& its Applications (GeoMAP)
and its Applications (GeoMAP) is an exciting National Science Foundation
project to introduce new discoveries and real-world applications of geometry
to high school students. The materials are flexible enough to be used
in almost any class from algebra and geometry through precalculus, and
are ideal for discrete mathematics or college preservice classes.
of these modules is available, free of charge, to COMAP members for use
in the classroom. Photocopying is permitted for use only within a single
class of students or teachers. The material may not be sold or modified
in any way without written permission from COMAP.
COMAP members can download
and use any of these units:
Models, by Joseph Malkevitch
Looking at the problems faced by delivery people, storeowners, coaches,
airline operations managers, and more, your students learn how to analyze
real situations using mathematical models.
Paths, by Nancy Crisler & Walter Meyer
Robots like SARAH, a robot that performs neurosurgical procedures, often
use graph theory to make "decisions" about where to go. Students
explore a variety of algorithms designed to calculate efficient routes
and try to find their own optimal solutions.
& Braced Grids, by Brigitte Servatius
Whether it's the Cathedral of Notre Dame or the Statue of Liberty, an
architect needs to create structures that won't collapse. Your students
will learn how to determine whether a grid (of steel or wood, for example)
is braced, or unstable and dangerous.
by Bridget Arvold & Peter Cromwell
From magic tricks to sailing, to Egyptian hieroglyphics, knots have appeared
throughout history and in virtually all cultures. Using topology, students
explore the nature of knots, a new and exciting area of mathematical research.
& Patterns, by Nancy Crisler
Through the eyes of an archaeologist, students learn about mathematical
patterns and how they can be used to help us understand ancient civilizations.
by Philip Mallinson
Tessellations are found in art, architecture, and the natural world. Students
work with increasingly difficult polygons (from triangles and squares
to pentagons, hexagons, decagons, and beyond) as they explore the mathematics
Probability, by Art Johnson
Through the visual world of geometry, students experience probability
as a tangible issue, allowing them to more easily grasp this important
but challenging concept.
Diagrams & Proximity Problems, by Matthew Dickerson & Scott
Students use the properties of Voronoi diagrams to explore issues such
as choosing a location for a restaurant and deciding which emergency unit
should respond to a crisis.