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March 1999, Volume 92, Issue 3


Exploding the Ellipse
Arnold Good
Readers are advised to proceed with caution. Those with a weak heart may wish to consult a physician first. What we are about to do is explode an ellipse. This risky business is not often undertaken by the professional mathematician, whose polytechnic endeavors are usually limited to encounters with administrators.

Extending a (TIMSS) Japanese Lesson Using Trigonometry
David Pagni, Harris Shultz
One of the Japanese mathematics lessons reported in the Third International Mathematics and Science Study (TIMSS) involves the concept of the area of a triangle. On the first day, students explore the area of triangles obtained by using the same base but translating the vertex opposite the base along a path parallel to the base, thus keeping the height constant. The next day the students are reminded of that property and are given a challenging problem that applies the property.

The Recurring Fibonacci Sequence: Using a Pose-and-Probe Rubric
Kenneth Shaw, Leslie Aspinwall
As amateur Fibonacci explorers, we have investigated a known problem involving the Fibonacci sequence and tried our hand at extending it. Not only have the explorations been fun, they have been mathematically rewarding. In this article, we share some explorations and then furnish several problems for further investigation.

Who's Winning at Monopoly Junior?
Donald Hooley
A "real" problem for many students with younger siblings, in the spirit of the NCTM's Curriculum and Evaluation Standards for School Mathematics  (1989). This article also illustrates the use of modeling and simulation, which Burrill (1997) notes that mathematicians in industry report using more than any other content area.

The Big Loser
Daniel Marks
The identity of the team in greatest jeopardy of becoming the big loser is the subject of this article. This article explores several facts about the big loser, offering them in a hierarchy that may be appropriate for creating various short- and long-term projects for a high school mathematics class.

Preparing Students for Modern Work: Lessons from Automobile Manufacturing
John Smith III
Take the mathematics that you find back to school. With a bit of adaptation, mathematical work can generate real-life problems and projects for your students.

Fractals in High School: Exploring a New Geometry
Randi Lornell, Judy Westerberg
A brief description of fractals and their characteristics, some examples from our unit, and an argument about the reasons for including fractals in the mathematics curriculum.