The southbound lanes of I-471 are backed up from the Big
Mac bridge at the Ohio river, to Nunn drive. How many
cars are stuck in traffic on that section?
What are some of the fundamental mathematical elements of the
estimate?
Collection of (quality) Data
Approximation using geometrical objects with
known characteristics; use of mathematical and
statistical models (e.g. a cylinder is a model of a
body).
Units and unit conversion
We need useful referents
Is one of your fingers three inches long?
Is a knuckle an inch long?
There are 2.54 centimeters in an inch: how many
kilometers are there in a mile? (factors of 10 and
English unit conversion)
Computation (putting it all together)
Make sure that you keep units in your
calculations;
add, subtract, multiply, and
divide units, too, so as arrive at an answer
that has the correct units.
Bound where possible (that is, capturing the true value between two
values)
Sometimes it pays to be rough! If you don't need an answer
to great accuracy, you can be rough:
Where multiplying or adding two numbers, round one up and
one down for balance.
Where adding many numbers, use rounding (e.g. at
the supermarket, just round everything to the
dollar -- this should get you in the ballpark
of your total).
When subtracting or dividing two numbers, you need
to either round them both up or both down to
stay in the ballpark (as a general rule).
Two things are important in estimation: an estimate and a bound (some idea of how bad your answer can be): e.g.
A CNN-Opinion Research Corp. poll of 1,041 adults conducted July
27-29 found that 62 percent favor a timetable for withdrawing
U.S. troops from Iraq, but 37 percent oppose setting deadlines. The
results had a margin of error of plus or minus 3 percentage points.
We estimated Ed's hair count as about 4-5 million - what can we say about bounds?
Back to the "the pidgeonhole principle"....
Have you ever played a game, perhaps at a birthday party
as a young child, that relies on the pidgeonhole
principle?
So let's review how do we know that there are two people on earth who have
exactly the same number of hairs on their bodies:
Let's generalize: how many people must have the
same number of hairs on the bodies, at the very least?
Problems to consider (exercises in estimation):
There will be fifty-seven people at your picnic -- how
much potato salad do you need?
The Republic of Georgia just received $1
billion in US Humanitarian aid in their conflict with
Russia. How much are you paying (on average)?
In the book "The Three Trillion Dollar War", by Joseph
E. Stiglitz (winner of the 2001 Nobel Prize in Economics) and Linda Bilmes,
they assess the true cost of the Iraq war at -- you guessed it
-- Three Trillion Dollars. About how much is that for each
American?
How many ordinary dice would it take to fill this
classroom?
Do you have a temporal twin (someone who was born on the
same day as you, and will die on the same day)?
Is there anyone who obviously does?
Is there anyone who obviously doesn't?
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Comments appreciated.