This worksheet is again about White Bear Lake and its shrinkage. This time, though, it's all about visualizing data. Data about surface elevation and surface area from the Minnesota DNR is again presented in the worksheet, and students are asked to graph it two ways. Which way is better for presenting the information?
I want to provoke an argument here! Getting students to argue in a constructive and respectful way is a great tool for pushing critical thinking and reasoning, as well as practicing language skills. Here, students need to think about the meaning of the information they're trying to present and then argue for which graphical representation is most effective. If I were teaching this in eighth grade I'd get students to write a news article about White Bear Lake, using mathematics and their own research!
White Bear Lake: Graphing surface area
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!
White Bear Lake: Rate of Change
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?
White Bear Lake has been in the news a lot recently: Minnesota Public Radio is doing a big project about our dropping groundwater levels, for instance. And now that the holidays are over (Happy New Year all!) I've got the first pass worksheet for exploring White Bear Lake mathematically. No calculus yet, just an exploration of the area and volume of the lake. On average, White Bear Lake is pretty shallow. I think that's one reason the drop is so noticeable, especially on the western shore of the lake. In the worksheet students can find out just how shallow WBL is and also deal with big numbers.
As a teacher, I think this is an appropriate worksheet for a class that's dealing with big numbers (scientific notation would be great here!) and units.
- Scientific notation!
- Changing units.
- Average depth from knowledge volume and area.
Precalc: Volume And Average Depth
If you've got suggestions for improving the worksheet, let me know! And check out my email subscription list on the side -- I will email you about the EarthCalculus book I'm putting together right now....