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?

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## About katenerdypoo

Middle Years and Upper Grades math teacher in the Netherlands teaching both within the Dutch national curriculum and the IB MYP and DP.

It’s a great exercise for the 9th grade. I think I’ll use it as an introduction for my 11th grade class, but off course they will have to find a function to approximate the values. This page is going into my bookmarks! 🙂

Thanks Martijn! The nice thing about a good task is it can be scaled up or down to fit the level of your students! 🙂

At some point I would get them to observe and record some real data, with a real thermometer, or lifted from the internet. Try http://www.intellicast.com and pick your location.

Thanks for the link, Howard. It’s maybe nice to show them this after they’ve done the assignment. What I want is for them to think critically about how the temperature actually works. They will not have the mathematical knowledge to actually model the function, so it’s not worthwhile for them to use actual data points. For me, what is much more important is that they learn to critically examine a model, make their own assumptions, and develop their own model that works with their assumptions, while still looking for the flaws in the model.