Algebra Gets "Real"


When imagining a headquarters for the fictitious social media development firm they created in a recent math class project, three students dreamed big. The Manhattan Company student "executives" gave themselves offices at 20 West 34th Street in New York City because, they said, "that's the Empire State Building!"

The lofty address was a fitting one considering the ambitious nature of the trio's challenge. The students — Caroline Samoluk '21, Yuto Sugiyama Lam '22 and Tristan Witz '21 — had to develop a specific social media plan to maximize the number of hits on Brooks School's website, factoring in the real-world constraints of time and resources, using algebraic formulas.


Their group was one of ten participating in the "Linear Programming in Brooks' 'Real World'" project created for Algebra II Honors students by mathematics teachers Tote Smith P'18, P'20, P'22 and Doug Burbank H'98, P'11. Each group was tasked with essentially acting as management consultants for various departments at Brooks School and transforming a real-life situation into mathematical inequalities.

The student groups began by interviewing one faculty or staff member from either admission, advancement, communications, the deans' office or student activities on campus to try to understand a challenge that the person faces in a single aspect of his or her job. (For the Manhattan Company, who met with Brooks' assistant director of communications, that meant coming up with a plan for how to best deploy social media posts about sports versus all other school-related news).


The students gathered information from each participating faculty or staff member about how to maximize or minimize that piece of the adult's job. (That translated for Communications into considering how many posts about sports it would be ideal to create each week — so that athletics isn't featured more than double the number of times that other areas of school life are highlighted, without increasing the total number of posts to audience fatigue — within the a 40-hour work week).

After that one-on-one, students met alone with their group to figure out how to use the data they'd gathered in formulas illustrating the situation on a graph. (The Manhattan Company created three main algebraic equations for Communications: one about audience fatigue; a second one representing the ratio of sports-themed social media posts to posts about all other things; and a third one focused on the number of hours required to create social media posts).

Once they devised their formulas, the students applied the data they'd gathered during their interview to the equations, and created a single graphic with information depicting a "feasible region," of successful activity. Each group was then able to identify the specific point at which the adult's efforts would be most successful for all three equations.

Learn more about academics at Brooks School on our overview page.

The students concluded their project with a presentation to the faculty or staff member sharing and explaining the group's findings. (The advice for Communications? Share 133 posts about sports a year and 67 posts about everything else).


"I hope from this experience students learn that there are no Xs and Ys outside of textbooks," said teacher Tote Smith. "I want them to know that these simple algebra tools we're learning about can really be used – and that they already have powerful tools, even as third- and fourth-formers."

As an added bonus, Smith said that talking with adults on campus about their jobs also provided students with a lesson. "It rounded out their understanding and appreciation for what it takes to make a place like Brooks run," he noted. "And it made them move outside their comfort zone... I think students got a great deal out of the whole exercise."

Brooks students can also intern in "the real world" by participating in our Students on the Forefront of Science program.

Oliver Kim '22 enjoyed the work because he said, "I felt like I was an actual consultant at a management firm." It also helped him improve his understanding of linear programming because "applying a math concept into a real-life situation is the hardest part, and I was able to practice that throughout the project," he explained.

Caroline Samoluk agreed, adding that, "this project helped me to understand linear programming better because it tied the numbers and formulas we had been working with to something easier to comprehend and that we all deal with in the real world."

What she enjoyed most was creating all of the supporting materials to pull off the consulting persona. "Making business cards, coming up with a company logo, and creating a formal business-meeting-style presentation was my favorite thing," she said. "I feel these parts of the project will be very helpful in the future and were a good introduction to the professional business world."

Before wrapping up for Thanksgiving break, the students got to watch some of their videotaped presentations, and get feedback from their teachers. "I want to impress upon them that the way your present a solution is as important, more important, than how you derive it," Smith said. "People who collaborate well in groups will inherit the world!"

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