Fermi Problems/Questions
- Fermi Problems are maths problems to which we will never know the exact answer;
- an example of a Fermi Problem is:
- to solve a Fermi Problem we need to make reasonable assumptions and estimates about the situation in order to come up with an approximate answer;
- solving Fermi Problems helps us to think mathematically and to use our problem solving skills;
Fermi Problems are named after Enrico Fermi, an American physicist who created the world's first nuclear reactor.
Some Fermi Problems
How many sheets of A4 paper are used at our school each week?
If all the people who live in Australia joined hands and stretched themselves out in a straight line, how long would the line be?
How many beats will your heart make in a lifetime?
How many books are read by children in our class in one year? About how many pages is that?
How many pizzas are eaten by our class in one year?
If all the people who live in Australia joined hands and stretched themselves out in a straight line, how long would the line be?
How many beats will your heart make in a lifetime?
How many books are read by children in our class in one year? About how many pages is that?
How many pizzas are eaten by our class in one year?
Remember ...
- make reasonable assumptions and estimates;
- you need to be able to explain and justify what you did when coming up with your solution;
- your answers may differ from each other's but if you have made sensible estimates and assumptions the different answers should be close to each other;
- different assumptions and estimates will influence your solution;
Can you invent your own Fermi question?
For teachers:
Peter-Koop, A. (2005). Fermi Problems in Primary Mathematics Classrooms: Fostering Children's Mathematical Modelling Processes. Australian Primary Mathematics Classroom, Vol 10(1), 4-8.
"The difficulties that primary students experience when dealing with real-world related word problems have been discussed extensively. These difficulties are not only related to complex, non-routine problems but already occur with respect to routine problems that involve the application of a simple algorithm. Due to difficulties with the comprehension of the text and the identification of the "mathematical core" of the problem, primary students frequently engage in a rather arbitrary and random operational combination of the numbers given in the text. In doing so, they fail to acknowledge the relationship between the given data and the real-world context. While traditional word problems often do not seem to provide a suitable context for the development of mathematical modelling skills, the use of Fermi problems in the middle and upper primary mathematics classroom can help to foster students' mathematical modelling strategies."