A few years ago, I encountered two different problems in which the number 3 played surprising roles. I found myself wondering, “Why 3? What's so special about 3?” Further investigation led to continuous extensions involving exponents, logarithms, a parametric equation, maxmin problems, and some history of mathematics. As you read, pause to try the problems and play with the applets (the article's title is a big hint!)

# Search Results

### 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.

### Flor Jacqueline Alarcón Mejía

Algebra, probability, and sequences—all important curricular material—can be connected by a question that will challenge students: What is the probability *P* that the function *f*(*x*) = *x*
^{2} + *rx* + *s* has real zeros when *r* and *s* are real numbers between 0 and 9, inclusive? This problem involves an infinite sample space, making it more interesting for students who have worked on probability problems with only finite sample spaces.

### Heather Lynn Johnson

This article explores quantitative reasoning used by students working on a bottle- filling task. Two forms of reasoning are highlighted: simultaneous-independent reasoning and change-dependent reasoning.

### Becky Hall and Rich Giacin

Tying your teaching approach to the Common Core Standard for Geometry and Congruence will help students understand why functions behave as they do.

### Jon D. Davis

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

### Teo J. Paoletti

This historically significant real-life application of a cryptographic coding technique, which incorporates first-year algebra and geometry, makes mathematics come alive in the classroom.

### G. Patrick Vennebush, Thomas G. Edwards and S. Asli Özgün-Koca

Students analyze items from the media to answer mathematical questions related to the article. This month's clips involve finding a mathematical error in an advertisement as well as working with ratios and proportions.

### Sheldon P. Gordon

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

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