# 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.

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### Fermi problems: ball bouncing

‘Ball bouncing’ is a series of 7 problems that looks at what happens if you put a tennis ball on top of a basketball and then drop them both. This is done through mathematical modelling. The series shows how to take a complicated problem and break it down into manageable parts. It is recommended that the sheets are...