# Modeling with Predator/Prey Populations

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## Objective

Students will be able to practice math modeling while applying a trig function to the population of rabbits and foxes.

#### Big Idea

Students act as wildlife biologists and discover the "periodic" connection between rabbits and fox!

## Roll Out

10 minutes

As the students enter the classroom, I have the Rabbit and Fox Cartoon playing on the projector screen.  Needless to say, watching cartoons at the start of class intrigues the students to ask the question:  What in the world are we doing today!? (MP1)

After the bell sounds, I begin to pass out the entry documents.  For this activity, I simply group the students according to whom they are sitting around (MP3).  My students sit in tables of four, so each table receives a Fox Entry Document or a Rabbit Entry Document.  After all of the entry documents have been circulate, I pause the video and ask the students to begin reading silently.  (I have found that stopping a video mid-stream is a great way to get the students attention, and get them quiet and settled in.)

After allowing 2-3 minutes of silent reading, I explain the situation to the students.  Today, they are going to play the part of a wildlife biologist at our local reservoir.  By the end of the period, they will not only reach a mathematical conclusion about their species of animal (fox or rabbit), but they will analyze the connections between the two mathematical models.

NOTE:  This lesson was adapted from This Illustrative Math Website - Foxes and Rabbits 2.

## Constructing a Model

15 minutes

During this time the students work to construct a model.  If you checked out the format of this lesson on the Illustrative Math Site you will see that I have modified it to fit my needs.  This is typically the case from resources that you pull off of the internet.  What is great for one set of kids (and one teacher) can often be even better if slightly modified and personalized before being used by another teacher!

By setting the stage of the investigation at our local reservoir, students interest is immediately peaked.  It also opens the door for a future guest speaker (in person or via google hangout) from the reservoir.  Who knows, now that the template has been created, perhaps we can even use real reservoir data in an upcoming year!  This activity could easily blossom from a 1 day lesson to a 3-4 day investigation.  I have found that often times, students have these contacts even if I do not.  More than once, the kids have actually helped me get ahold of a great guest contributor.

As the students work on constructing a model (Circulate Constructing a Model - RabbitConstructing a Model - Fox) I rotate the room and offer support where needed.  For the groups that finish within the first 10 minutes, I encourage them to attempt the challenge problem where they seek to come up with the other trig function to model the data.  Having the students do this in a real world context drives home the fact any sine function can also be expressed as a cosine function.

15 minutes

5 minutes