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

### Kasi C. Allen

In this favorite lesson, students must engage in cooperative problem solving and think outside the algebra box as they work to make sense of the Purple Milk problem.

### Tony Gong and Adam Lavallee

There seems to be a trend toward using creative terminology for mathematical properties and procedures as teachers attempt to engage their students. This short article explores potential issues and concerns related to the use of creative terminology and its effect on students' ability to meet the CCSSI standards of mathematical practice.

### 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.

### 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.

### 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.

### Jon D. Davis

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

### S. Asli Özgün-Koca

Student interviews inform us about their use of technology in multiple representations of linear functions.