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## Puddle Play!

For the Love of Mathematics

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## Student Engagement with the “Into Math Graph" Tool

We introduce the Into Math Graph tool, which students use to graph how “into" mathematics they are over time. Using this tool can help teachers foster conversations with students and design experiences that focus on engagement from the student’s perspective.

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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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## 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 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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## Authenticity of Mathematical Modeling

The choice and context of authentic problems—such as designing a staircase or a soda can—illustrate the modeling process in several stages.

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## Working the System

Two teachers discuss the planning and observed results of an introductory problem to help students nail a conceptual approach to solving systems of equations.

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## Students as Mathematics Consultants

Five problems—relating to gas mileage, the national debt, store sales, shipping costs, and fish population—require students to use functions to connect mathematics to the real world.

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## Equivalence Relations across the Secondary School Curriculum

An analysis of problems from state assessments and other sources helps preservice teachers discover analogous mathematical representations.