Lesson Plan:
Hook: Fermi brief introduction and story about estimating TNT in atomic bomb. Talk about in everyday life when we use estimation: tipping, tax, time, distances (driving).
Pretest: How many 10-dollar bills would it take to cover the surface of Canada? Answer: 950 trillion!
Canada: 9 984 670 km^210
Dollar bill: 1.05*10^-8 km^2
950 trillion.
Lesson Part 1: Understand the problem -> Think of a plan -> Carry out the plan
Go through the example and how we would solve it using those three steps.
Activity: In groups of 3-4, hand out one problem to be solved by the group in the same way we have just shown. Each group will have basically the same problem, but one group has access to computers, one has access to calculators only, one has no computer/calculator, and one has limited information from the problem. Question: How many songs does a radio station play per week? Groups 1-3 will be told it is a classical station.
After 5 mins, have groups share their answer and how they got it. After they've all shared talk about error and which group they think was closest in their estimation.
Post-Test: Assign a few problems for homework.
Summary/Conclusion: Scientists often look for Fermi estimates of the answer to a problem before turning to more sophisticated methods to calculate a precise answer. This provides a useful check on the results: where the complexity of a precise calculation might obscure a large error, the simplicity of Fermi calculations makes them far less susceptible to such mistakes. (Performing the Fermi calculation first is preferable because the intermediate estimates might otherwise be biased by knowledge of the calculated answer.)
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