## Devoured by Wolves (Plotting a exponential between two points)

This has been one of my most popular lessons. I adapted it from a much less colorful variant (just the dice, no sinister howling).

Supplies: lots of dice. Spooky music optional.

1. Students get into small groups, each group with optimally 15-20 dice. Each die represents a villager. Every night the wolves come, and some of the villagers don’t make it out alive.

On Day 0 all the villagers are alive. Students should simulate each day by throwing all the dice. The dice that roll up a 6 get sent to the graveyard.

2. After all the villagers are dead and the results recorded, the experiment should be repeated two more times and graphed.

3. Large village apocalypse: The entire class gets in a circle with all the dice. The total number of villagers is recorded, and then all the dice are thrown simultaneously in the center of the circle. All the sixes are gathered and put in the graveyard [I had one student calling himself the “Grim Reaper”] and the rolling continues until there are no survivors. The data this time can be put on the class white/chalkboard.

The data gathering culminates in students finding a graph first, modeling the situation experimentally, and then deciding on an exact model based off of the probability.

[SHORTER CLASS VARIANT] Each student is themselves a villager and has only one single die. They start standing up and roll after each day, sitting down if the wolves get them.

### 8 Responses

1. Thank you! I don’t completely ‘get’ this. I’ll have to play it out a few times to understand what’s involved. It sounds fun, though. Maybe I can get my teenage niece and nephew to play over the holidays.

• Math explanation (although if you’re having fun trying to figure it out it’s perfectly fine to ignore this comment):

Each iteration, 1/6 of the villagers expire, so 5/6 are left over. So each time the number of villagers is multiplied by 5/6. So if you started with 100 villagers, the formula would be

100 * (5/6)^(Days passed)

When doing it it with dice, using actual probability it won’t match exactly, plus only whole villagers can survive so there will be some rounding.

2. Sounds like a very worthwhile activity next time I teach exponentials. A colleague of mine does a similar thing where rabbits are killed off by mixymatosis, all in an Excel spreadsheet. The nice thing about that is the graph is constantly updating. I like the hands-on approach described here, though.

3. Thanks for posting this. We just finished exponential functions in my College Algebra class. It is the day before Thanksgiving, so I don’t know how many students will show up. To make matters worse, most of the class is dual-credit high school students, and the local high school is out today. It’s good to have a fun activity for the students who do come. We’ll be using an exponential regression to model the data the students generate.

4. I’ve done a similar activity with a Chocolate Monster eating m&ms (they are devoured if the monster can see the m), but I think having these two activities together might help understanding both the probability involved and the exponential aspects. Thanks for the idea!

5. […] Devoured by Wolves (Plotting a exponential between two points) […]

6. Jason, What spooky music do you recommend?

• That depends a lot on your class and just how spooky you want it to be. Something like Michael Jackson’s “Thriller” or Bobby Pickett’s “Monster Mash” would be on the lighter side, something like the Goldenthal movie soundtrack to Alien 3 would be on the darker side.