Title
March Madness (Dan Snook)
Goals
1. Students will explore the concept of trees as it relates to tournaments.
2. Students will be able to generalize patterns inside of single elimination tournaments.
3. Students will use LOGAL software to run sample tournaments based on the odds of each team winning the tournament.
Abstract
This activity, which is set in the context of the NCAA basketball tournament, asks students to determine such items as the number of rounds needed, the number of games each team must win, and the total number of games for tournaments ranging from 4 to 128 teams. Students will also learn how to deal with byes. This activity is designed to be part of a 3 or 4 day unit implemented the week prior to spring break which coincides with the NCAA tournament.
Problem Statement
Student understanding of the nature of this problem may be diverse, ranging to basketball players who understand how tournaments work, to students who have never seen a tournament bracket. It may be useful to set up a friendly classroom tournament to illustrate seeding, and how teams advance through a tournament. It is also important to note that not all students will feel that it is fair that the top seed will open up the tournament against the bottom seed.
Instructor Suggestions
1. Begin with the problem statement. It may be necessary to review the tournament process. One may wish to determine how a tournament compares to the election process.
2. Distribute the "March Madness" worksheets. Allow students to work individually on the activity.
3. When all of the students are finished, have individual students share their results with the class.
4. Discuss student results.
5. Continue activity choosing from "Further Investigation" and "Variations".
Materials
"March Madness" worksheets, dry erase board, Math lab with access to WWW and LOGAL
"Probability Constructor" software, Rocky Mountain News
Time
Introduction of problem statement (5 minutes), Individual work (10 minutes), Presentation of individual work and large group discussion (20 minutes), Lab time to search the web for related topics (20 minutes)
Mathematics Concepts
Discrete Mathematics Concepts:
Binary Trees, Roots, Stems, Leafs, Counting
Related Mathematics Concepts:
Variables, Exponents, Representing Patterns
NCTM Standards Addressed
Problem Solving, Algebra, Geometry, Communication, Reasoning, Connections,
Discrete Mathematics
Colorado and District Standards Addressed
Number Sense (1), Algebraic Methods (2), Data Collection and Analysis (3), Problem Solving Techniques (5), Linking Concepts and Procedures (6)
Curriculum Integration
This activity could be used with any level of high school math. This would be a good activity
to incorporate in the days prior to spring break. This time usually corresponds with the regionals
of the NCAA tournament.
Further Investigation
This activity could be extended to include a probability experiment based on the NCAA tournament. The odds of each team winning the tournament could be pulled off of the web. Then, the LOGAL "Probability Constructor" software could be used to run an experiment. The software will allow a weighted probability to be assigned to each team, and then will run he tournament any numbers of times, collecting and storing the results. Many tangents of this experiment can be addressed.
Variations/Comments
It should be noted that the championship game usually occurs the Monday night that school resumes after spring break. It would also be possible to utilize the Rocky Mountain News school program so that students can follow tournament results during the instruction period. Another variation would be to use the NCAA women's tournament results.
References/Resources
Colorado Model Mathematics Standards Task Force. (1995) Colorado model content standards for mathematics.
National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: Author: