The Foundation for a Meaningful Life
Kindergarten - Grade 9 in Southborough, MA

Fermi Problems

Primary School students learned about Fermi problems in a special morning meeting led by Math Department Chair Maura Oare this month. Fermi problems use estimation to solve large-scale math problems where exact measurement is difficult. For example, how many dump trucks would it take to cart away Mount Everest? While this might seem an impossible problem to solve, Fermi's strategy was to use information gleaned from smaller-scale resources to make a reasonable estimate, or in the words of one Primary School student,  "a really smart guess." Iterative refinement is at the heart of solving a Fermi problem. After setting initial parameters for the solution, a mathematician might make a preliminary estimate, but then, as they gather additional information, that estimate is refined. Maura described the process of solving a Fermi problem to students before posing a Fermi problem of her own for the students to work on: How many snap cubes laid end to end would it take to stretch across the Primary Multipurpose Room? 
Working in their community groups of mixed grades, students were given a handful of one-inch snap cubes—not enough to measure the room, but enough to develop some estimation strategies. Students started by setting parameters, picking numbers they thought would be too small or large, and making preliminary guesses at numbers that might be close to correct. Then, they worked in pairs to brainstorm strategies. Several students came up with the idea of measuring the length of their feet in snap cubes and then walking heel to toe across the room to estimate how many it would take to span the room's length. The idea caught on, and multiple students could be observed walking across the room and counting out their steps. Other groups started small by measuring how many snap cubes are in a foot's length and used that information to graduate to larger units of measurement. Having determined how many snap cubes in a student's foot and how many of those feet measured the length of a student, one group set out to calculate how many "Janies" it would take to cover the room's length.  
Students came together after the activity to reflect on what they had learned and to compare their final answers. While no group came up with the same answer, they found that the range of answers from 400 - 770 snap cubes was relatively small, suggesting that students had employed some good estimation strategies!
main number 508-490-8250
admission 508-490-8201