Background: doing a freehand macrame project with a craft circle. Kids kept asking whether or not an object could be tied in. When I started to explain the general principles of how one can decide this… Whoohoo!
This parking meter is a contribution to What Can You Do With This, or WCYDWT, project. Dor Abrahamson sent it to me, together with this story for WCYDWT people:
“I’m co-teaching w/ Prof. Alan Schoenfeld an undergraduate course for future teachers, at UC Berkeley. It’s a problem-solving based course, and the problems are often based on mundane situations. We used this authentic document - a Berkeley parking meter - to explore multiplicative structure and rational numbers. Rate, I guess. Basically, we show this picture and ask what the best bang for the buck is. To our great surprise there was much confusion in terms of concepts, notation, vocabulary. Diverse approaches, some we couldn’t make sense of.
Judging by your blog, I need not demonstrate what a talented math teacher could do with this material. The mind reels, right? One of the interesting angles here is that some kids calculate min/cent, and others go for cent/min. We all wish to equalize the “denominator” so that we can compare the “numerators” directly. However, for me the min/cent feels intuitive, b/c I want to know how much bang I get for the buck. And yet, think of those ‘value’ numbers we see in the supermarket, which help us choose between comparable products that come in different volumes — they tell you, e.g,. 39c/ounce. So the equivalent here would be cent/min, right?
And so on. We played with polynomials so as to figure out what exact minute totals we could produce and how much they would cost us.
Time is money.
Oh, and the person whose image we can just discern in the display area of the parking meter is Becky Blessing — this is her, errr, reflection piece.”
UPDATE: Becky already submitted this picture in February, and there is a very nice discussion there at dy/dan blog.
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