BY JOHN PAWLAK
White Rock
The trouble with numbers is that they can be hard to relate to. And the bigger the number, the harder it becomes. People tend to prefer small numbers. Well, not when talking about salaries though!
When teaching math, students would complain to me about having to learn concepts that were “totally useless, Mr. Pawlak!”. For example, they hated irrational numbers and imaginary numbers, stating that they would never have to deal with things that confusing in real life. I told them that in many ways, I agreed. With the average number of children under 18 per family now being 1.94, it was very confusing indeed when figuring out deductions during tax season!
It became painfully clear that many students saw little relevance to numbers in their day-to-day activities. To launch them on a journey of numerical perception, I would start with a simple example that addresses a real-life situation. I taught the following lesson: You’re driving at 50 mph and you get a text message. You pick up your phone and read it for just 4 seconds. How far did you just drive without looking at the road?
Four seconds isn’t a very long time. 50 mph equals about 75 feet per second, so in four seconds, you’ve traveled 300 feet, the length of a football field! This made them think twice about texting while driving! Well, okay. Knowing my students, maybe not all of them.
When teaching Physics, the text book showed a depiction of our solar system, looking pretty much like every other picture I’ve seen. This was another opportunity to teach perspective. I put a one-foot-wide yellow ball out in the hallway and told my students it represented the Sun. Now, constructing our picture with proportional measurements, how big would Earth be and how far down the hallway should we place it? The Earth would be bit smaller than a 1/8 inch ball bearing and 107 feet away from our one-foot Sun. Maybe the pictures in the science books are a “little” misleading?
Another favorite problems I would assign to my students was for them to calculate the weight of 1/4 inch of rainwater on an acre of land. Before doing the math, they would shout our guesses like “A couple hundred pounds!” Okay, an acre has 43,560 square feet. A 1/4 inch is 1/48 of a foot, and hence this gives us 907.5 cubic feet of water. One cubic foot of water weighs 62.4 pounds, giving us an answer of 56,628 pounds, a little over 28 tons.
To associate a bigger number with the real world, we looked a hamburgers. McDonalds sells about 2.5 billion hamburgers every year. We hear the word “billion” used often these days, but it’s just a big number. It doesn’t seem to have any correlation to real life, right? Another way of looking at this figure is to divide by 365 (days in a year) and divide by 86,400 (seconds in a day). This gives us a slightly better understanding when we see that McDonalds sells 80 burgers every second of every day. Yum!
Now, what about really BIG numbers. Politics aside, let’s look at our nation’s National Debt. My favorite quote regarding federal spending is by Senator Everet Dirksen, who said, “A billion here, a billion there, and pretty soon you’re talking about real money”. At the time of this writing, our National Debt is $37.2 Trillion (a trillion is a thousand billion). Most people shrug off this fact because a number that big simple doesn’t mean much to them. A billion is big. A trillion is, well, bigger. So exactly how big is this big?
A conical pile made from 37.2 trillion grains of rice would be 450 feet in diameter and 450 feet high. Stack 37.2 trillion $1 bills. The pile would reach to the moon, and back, fives times! If you spent $100 every second, 24 hours a day, it would take you 11,800 years to spend it all. Does this make you feel like crying? 37.2 trillion human tears would fill 92 Olympic sized swimming pools!
I think I did make my students cry though when I had them divide the debt by our country’s population. Calculating that every single person in the country “owes” about $108,000 of that debt is a perspective that really makes math lessons unpleasant!