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October 2007, Volume 101, Issue 3

FEATURES

Ecosystem Simulations and Chaos on the Graphing Calculator
Robb Sinn
An eighth grade algebra class used graphing calculators to simulate ecosystems. One simulation introduced mathematical chaos.The students were able to explore the iteration theory using a graphing calculator. Three classroom-ready worksheets are included. Science connections include equilibrium, and carrying capacity of ecosystem.

Who Will Win? Predicting the Presidential Election Using Linear Regression
John Lamb
Article outlines a linear regression activity that engages learners, uses technology, and fosters cooperation. Students generated least-squares linear regression equations using TI-83 Plus™ graphing calculators, Microsoft© Excel, and paper-and-pencil calculations using derived normal equations to predict the 2004 presidential election. This data-analysis activity supports students by engaging them through meaningful, relevant mathematical experiences.

Creating and Exploring Simple Models
Miles Hubbard
Students manipulate data algebraically and statistically to create models applied to a falling ball. They also borrow tools from arithmetic progressions to examine the relationship between the velocity and the distance the ball falls. A supplemental option is to use a Computer Based Laboratory (CBL) for this activity. Students use graphing calculators to manipulate the sequences (in the statistics editor). Students can plot their data and superimpose their model on the calculator.

Redefining a Model
Thomas Hodges
This article describes an alternate way to utilize a circular model to represent thirds by incorporating areas of circular segments, trigonometric functions, and geometric transformations. Students start activity with pencil and paper, but eventually verify solutions using technology. This task provides opportunities for higher levels of thinking.

Using a Before-During-After (BDA) Model to Plan Effective Secondary Mathematics Lessons
Jane Wilburne, Winnie Peterson
Article describes what a before-during-after (BDA) format is and provides two examples of how it is implemented in high school mathematics classes. Each component of the lesson plans is detailed and explained in order to maximize the students' engagement. Includes a teacher outline for constructing your own BDA lessons.

Read how you can use this article as part of a Professional Development Experience.