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Step 1: Guess!

Any idea how many people are picking their noses right now? Or, what fraction of land in the United States is covered by either a roof or pavement? Known as Fermi problems, these types of questions require the use of reasonable estimation, which is the focus of Lawrence Weinstein and John Adam's Guesstimation: Solving the World's Problems on the Back of a Cocktail Napkin.

The book's initial chapters briefly overview good “guesstimation” techniques involving numbers (i.e. scientific notation, accuracy, unit conversion). Mathematics and science teacher's can share this useful information with students, especially the explanation as to why the geometric mean is preferred when making estimates over the expected use of the arithmetic mean.

The book meanders through a wide variety of fascinating problems, roughly arranged in categories of “world-type” problems:

  • General questions (e.g. How long would it take a running water faucet to fill the inverted dome of the U.S. Capitol building?)
  • Animals and People (e.g. How far does a soccer player travel during the course of a 90-minute game?)
  • Transportation (e.g. How much total extra time would Americans spend driving each year if the highways speed limit was lowered from 65 to 55 mph?)
  • Energy and Work (e.g. How much energy could we get from flattening the Rocky Mountains?)
  • Hydrocarbons and Carbonhydrates (e.g. How much energy does a typical well-fed human consume in one year...more or less than a typical car?)
  • Earth, Moon, and Lots of Gerbils(e.g. How much would the ocean surface rise if the ice caps meltedc?)
  • Energy and the Environment (e.g. How much land would be needed to supply the U.S. elecrical energy needs with solar energy?)
  • Atmosphere (e.g. How many molecules of Alexander the Great's last breath do you inhale with each breath?)
  • Risk (e.g. Compare the risks of getting killed by a shark at the beach and of driving to the beach?)
Some of the problems are easy, some are hard…and most will grab your interest. Again, the goal for students is not to produce “the answer” to these questions but rather to produce a reasonable “guesstimate.”

The authors also offer a collection of thirty-three unanswered questions for readers (i.e. your students) to explore on their own. Enjoy...and be sure to look at my previous review of Fermi problems!