Just measure the width (or height, if you'll be stacking the pennies a mile high) of a penny, then divide 5280 feet by whatever you find. This is a great activity for a class, and in fact a good way to start the project. First take one penny, and work out an answer. Then get 100 pennies, and measure them; do the same calculation to see how many pennies it will take to make a mile. There will probably be a difference, because you can measure 100 pennies more accurately than a single penny. Or maybe you have a micrometer that will measure one penny precisely. Which is better can be a good discussion starter. And don't forget to try it in metric, too.
Just to illustrate, using a very rough estimate of a penny's width, let's say a penny is about 3/4 inch wide. The number of pennies in a mile will be
5280 ft 12 in 1 penny 1 mile * ------- * ----- * ------- = 5280 * 12 * 4/3 pennies 1 mi 1 ft 3/4 in
This gives about 84,480 pennies. (This method of doing calculations with units is very helpful, and would be worth teaching.)
If we measure 100 pennies as 6 ft 1 in, we will get
5280 ft 100 pennies 1 mile * ------- * ----------- = 5280 * 100 * 12 / 73 pennies 1 mi 6 1/12 ft
