For math, taught by Mr. Regele, we work on math modeling. Math modeling is a way to use math and math concepts in order to model solutions to real-world problems. This class is designed to foster collaboration and for students to be able to talk out problems in order to come up with the solution in a variety of manners. When it comes to the math that we actually do, it tends to vary. One of the biggest things is the Exeter math problem sets which are booklets of problems that cover topics ranging from distance formulas to circles. We are assigned problems from these books at the end of class and start the next day by talking about them with the other kids at our table. Through this, we are able to try problems on our own, get help if we need it, and see other possible ways to get to the solution.
The first piece I have here for math is my group’s write-up for the HiMCM, aka the High School Mathematical Contest in Modeling. The HiMCM is a competition that Mass Academy competes in every year. Here, it is also called the 36-hour math competition. Fun fact, this math competition is now 2 weeks long, though we still have 36 hours to do it. This year, the question was about solar panel energy usage for a home somewhere in rural USA. My group broke our solution model into two parts, one being a survey which the user would fill out in order to get an estimate of their energy sources and the other being a code which took the energy usage of the user and their climate zone and gave them the best possible set of batteries along with their cost.
This Mathematica assignment shows how to find a median-median line. A median-median line is a way to fit a line to a set of data and can be used as an alternative to the more common least-squares line. In order to find a median-median line, you must break the data set into three separate parts, find the median of each part, and draw two lines (one connecting the first and third median and the other being a parallel line that goes through the middle point). With these two lines, you take the y-intercepts and find their averages, adding the y-intercept of the line which connects to the first and last points twice in order to account for the two points being on the line. This average is your new y-intercept. With the slope of the earlier lines and the new y-intercept, you now have your median-median line.