http://www.7x7.com/arts-culture/real-top-10-list-steepest-streets-san-francisco
Maybe the math problem isn't that interesting, at least not at high school, but talk about a real-life application of slope. I think it's interesting to think about slope as a percentage--you never see a 30% line in math class, but you might see things like 30% grade on street signs. I wonder if kids notice those signs (especially if they don't drive yet and especially if they don't live in a hilly area), and I wonder what they think that grade means. It might be interesting to connect trig to this somehow and think about the angle that the street is tilted at. There always seem to be trig problems about wheelchair ramps--are road grades another piece of this? Is it even interesting?
Sort of related, I have to say I'm always kind of amazing at how steep a road or hill actually feels when I think of the grade mathematically. In my math class mind, a slope of 3/10 is definitely not steep (really, anything below a slope of 1 doesn't seem that steep. I wonder if this is because I often think about slopes in terms of pile patterns, so a slope <1 means that you're not even adding one block per pile...). But driving on a 30% grade is terrifying and just walking up it is painful. Would a kinesthetic experience with slope actually support students' understanding?
Update:
I finally decided to turn this into a student activity, but the article above doesn't really give enough information to make something interesting. With a little more research into Stephen Van Woorley (the guy who did the calculations the article was based on), I found some much more interesting stuff:
- The story of how he came up with these measurements. I think this will be my basis for the student activity.
- More steepness calculations, including some good history. An interdisciplinary opportunity??
- A sweet map! I mean, really, who doesn't love a good map-based data visualization?
