One of my classes have just sat a pretty hard exam and are a bit disappointed with their results.
One question they all did poorly on asked:
A wheel with a diameter of 20cm rolls for 30m. How many times did it spin?
Frankly, they didn't know what the hell they were expected to here, and several just did 30 / 20 = 1.5
So we decided to revisit this but let them control it.
Firstup: show this video.
Ask class: How fast is the car going?
Take bets Vegas stylee.
The clip lasts about 5 seconds. Several kids asked how far the car went.
It told them i wasn't going to tell them, but that i would tell them that i have 18 inch wheels on my car.
I put the clip on loop.
Because they were now looking at the wheels, one of them noticed that there a "white thingy" as he so eloquently put it on my wheel. This was true, i'd stuck a piece of tin foil on the front driver tyre.
One said we could count how many times the wheel actually spun, but we tried this and it was too difficult to see.
"Sir, can you slow the video down?"
Hell yes I can, god bless the VLC gods, this was nothing more than a click away.
We counted that the wheel spun about 20 times in the clip.
(one pair of pupils just counted one seconds worth, which i thought was clever as the first and last second of the clip are pretty hard to count.)
There was some dispute about this, so half the kids worked this as 3 spins per second, half worked as 4 spins per second.
Which brings us back to the exam question, as the kids are now asking how far do we go every spin? Several notice that this would be the circumference of the wheel, and we run on.
This all led us nicely into miles per hour (although we had to google how many inches there were in a mile)
The kids managed to calculate the exact speed of the car (i had a video of my tom tom showing current speed to prove it!) and i think now feel confident that they can deal with "rolling" questions.
Interestingly, kids at 3 spins per second came out about 10 mph, kids at 4 spins came out at around 13 mph which led us to a nice little debate about errors in measurement.
At this point, students felt happy that if the car had rolled for 30 feet, they could find out how many times the wheel spins.
Then we trotted out to the car park, measured some wheels and worked how how much faster Mr C's car would be going than mine if his wheels also span at 3 spins per second.