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## Quick Reads: Using Technology to Build a Pen for Browser

### a good idea in a small package

Making mathematics meaningful is a challenge that all math teachers endeavor to meet. As math teachers, we spend countless hours crafting problems that will energize students and help them connect mathematical topics to their everyday lives. Being successful in our efforts requires that we allow students to explore ideas before we provide explanations and demands that we ask questions to promote a depth of thinking and reasoning that would not occur without such probing (Marshall and Horton 2009).

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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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## An Unexpected Influence on a Quadratic

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

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## Delving Deeper: Chordic vs. CORDIC: How Calculators and Students Compute Sines and Cosines

Students who have grown up with computers and calculators may take these tools' capabilities for granted, but I find something magical about entering arbitrary values and computing transcendental functions such as the sine and cosine with the press of a button. Although the calculator operates mysteriously, students generally trust technology implicitly. However, beginning trigonometry students can compute the sine and cosine of any angle to any desired degree of precision using only simple geometry and a calculator with a square root key.

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Interesting solutions and ideas emerge when preservice and in-service teachers are asked a traditional algebra question in new ways.

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## Investigating the Effects of Parameters on Quadratic Functions

Technology is in a constant state of flux. As a result, if we seek to use the latest forms of technology in our teaching, our teaching with technology must be ever changing. Edwards and Özgün-Koca (2009) describe an investigation involving the TI-Nspire CAS to understand the effect of b on the graphical representation of a quadratic function of the form f (x) = ax2 + bx + c. Adapting this idea, I show how updates to technology can enhance this investigation to create an even more motivating and compelling experience for students. The investigation will make use of sliders and the spreadsheet capability of the TI-Nspire (the directions provided here apply to the TI-Nspire CX CAS).

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## Using Radioactive Decay to Investigate Exponential Functions

During the thirteen years that I taught high school physics and mathematics, I found that my physics students typically came to class excited to learn. As in all science classes, they interacted with fellow classmates while performing laboratory investigations and other group activities requiring higher-order thinking skills. To create a similar experience for my mathematics students, I developed a laboratory investigation for my precalculus class. These students responded just as favorably as my physics students to hands-on data collection activities.

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## Exploring Conics: Why Does B 2 – 4AC Matter?

An introduction to definitions and equations of conic sections can be extended to explain the significance of the determinant.

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## A Natural Approach to the Number e

Building on prior knowledge of slope, this approach helps students develop the ability to approximate and interpret rates of change and lays a conceptual foundation for calculus.

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## The Shape of an Ellipse

Ellipses vary in shape from circular to nearly parabolic. An ellipse's eccentricity indicates the location of its foci, but its aspect ratio is a direct measure of its shape.