## Monday, December 1, 2008

### Lesson Idea: Model Exponential Decay with Skittles (or M&Ms)

Lessons on exponential functions don't have to be all about tedious calculations. You can also use Skittles (or M&Ms, depending on your preference). This activity is pretty easy to set up, and your students will love it just like mine did. You'll have to split your students into pairs, so first estimate how many pairs you'll have.

Supplies Needed:
• 1 lb bags of Skittles or M&Ms (one bag should be enough for about 5 pairs of students, so figure 2 bags for a class of 20-25 students)
• paper plates (1 per pair)
• paper towels or napkins (1 per pair)
• small plastic cups (1-2 per pair)
Each pair of students gets a cup, plate and napkin. Fill each cups about 2/3 or 3/4 full of your candy of choice. Let students know they're free to eat everything AFTER the activity is complete.

Student Procedures:
1. Create a table with two columns: Trial and Number of Candies Left.
2. Pour out your candy onto the plate and count all of them. Record this as Trial 0 in your table.
3. Put all the candy back into the cup. Pour out the candy onto the plate again, but this time only count the ones that are face up--that is, have the "s" or "m" showing. Record this in your table.
4. Put only the candies that were face up back into the cup. Remove all of the candy that was face down--you can eat those now.
5. Repeat steps 3 and 4 until you have no candy left.
6. On a coordinate plane, plot your data as coordinate points. (Ask yourself, "Which is the independent and dependent variable in this experiment?" Your answer will help you decide how to graph the data.) What do you notice about the graph this data creates?

What happens in this activity is an example of exponential decay. When your students plot the data as coordinate points on a graph, they'll see an exponential curve. This doesn't even really require fiddling around with Stat Plot on a TI graphing calculator, although they can use it to help create an exponential function that fits the data they found as a final step (or extension).

I based my graphic organizer on this Exponential Functions module from Kennesaw State University's Transitions Project, a website designed for teachers in training and obviously worth exploring for everyone else. The only thing I really added to their worksheet was a coordinate plane for students to use to graph the data.

I first learned about this lesson at a Texas Instruments training, as we were practicing collecting data, plotting points and curve fitting using the TI-Navigator system (here's two similar TI lessons with and without the TI-Navigator). I never found time to use it last year with my Algebra I students, but it was perfect for my Algebra II students as we started exploring exponential functions. I hope you enjoy using it as much as I did!