I needed a polar-coordinates-based assignment for my Calculus 2 students, so I pounced on it. The question they have been working on is, How long will it take to mow the lawn?
I read their work today. The following are some quotes from their writing.
“Establishing the polar function was difficult at first, until I thought about it as just a plain linear function.”
“I tried going on the treadmill to see what a comfortable walking speed for mowing would be.”
“Sorry for making this 13 pages. I really got into it.”
“Sometimes math needs a little touch up; this is when Photoshop is there to save the day.”
“The real real-world problem is how to convince your wife to upgrade mowers.”
“Rather than dealing with negatives and reciprocals, this paper will assume the lawnmower ‘un-mows’ the lawn from inside to out.”
“After realizing that the point on the outer ede of a circle has to cover more linear distance than a point near the center, angular velocity seems like it might have some flaws.”
I see in these excerpts students making mathematical connections that result from their struggles with the problem. I see them posing and refining mathematical models based on correspondence to the real world. I see them looking at this small slice of the world through a mathematical lens.
I am so proud of them.
NOTE: In original post, I did not know who had posted the video to 101qs. David Cox came through for me on Twitter. Credit given in revised post.