Mathematical Modeling

What is Mathematical Modeling?

Mathematical Modeling at Mass Academy is unlike any other math course I have ever taken. There is a large focus on problem-solving and collaboration rather than preparing for some unit test. The class was being asked to constantly solve problems with interesting real-life applications. Below are two examples of math modeling problems I found interesting.


A prime example of teamwork would be HiMCM, or the High School Mathematical Modeling Competition. This competition is a 36-hour experience, where groups of students picked between 2 mathematical modeling problems and write a 25-page solution. Normally, students would gather at each other’s houses to help each other work on the problem. However, due to the COVID-19 pandemic happening at the time, this was not as feasible; although Mass Academy did allow us to go into school on the last day of the competition. The 36-hour deadline was also extended, although our group did not end up using that too much, as our paper only needed polishing by the end of the 36-hour deadline.

The problem our group chose was asking us to help teens find their ideal summer jobs. Our group first researched summer jobs generally available to teenagers in the US. We considered criteria that teens might consider when looking for a job, such as how much money they want to save by the end of the summer, who this teen might want to work with, how many hours they want to work per week, whether they are looking for an active or sedentary job, etc. We set up a Java program that asks the user about what values for the criteria they would want (such as, “I want to save $1000 by the end of summer” or “I want a job where I get to do physical activity (an active job)”). If a job matches those values, that job ranks higher than jobs that do not match as many values. The program displays the top 5 jobs as recommendations, so that the teens still get a choice in what they want to do. The paper we wrote for the contest can be found below.

Euler School Problem

Another example of a math modeling problem is the Euler School problem. The problem described a school which is having a new wave of incoming students, as such they are getting new teachers. It was our job to decide how many teachers should be allocated to each subject, given data about how many students are currently enrolled in each subject, and how many teachers there currently are for each subject. Our goal was to lower the student to teacher ratio to maximize one on one learning, and thus have a better education at the Euler School. The PowerPoint my group made can be found below.