Project AMP Dr. Antonio Quesada – Director, Project AMP

Influenza Outbreak Abstract

Subject: Advanced Algebra, Precaclulus, Calculus, Statistics

Strand: Data Analysis

Topic: Regression

Grade: 11-12

Objectives:

1.  Use a graphing calculator to calculate and graph a suitable regression for a given problem situation.

2.  Determine the reasonableness of a mathematical model by relating it to the problem situation.

3.  Synthesize findings in a written report and/or electronic presentation including charts and graphs

Materials: TI-83, Worksheet

Expected Time: 2-3 days

Influenza Outbreak

Overview

Authors: Dave Erb & Donna Duve

Description: Graph, explore, interpret, and calculate data pertaining to a logistic equation.

Keywords: Regression, logistic, calculus, precalculus, disease control, statistics

Prerequisites: Some knowledge of how to calculate a regression equation on a TI-83

Grades: 11-12

Subjects

Economics

Social Sciences

Life Science

Mathematics

Speech

Writing

Concept

1.Estimation and prediction by use of mathematical models is an essential skill in a competitive market place.

2. Available technologies have a large impact on society.

3. Effectively communication of ideas is a necessary life skill.

4. Working cooperatively with peers is essential to the success of individuals and companies.

Assessment

Rubrics

Student presentation

Written explanation

Sharing

Electronic presentation software or overhead projector can be used for students to present their regression models and analysis of the model of best fit. Presentations will be made to other teachers and classes as well as in class.

Results

Students will have explored the effects of the introduction of a disease to a fixed population. They will have a better understanding of how the Centers for Disease Control and Prevention (CDC) are able to predict outcomes and epidemics. Students will also have a better understanding of regression models and the logistic function in particular.

Learning Objectives

4.  Use a graphing calculator to calculate and graph a suitable regression for a given problem situation.

5.  Determine the reasonableness of a mathematical model by relating it to the problem situation.

6.  Synthesize findings in a written report and/or electronic presentation including charts and graphs

The following is a list of the Learning Outcomes associated with this lesson lab

OPO Ninth-Grade Math 12

OPO Twelfth-Grade Math 5

OPO Twelfth-Grade Math 6

OCBM Grade Eleven – Integrated Strand One – 3

OCBM Grade Eleven – Integrated Strand Five – 8

OCBM Grade Eleven – Integrated Strand Five – 10

OCBM Grade Eleven – Integrated Strand Eight – 2

Project/Task

Graph, interpret, and calculate a regression model related to the spread of disease in a fixed population

Learning Strategies

1. Begin by having students explore the CDC website (http://www.cdc.gov)

2. Present project through worksheet

3. Group students to analyze data and prepare presentations

4. Have students prepare presentations for CDC “experts”

5. Conduct presentations.

Tools/Resources

TI-83 or TI-83+ Calculator

TI-Graph Link

Teacher prepared data and problem statement

Computer programs for web browsing and electronic presentation

Do and How

1. Access CDC website for information on disease spread prediction

2. TI-graph link is a cable and software package from Texas Instruments, which allows the user to place calculator screens into word processing documents and presentation software.

Classroom Management

Assign small groups of three students. Discuss teamwork and cooperation by helping students set up team structure and accountability processes.

Teacher should introduce problem and emphasize what is to be accomplished. Teacher will oversee completion of analysis and development of presentation materials.


Addendum

The Spread of Disease

Epidemics are a major threat to human, animal and plant population. The worst epidemic in recent times was the global influenza epidemic of 1918 and 1919. About 2o million people died worldwide, including about 500,000 in the U.S.

The Center for Disease Control (CDC) was established to promote health and quality of life by preventing and controlling disease, injury, and disability. As a result, they are very interested in studying diseases and how they spread.

Recently, on a local college campus of 5000 students, one student returned from vacation with a rare strain of a very contagious 3-day flu virus. The virus was so easily transmitted that any contact with an infected person resulted in the virus being passed. The situation became even more complex when it was discovered that the virus carries a twenty-four hour incubation period, during which the infected person is contagious but often shows no symptoms. Thus, many people did not even know they had come into contact with the virus. The only good thing about this virus is that once you had contracted it and been ill, your body’s immune system was able to build antibodies that would prevent you from getting the virus again.

The records of the number of people infected were just recently found, but they were incomplete. It appears the Campus Medical Center was so over run with infected patients and staff members, that accurate records were not recorded. The only data that could be found was the following table written by the Doctor at the Campus Medical Center.

Day # of people infected

1  2

2  5

3  11

5  54

10  1868

15  4851

The CDC would like to know more about this virus and how it spread through this population so they can possibly prevent it from happening again. As your math teacher, I gladly volunteered your services to them in order to create a mathematical model that reasonably fits this data. My friend Dat, who is a data analyst for a major corporation, suggests that you examine the quartic, exponential, and logistic regression models to determine which one best fits the data and the circumstances.

Since these results must be presented to the CDC, you will need to compile your information into a report to be presented to them. They’ve informed me that they will be in our area within the next three days and that they will need to review your models at that time. Your presentation can be done using a computer presentation system or by creating your own visual aids. Be sure to include some screen shots from your TI-83, the CDC really likes to see proof of what lead you to your conclusion of the model of best fit.

Since this is such a large and important project, I think I will put you into groups of three to prepare your presentations. The groupings will be posted soon, so prepare to get busy on this project.