Coloring Discrete Structures

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Lesson synopsis

coloring conceptIs it true or false that Discrete Structures and Discrete Mathematics are the same thing? This is the kind of question that is asked in this field – or both fields if they are indeed different. Most Middle School students see a mix of discrete and continuous math without ever noticing the difference. This lesson introduces them to areas of mathematics that computer scientists use to do computational problems. Search techniques through discrete structures are illustrated through graph traversal and graph coloring.

Age Levels

11 - 13 years

Objectives

Introduce students to:
the relationship between Discrete Structures and Discrete Mathematics.
the difference between discrete and continuous phenomenon.
how to answer a question with sets.
how a discrete problem is solved through search: specifically graph coloring.

Anticipated learner outcomes

Students will be able to:
explain the difference between continuous and discrete structures.
discuss the difference in perspective of discrete math and discrete structures.
form a problem statement as a logical proposition, a Venn diagram, and an adjacency graph.
color a map with the least number of colors.

Internet Connections

Continuous vs. Discrete
https://youtu.be/WX0hnuniLpI
Map Coloring
https://youtu.be/ANY7X-_wpNs

Recommended Reading

http://wiki.acm.org/cs2001/index.php?title=Discrete_structures
http://www.cse.buffalo.edu/~rapaport/191/S09/whatisdiscmath.html
http://www.purplemath.com/modules/venndiag4.htm
https://en.wikipedia.org/wiki/Set_(mathematics)
https://en.wikipedia.org/wiki/Intersection_(set_theory)

Optional Writing Activity

Is it true or false that Discrete Structures and Discrete Mathematics are the same thing? Defend your answer.

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As an award-winning teacher and researcher, Liz has touched the lives of more than 6,000 students through her teaching at Northwestern's Segal Design Institute and Stanford University's Hasso Plattner's Institute of Design and through her paradigm-shifting creation, Design for America, a national network of students using design to tackle social challenges.

Image credit - Lisa Beth Anderson

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