This "Activity for Students" article presents a taxicab geometry problem that engages students in plotting points and observing surprising shapes and underlining reasons for the appearance of figures when working with street grids. With this activity, teachers can provide an extra challenge by writing additional problems introducing a…

What if Stephen Douglas instead of Abraham Lincoln had won the U.S. presidential election of 1860? What if John F. Kennedy had not carried some of the eight states he won by 2 percentage points or fewer in 1960? What if six hundred more people in Florida had voted for Al Gore in 2000? And what if, in that same year, the U.S. House of…

Certain dates stand out in history--October 12, 1492; July 4, 1776; and May 8, 1945, to name a few. Will December 21, 2012, become such a date? The popular media have seized on 12/21/12 to make apocalyptical prognostications, some venturing so far as to predict the end of the world. Scholars reject such predictions. But major archeological finds…

Students frequently have difficulty determining whether a given real-life situation is best modeled as a linear relationship or as an exponential relationship. One root of such difficulty is the lack of deep understanding of the very concept of "rate of change." The authors will provide a lesson that allows students to reveal their misconceptions…

Every two years in the United States, districts in each state elect representatives to the U.S. House of Representatives. The district boundaries are not permanent; rather, they are redrawn every ten years in a process known as redistricting. Mathematics is useful in understanding this important and often contentious process. Redistricting is a…

This article will describe two activities in which students conduct experiments with random numbers so they can see that having at least one repeated birthday in a group of 40 is not unusual. The first empirical approach was conducted by author Cauto in a secondary school methods course. The second empirical approach was used by author Flores with…

The 2012 U.S. presidential election is the perfect opportunity to present a timely civics lesson on how a U.S. president is elected. More important, it offers opportunities for students to reason mathematically about election issues--for example, about how much time and resources the candidates should invest in particular states. The results of…

By working through well-designed tasks, students can expand their thinking about mathematical ideas and their approaches to solving mathematical problems. They can come to see the value of looking at tasks from different perspectives and of using different representations. This article discusses four tasks that encourage high school students and…

This article describes an alternate way to utilize a circular model to represent thirds by incorporating areas of circular segments, trigonometric functions, and geometric transformations. This method is appropriate for students studying geometry and trigonometry at the high shool level. This task provides valuable learning experiences that…

Describes how the concept of similar triangles was taught using an optical method of estimating large distances as a corresponding activity. Includes the derivation of a formula to calculate one source of measurement error and is a nice exercise in the use of the properties of similar triangles. (Author/NB)

Emphasizes the commonalities among classes of polynomial functions. Provides exploratory activities for students as well as a teacher's guide. (KHR)

Presents activities designed to engage students in an experiential and theoretical application of problems in precalculus and to study geometry, coordinate systems, rates, linear applications, and the concept of function. Illustrates problem situations and includes student worksheets and a teacher's guide. (KHR)

Presents a mathematics game appropriate for middle school or high school students that aids in the teaching and understanding of closure properties. (Author/NB)

Uses a probability tree to predict the most likely wild card team for a National League Championship. (KHR)

Describes an instructional sequence that promotes student understanding of a coordinate system while simultaneously facilitating understanding of linear relationships. (Author/NB)