Math Modeling Class Presentations

From Peter Mannisto, Math Modeling Teacher:  

This year, the Grauer School introduced a new math class, Mathematical Modeling. This is the only fully project-based mathematics class at Grauer, and it is centered around a series of real-world problems that students study the mathematics necessary to solve. But solving the problem involves more than mathematics! One must use good judgement to decide what are the important factors to consider, one must make approximations where an exact answer is impossible or to hard to obtain, and you need to be able to present your results to a wide variety of audiences. 

Recently, students spent several weeks preparing a solution to a complex math modeling problem. They were given a list of 6 airports in the United States, as well as population and geographical information about each. Their goal was to decide the best way to connect the cities via airline routes, considering two competing factors: more routes would be better for consumers as it would lead to fewer connecting flights, but would also be more expensive for the airlines. The students had to come up with a method for measuring customer satisfaction and cost to the airline for a network of routes, and then come up with what their model viewed as the "best" network. They then presented their results to the class.

All of the teams did extensive in-depth analyses of the problem, including coming up with some impressive mathematics to solve the problem. Each of the teams approached the problem in their own way, and their solutions were all different. It's important to remember with math modeling that there is no right answer, and that every team's work presented a viable solution for this problem. The students all did a great job, and showed that they possess the teamwork skills and resourcefulness needed to succeed in a quickly changing job environment!