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## Introducing Roots and Extrema in Calculus

Use cubic polynomial functions before increasing the difficulty with irrational values.

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## Addressing the Standards for Mathematical Practice in a Calculus Class

A two-part calculus activity uses true-false questions and a descriptive outline designed to promote active learning.

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## Delving Deeper: Areas within Areas

Consider the following problem, which was the MT Calendar problem for December 3, 2006:

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## Reader Reflections – November 2012

Readers comment on published articles or offer their own mathematical ideas.

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## Reader Reflections – December 2012 / January 2013

Readers comment on published articles or offer their own mathematical ideas.

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## Ferris Wheel Graphs

To introduce sinusoidal functions, I use an animation of a Ferris wheel rotating for 60 seconds, with one seat labeled You (see fig. 1). Students draw a graph of their height above ground as a function of time with appropriate units and scales on both axes. Next a volunteer shares his or her graph. I then ask someone to share a different graph. I choose one student with a curved graph (see fig. 2a) and another with a piece-wise linear (sawtooth) graph (see fig. 2b).

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## Formative Assessment at Work in the Classroom

Assessment tools–a rubric, exit slips–inform instruction, clarify expectations, and support learning.

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## Strategically Fostering Dynamic Interactive Environments

Student interviews inform us about their use of technology in multiple representations of linear functions.

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## The Joy of Paper Folding

A paper-folding problem is easy to understand and model, yet its solution involves rich mathematical thinking in the areas of geometry and algebra.

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## Instruction and Learning through Formative Assessments

Teachers can use rich mathematical tasks to measure students' conceptual understanding.