1. Upon completion of the simulation,

students will be able to explain what factors affect the spread of viruses, 90 percent of the time.

students will be able to identify the type of graph that models the spread of infection in a population, nine times out of ten.

students will be able to explain what the graph means and make predictions from a graph, 90 percent of the time.

2.  This lesson is part of our unit on quadratic and exponential functions.  We have already discussed quadratic equations.  This activity will introduce you to exponential functions and logistic functions and how they are used to model growth and decay.  

3. You will be permitted 15 minutes of class time each day for the next week to complete the simulation and prepare their conclusions.  Conclusions will be presented the following week during one class period. 

4. The main questions that you need to answer during and after this simulation are:

What factors cause viruses to spread quickly over time with a high percentage of the population infected?

What type of equation produces a this type of graph?

What can you learn from the graph?  What can you predict with the graph?

1. Procedure: 

  1. Go to the simulation at http://www.nctm.org/mathhereandnow/pandemic/

  2. Work through the activities on the first page.  Record your answers and observations.

  3. Read about what pandemics are http://www.nctm.org/mathhereandnow/pandemic/birdflu.asp and the history of pandemics  http://www.nctm.org/mathhereandnow/pandemic/history.asp

  4. Read and work through the questions posed on this page about how to minimize the threat of pandemics http://www.nctm.org/mathhereandnow/pandemic/threat.asp

  5. Read this page about the math behind this model  http://www.nctm.org/mathhereandnow/pandemic/whatismath.asp

You should be able to get through these steps in the forty minutes.  The remaining forty minutes should be spent on drawing conclusions and planning your presentation of those conclusions.

What are the specific step-by-step activities or procedures that the students will participate in during the web-integrated activity?  What is the timeline for these activities?

2. You will work in groups of 2 to complete this simulation.  You will work on the computers together, making observations, interpreting your findings, and drawing conclusions.  Then you will work together to present your conclusions.

3. Ms. Au will observe the groups throughout the activity to make sure that you are on task.

1. Website Resources

NCTM Math Here &Now

http://www.nctm.org/mathhereandnow/pandemic/

This is an activity provided by NCTM that investigates the mathematics behind the spread of viruses. 

This is the site of the simulation.

World Health Organization

http://www.who.int/mediacentre/factsheets/fs211/en/

This is an influenza fact sheet produced by WHO.

Nobilion International

http://www.nobilonvaccines.com/htm/coreactivities_influenza.htm

This website contains frequently asked questions about influenza. 

Other Resources

Cartwright, Frederick F., and Michael Biddiss. Disease and History, 2nd revised edition. Darby, PA:

Diane Publishing Company, 2000.

2. Ideally there would be enough computers available for all of the students.  However, at least four computers are needed.  Groups of two will work together on the computer.  The groups may have to take turns using the computers.  

3. Supplemental activities can include a discussion with an epidemiologist from the University of Pittsburgh in person or through email, a field trip to a lab where diseases are studied to see what an epidemiologist does, and vaccines administered or antibodies awarded to those who successfully survive the simulation. 

1.  After you have completed the simulation, you may choose one of the following methods to present your conclusions: 

Write a 2 page lab report.

Create a PowerPoint presentation to report your findings at a conference on pandemic flu prevention.  

Create a video where one partner is a reporter interviewing the other partner who is an expert epidemiologist.

Any other creative way of sharing your findings with the class, as approved by the Ms. Au.

2. Following the simulation we will learn more about logistic curves and their symmetry.  We will also discuss what natural occurrences can be modeled by logistic curves.  

3. Students will be evaluated on their active participation and completion of the simulation.  Reports and presentations will be evaluated on the conclusions made and their presentation of those conclusions.

4. For further study you may wish to Ask Dr. Math about this topic: http://mathforum.org/library/drmath/view/53729.html