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Lesson title:  A study of world population

Subject and Grade Level:  9 - 12th grade Mathematics ;  Science ;  Social Studies ;  Environmental Studies

Brief Description:   An introductory investigation of exponential functions through a study of world population.

Objectives —The students will be able to:

    1.   Solve real life mathematical problems.

    2.   Graph results of their problem solving to give visual representations of their results.

    3.   Recognize the difference between linear and exponential relationships by studying data.

    4.   Speculate on the reasons for changes in population in the U.S.A and the world.

Educational/Skills Goals (Mathematics):

    1.   Mathematics as Problem Solving,  Communication,  Reasoning and making Connections

    2.   Investigation of Statistics and projections based on an analysis of the data.

    3.  Explore  real-world phenomena representing situations that involve variable quantities with expressions, equations,  and  inequalities.

    4.  Use tables and graphs as tools to interpret expressions, equations, and inequalities.

    5.  Use the Internet to search for information at selected sites.


Internet resources involved (web addresses)

          URL:   Reference:

Other Resources:   National Geographic December 1988;  World Almanac;  Encyclopedias; Encarta

Procedure:   In groups of  2-3 students,  prepare a report on the population explosion.  Include statistics and graphs as requested ,  with comments suggesting reasons and explanations as detailed below.

  • Draw a graph of the U.S. population for the years 1650-2000,  using population figures (in millions) for the vertical axis and  years on the horizontal axis (in 50 year intervals).
  • For the years 1790-1860 find the percentage growth rate.  [(1860 pop)/(1790 pop)] X 100.  Suggest reasons why you think the growth rate is that figure.  Estimate the 2000 population if the population had continued to change at this rate. Compare this figure to the actual estimate.
  • Find the mean (average) yearly growth rate of the U.S. population from 1970-1980 and from 1980-1990.  [(1980 pop)/(1970 pop)] X 0.1.   What do you find in your results?
  • If the 1980's growth rate continues in the 1990's estimate the 2000 population.  Estimate the time it  will take the U.S. population to be double the 1990 figure.  When do you think the population in the U.S. will reach 1 billion?
  • For what reasons,  do you think,  may a population's growth rate increase or decrease?  Which of these factors were present during the different 50 year periods from 1650-2000?

Timeline:   1 week.

Non-Internet Activities:  Class work on linear functions and exponential functions (interest rates)

Internet Activities:

    • Visit and explore the U.S. Census site and determine the estimated population of the U.S.A at 50 year intervals from 1650 - 2000.
    • Study the exponential growth graphs at the appropriate site.
    • Visit the Fibonacci Rabbit site to see a population explosion.

Assessment (Evaluation):

Holistic Scale

  • 6         Fully achieves the purpose of the task, while insightfully interpreting, extending beyond the         task, or raising provocative questions.  Demonstrates an in-depth understanding of concepts and content.   Communicates effectively and clearly to various audiences, using dynamic and diverse means.
  • 5         Accomplishes the purposes of the task.  Shows clear understandings of concepts.  Communicates effectively.
  • 4         Substantially completes purposes of the task.  Displays understanding of major concepts, even though some less important ideas may be missing.  Communicates successfully.
  • 3         Purpose of the task not fully achieved; needs elaboration; some strategies may be ineffectual or not appropriate; assumptions about the purposes may be flawed.  Gaps in conceptual understanding are evident.  Limits communication to some important ideas; results may be incomplete or not clearly presented.
  • 2         Important purposes of the task not achieved; work may need redirection; approach  to task may lead away from its completion. Presents fragmented understanding of concepts; results may be incomplete or arguments may be weak.  Attempts communication.
  • 1         Purpose of the task not accomplished.  Shows little evidence of appropriate reasoning.  Does not successfully communicate relevant ideas; presents extraneous  information.

Follow-up Activities and Extensions:  Extend the project to include other variables such as improved medical help contributing to a declining death rate,  possible food shortages,  global warming,  overconsumption of natural resources  and .....

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After the lesson is taught, review the following:

    Set-Up Time Required

    Class Time Required

    Problems and Issues that were encountered


    Recommendations for Improvement


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