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## Learning What Works: Promoting Small-Group Discussions

Elicit productive discourse from students as they work through a bicycle rate problem.

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## GPS: Rewriting Quantities and Expressions

.7.EE.A.2 Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. CCSS.MATH.CONTENT.HSA.SSE.A.2 Use the structure of an expression to identify ways

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## Coordinate an Attack Using the Calculator

Teachers using these graphing tasks experienced engagement in understanding the need for the coordinate system.

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## Math For Real:The Half-Lives of Medicines

### when will I ever use this?

Calculating a half-life, the approximate time it takes for the body to remove one-half the active ingredient in a medicine, provides the real-life tie-in to this activity.

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## A Framework for Computational Thinking Dispositions in Mathematics Education

This theoretical article describes a framework to conceptualize computational thinking (CT) dispositions—tolerance for ambiguity, persistence, and collaboration—and facilitate integration of CT in mathematics learning. CT offers a powerful epistemic frame that, by foregrounding core dispositions and practices useful in computer science, helps students understand mathematical concepts as outward oriented. The article conceptualizes the characteristics of CT dispositions through a review of relevant literature and examples from a study that explored secondary mathematics teachers' engagement with CT. Discussion of the CT framework highlights the complementary relationship between CT and mathematical thinking, the relevance of mathematics to 21st-century professions, and the merit of CT to support learners in experiencing these connections.

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## CCSSM Challenge: Graphing Ratio and Proportion

A Cherry Syrup problem can build links between ratio and graphing.

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## Tracking Trout: Engaging Students in Modeling

After months of solving real-world problems, high school students enact the full modeling cycle supported by peers, teachers, and technology.

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## Tiling the Cube

The Tiling Tubs task is a middle school activity published in NCTM's Navigating through Algebra in Grades 6-8. Students examine a drawing that shows a square hot tub with side length s feet. A border of square tiles surrounds the tub, with each border tile a 1-foot square. Students determine the number of border tiles required to surround the tub and express that number in as many ways as they can, thereby creating various equivalent algebraic representations. A valuable component of Tiling Tubs is its requirement that students contextually justify their algebraic representations. Students also realize that more than one correct representation and justification exists.

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## Informing Practice: Mathematical Practices That Promote Twenty-First Century Skills

Skills that students will need in the twenty-first century, such as financial literacy, are explored in this classroom-centered research article.

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## Solve It! Student Thinking: Aunt Martha's Cupcakes

### big solutions to little problems

Solutions to a February 2013 Solve It! problem are discussed, and the procedures used with problem solving are explored.