PBI Unit lesson plan

Author: Samantha Abeln

Title of Lesson: Population Decay Model

Date written: 10-10-06

Length of lesson: 100 mins (2 - 50 min periods)

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

Sources:

• http://www.utdanacenter.org/mathtoolkit/downloads/scope/OLDalg2scope/buzzbugs.pdf

Overview: Students work in groups to create a reverse model of the buzz bugs/m&m’s activity for population growth. Students will use what they have learned about population effects and exponential functions to create a model for population decay.

TEKS addressed:

(2A.11)  Exponential and logarithmic functions. The student formulates equations and inequalities based on exponential and logarithmic functions, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation.

The student is expected to:

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

(F)  analyze a situation modeled by an exponential function, formulate an equation or inequality, and solve the problem.

Objectives:

Students will be able to:

• Explain population decay
• Create a mechanism for decreasing population
• Determine a regression line to fit their data

Materials:

• 1 set of buzz bugs per group
• 1 graphing calculator per person (for extension, not absolutely necessary)

Teacher Does	Students Do	Probing Questions
Engage: Remind students of buzz bugs activity they did at the beginning of the unit. Recap of procedures of activity and findings/results.	Engage brains and attempt to remember what they did in math class a week and a half ago.	Do feel like the model used to represent population growth was good? Were there any flaws?
Explore: Using the same tools we used to create a model for population growth, create a model for population decay. Work through it a couple times to make sure it works.	Work in groups of 3 or 4 to create a system that uses buzz bugs and decreases the population.	What trends do you notice? Is your model exponential like the growth one was or is it more linear? How many times does it take for the population to become half its original size? A fourth its original size? Is this correct based on what you’ve learned about exponential functions?
Explain: Have students present their models to the rest of the class and explain their reasoning and why it works to decrease the population.
Extend/Elaborate: Have each student complete a population decay simulation and record their data along each step of the way. Then have the students graph their results. Then have students plug their data into a graphing calculator and find an exponential regression line for their data. Discuss trends in the lines and address any question students may have.		Does this line make sense with what you know about exponential decay functions? Does the exponential line fit your data or is there a large amount of error?
Evaluate: The model for population decay that students come up with is the main thing to be evaluated. However, if teacher feels like students need to have the concept cemented further, students could write a short summary of their model and be asked to extrapolate other data points and draw conclusions.