In this class, the primary goal is to grow our toolbox of strategies that we can utilize to solve novel, difficult math problems and be able to explain our thinking in effective ways. Our classes are generally structured in a way where we go over homework or past assessment questions together with a few students presenting their work on the board, then we solve challenge problems in our groups which enables us to identify patterns and pull from strategies we learned in other units. Sometimes we don’t even finish solving the problem in one class, and from my experience, there have been many times where I tried using a strategy that I thought was working, but then it ended up not working. Nevertheless, it is really rewarding when it does, and it is also very interesting to see other people’s approaches to the same question. Below you can find some examples of the work we have completed in this course.
HiMCM, which stands for High School Mathematical Contest in Modeling, is an annual math modeling competition in which Mass Academy students participate. We were put into groups of 4, and then given 50 hours to develop a mathematical system that would allow us to illustrate a real-world situation. The scenario we chose was regarding the transition of typical diesel buses into an all-electric fleet in a major city. To say the least, I learned a lot more about public transportation buses in those 50 hours than I probably ever will for the rest of my life. Nevertheless, it was a very memorable and enjoyable experience and challenged me to manipulate data and equations at a high level.
In addition to HiMCM, another competition we are currently competing in is the Modeling the Future Challenge, also known as MTFC. This competition gave us an insight into the actuarial process which is the use of statistics and data to optimize insurance and premium rates. We started by calculating insurance rates for phones based on user data, then analyzing the profit margins of farms based on patterns in weather conditions, and then we finally analyzed a ski resort and how their profits would be influenced by the changing climate, and how insurance should be changed accordingly. Additionally, alongside the analysis of the ski resort, each group (our group is called the Scheme Team) came up with their own situation/issue for which a mathematical model can be made based on previously found data, and then hypothetical solutions can be identified and tested through simulation. Here is the work regarding our analysis of the ski resort and some initial brainstorming we did for our topic, which was drowsy-driving-induced car crashes.
Occasionally, we have a problem of the week, also known as a POW. Our first POW challenged us to create a mathematical approach that would allow us to identify what day of the week a person was born based on their birth date. Although there were many different approaches to figuring this out, our group specifically built off our knowledge of modding that we had learned in a previous unit, shuffling. It took us a few ordeals of trial and error to create a method that works every time, but when we realized we had found a solution it was very satisfying and we tried it with many different birthdays. As an extension, we also coded the method so that the user could just type in the inputs (month, date, and year they were born) in order to get the corresponding day of the week.