The worksheet up today is a short one-pager about rate of change. It's technically not using any calculus, but it asks students to compare rates of changes and draw conclusions about the shape of White Bear Lake.
Using some data from a 1998 Minnesota DNR report about surface area and elevation, the worksheet asks students to compute average rate of change of surface acreage for elevations 903 and 913 feet above sea level and then for elevations 925 and 926.5 feet above sea level. Change of acreage is really dramatically different for these elevation ranges: you can really see how shallow the shoreline of White Bear Lake is, and how much effect simply losing one foot of water surface elevation has. No wonder the current drop is so noticeable!
I have some more ideas for White Bear Lake worksheets, so we'll see what happens. I'm thinking about
- modeling surface area vs elevation using a spreadsheet
- numerical integration to calculate volume of the lake
- graphing: what's the best way to convey mathematical information?