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Home Education Magazine

September-October 2000 Issue

Shooting Hoops, Riding Bikes - Sue Smith-Heavenrich

Science and Math in a Kid's World

My younger son loves to play basketball. Or ride his bike through the just-melted mud patches on the logging road. Or follow frogs or kick a soccer ball or just about anything except sit for long periods of time trying to figure out useless math problems from a workbook. Like this one: You want to measure exactly five cups of water but you have only two measuring beakers. One holds exactly three cups and the other exactly seven cups.

"So fill up the three-cup measure, dump it in the seven-cup measure and scratch a line to mark it," says my son. There are easier ways to solve this problem than the answer the book gives.

"Or go buy a one-cup measure at the dollar store." I see his point. Anyway, who needs to measure things exactly? Why not just double the recipe and estimate?

So we tossed the book aside and went out to shoot hoops. I didn't want to wash the dishes... and the sun was shining. We played "PIG" and I was losing big time.

"How does the angle you shoot the ball affect how the ball travels?" I asked, trying to mimic a left-handed hook shot he'd just scored on.

"If you're closer, you shoot higher." He demonstrated how he shot the ball at different distances from the net.

"This would be neat to study," I mentioned. We started talking about how we might quantify the angle of shooting and compare the distance traveled by the ball. To measure the shooting angle we made a large protractor from a cereal box and marked the angles at 15, 30, 45, 60, and 75 degrees. Our idea was to hold the protractor at shoulder height, level with the ground, and have Toby shoot at various angles.

To measure distance, we marked off 50 feet at one-foot intervals. We figured we could estimate to the nearest half-foot. After testing the basketball and baseball, we walked to the mailbox and talked over our "study." The mailbox is a half mile walk, so by the time we got back we were hot and sweaty.

"Let's do it with squirt guns," Toby suggested. You can get pretty wet testing super-soakers aimed at a 75-degree angle. Later in the week, when it got cold and rainy, we sat down with mugs of hot cocoa and sheets of graph paper and plotted the data in a way that would represent "horizontal distance traveled compared to the angle of launch." Our graphs, though crude, showed a definite relationship between the two a lovely curve that resembled the arc of travel a ball makes when flying from hand to basket.

The amazing thing is that by shooting baskets, moving back, shooting again, kids get the feel for the mathematical relationship between launch angle and distance. Furthermore, they must calculate where, on the re-entry curve, the ball will swish through the net. And they do it without calculators!

Bicycling through the mud is another study altogether. That one began a few years ago when my older son (who was then six) noticed my bike went faster than his. We got off the bikes and looked at them.

"What's different?" I asked.

"Your bike has bigger wheels."

"So?" I challenged him to design a way to test whether big wheels made bikes go faster. We measured the distance traveled by one tire rotation for each bike. Sure enough, my bike went farther.

As he grew, he got larger bikes. But still, my bike won the races and not because I was pedalling harder!

"It's the gears!" he shouted one day after a lazy pedal on the flatlands.

"Yes, but why?"

Soon my bike was upside down and we were looking at how gears work. If you have a bike with gears, it's a simple experiment. You need a buddy (a mom or sibling will do) and a roll of masking tape. Your buddy holds the upside-down bike frame steady. Shift the bike into high gear (that's the chain going around the largest front chainwheel and smallest rear sprocket) and turn the pedal so the crank arm points up. Mark a spot on the rear wheel with a piece of masking tape. Turn the crank one full turn and count how many times the rear wheel turns.

Now, shift into low gear (chain goes around the small front chainwheel and largest rear sprocket). Again, start with the crank arm pointing straight up, and turn it one full turn. Count how many times the rear wheel turns. When you're riding in low gear, the rear wheel turns fewer times, but gives you more force. This is great for going up hills.

"So why don't you ever ride up our hill?" he asks. I don't have a gear that low!

There's a cool equation using the ratio of number of teeth on the chainwheel and the sprocket, multiplied by the wheel diameter to give you something called "gear inches." If you multiply gear inches by pi you come up with the distance you travel in one turn of the crank. We haven't done this yet maybe next summer. Right now my kids are shooting hoops.

2000, Sue Smith-Heavenrich

September-October 2000 Issue

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