Tag: math models

Prof. Andrew Stapleton teaches OM at U. Wisconsin-LaCrosse

Many of us have experienced the anxiety some of our students feel whenever we teach OM techniques. I have found a very effective manner to alleviate it by beginning my lectures with Math Magic.

First, start off the semester with the Phone Number. Tell your students to: (1) Grab a calculator; (2) Key in the first three digits of their phone number (NOT the area code); (3) Multiply by 80; (4) Add 1; (5) Multiply by 250; (6) Add the last four digits of the phone number; (7) Add the last four digits of their phone number again; (8) Subtract 250; (9) Divide by 2. Recognize the number?
Here is why it works:
X = first three digits of your phone number
Y = last four digits of your phone number = [250(80x+1) + (2y-250)]/2 = [20000x + 250 +2y -250]/2 = [20000x + 2y]/2 = 1000x + y = your phone number  (this trick doesn’t work if the first digit of the last four is a zero).

Hers is another one: The Rope Around the World.  Imagine an un-stretchable rope wrapped completely around the Earth at the equator. Imagine the Earth is as smooth as a cue ball. Here is the question: If you lift that rope exactly one foot above the earth’s surface (ignoring gravity), going all the way around the planet, how much extra rope will you need? The answer is amazing. Students may think they need to Google the diameter of the Earth to figure this one out. Surprisingly, you don’t need to know the Earth’s diameter or radius. You only need to know the formula for the circumference of a circle, i.e., Circumference = 2πr, where the value of π is approximately 3.14 and r stands for the radius.

Answer: You realize you can plug in that extra foot into the circumference formula. When the rope was wrapped around the Earth at the surface, you just have 2πr. When you add in the extra foot, it extends the radius of the Earth by one foot, so you now have 2π(r+1). If you want to find out the difference between the lengths of the two ropes, you subtract the shorter rope on the Earth’s surface from the longer rope suspended one foot above the Earth. 2π(r+1) – 2πr or 2πr + 2π – 2πr = 2π. The two circumferences in the equation cancel out, which leaves just the 2π. Really? It’s true! The rope that is suspended a foot higher all the way around our planet only needs to be 2π or 6.28 feet longer than the rope lying flat on the Earth’s surface.

Challenges like these take help take students’ minds off anxiety they may have felt when we go over a new OM model, making them more receptive to learning a new technique.