The choice and context of authentic problems—such as designing a staircase or a soda can—illustrate the modeling process in several stages.

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### Erik Jacobson

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

### Sonali Raje, Michael Krach, and Gail Kaplan

Stereochemistry and three-dimensional analysis constitute significant parts of this student activity.

### Ron Lancaster

Students analyze items from the media to answer mathematical questions related to the article. This month features two news clips on a lottery winner; the mathematics involved includes probability and combinatorics and some locus problems.

### Amy L. Nebesniak

When it comes to student achievement, teachers and instruction matter most.

### Patrick Kimani and Nicole Engelke

In a new approach, rate problems—the bane of students—can connect to higher-level concepts.

### Martin Griffiths

Two seemingly unrelated problems—one posed to a class of eighth graders, the other posed to a class of high school juniors—uncover a connection through Stirling numbers of the second kind.

### Douglas Wilcock

Can you imagine riding a tricycle with square wheels? Can you imagine that this tricycle would give you as smooth a ride as a traditional tricycle? A *New York Times* article (Chang 2011) described a tricycle that had square wheels but that could be ridden “smoothly around a circular path ridged like a flower's petals.” It then explained that the ridged surface on which the tricycle rode undulated such that “the tricycle's axles—and the rider—remain in the same height as they move.”

### 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.

### Dick J. Smith and Eric F. Errthum

Many mathematics instructors attempt to insert guided exploration into their courses. However, exploration tasks frequently come across to students as contrived, pertinent only to the most recently covered section of the textbook. In addition, students usually assume that the teacher already knows the answers to these explorations.