Lesson Plan 1

Name: Lauren Thibodeaux

Title of lesson: Exponential Epidemic

Date of lesson: April 27, 2004

Length of lesson: 45 minutes

Description of the class:

                     Name: Algebra I

                     Grade level: 9th Grade

                     Honors or regular: Either

TEKS addressed:

(3) The student understands there are situations modeled by functions that are neither linear nor quadratic and models the situations. Following are performance descriptions.

(A) The student uses patterns to generate the laws of exponents and applies them in problem-solving situations.

(B) The student analyzes data and represents situations involving inverse variation using concrete models, tables, graphs, or algebraic methods.

(C) The student analyzes data and represents situations involving exponential growth and decay using concrete models, tables, graphs, or algebraic methods.

Sources:

http://www.byu.edu/ipt/projects/middleages/LifeTimes/Plague.html

http://www.pbs.org/weta/thewest/lesson_plans/lesson09.htm

The Lesson:

I.  Overview

Students will discover that some diseases spread exponentially. Students will demonstrate the spread and then discover a pattern for the spread modeled. Finally, students will graph the spread on graph paper.

II.   Performance or learner outcomes

          The students will be able to:

á      Find number patterns

á      Discover a formula for the number pattern

á      Make a chart based on the formula

á      Graph the equation on grid paper

             

III. Resources, materials and supplies needed

 Red cards, colored stickers, grid paper, paper, pencils, overhead, overhead pens, blank transparency

 

IV. Supplementary materials, handouts.

             

                        Teacher Does                                               Student Does

Engage:

Learning Experience

The teacher will begin class by giving a brief history lesson: ÒIn the early 1330s an outbreak of deadly bubonic plague occurred in China. Plague mainly affects rodents, but fleas can transmit the disease to people. Once people are infected, they infect others very rapidly. Since China was one of the busiest of the world's trading nations, it was only a matter of time before the outbreak of plague in China spread to western Asia and Europe. After five years 25 million people were dead--one-third of Europe's people.Ó The teacher will explain that the stack of red cards at the front of the room represent the bubonic plague. The teacher will explain that the class is going to simulate the spread of the bubonic plague throughout the classroom. The teacher tells the students that each time someone comes into contact with the disease or a red card, they will catch the disease. The teacher explains that she is the first to come into contact with the disease, so she takes one card for herself, then breaks the remaining stack into two even piles and gives the two new stacks to two students. The teacher tells each of the students that they have now come into contact with the disease, so they must take a card for themselves, then divide their pile into two even stacks and pass them to two students who have not yet received the stack. The teacher will tell the entire class that each of them must follow the same procedure until all students have a card.

 

 

What the students are doing

Listening attentively.

 

 

 

 

 

 

 

 

 

 

 

 

Taking one card, dividing the remaining stack of cards into two piles, and passing the piles to two classmates who have not yet received a card.

 

 

Evaluate

The teacher will ask the students to draw a diagram showing how many people are infected with the bubonic plague while the stack of cards is being passed.

            Teacher Does                                                   Student Does

Explore:

Learning Experience(s)

As the students are passing around the cards, the teacher will make a diagram on the overhead representing the pattern that is occurring while the cards are being passed. The teacher will ask the students, ÒHow many people are infected right now?Ó each time the cards are passed. The teacher will then record the number of people holding a card at each step on the overhead diagram. Once all students have a card and all numbers are recorded on the overhead diagram, the teacher will break the students into small groups using a small color coded sticker that has already been placed in the corner of all red cards. The teacher will ask the students to find and discuss all number patterns in the diagram and find a formula for the number pattern they have discovered. If students have problems, the teacher will encourage the students to find another number pattern by examining the number of people who are given a stack each time the cards are passed instead of the total number of people with cards. 

       Questions

1.     How many people are infected right now?

2.     How many people catch the disease at each pass of the cards?

3.     What is the formula?

 

What the students are doing

Passing cards.

 

Answering questions

 

 

 

Move into groups.

 

Discuss all patterns found and find a formula for the number pattern. 

     

 

 

Expected Student Answers

  1. 1, 3, 7, etc.
  2. 1, 2, 4, etc.
  3. 2x

Evaluate

If the stack was broken up into three piles every time and passed to three more students each time, what would the formula be?

            Teacher Does                                                   Student Does

Explain:

Learning Experience(s)

Once the students have found the formula for the number pattern, the teacher will ask the students to make a t-chart labeling one side of chart x and the other side 2x. The teacher will ask the students to fill out the chart from x=0 to x=10. Then the teacher will ask the students to graph the equation on large grid paper. The teacher will tell the students that each group will post their large grid paper at the front of the room. The teacher will ask each group to decide what happens to the graph as x gets larger and to predict what the graph will look like when x = 25.

        Questions

1.     How would you describe the shape of this graph?

2.     Would you characterize this graph as linear? Why or why not?

 

What the students are doing

Making a chart and graphing the equation on grid paper.

 

 

     

 

Posting grid paper at the front of the room and answering questions.

 

Expected Student Answers

  1. Half of a rainbow
  2. No, it is not a straight line

Evaluate

To make sure that all students can plot graphs appropriately, each student will be asked to plot the graph of the equation 3x.

                                                                   

            Teacher Does                                                   Student Does

Extend / Elaborate:

Learning Experience(s)

 The teacher will have the students research different diseases on the internet. The teacher will ask the students to find out how the disease spreads through a population. The teacher will ask the students to plot graphs of the spread of various diseases. The teacher will hold a class discussion about their results.

       Questions

1.     What diseases did you research?

2.     Do all diseases spread exponentially?

3.     How do different diseases spread?

 

What the students are doing

 Researching on the internet.

 

Plotting graphs of the spread of diseases.

Discussing as a class and answering questions.

      Expected Student Answers

  1. Cholera, AIDS, etc.
  2. No
  3. Linearly

     Evaluate

Each student will write a paragraph about one disease they researched on-line. The paragraph should include how the disease is spread throughout the population as well as a picture to represent this spread.