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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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LouAnn H. Lovin

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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Tracy E. Dobie and Miriam Gamoran Sherin

Language is key to how we understand and describe mathematics teaching and learning. Learning new terms can help us reflect on our practice and grow as teachers, yet may require us to be intentional about where and how we look for opportunities to expand our lexicons.

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Julie M. Amador, David Glassmeyer and Aaron Brakoniecki

This article provides a framework for integrating professional noticing into teachers' practice as a means to support instructional decisions. An illustrative example is included based on actual use with secondary students.

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Erell Germia and Nicole Panorkou

We present a Scratch task we designed and implemented for teaching and learning coordinates in a dynamic and engaging way. We use the 5Es framework to describe the students' interactions with the task and offer suggestions of how other teachers may adopt it to successfully implement Scratch tasks.

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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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Debasmita Basu, Nicole Panorkou, Michelle Zhu, Pankaj Lal and Bharath K. Samanthula

We provide an example from our integrated math and science curriculum where students explore the mathematical relationships underlying various science phenomena. We present the tasks we designed for exploring the covariation relationships that underlie the concept of gravity and discuss the generalizations students made as they interacted with those tasks.

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Gabriel Matney, Julia Porcella and Shannon Gladieux

This article shares the importance of giving K-12 students opportunities to develop spatial sense. We explain how we designed Quick Blocks as an activity to engage our students in both spatial reasoning and number sense. Several examples of students thinking are shared as well as a classroom dialogue.

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Elizabeth T. Walker and Jeffrey S. Molisani

Multiple entry points on the road to assessing students can tell teachers if students can do math and therefore apply math to real-world problems.

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Janet B. Andreasen and Erhan S. Haciomeroglu

Dynamic software is used to teach geometry, tying into the Common Core's Standard 5, “Use appropriate tools strategically.”