Math Modeling

Course Description

Mrs. Burns teaches math modeling.

In math modeling, we use math– everything from algebra to statistics– to simulate and generate solutions to real-world problems. Through working independently and with peers, we learn from each other and challenge ourselves to explore various mathematical concepts and solutions. The year begins with a discussion of our summer reading book, Fermat's Enigma by Simon Singh. Next comes a unit starring a deck of cards; a 72-hour math competition, HIMCM; and some problems we model using Mathematica. We are constantly encouraged to challenge ourselves with the problems we encounter, whether as homework, classwork, or part of a math competition. Collaboration is key to this class, where the solution is never clear at first glance.


At MAMS, we participate in a number of math competitions. The first is HiMCM (High School Mathematical Contest in Modeling), where we work in small groups and have 72 hours to propose a solution to one of two problems provided by the competition. My partners were Amy and Shuling; we chose to do problem A, which had us model the population of a bee colony over time, determine the factor that impacts bee colonies the most, and calculate how many hives are needed to pollinate a 20-acre farm. We chose this problem because we liked bees and already knew a decent amount of information about them. Or so we thought. Once we started researching, we found many facts about bees that we didn't know, with each adding a layer of complexity to the problem. Thus, we decided to begin with a simplified model, which we would then build on by factoring in variables we identified during our research.

Epsilon School

The Epsilon School problem was one of the first modeling problems we did this year. It challenged us to decide how seven newly hired teachers would be divided between each of eleven subjects for the coming school year. We were given information such as the number of students in each subject, the number of grades in the school, the percentage of students that would drop out, and that the number of incoming students would increase for the coming year due to a school expansion.

We worked on the problem in groups then presented results to the class. My partners were Lily and Travis, and we made a model where we focused on maintaining the same ratios (such as the ratio of subject enrollments to the number of teachers for the subject) year to year. Our method of deciding the number of new teachers alloted to a subject involved several steps. Thus, for the benefit of our audience during presentations, we demonstrated our process by using an example, biology, which we highlighted in green in each table in the slideshow below.

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