Wayne's Wheel
(page 144)

Here is a solution from Bo ("the Best Person"), submitted October 2013

.1266514796 meters squared

We got it because 10/4= 2.5 2.5= circumference. And the problem wants the diameter.
The diameter of the wheel is 0.795774715 that equals the circumference of the hub.
.795774715/ pie =0.253302959.
Then .253302959/ 2= 0.1266514796 meters squared or to round it up 0.126

Okay, thanks for the solution. Now: the other answer is different. Who is right, and how can you tell?

Clearly, both solutions have some good thinking behind them. But what more do you want to know from these students? What questions could you ask them to put them on the right track?

Now, the first solution to this problem, from Beverly Bogden's class, which appears to be in New Jersey...

Member's Names: Matt N, Lee O, Brent P, Jack A

Question of the task: What is the thickness of Wayne's wheel?

Our Answer: 12.6651478 cm

How we came up with our confident answer:

When Wayne's Wheel rolled forward four times, it covers a distance of ten meters. Therefore, it travels 2.5 meters per one rotation. The second clue stated that the circumference of the hub was the same as the diameter of the wheel. Then we concluded that the diameter of Wayne's wheel was 0.795774715 meters. We discovered this by dividing 2.5 (circumference) by Pi, getting the diameter. The next clue explained that the thickness of the wheel was the same as the radius of the hub. We took 0.795994715m and divided by Pi. The result was 0.12665148 meters, or 12.6651478 centimeters.

So I got this answer (I especially like "confident answer"!) but the thing that troubled me was the number of decimal places. So I wrote back: " My question is, how many decimal places do you think you're entitled to keep? Put differently, how many are practical?" And THEY wrote back:

Dear Tim,

Thank you for your e-mail. We want to keep 3. We think that 3 decimal places are practical for our answer.

Matt, Lee, Brent, and Jack

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