Last week I suggested that you can give your children an understanding of "a mile a minute" by having them time the interval between two mile markers as you hold a constant 60 mph. Today let's add a little mathematics to this situation, along with a calculator, and the result will be an entertaining and enriching family activity for long automobile trips.
Without looking at the speedometer, your children can tell exactly how fast the car is going. If your children use a watch (a stopwatch is excellent for this but isn't really necessary) to measure the time between one interstate mile marker and the next, they can determine your average speed over that mile with considerable precision.First, and before you start out on the trip, your children must understand that "miles per hour" means "miles divided by hours." Calculating miles per hour, therefore, is simply a matter of dividing the number of miles you travel by the number of hours needed to travel that distance.
Let's say that their watch shows exactly 65 seconds as the time between the two markers. They know they've gone exactly one mile, but how many hours is 65 seconds? Well, there are 3,600 seconds in an hour (60 seconds x 60 minutes), and so 65 seconds is exactly 65/3,600 hours. Our equation (miles hours\ mph), therefore, is one mile 65/3,600 hours\ mph.
The procedure for dividing by a fraction is simply to invert that fraction and multiply, so 1 65/3,600\ 1 x 3,600/65\ 3,600/65. Just divide 3,600 by 65 on your calculator and voila! - the result is 55.3846 mph.
So, however many seconds they measure your time between markers, they simply divide 3,600 by that number of seconds, and the result is your average speed in miles per hour over that distance. (This, by the way, is precisely the method used by the police officer in the patrol plane that may be flying directly overhead as you are performing this activity.)
You don't have to use a calculator, of course; the division can be worked out with pencil and paper quite simply. But if children first understand what they are doing - that is, what the numbers mean and why they are performing various operations on them - then a calculator can actually improve their math skills by allowing them to work more problems and to use bigger numbers without tedium or frustration.
Now, about the answer to last week's puzzler - did you guess 90 mph? 120 mph? 180 mph? You will recall that the driver was to average 60 mph for two miles but managed only 30 mph for the first, and the question asked what speed he must now average during the second mile in order to accomplish his original goal.
The first question to ask yourself is, how long would it take him to go two miles at a 60 mph average? Well, 60 mph is a mile a minute, so two miles would take exactly two minutes. He could stop and start again, slow down, speed up, do anything he wanted; if he makes the trip in two minutes, he's averaged 60 mph.
Now, how long did it take him to go the first mile at 30 mph? Well, 30 miles in an hour is 1 mile every two minutes, so that first mile took him exactly two minutes.
Do you see what has happened? He's already used up his two minutes, and so no matter how fast he travels during that second mile, it is impossible for him to average 60 mph for the entire two miles.- William F. Russell's books for parents and children include "Classics to Read Aloud to Your Children" and "Classic Myths to Read Aloud." Send your questions and comments to him at Family Learning, 2400 E. Main St., Suite 266, St. Charles, IL 60174-2414.