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Growing, Growing, Graphing!

Procedures for Teachers is divided into three sections:
Prep -- Preparing for the Lesson.
Steps -- Conducting the Lesson.
Extensions -- Extending the Lesson.
Tips -- Managing Resources and Student Activities.

Prep

Student Prerequisites:
Students should have knowledge of basic math applications, including addition, subtraction, multiplication, and division. Students should know the difference between linear and exponential growth functions. Students should be able to plot data points and make line graphs of data using graph paper, a graphing calculator, or if available, spreadsheet software such as Microsoft Excel.

Materials:
• notebook paper
• pens
• pencils
• markers
• graph paper
• poster board
• calculator (preferably graphing, like a TI-92 or Casio Algebra FX 2.0)
• rulers
Computer Resources:
You will need at least one computer with Internet access to complete this lesson. While many configurations will work, we recommend:

• Modem: 28.8 Kbps or faster.
• Browser: Netscape Navigator 3.0 or above or Internet Explorer 3.0 or above.
• Macintosh computer: System 7.0 or above and at least 16 MB of RAM.
• IBM-compatible computer: 386 or higher processor with at least 16 MB of RAM, running Windows 3.1. Or, a 486/66 or Pentium with at least 16 MB of RAM, running Windows 95.

For more information, visit What You Need to Get Connected in wNetSchool's Internet Primer.

Software:
• Any Word Processing Program (i.e., Microsoft Word, Corel WordPerfect, Apple Works, etc.)
• Any spreadsheet software (i.e. Microsoft Excel or Claris Works) (*optional: may opt to use only graph paper and a calculator)

Bookmarks:
The following sites should be bookmarked:

• Population.com
http://www.population.com/

Here you will find current information about population in 200 countries around the world.

• China Population Information and Research Center (CPIRC)
http://www.un.org/Depts/escap/pop/china/welcome.htm

CPIRC is the leading unit of the China Population Information Network (CHINA POPIN), a member of the Asia and Pacific POPIN, and the Global POPIN. This Home Page is designed to provide accessible information about its organizations, tasks, publications, Data User Service, and other related issues.

• Introduction to China
http://www.china-embassy.org/eng/gyzg/default.htm

This site provides links to geographic, historic, and population data of China.

• China Data Center - University of Michigan

This is an interdisciplinary center for China data development, GIS researches, and spatial studies. Click on "population" and then "Fourth National Census."

• Statistics on China
http://www.umsl.edu/services/govdocs/wofact99/102.htm

• Population Reference Bureau
http://www.prb.org/

A site providing timely and objective information on population.

• PopNet
http://www.popnet.org/

The source for global population information.

• United Nations Population Fund (UNFPA)
http://www.unfpa.org/index.htm

The state of world population in 1999.

• China Statistics
http://www.stats.gov.cn/english/

Surf China, Inc. provides up-to-date China statistical data.

• Statistical Data on the Republic of China
http://www.taipei.org/info/98html/stat-e.htm

• ABC Country Book of China
http://www.theodora.com/wfb/china_people.html

China interactive fact book.

• Interest and Exponential Growth Table
http://www.math.com/tables/general/interest.htm

Equations of different types of compound interest.

• Suzanne's Math Lessons: Graphing

This site has two great lessons on graphing linear functions and graphing exponential functions. Use this site to introduce these two concepts.

• Exponential Growth and Decay
http://www.physics.uoguelph.ca/tutorials/exp/Q.exp.html

 Steps Time Allotment: This lesson requires approximately 3 class periods. The extension lessons for other subjects will vary in length of time required for completion. Review the concepts of linear and exponential growth functions. Refer to Suzanne's Math Lessons: Graphing mentioned in Bookmarks. This site illustrates these two concepts. If using Excel or graphing calculators to graph data, briefly review how to use these tools, if necessary. Discuss world population growth, and why this is such an important world issue. Encourage students to provide input to the discussion. Organize the class into groups of preferably three students each. Students in each group should equally contribute to the tasks that follow. Preview a few of the bookmarked sites with the students (on a presentation monitor, if available), and explain how the sites can be used to find Chinese population information. Students should research and collect data on China's population, for a period of at least 10 years. If possible, find population data (estimated) for the past few decades. Record data in a table (either using spreadsheet software, remembering to save, or making a neat chart using a ruler and paper). Analyze the data so far. Is there a pattern? Is there a noticeable increase in the population of China over the time selected? If there are any drastic changes from one year to another, do some research to see if there is a reason for this change (due to a war, a disease breakout, natural disaster, etc.). Graph the data using graph paper and ruler. Make a line graph with population vs. time, plotting points for each piece of data, and then connecting the points with straight lines. Is there a noticeable trend in the graph? Does the population growth appear to be an exponential or linear pattern? (Students may instead want to use the graphing tools in the spreadsheet software, or a graphing calculator.) Compare the data to an exponential function like y=2x. Can you write an exponential function that closely mimics the data you found? Look at the graph and extrapolate what the population in China will be 5 years from now, 10 years from now, and 20 years from now. How about in the year 2100? Are you worried about the population growth in China, and in the entire world? Why or why not? Conduct a class discussion after assignments are complete about general findings, observations, and any surprises from the research. What possible scenarios could occur due to exploding population growth?

Extensions

Social Studies: Students may research population control policies of foreign countries. Are these policies necessary? Are they fair? What about our town efforts? Students may debate these questions.

Science: Students may research and graph data of bacteria growth, which is an exponential phenomenon. Students may also explore the half-life of a radioactive substance, which is an example of exponential decay. Find out how long it would take specific radioactive materials found in toxic waste to decay. What are the impacts of this?

Economics: Students may analyze the effect of population growth on the world's finances. Local and foreign economies, job markets, and food supplies are elements that can be affected by increasing populations. Also, students may explore the exponential phenomenon of compound interest over time. Start saving those pennies!

Speech: Students may write and present a persuasive speech for or against government-regulated population control. Is it necessary? Is it humane?

Tips

One Computer in the Classroom
If you have access to one computer in your classroom, you can organize your class in several ways. Divide your class into two groups. Instruct one of the groups to do paper research while the second group is working on the computer. Bring in books, encyclopedias, etc., from the library for the group doing paper research. Lead the group working at the computer through an Internet search or allow the students in the class to take turns. (Always have a set of bookmarks ready for the students before they start working on the computer, in order to show them examples of what to look for.) When the groups have finished working have them switch places.

If you have a big monitor or projection facilities, you can do Internet research together as a class. Make sure that every student in your class can see the screen, go to the relevant Web site(s), and review the information presented there. You can also select a search engine page and allow your students to suggest the search criteria. Again, bookmark and/or print the pages that you think are helpful for reference later.

Several Computers in the Classroom
Divide your class into small groups. Groups can do Internet research using pages you have bookmarked. Group members should take turns navigating the bookmarked sites.

You can also set the class up so that each computer is dedicated to certain sites. Students will then move around the classroom, getting different information from each station.

Using a Computer Lab
A computer center or lab space, with a computer-to-student ratio of one to three, is ideal for doing Web-based projects. Generally, when doing Web-based research, it is helpful to put students in groups of three. This way, students can help each other if problems or questions arise. It is often beneficial to bookmark sites for students ahead of time.

Submit a Comment: We invite your comments and suggestions based on how you used the lesson in your classroom.

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