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A hands-on approach to studying quadratic functions emphasizes the engineering design process.

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## A Graphic Organizer for Polynomial Functions

Students often view questions about polynomials—finding the zeros of a polynomial function, solving a polynomial equation, factoring a polynomial, or writing a polynomial function given certain properties—as discrete, unconnected processes. To address students' confusion about the many directions given for working with polynomial functions and to enable them to gain a true, conceptual understanding of polynomial functions, I created a graphic organizer (see fig. 1).

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## Media Clips: The Worst Day of the Year? – Chopsticks

Students analyze items from the media to answer mathematical questions related to the article. This month's clips discuss misrepresented formulas.

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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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## 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.

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## Investigating Functions with a Ferris Wheel

A computer activity helps students make sense of relationships between quantities.

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## An Unexpected Influence on a Quadratic

Using technology to explore the coefficients of a quadratic equation leads to an unexpected result.