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## Asked & Answered

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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## Supporting Probability Understanding through Area Models

Moving beyond memorization of probability rules, the area model can be useful in making some significant ideas in probability more apparent to students. In particular, area models can help students understand when and why they multiply probabilities and when and why they add probabilities.

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## Asked & Answered

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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## Linking Factors and Multiples to Algebraic Reasoning

In this paper we illustrate how a task has the potential to provide students rich explorations in algebraic reasoning by thoughtfully connecting number concepts to corresponding conceptual underpinnings.

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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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## Asked & Answered

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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## Is the Last Banana Game Fair?

Is the “Last Banana” game fair? Engaging in this exploration provides students with the mathematical power to answer the question and the mathematical opportunity to explore important statistical ideas. Students engage in simulations to calculate experimental probabilities and confirm those results by examining theoretical probabilities

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## Thinking with Our Hands

Through the use of rich examples, we examine the non-verbal ways in which teachers and students may communicate with one another. We will explore how gesture may be used to clarify and enrich interactions in the mathematics classroom.