**Procedure 1 – Using Geometric Dimensions to Determine Carrying Capacity ***(One 45-minute class period)*

In this part of the lesson, students will work together to determine if specific populations would be able to survive in a given area.

- Ask the students to brainstorm about which factors may contribute to the carrying capacity of a population. Acceptable answers may include: available resources (food, water, etc.), competition for resources, # of predators, physical space, etc. Explain that the students will have to find a sustainable habitat for specific groups of animals, based primarily on the geometric dimensions of a given area.
- Distribute a copy of Handout 1 to each student.
- Refer the students to the groups of species (from the handout) that will require a new sustainable habitat.
- Given that the students will be working with the dimension of acres, demonstrate on the board how to convert the measurements of a given area to acreage (as outlined on Handout #1).
- Divide the class into 4-6 groups (of about 6 students each)
- Have students follow the directions on Handout 1 to calculate the range requirements for each species (given 25 breeding pairs for each species, as per the directions) and complete the chart.
__Note__: There are six different animal species which require a sustainable habitat. Depending upon the amount of time that you would like to devote to this part of the lesson, you may choose to shorten the activity by having each group do the calculations for only one or two of the given species. When complete, each group can provide the acreage requirements for each assigned species to the rest of the class.

- Provide each group of students with
__either__:
- A map of a local or national park
- The chance to choose a local park area that they believe would be a sufficiently-sized environment for the provided populations. Then, look up the dimensions of the area/acreage online. (Ex/ The Jamaica Bay Wildlife Refuge in Queens, NY is 9155 acres)

__Note__: If it is not feasible to obtain or locate a local map, then any park map (or even the dimensions of an imaginary park) will suffice.

- Have each group calculate or look up the acreage for their given/chosen area.
- Each group should then compare the calculated acreage of their park to range requirements for each species. Challenge the students to choose sub-areas within the park that may be best suited and sufficiently sized for each species (based upon the terrain and other needs, as indicated on Handout #1). For a more thorough analysis of habitat sustainability, any information obtained about the park can be used to complement the students’ geometrical data calculations.
- On a separate piece of paper, have the students complete Questions 1-6, based upon each groups’ park dimensions, calculations & overall analysis.
- When there are 10 minutes remaining in class, have each group share the details of their findings with the rest of the class. Encourage students to elaborate on other factors that will influence the carrying capacity of the park that they have chosen.
- In the interest of time, some questions may be omitted or assigned for homework.

__Procedure 2__**- Using Technology to Graphically Demonstrate & Analyze Population Mechanics**

*(Two – Three 45-Minute Class Periods)*

__Note__: Although the following two graphing activities (a & b) are related, each may be completed independently and can be done in any order (or one may be omitted).

**Procedure 2a – Graphing Population Growth**

In this part of the lesson, students will be presented with an opportunity to graphically demonstrate population growth, based upon the Logistic Model (see Background section for full details). Given a basic understanding of carrying capacity, students will analyze and make predictions through the graphical depiction of a rabbit population’s growth, as it approaches carrying capacity.

__Differentiated (Technology) Learning Options__:

__Option 1__– (Length= Two 45-minute class periods)

(For Students to __design__, __implement__ & __manipulate__ a Population Growth Model- Excel Spreadsheet)

- Each group of students (2-3 students per group) should have a computer setup with MS Excel
- First, ensure that students have a basic understanding of carrying capacity and the Logistic Model of Population growth (see Background). Then provide an overview of the activity’s goal: to design & create a working model of population growth of a rabbit population using the discussed Logistic Model.
- Provide each group with a copy of
*“Handout A” *and read through the guidelines for the proper completion of their Excel Model of Population Growth.
- Provide each group with either a digital or a “hard-copy” of
*Handout 2 (Excel Tutorial)*, which will provide them with detailed assistance with some Excel tools that will be useful for creating their population growth model (especially Scroll Bars).
- Instruct the students to complete the Prediction Section of “
*Handout A”, *before beginning the design for the population growth model.
- The design of the model should take at least the entirety of the 1
^{st} lesson period. “Finishing touches” may be applied during the beginning of the 2^{nd} lesson period.
- Once the students have created their Population Growth Model, instruct them to continue with the
*Analysis Section *of “*Handout A” (*allowing them to manipulate and analyze their model) and complete Questions 1-6.
- Students should be able to submit their findings on
*Handout A* by the end of class

__Option 2__– (Length= Two 45-Minute Class Periods)

(For Students to follow directions to __implement__ & __manipulate__ a Population Growth Model- Excel Spreadsheet)

- The instruction of Option 2 is almost identical to Option 1, with one exception:
- You can opt to provide step-by-step support to your students (perhaps through interdisciplinary collaboration with the computer/technology department) guiding them through the spreadsheet creation process.
- Within Excel, the formula that will model the Logistic equation can be expressed as:
- =B2+B2*Birthrate*((Capacity-B2)/Capacity)
- where B2 represents the population size of the preceding month (to be sequentially compounded within each subsequent month)
- Birthrate & Capacity represent the cell “name” for each respective parameter

- Once the students have completed their spreadsheet models, they will complete the rest of the lesson using “
*Handout A” *as described above within Option 1.

__Option 3__(Length= One 45-Minute Class Period)

(For students to (only) __manipulate__ a Population Growth Model- Excel Spreadsheet)

- The instruction of Option 3 omits the spreadsheet design section of the lesson.
- Instead, instruct the students to open the supplied
*“Logistic Model” Spreadsheet* using MS Excel. They will then manipulate the supplied model in order to complete the questions on *“Handout A3”.*

**Procedure 2b- Using Technology to Graphically Analyze the Predator-Prey Relationship **(Length= One 45-Minute Class Period)

In this part of the lesson, students will be presented an opportunity to graphically analyze a model of the predator-prey relationship. Since the Lotka-Volterra Model is based upon a higher-order pair of inter-dependent equations, advanced programming knowledge is required in order to execute proper spreadsheet design, the students will instead manipulate and analyze a supplied spreadsheet model of the Lotka-Volterra Equations.

- Each group of students (2-3 students per group) should have a computer setup with MS Excel.
- First, ensure that students have a basic understanding of the predator/prey relationship, as exemplified by the Lotka-Volterra Equations (see Background). Then provide an overview of the activity’s goal: to manipulate and analyze a working model of the predator/prey relationship .
- Provide each group with a copy of
*“Handout B” *and read through the activity directions, explaining how to manipulate and analyze the Predator-Prey Relationship Model.
- Open
*Spreadsheet 2 (Predator-Prey Relationship) using MS Excel.*
- Instruct the students to complete the Prediction Section of “
*Handout B”, *before manipulating the Lotka-Volterra model.
- Once predictions have been made, the students must complete Questions 1-6 on “Handout B” as indicated.
- Students should be able to submit their findings on “
*Handout B”* by the end of class