Estimating volume: the Money Munchers

This is a problem solving lesson, designed to help you assess how well students are able to:

• Model a situation.
• Make sensible, realistic assumptions and estimates.
• Use assumptions and estimates to create a chain of reasoning, in order to solve a practical problem.

This is a ‘Fermi type problem’. Fermi was a 20^th century Italian physicist who loved setting estimation problems for his colleagues and students. A Fermi problem is a question for which a rough, but sensible estimate is produced, without knowing exactly all of the measures involved.

The problem is set in the context of $24 000 being stored under a mattress in $1 bills. The money is removed and taken to a bank. The first problem is to work out how much lower the mattress is once the money has been removed. The second problem is to work out how many trips to the bank are needed if a single suitcase is used to carry the money.

This is a problem solving lesson from the Mathematics Assessment Resource Service, a collaboration between UC Berkeley and the Shell Centre team at the University of Nottingham. Further information on the collection is given here.