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!)
Debra K. Borkovitz
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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