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PROFESSIONAL COMMENTARY

On the surface, this activity is a simple game that gives students practice with coordinates, but it is also an introduction to taxicab geometry, a gateway to non-Euclidean geometry. If that sounds formidable, fear not. Here's the difference: In regular (Euclidean) geometry, the shortest distance between two points is a straight line, but in driving a taxicab, a straight line is not usually possible. So the shortest distance between two points is the number of blocks traveled along streets. The taxicab game is simple enough for very young students to play by trial and error. The underlying mathematical ideas are intriguing enough to challenge high school students. The site includes background for the teacher, as well as links to related sites and additional resources. (author/sw)

CAREER APPLICATION

Drafting, construction, and engineering students all need to have a sound grasp of geometry. This lesson helps students not only practice their mathematics and geometry skills, but also develop their ability to visualize a construction using principles of mathematics. Transportation students might also make use of their skills in map reading and routing as they play a deceptively simple game. Teachers should ask what skills students believe are necessary to win this game.

OHIO STANDARDS
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Mathematics Academic Content Standards
Geometry and Spatial Sense Standard
Mathematical Processes Standard
NATIONAL STANDARDS
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Principles and Standards for School Mathematics
Geometry Standard
Reasoning and Proof Standard
RESOURCE TYPE
Content Resource
STANDARDS ALIGNMENT
Grades 3–12
CAREER FIELDS
Manufacturing Technologies;
Transportation Systems;
Arts & Communication;
Construction Technologies
TOPICS
Mathematics --
Geometry;
Non-Euclidean geometry;
Coordinate systems;
Reasoning and Proof;
FOUND IN
KEYWORDS
taxicab geometry;
game;
applet
Publisher: Annenberg/CPB