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## Multiple Representations and Connections with the Sierpinski Triangle

A task using multiple representations helps students write explicit algebraic equations.

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## Technology Tips: Teaching Inverses with Technology Is “Sweeeet”

A wonderful experience occurred in a class that I was teaching recently. It was a precalculus class, the last period of the day. The local university had brought over its cadre of preservice secondary school mathematics teachers to observe my class, so there were twenty-four additional eyes on me that day.

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## Using Covariation Reasoning to Support Mathematical Modeling

Table representations of functions allow students to compare rows as well as values in the same row.

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## The Back Page: My Favorite Lesson: Modeling Exponential Decay

Our favorite lesson, an interactive experiment that models exponential decay, launches with a loud dice roll. This exploration engages students in lively data collection that motivates interest in key components of the Common Core State Standards for Mathematics: functions, modeling, and statistics and probability (CCSSI 2010).

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## Connecting Algebra to Economics

Economics can be an avenue for teaching such algebra concepts as graphing curves, writing linear equations, solving systems of equations, and shifting graphs.

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## Connecting Research to Teaching: Linked Representations in Algebra: Developing Symbolic Meaning

Algebra involves negotiating meaning between the worlds of mathematical ideas and the symbols that represent them. Here we examine classroom interactions and explorations as they relate to the connection of these worlds through the use of dynamically connected representations in a technology-rich environment.

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## Connecting Slope, Steepness, and Angles

Students must be able to relate many representations of slope to form an integrated understanding of the concept.

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## Extreme Numbers and Estimation Skills

Using estimation helps increase numerical fluency and gives meaning to large numbers.

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## Spaghetti Sine Curves: Virtual Environments for Reasoning and Sense Making

The Spaghetti Sine Curves activity, which uses GeoGebra applets to enhance student learning, illustrates how technology supports effective use of physical materials.

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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.