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.

What a great selection of Fermi questions. I can understand why students would enjoy them, and see their potential to get students thinking and discussing.

can you post some of the possible answers?

Haha – which one?

the Earth to Moon one is 8.770248688 Years walking 5Km/h. the distance is 384,400Km

I have a bottom set of dispirited kids who talk or draw and reject the formal learning. I’m going to try a question from this list, to see if it sparks their attention. Thanks!

Let me know if you need anything else…

Thanks, I wrote the list and there’s plenty more where they came from!

Fermi questions are on the syllabus for the Core Maths exam. Some great ideas here for the next time I teach it.

Good to know!

“When you take a single breath, how many molecules of gas you intake would have come from the dying breath of Mahatma Gandhi ?”

How much air has been exhaled by Mahatma Gandhi in his last breath?

What is the volume of air in earth’s atmosphere? Radius of the Earth(RE) is approximately 6,400 km and 100 km is often used as the border between the atmosphere and outer space. But, 75% of the atmospheric air is within about 11 km of the surface.

What fraction of Gandhiji’s last exhaled air is present in a unit volume of atmosphere? we assume that during these 70 years it’s evenly distributed in earth’s atmosphere.

How many air molecules you inhale in each breath?

What are the chances that your current inhaled air contains air from Gandhiji’s last breath?

Can you please share possible answers of these questions

There are so many possibilities, that would make it too easy for you and others reading…

Very good and resourceful

I put one on the wall (and on Google Classroom) each Monday morning for my students to discuss and play with during our staggered starts and finishes. I have a year 6 class and about half of them really enjoy it. The rest either ignore it or think it’s silly. I don’t make a fuss, just support and encourage the ones who want to try them. It has made some of my less mature children think a bit more critically and organise their thinking in problem solving during maths lessons.

A good effort nonetheless; perhaps an engaging image alongside the fermi question will work wonders?

Great to see some many people interested in this Topic – Fermi questions are so valuable for maths thinking and inclusive of all as you can respond with simple or complex solutions.

One thing to consider is relevance. Shouldn’t we try and ask questions that are worth answering.

Why ask – “How many pieces of popcorn does it take to fill a cinema?” (who cares!!) – when you can ask “How many people can you fit in a cinema and still observe social distancing rules?”

I usually have some criteria for my Fermi questions – they need to be

Meaningful (worth knowing)

Achievable

Relevant (to the student cohort)

Challenging (involving enough maths for complex answers as well as simple solutions”

Agree – it’s a fantastic methodology.