Math Modeling at MAMS aims to teach advanced problem modeling skills while teaching a thorough variety of subjects including trigonometry, statistics and geometry to name a few. A typical math class starts with either a challenge problem followed by presentations of solutions or group review of homework questions paired with presentations of particularly challenging problems. Oftentimes, the next homework set will be assigned and started in groups until the end of class. Occasionally, multi-day modeling projects will be assigned for completion in groups. Two examples of multi-day modeling projects can be found below. Every year, Mass Academy Juniors participate in the HiMCM math modeling competition; an explanation of this competition and my team’s final paper can be found below.
The first group modeling project that we completed was The Epsilon School modeling question. In this problem, the Epsilon School is expanding in size to accommodate an incoming class of sophomores with a population 140 students higher than the graduating senior class. This would increase the student population from 490 to 630 at the start of the new school year. At the Epsilon School, there are only three grades, Sophomores, Juniors and Seniors. In order to respond to the increasing student population, seven teachers will be added. The question of how the teachers will be distributed throughout the departments remains. With a 5% dropout rate, this question becomes even more challenging. Below is my summary of our group’s efforts to find an equitable solution to this problem and a link to our unannotated spreadsheet can be found HERE.
The next modeling challenge I participated in was the Birthday POW or Problem of The Week. We were once again placed in groups and challenged to build a model to mathematically determine the day of the week that a person was born on given only the date that they were born on. This model worked for all birthdays between 1900 and 2100. Below is a link to our write up and explanation, and a link to the working spreadsheet can be opened HERE.
The most in-depth, aggressive modeling problem that I have completed at MAMS is the HiMCM or High School Mathematical Contest in Modeling. Given a 48 hour time period, my team and I attempted to accurately model the spread of the common dandelion in a one hectare sized plot of land over the course of 1, 2, 3, 6, and 12 months. We then had to produce a model that rated a plant’s impact factor on its environment. Two very late nights and two very long days later and we were able to produce a working solution to these challenges. A link to the official challenge PDF can be found HERE and below is our 25 page written up solution to this challenge.