# Fermi problems

A Fermi problem involves making estimates and using mathematics to answer a question, in more colloquial language they might be termed ‘back of envelope’ calculations.

Many of the questions don’t have clear cut answers, and sometimes alternative paths to solutions are possible.

The level of mathematics required is around that of level 2. The problem solving element is around level 3, making the materials ideal for students studying Core Maths, or as an extension for students preparing for the AO3 element of GCSE mathematics.

An essential element of problem solving is to be able to break down the problem into parts and decide on an order for working on those parts.

In order to give students the experience of seeing a problem broken down, it is recommended that they initially tackle either the ‘A secret of bees’ problem or the ‘Ball bouncing’ problem. From a mathematical perspective, ‘A secret of bees’ is a more gentle introduction, ‘Ball bouncing’ would be suitable for ‘A’ level students.

For each problem a full solution is provided in the teachers’ notes.

## Resources

### Fermi problems: the top-notch burger joint

This question asks us to consider a person opening a burger bar, doing all of the cooking themselves, and then estimate how much space should they rent?

The main topics required are rates (number of burgers per hour that one person could cook, number of customers per hour), and areas.

### Fermi problems: moving Mount Fuji

This problem serves as an introduction to the ideas of Fermi problems. The question posed is ‘how many dump trucks would you need to move Mount Fuji, a major mountain in Japan?’
The topics required to complete this problem are calculating the volume of a pyramid, working out mass from density and volume, and...

### Fermi problems: Fermi challenge

This problem assumes that students have completed the ‘Moving Mount Fuji’ problem and is intended to be used as a competition. The problem consists of three separate short problems:

1. How many bricks are needed to build a house.
2. What is the value of...

### Fermi problems: a secret of bees

‘A secret of bees’ is a series of 7 problems that looks at an interesting feature of the family tree for bees. The series shows how to take a complicated problem and break it down into manageable parts. It is recommended that the sheets are given to students one at a time.

Initially a family tree for bees is...