** Rules of Thumb.** Here are two rules of thumb for converting
Centigrade to Fahrenheit: "Double C and add 30;" or "Double C, subtract
10%, then add 32." How well do these work? Which is more suitable to
the northern states, which to southern?

** Tailgating.** Compare via calculation, formula, and graphs two
common rules for safe driving: to stay one car length behind the car
ahead for every 10 mph, or stay two seconds behind the car ahead.

** Digitizing Libraries.** Estimate how many words there are in
all the books in the school library. Then figure out how many megabytes
of disk storage would be required to store the entire library on a
computer. Finally, if all these books were digitized, how long would it
take to transmit the entire contents of the library via a 56KB computer
network?

** Bumps.** Suppose an orange were blown up to the size of the
earth? How high would be the tallest mountains? Or, imagine the earth
shrink the size of an orange. Which would be smoother?

** Estimating Area.** Estimate the areas of several states of
different shapes, given only a map (with scale) of each state. Compare
with accurate values (from an almanac) to see how the the shapes of the
states affest the accuracy of the estimates.

** Fermi Estimates.** "Back-of-the-envelope" estimates are based on
rough approximations that can be derived from common sense or everyday
observation. Examples:

- How many school teachers are there in New York City? How many electricians? How many morticians?
- How many gallons of water are there in Lake Superior? How does that compare with the amount of water used by U. S. households each year?
- How many miles of streets are in your city or town?
- What is your share of the national debt?
- When will your town fill up its landfill?
- How far do you walk if you dance all night?

** Order of Magnitude.** Estimate how many cups of
water there are in Lake Superior.

** Making Estimates.** Each year visitors to Disney World eat 7
million hamburgers, 5 million hot dogs, 5 million pounds of French
Fries, and 46 million Coca Cola drinks. What can you infer from these
data about the likely number of visitors?

** Mental Arithmetic.** Using only mental arithmetic (no fingers,
pencil or a calculator), double and halve any integer or simple fraction.

** Restaurant Bill.** Without pencil or calculator, mentally round
off a restaurant bill in order to estimate to the nearest 50 cents the
amount of a 15% tip.

** Estimating Volume.** A large load of topsoil forms a conical
pile. Because of its size, you cannot directly measure either its
diameter or its height. Find a strategy for estimating how many
truck-loads of topsoil it contains.