Activities on Special Topics:

 

This section lists books and modules which each give activities related to one special topic. The activities can usually be integrated into a wide variety of courses, on many levels.

The Mathematician's Coloring Book   (Module, 4-10)
Richard L. Francis; COMAP, HiMAP Module 13, 1989; $12. This entertaining unit, developed around the Four-color Theorem, is especially appropriate for general math or geometry students. It includes maps, pictures, and worksheets to explore map coloring (which have been used in the LP K-8 programs). Many of the coloring activities are appropriate for young students. At the end there are challenging problems on coloring maps on doughnut-shaped and other surfaces, suitable for advanced students.

Drawing Pictures with One Line: Exploring Graph Theory  
(Module, 4-10)
Darrah Chavey; COMAP, HistoMAP Module 21, 1992; $12.

This popular module introduces Eulerian tours and other topics. Here is an excerpt from a teacher's review [29]:

[The book takes the reader] through the historical beginnings of graph theory as recreational puzzles, to the array of applications for which graph theory is used today. Included are multicultural aspects of graph theory as it exists in cultures in Africa and Oceania as part of a heritage of sophisticated story-telling.

Problem Solving Using Graphs   (Module, 6-10)
Margaret B. Cozzens and Richard Porter; COMAP,
HiMAP Module 6, 1987; $10.

This is an excellent source of problems on a variety of graph topics, including Eulerian tours, shortest paths, minimum spanning trees, and the Traveling Salesperson Problem. The problems can be used for teaching modeling, problem-solving, or algorithm design. Many of these problems have been used successfully in the Leadership Program, and subsequently by the participating teachers when they return to their classrooms.

Fractals for the Classroom: Strategic Activities   (Workbook, 7-12 )
Heinz-Otto Peitgen, Hartmut Jürgens, Dietmar Saupe, Evan Maletsky, Terry Perciante, and Lee Yunker;
Springer-Verlag, 1991; two volumes, $20/vol. (available from NCTM).
Vol. 1 includes slides of 2- and 3-D fractal images.

This is a set of ready-to-use classroom activities, designed to introduce the concepts of self-similarity, fractal generation via the Chaos Game, and fractal complexity (or dimension). The book is the result of a collaboration between researchers on the mathematics of fractals (the first three authors) and specialists in mathematics education.

Authors Maletsky (see [23]) and Perciante have each used some of these activities successfully with teachers at all levels in the Leadership Program. William Bowdish LP `92 reported using the material in a classroom activity in which his 9th-grade Honors Algebra students estimated the fractal dimension of the coastline of Martha's Vineyard [1].

Codes Galore   (Module, 9-12)
Joseph Malkevitch, Gary Froelich, and Daniel Froelich;
COMAP, HistoMAP Module 18, 1991; $12. This module begins with a historical account of codebreaking and its impact on WWII. Its main focus is on common error-detecting and error-correcting codes (such as the zipcode and ISBN numbers), and their many applications (such as compact discs, or transmitting images from spacecraft to Earth). These codes use the idea of check digits, and are a good introduction to modular arithmetic. There are many activities, many of which require a calculator. A number of the activities lend themselves to cooperative group work--like decoding a simulated picture from space. A good complement to this module is the segment on codes in the COMAP Geometry video, described in Section 6.