I spent four days this week on a deserted island with my precalculus students.
It all started when I read this post by Sue Vahattum. If you’re looking for a good exponential modeling activity, I’d check it out. She explains it pretty well on her blog, so I’ll just recap my experiences this past week.
The basic premise is that you present your students with a scenario where the entire class has been shipwrecked on a deserted island. Suddenly there is a murder and one member of the class is the culprit. The class will need to use body temperature and logarithmic equations to determine the time of death and, eventually, the murderer. Here’s the handout I gave my students that frames it all. Of course, you would customize the names to the students in your class.
UPDATE 1/9/17: Improved handouts and storyline are here.
This is the second time I’ve done this activity, and both times it’s been a total hit with the kids. It’s pretty engaging, out of the ordinary, and totally applicable to the curriculum. To get into the spirit of the activity, I come in wearing sandals, shorts and sunglasses during first couple of days and they enjoy that. Besides, we are on a tropical island. They work in groups and I use this whole thing as a culminating activity to my exponential/logarithmic functions unit. The modeling goes beyond just a simple regression, of which a data table can be put into their graphing calculator. What is great here is that the modeling contains a vertical shift in the function, so they have to do the modeling by hand. To tie into their unit assessment, I also will include a problem on their exam relating body temperature and time of death.
The only hiccup this year came on the third day when they couldn’t actually find the murderer! The students overlooked a detail related to the time intervals and we had to conclude on a fourth day. Since I was actually “murdered” on the third day, I couldn’t help them (which was perfect to assess mastery). This actually made it even more dramatic as they had to wait the entire weekend to figure out who the murderer was! Oh, by the way, before the activity I did secretly “choose” a student who could play a good murderer before we started – and he consented to this part in the activity. No one in the class knew who it was beforehand, so when he was revealed at the end he could come up with a little skit as to why he did it. It was a fun touch.