discrete mathematics: - dimacsdimacs.rutgers.edu/ysp/documents/chicago06res.doc · web viewan...

After playing the bean game, try to color the map above using the rule that two regions of a map that share a border must be assigned different colors. What is the least amount of colors you need to color this map? Can it be colored in 5 colors, 4 colors, 3 colors or less?

Discrete Mathematical Modeling Using Graphs HO #1

Some Maps to Color

Try to color the maps above using the rule that two regions of a map that share a border must be assigned different colors. What is the least amount of colors you need to color each of these maps? Can they be colored in 5 colors, 4 colors, 3 colors or less?


From Get It Together * EQUALS* Lawrence Hall of Science, p 116


What is Discrete Mathematics?

Look at all the things that you can see…And ask, “Can these be counted individually?”

Ice cubes stack, count 1, 2, 3.Each cube sits alone, so discretely!

Water falls down, as a cascade from the top.It is not so discrete, unless you count each drop.

Look for patterns. They are everywhere.On ceilings, floors and tables, and in numbers that are square.

Place your sharp pencil, on any point at the base.Can you go over an alphabet letter, without having to retrace?

Sequence all the steps, leading to a final result.This defines an algorithm, with numbers, or without.

When completing these examples, your solutions may be many.Can you justify why your answer is the best one of any?


By Joan Fitton from the previous version of the Massachusetts Mathematics Curriculum Frameworks

Map Coloring and Conflict Resolution

Web Resources

The Most Colorful Math of All - MegaMath

http://www.c3.lanl.gov/mega-math/workbk/map/map.htmlColoring is a profound mathematical topic with multi-million-dollar industrial applications. The problem presented here has been of interest to mathematicians for over a hundred years. How many colors do you need? With a few crayons or markers and some hand-drawn maps, children can quickly find themselves grappling with some of the same conundrums that contemporary mathematicians do. Four-color map problems, activities, background information, from the MegaMath Test and Development Site.

Colorful Mathematics - Canada's SchoolNet

http://www.math.ucalgary.ca/%7Elaf/colorful/colorful.htmlAn educational software series presenting advanced mathematical concepts to K-12 students in a game-oriented approach. The five games offered use simple coloring and/or drawing techniques to illustrate mathematical concepts from graph theory. Downloadable software and a "teacher's corner" are provided. From Canada's SchoolNet. Games: The Four Color Map Problem; the Chromatic Number of a Graph; the Edge Chromatic Number of a Graph; the Two-Player Chromatic Game; the Dominating Number of a Graph. Available for IBM compatibles only. Version in French.

Graph Theory Tutorials - Chris K. Caldwell

http://www.utm.edu/departments/math/graph/A series of short interactive tutorials introducing the basic concepts of graph theory, designed with the needs of future high school teachers in mind and currently being used in math courses at the University of Tennessee at Martin. An Introduction to Graph Theory tutorial uses three motivating problems to introduce the definition of graph along with terms like vertex, arc, degree, and planar. Includes a glossary and a partially annotated bibliography of


graph theory terms and resources. Euler Circuits and Paths; Coloring Problems (Maps). (http://www.utm.edu/cgi-bin/caldwell/tutor/departments/math/graph/color)

Perry-Castañeda Library Map Collection - The University of Texas

http://www.lib.utexas.edu/maps/index.html A large collection of maps stored as JPEG and GIF images which can be printed for classroom use. Since the maps scanned by the General Libraries are in the public domain, no permissions are needed to copy them. You may download them and use them as you wish giving the site credit.


discrete mathematics: - dimacsdimacs.rutgers.edu/ysp/documents/chicago06res.doc · web viewan...

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