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By Gabriel Xu, VI Form
What if math students no longer had to study similar triangles because they simply don’t exist?
What if you could draw as many lines parallel as you want to a given line from only one point?
What if angle-angle-angle was enough to prove congruence of triangles?
Would these changes to our known geometric system finally make it easier, or would they further contribute to its fascinatingly intricate nature?
Studying Non-Euclidean Geometry aims to answer these questions. (more…)
By Kate Sotir, Cooper Sarafin, Anderson Fan, Shep Green, VI Form and Mo Liu, V Form
Math Modeling: Using Math for Flight Path Safety
The problem at hand is to create a model, a rating system, that would inform potential flyers of the safety of a particular flight. Our solution includes a mathematical equation that gives us a number between 1 and 100, depending on the inputs. Although the values themselves indicate the safety level of flights, we do not want to our audience to read into the numbers: a flight with a safety index of 63 should not be considered a more dangerous flight than a flight with a safety index of 67. Therefore, to make our model directly presentable to our audience, we classified the possible outcomes into ratings. A safety index ranges from 1 to 20 would have a rating of ★, from 20 to 40 would have ★★, 40 to 60 would be ★★★, 60 to 80 ★★★★, and finally, 80 to 100 would have the highest rating of ★★★★★, and flights that fall under this rating would be the safest choice based on our model. (more…)
By Nathan Cunningham, Ryan Ferland, and Freddy Masri, VI Form
Best Cities to Work and Live
We were tasked with creating a ranking function on a subject of our choice. We decided that our equation would rank US cities and would output an index indicating the best cities to work and live in. Our ranking is only intended for cities within the United States and does not include surrounding suburbs. The equation takes into account annual salary, annual cost of living, unemployment rate, and poverty rate giving an index anywhere from 0 up to several hundred. The higher the index, the better the city. (more…)
By Steven Li & Gabriel Xu, V Form and Finn Reams & Thee Ngamsangrat, VI Form
Math Modeling: Improved System for Ranking Colleges
Our task was to rank undergraduate colleges based on major elements that were most important to us. To solve the problem at hand, we first came up with six general elements of a college that held significance and found specific variables that would quantify each element. After putting all the variables into a ranking function, we adjusted the weights put on each category in correspondence with the importance we believed they contributed. We applied our model to both normal and extreme cases for testing, and we drew a 3D graph that showed the relationship between the final result with two of the variables as well. (more…)
By Mr. Scott Dolesh, Mathematics Faculty
Outcomes in Team Based Learning in Algebra II
My project compares the outcomes of students in Team Based Learning (TBL) Algebra II courses versus students in traditional teacher directed Algebra II courses. I had one Algebra II course that I used the TBL approach, and I had one Algebra II course that I used a traditional teacher directed approach. I also had a colleague who had two Algebra II courses that she taught using the TBL approach, and another colleague who had one Algebra II course that she taught using a traditional teacher directed approach. I compared the outcomes on our two common assessments that we give in Algebra 2: the first being the midterm exam and the second being the final exam. (more…)