After yesterday’s flurry of thought I settled down today to actually write up the new modeling task. In my document, I included Geoff Krall‘s screen shot with the introduction that this problem was taken from an American book.
I then gave them the exact conversions (at this point in the year, they’ll have done a whole report on converting temperatures) but for ease’s sake told them to change the problem so that the temperature at sunrise was 18 degrees Celsius and the temperature rose (by the way, hate the repetition of sunrise and rise in the problem) 3 degrees Celsius per hour.
Here’s the new assignment:
1. As instructed in the American problem, find the equation of this scenario.
2. Model this situation on a graph. Make sure you label your axes and pick an appropriate scale. Indicate any important points.
3. Critically look at your model – this can not be correct…why not? What’s wrong with this model?
4. Is it realistic to assume that the temperature rises 3℃ per hour? Why or why not?
5. What other assumptions are you and the model making? What isn’t the model taking into account?
6. Create a new model. You can either first create a table that relates temperature, T, with hours during the day, h, or first create a graph of how the temperature should look. (You can use actual times of day to help you orient yourself). Briefly explain how you picked your temperatures/graph.
7. If you were to continue this over a couple of days, how would your graph look? Give a small sketch.
8. What is better about your new model? What is still weak about your new model?
9. How would the graph compare if you were the daily temperatures in another country (like for example Saudi Arabia or Greenland)? What would be the same, what would be different?
I envision this taking an entire class period for my MYP 4 (9th graders). I do not expect them to come up with an appropriate equation for their new model, but they should still evaluate its validity. What do you think?