# Making Assumptions in Class 6 Math

How many watermelons fit in Vatican City? How many ounces of coffee does the average person in the United States drink in a lifetime? How many basketballs can squeeze into Gym 6?

To arrive at answers to these and a multitude of other perplexing questions, one need look no further than Room 704, where Math teacher Fanny Sosenke’s Class 6 students have been experimenting with a nimble calculation tool called the “Fermi” method.

Named for Italian physicist Enrico Fermi (1901-1954), who excelled at making correct computations with little or no actual data, this technique helped these Middle School mathematicians learn how to accurately estimate, while also honing their measurement, analytic and critical-thinking skills – and having a lot of fun in the process.

On a recent “I-Day” afternoon, after Ms. Sosenke introduced the unit to her class, the students quickly rearranged themselves into groups of two or three and got busy brainstorming their own Fermi questions. As Ms. Sosenke emphasized, a provable question is such that to be able to solve it, one needs to make assumptions using knowledge gained from everyday experiences.

A query easily answered by an Internet search would not qualify as a “Fermi question.” Rather, a series of steps must be followed to find the solution. For example, to solve the question, How many times do sixth graders open their lockers per year?, a combination of facts (There are 61 students in the grade.) and assumptions (Students go to their lockers about five times a day.) contribute to the final solution.

Lively chatter filled the room as the groups tossed suggestions back and forth and jotted ideas down in their orange notebooks. “What should we do?” one student asked. Her partner suggested, “How about, how many girls in our grade have Nike sneakers?”

After checking with their teacher, the students formulated the steps they needed to follow based on their own assumptions, their prior knowledge and facts discovered through research. Ms. Sosenke helped the girls look up various questions on the classroom laptop and reminded them to properly acknowledge any sources they used.

For the rest of this energetic class and the next meeting time, the students demonstrated impressive problem-solving acumen, perseverance and no shortage of imagination. They collaborated and compromised well and seemed to genuinely enjoy tackling this challenging assignment, which concluded with a poster from each group that illustrated their Fermi question and the steps needed to solve it.

“Every little step you take, you need to justify your reasoning,” Ms. Sosenke explained, as she circulated around the room checking in on each group’s progress. Although some pairs were still tweaking their questions with the help of hand-held calculators and others had moved on to designing their posters with colored pencils, everyone in the room was fully engaged in the activity.

Employing the Fermi method and their own ingenuity, these math scholars ultimately created a myriad of interesting questions and subsequent solutions that covered all manner of topics, Chapin-related and otherwise. Their informative posters will be displayed in and around Room 704 for all to admire.

A sampling of Class 6’s far-reaching inquiries included:

• How many students in Chapin’s Middle School get a snack from a store after school?
• How much money do Chapin students spend on Hydro Flasks in a year?
• How many books have members of Class 6 read since learning to read?
• How many Netflix movies are watched by New Yorkers every year?
• How many water bottles are thrown away every day in New York City?
• How many deep-dish pizzas can fit inside the Chicago “Bean”?