Circumference of the Earth
Lesson Plan

Developed byDavid McAdams
Based on a lesson plan by Mr. Duff of Kickapoo H.S. Springfield, Mo
Last update3 Dec 2005
Grade Level9
SubjectGeometry
Digital versionhttp://www.lifeisastoryproblem.org/lesson/index.html
CopyrightUnpublished copyright work 2005, David McAdams, Orem Utah

Permission is hereby granted for noncommercial reproduction of this document unchanged and in its entirety. Also, worksheets and rubrics may be reproduced for noncommercial purposes. Portions may be included in other works if the statement "Portions copyright © 2005 by David McAdams, Orem, Utah" is included.

Contact
Contact the author at DEMcAdams@usa.net.
  1. Goal(s)/Standards
  2. Specific Objectives

    At the end of the lesson the student will be able to:

  3. Materials/Preparation
  4. Prerequisite Vocabulary
  5. Prerequisite Methodology

    None

  6. Instructional Procedure
    1. Review
      1. Review the circumference of a circle.
      2. Review that angles adding up to full circle make 360 degrees.
      3. Review the postulate for corresponding angles (Euclid's Postulate 5).
    2. State the problem and objective
      1. State the problem: "How could we calculate the circumference of the earth?" Allow the students to explore ways. Some possible ways include:
        1. Measure the width of the earth from space/the moon.
        2. Travel around the earth at a constant speed.
        3. Eratosthenes method
        Do not reject invalid methods at this time. The students will have the opportunity to evaluate each method later in the lesson.
      2. State and write on the board that at the end of the lesson, students will describe in their math journals at least one method of measuring the circumference of the earth, including samples; and complete a worksheet using Eratosthenes method of calculating the circumference of the earth.
      3. Evaluate the proposed methods.
        1. Form several groups, at least one for each method that will be explored.
        2. Assign each group a single proposed method. Explain the ground rules:
          1. Each group is to determine if this method is valid (if it will give reasonable results). The group is to explain why it is valid or invalid.
          2. Each group will be responsible for explaining the math involved, including a sample.
          3. If the person proposing the idea disagrees with the group they are allowed to give a dissenting opinion after the group presentation.
          4. After the presentation, all students are allowed to ask clarifying questions first, and then offer additional opinions.
          5. The teacher will then assist the students in developing the idea, filling in any missing parts.
        3. Give the groups sufficient time to work, perhaps 30 minutes.
        4. Group presentations
      4. Lecture on Eratosthenes and his method of calculating the circumference of the earth.
        1. Differentiate between negative sign and minus sign. Point to negative sign and ask, "Is this a minus sign?" Lead discussion to conclusion that since backward is not being subtracted from anything it can not be a minus sign. State that it is a negative sign. Have students form groups and make a group statement of the difference between a minus sign and a negative sign.
    3. Develop the experiment.
      1. Tell the class that they will duplicate Eratosthenes experiment. Ask them what we need to have and do to duplicate the experiment. As they develop the ideas, introduce or reinforce the arrangements you have made. The arrangements include:
        1. A staff of know length
        2. A tape measure or ruler
        3. A clock, synchronized with the other class
        4. A plumb bob to make sure the staffs are upright.
        5. A worksheet to record the data.
      2. Complete a phone call to the cooperating class to synchronize clocks.
    4. Perform the experiment.
      1. Assist the students in setting up and performing the experiment at the appointed time and recording the experiment.
      2. Average the experimental data for the entire class.
      3. Complete a call to the cooperating class and exchange data.
      4. Have the students assist each other in completing the worksheet.
    5. Allow the students sufficient time to describe a method of calculating the circumference of the earth in their math journals.
  7. Differentiation for Diverse Student Needs
  8. Assessments
  9. References

    1National Council of Teachers of Mathematics, Principles and Standards for School Mathematics, 2000

  10. Other Resources
    1. About.com, Eratosthenes, The Father of Geography
    2. Livio C. Stecchini, Ancient Measurements of the Circumference of the Earth
    3. J J O'Connor and E F Robertson, Eratosthenes of Cyrene
  11. Materials Masters

    Download Worksheet for Calculating the Circumference of the Earth
    Download Rubric for description of a method to calculate the circumference of the earth