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

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### Steven R. Jones

An applied approach to understanding the integral—using a burst pipe—involves physical quantities and helps deepen the concept for students.

### Alison L. Mall and Mike Risinger

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).

### S. Asli Özgün-Koca, Michael Todd Edwards, and Michael Meagher

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

### Dan Kalman and Daniel J. Teague

Using ideas of Galileo and Gauss but avoiding calculus, students create a model that predicts whether a fly ball will clear the famous left-field wall at Fenway Park.

### Yong S. Colen, Channa Navaratna, Jung Colen, and Jinho Kim

The 2000 presidential election provides an ideal backdrop for introducing the electoral voting system, weighted voting, and the Banzhaf and Shapley-Shubik Power Indices.

### Jeffrey J. Wanko, Michael Todd Edwards, and Steve Phelps

The Measure-Trace-Algebratize (MTA) approach allows students to uncover algebraic relationships within familiar geometric objects.

### Rose Sinicrope and Daniel V. Bellittiere

The orbits of planets about the sun and satellites about the earth are elliptical. The shape of the orbit can be described by its eccentricity and can be modeled algebraically and graphically. The exploration of orbits enriches our understanding of the mathematical representations, definitions, and connections for ellipses.

### Sheldon P. Gordon

We tell students that mathematical errors should be avoided, but understanding errors is an important tool in developing numerical methods.