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• Author or Editor: Kathleen Cage Mittag
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Activities for Students: As the Ball Rolls: A Quadratic Investigation Using Multiple Representations

Using activities to create and collect data is not a new idea. Teachers have been incorporating real-world data into their classes since at least the advent of the graphing calculator. Plenty of data collection activities and data sets exist, and the graphing calculator has made modeling data much easier. However, the authors were in search of a better physical model for a quadratic. We wanted students to see an actual parabola take shape in real time and then explore its characteristics, but we could not find such a hands-on model.

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Easy Absolute Values? Absolutely

When we ask algebra students to tell us about absolute value, we usually get an answer along the lines of “something that is always positive.” Students immediately question their answer when asked about the absolute value of zero (0). Sometimes our more advanced students say that it has a V-shaped graph or mention the piecewise definition. Despite the varied answers given by our students, seldom do we hear the answer “distance from 0.” However, using distance from 0 is the perfect way to help students understand absolute-value computations. Distance from 0 also provides a foundation for solving equations and inequalities.

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Mathematical Exploration: Tennis Balls, Lines, and Geometric Transformations

Activities that use linear data as a model will help students understand linear functions. In this activity, students collect data and make connections to concepts used in geometry and measurement. Rather than teaching introductory algebra and geometry, this activity is intended to serve as a culminating task to reinforce material already learned.

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Hitting the Bull's-Eye: A Dart Game Simulation Using Graphing Calculator Technology

What do plotting points, making decimal representations, graphing circles, using a random number generator on a calculator, calculating the Pythagorean theorem, studying probability, and throwing darts have in common? We did not know the answer to that question either until we accidentally discovered an activity that incorporates all these elements.

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Sharing Teaching Ideas: Seven Wonders of the Ancient and Modern Quadratic World

After teaching algebra for many years in both high school and college, we noticed that our students were still having trouble understanding the concepts derived from the fundamental theorem of algebra. With the increased emphasis on multiple representations—graphical, numerical, and algebraic, we decided to design a classroom activity that examined solving quadratic equations by using a variety of methods.

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Mathematical Exploration: Mean, Median, or Mode: Which One Is My Pencil?

Methods for finding measures of central tendency are usually taught in middle school. Determination of mean, median, and mode are often presented as rote processes. In addition, graphical representations of data, such as stem-and-leaf and box-and-whisker plots, are also introduced. However, in many instances, no conceptual meanings are associated with the algorithms or graphical methods.