TEMPLATE FOR LESSON PLANNING

PBI -- Mathematics

LESSON PLAN # 1

Name(s): Christie Anderson

Title of lesson: Buzz Bugs – Introduction to Exponential Growth

Length of lesson: 2 days: each 50 minutes

Description of the class:

Name of course: Algebra II

Grade level: 10^th &11^th

Source of the lesson:

IPG’s from Austin Independent School District.

TEKS addressed:

(b) Foundations for functions: knowledge and skills and performance descriptions.

(1) The student uses properties and attributes of functions and applies functions to problem situations. Following are performance descriptions.

(B) In solving problems, the student collects data and records results, organizes the data, makes scatter plots, fits the curves to the appropriate parent function, interprets the results, and proceeds to model, predict, and make decisions and critical judgments.

(f) Exponential and logarithmic functions: knowledge and skills and performance descriptions. 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. Following are performance descriptions.

(2) The student uses the parent functions to investigate, describe, and predict the effects of parameter changes on the graphs of exponential and logarithmic functions, describes limitations on the domains and ranges, and examines asymptotic behavior.

(5) The student analyzes a situation modeled by an exponential function, formulates an equation or inequality, and solves the problem.

I. Overview

Math is related to the real world, and students can appreciate the application of the activity that involves both graphs and equations. The data is used in both explanation and extension of exponential functions.

II. Performance or learner outcomes

Students will be able to:

1) Use a mathematical model for population growth.

2) Determine the growth rate of a population.

3) Graph and interpret an exponential function.

4) Make predictions for growth population trends.

III. Resources, materials and supplies needed

· 6 King Size Bags of Skittles

· 7 Boxes with lids

· 25 Colored pencils

IV. Supplementary materials, handouts. (Also address any safety issues

Concerning equipment used)

· Buzz Bug Worksheets

· pieces of “Big Paper”

V. Safety Issues:

Please do not eat the skittles due to the fact everyone will be touching them.

Five-E Organization

Teacher Does Probing Questions/Remarks Student Does/Says

DAY 1:

Engage:

Teachers split class into 6 groups of 4 students. They will be assigned group numbers 1-6. Teachers have groups discuss and guess a) how many people inhabited the Earth 1000 years ago, b) how many people inhabit the world now, 3) how many people will inhabit it in 15-50 years, while writing their predictions down on notebook paper. Teachers pose problem: How can we guess population growth trends?

Teachers then inform them: “What if we tell you that there are approximately 5.4 billion people that inhabit the Earth today and approximately 1.8 billion people in 1900.” Also teachers will hand out a table of data from 1900 to present time with the avg. population for years in intervals so they can graph the data on their paper and observe what type of function it is.

Given this new information split into your groups again and discuss any changes you want to make to your predictions and what strategy you use to come up with the number. Teachers will then call on groups by number to have them present their data to the class while teachers write the provided data on the board.

How can we guess population growth trends?

These are all good responses.

Scientists are concerned about population growths and actually generate models based upon such data figures.

Today we will look at a simple case of Buzz Bugs before we later discuss our world population.

Varied figures such as 4 billion, 8 billion, 1 million, 1.3 trillion, etc.

Why does this matter?

Explore:

Objective for the day: Make predictions for growth population trends and develop and use a mathematical model for population growth.

Students will collaborate in 6 groups of 4, with their desks turned together.

Teachers will distribute materials needed for the buzz bug activities.

Each group will need a box with a lid, containing 50 Skittles. Each student will need a worksheet, graphing calculator, and colored pencil.

While teachers walk around supervising, they ask such probing questions as follows: What relationship do you see among your data What is the data showing us?

“What are we doing to the population each time, what is happening to it each shake?”

Students sit in appropriate groups and work with others on lesson, thinking about and answering teacher questions while recording their data on their worksheet then later transferring it to big paper to display to class.

For the activity, teachers will explain to students that they will place 2 buzz bugs in their container. (This is the initial population.) They will then close the lid, and shake the container.

Students will open the lid, and count the number of buzz bugs with marked side up and record their data on their worksheet. Teachers will emphasize buzz bugs reproduce asexually (i.e. by themselves), and that their reproduction is triggered when the marked side up of a buzz bug is exposed to light. Students will add one buzz bug to the container for each mark counted. They will then record the total number of buzz bugs now in the container in the table of their worksheets. They will later transfer this information on to big paper that they will later tape to the board and present to the class. This is the end of one "shake." The end of each shake represents the end of one time period. The number of buzz bugs presented at the end of a shake is the total population at that time. This continues until shake number 10, which should yield approximately 90 buzz bugs. When they are completely done with the buzz bugs activity they will take their data and draw a graph also on their big paper and tape their big paper onto the board and as a group present it to the class.

Teachers will then ask them questions like “What account for the differences in the results among groups? and etc.”

Teachers emphasize to the students that they should record the TOTAL number of bugs, not just how many got added on the last round.

What accounts for differences in results among groups?

How would these differences correspond to “real world” simulations in population growth?

What do you think scientists take into consideration for their assessments with in their models?

We’re out of skittles and we are only on shake 5.

DAY 2:

Explanation:

Teachers will ask students to get in old groups and devise an equation that will mirror the data gathered from the buzz bugs activity and present to class.

Once students have a suitable equation, teachers will have them predict what would happen on the 12^th toss of the buzz bugs and then see if the class equation works for the prediction and explain why their predictions were right or wrong.

Why was your equation wrong and what was you equation representing?

Elaboration:

Teachers remind students of initial human world population growth problem.

Teachers present graph of human populations to the students and have students reflect on predictions. Teachers give students the exact population of year 2020 as predicted by the U.N.

Evaluation:

Teachers will hand out a short in-class quiz.

Shake No.	Population
0	2
1
2
3
4
5
6
7
8