Devising a plan to solve Fermi problems involving large numbers

Fermi problems are open, non-standard problems that require the students to make assumptions about the problem situation and to estimate relevant quantities before engaging in, often, simple calculations (Ärlebäck The Montana Mathematics Enthusiast, 6(3):331-364, 2009). Our study focuses on the plans—schemes aimed at solving—devised by students aged 12-16 years to solve Fermi problems involving big numbers. The strategies which appear in these schemes are characterized herein and analyzed to find out to what extent they would be suitable to solve the problems. Some of the identified strategies are related to magnitude estimation (use of a reference point), whereas others correspond to modeling processes (grid distribution, use of a concentration measurement, reductions of a problem, and use of a proportion). We conclude that Fermi problems involving large numbers may constitute a good opportunity to discuss heuristics and problem solving strategies in compulsory secondary education classes.