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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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## Envelope Curves Unify Sinusoidal Graphing

Transferring fundamental concepts across contexts is difficult, even when deep similarities exist. This article leverages Desmos-enhanced visualizations to unify conceptual understanding of the behavior of sinusoidal function graphs through envelope curve analogies across Cartesian and polar coordinate systems.

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## Now: The Metamorphosis of the Educational World

“It's a YouTube World” (Schaffhauser, 2017), and educators are using digital tools to enhance student learning now more than ever before. The research question scholars need to explore is “what makes an effective instructional video?”.

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## Using Scratch Programming to Explore Coordinates

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 Innovative Impact of NCTM Journals

NCTM has provided rich resources through the publication of practitioner journals for decades and is now leading the way once again with a digital first dynamic publication focused on the learning and teaching of mathematics. This is a rich opportunity for teachers to engage, to learn and to go.

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## Quick Blocks: Developing Spatial Sense

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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## Driving Students to Performance Assessments: Learning What Students Can Do

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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## Sharing Cookies: A Case Study

Gain insight into students' understanding of the concept of fraction as operator as well as their reliance on rote procedures to convert fractions to decimals.

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## Open-ended Questions and the Process Standards

Educating students—for life, not for tests—implies incorporating open-ended questions in your teaching to develop higher-order thinking.

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## Quick Reads: Journaling: Out with the Old

### a good idea in a small package

Students' writings in math class can be used for both reflection and assessment.