Fermi Questions

John Dabell

I trained as a primary school teacher 25 years ago, starting my career in London and then I taught in a range of schools in the Midlands. In between teaching jobs, I worked as an Ofsted inspector (no hate mail please!), national in-service provider, project...
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Have you ever tried asking some Fermi questions?

One questioning strategy worth trying in class is ‘Fermi questions’.

Fermi questions are named after the physicist and Nobel Prize winner Enrico Fermi.

He challenged his students to use estimation, common sense and numerical reasoning to work out quantities that were difficult or impossible to measure. He deliberately posed questions with limited information so that students had to ask more questions. His questions emphasise the process rather than the answer.

Examples of Fermi questions

* How many times could you say the alphabet in 24 hours?

* How many metres of spaghetti would be needed if all of the children in a school had spaghetti bolognese for lunch?

* How many ping pongs balls would it take to fill the classroom?

* How many balloons would it take to fill the school hall?

* How many people would fit shoulder to shoulder in the corridor outside our class?

* If all the people in the world moved to Wales, how crowded would it be?

* How many litres of water does the school use each week?

* How many sweets in a 2 litre jar?

* How many hairs on your head?

* How long would it take to count to one million?

* How many blades of grass are there on a football pitch?

* How many Mars bars would it take, lined up end to end, to reach from London to Birmingham?

* How many grains of rice in a 25kg bag?

* What distance will a ball point pen write?

Fermi showed that by making sensible assumptions, reasonable estimates and using simple calculations, remarkably accurate answers can be reached.

Why use them?

Fermi questions encourage creative thinking involving different solution strategies so they promote a range of problem-solving skills requiring students to be logical and inventive. Students like Fermi questions because they are:

• Open-ended problems
• Have no exact answer, no definite solution
• Interesting and motivating questions
• Challenging and rewarding
• Create a culture of questioning and curiosity

Fermi questions help develop much-need estimation skills and support the ‘feel’ of whether an answer is reasonable or not. Scientists, economists and engineers regularly use Fermi questions in their work as a way of getting  a ballpark idea of the viability of their plans and projects.

More examples

* How many Rubik’s cubes could you fit inside a double-decker bus?

* How many people would it take to surround our school if they held hands?

* How many 10 year olds are there in the UK?

* How many peas would you need to fill a bath?

* How many pieces of popcorn does is take to fill a cinema?

* How much dental floss does a prisoner need to escape over a wall?

* How many hours will you sleep in a lifetime?

* How many marshmallows would it take to cover the classroom floor?

* How many multi-link cubes would you need to fill a fridge?

* How far does a bee fly each day?

* How many people are airborne over Europe at any one moment?

* How many £1 coins could you fit inside a suitcase?

* How many times does a typical teenager say “basically” in one day?

* If all of the books in a school were stacked on top of each other in one pile, how tall would the pile be?

* How many years would it take if it were possible to walk to the moon?

It is great fun to observe students try solving ‘back of the envelope’ Fermi questions because they quickly become engrossed in contemplating the various issues, guesstimating, brainstorming ideas, discussing different approaches,  assessing each other’s thinking and reflecting on and refining assumptions. Students can develop logic and math skills without the fear of being ‘wrong’.

Have students come up with their own Fermi big picture questions and solve them together. They can be related to any aspect of life and even thinking of the question itself is a worthwhile challenge. Why not set a Fermi question of the week and see where it takes you!

Fermi questions are just one of the many questioning ideas that I have found useful from Questioning Technique Pocketbook by Gorden Pope.