–Grade 2 Mathematics Classrooms

Children experience joy in well-designed mathematics classrooms. This article describes five research-based practices for bringing joy into PreK-Grade 2 math lessons.

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## Riding the RAFT

Writing about mathematics holds a wealth of benefits for students. When students are given opportunities to write in math class, it helps develop mathematical thinking and language (Carter 2009; McCarthy 2008; Yang 2005), encourages self-reflection (Carter 2009; Danielson 2010; O'Kelley 2013), and provides a better way to organize ideas (Linhart 2014; Rogers 2014). Many teachers incorporate journaling and other types of reflective writing into their instruction already (Sjoberg, Slavit, and Coon 2004; Sanders 2009), but what about other forms of writing? NCTM states the importance of writing, in that students in the middle grades should be “more explicit about basing their writing on a sense of audience and purpose” (NCTM 2000, p. 62). How can we help students develop this important skill in math class?.

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## Conceptualizing Mathematics Using Narratives and Art

To support mathematical investigations, use this framework to guide students in constructing art-based and technology-based literature.

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## Learning to Write about Mathematics

This student-friendly rubric helped improve third graders' competencies when explaining solution strategies in writing.