PBI Unit lesson

Author: Samantha Abeln

Title of Lesson: Computer simulation of various effects on population

Date written: 10-10-06

Length of lesson: 50 minutes

Class description: 10^th or 11^th grade math

Sources:

• http://www.aetheling.com/NL/sim/population/population1.html

Overview: Students will learn the effect that various parameters can have on a population.

TEKS addressed:

(2A.11) The student is expected to:

(A)  develop the definition of logarithms by exploring and describing the relationship between exponential functions and their inverses;

(B)  use the parent functions to investigate, describe, and predict the effects of parameter changes on the graphs of exponential and logarithmic functions, describe limitations on the domains and ranges, and examine asymptotic behavior;

Objectives:

Students will be able to:

• Explain trends in a graph
• For example, explain the effects increasing or decreasing the infant mortality rate has on a population

Materials:

• Set of computers for the class

Teacher Does	Students Do	Probing Questions
Engage: (~5 mins) Have students go to the website http://www.aetheling.com/NL/sim/population/population1.html Click on the heading above the graph that says “population.” Have students just play around with the parameters and see what happens.	Play around with the controls and see the different resulting graphs.	Did anyone get a graph that doesn’t go up to the right? If so, write down the parameters for later.
Explore: Place all controls in the middle, except for iterations in the bottom left. This one simply controls the speed of the graphing and moving it to the left will make it go faster. Place this control wherever you like. With all controls in the center, press “Reset” and then “Start.” Pause the graph at year 200. Sketch this graph on your paper and write the values of each parameter beside it. Pick one parameter. Move it some amount to the left. Reset the graph and start it with this different parameter. Pause it at 200 years and draw the new graph and record the value of the changed parameter. Using the same parameter move it to a value to the right of the center. Redraw the graph and record the parameter value and the graph on your paper. Repeat this for the 4 remaining parameters.	Complete activity.	How are each of these new graphs different from the original one with all parameters in the middle? Why do you think this is so?
Explain: Class discussion of findings.	Share findings.	What is fertility rate? What, if anything was different about the graph when you decreased of increased fertility rate? Infant mortality? Mother’s age at first birth? Increase in adult mortality? Mortality at age 10? Was the graph what you expected?
Extend/Elaborate: Is there a situation you can create where the population is constantly decreasing, one where there are no bumps upward in the curve? The graph is simply theoretical. Do you think a population can ever be completely wiped out gradually like this?
Evaluate: Grade for the day simply based on student participation. Have students turn in graphs from the activity.