Utilization Strategies

Lesson Plans

Meet the Teachers




by Deanne Clifford
University of Idaho


GRADES 10 - 11


The first part of this unit will present circles and the various angles, arcs, sectors, rays, lines, and segments associated with them. The lesson continues with the study of surface area and volume of spheres and closes with a presentation of spherical geometry. These lessons and activities can take from 3-5 class periods. The primary source for this lesson plan is Life by The Numbers video and web site: www.pbs.org/wqed/lifebythenumbers/


Students will be able to:

  • Identify types of arcs and angles in a circle.
  • Find the measure of arcs and angles.
  • Find arc and angle measures when segments intersect circlesSolve real world problems involving segments that intersect circles.
  • Identify relationships among arcs and chords of circles.
  • Solve real world problems involving arcs and chords of circles.
  • Find lengths of segments formed by chords, tangents and secants.
  • Solve real world problems involving lengths of segments in circles.
  • Find lengths of arcs and areas of sectors.
  • Find lengths and areas in real world situations.
  • Calculate the surface area and volume of a sphere.
  • Compare volumes and surface areas of similar solids
  • Represent lines and shapes on a sphere.
  • Explore geometry on real world spheres.


For group of 25 students


We begin these lessons with a review/discussion of geometric terms: central angle, inscribed angle, chord, tangent to a circle, arcs and spheres. Students will be given Vocabulary worksheet #1 to take notes. Introduce the idea of spheres with the Danny Glover introduction.



To give students a specific responsibility while viewing, tell students to identify the 3 ways cartographers make maps and also to note the definition of geometry.


BEGIN video at beginning with Danny Glover's discussion of spheres. Pause after the demonstration of the corridor boundaries by the terrain visualization equipment. Discuss with students how the earth is measured and the definition of geometry and why spheres are so interesting.

RESUME the video when Robert Osserman, of the Mathematical Sciences Research Institute, Berkeley begins talking. To give students a specific responsibility for viewing have the students note why circles and spheres are important. Also ask students to identify any new vocabulary words they hear during this segment and to explain why the Greeks were so important to mathematics.

PAUSE the video when they show photographs of mountains. Discuss with the students what the Greeks had to do with Geometry and why geometry is essential to map-making. How did the Washburns' determine the height of mountains using geometry? Complete vocabulary worksheet # 2 and the Chord worksheet in class.

NOTE: Plan a day to go outside and apply this technique to measuring the mountains range nearby. Check with a local forest service or BLM office to see how close the estimates are to the actual numbers.

RESUME the video where you hear Danny Glover discussing how we find our position on the earth. Student's specific responsibility while viewing is to define what GPS is and how it was defined. Why is GPS important? Stop the video when you see the car with the GPS system driving away. Introduce the Global Positioning Worksheet. Discuss with students the properties of GPS and as a class complete the Global Positioning Worksheet.

RESUME the video when you see Robert Kirschner enter the observatory to fix the telescope. Have students note how scientists are mapping the universe. STOP and review the video as needed for the processes of measurement. Definitely repeat the portion of the video when the doctor says, "projects a circle on the earth that only could have that angle…" this section is ideal for discussion of angles and segments from satellites to the earth!




Finding out that there are geometries other than the one they are familiar with opens new worlds of interest for students and they are able to see the value of Math for a variety of purposes. Allow students to share their overall impressions from the past week via whole group discussion. After discussion allow students to write a brief essay that expresses their ideas and feelings about this significant fact.


Completing the "Exploring of Earth from Space" Student Worksheet is a great way to apply this unit to science and geography. On the links provided there are also contests that students can enter with NASA Student Involvement Program at: http://www.nsip.net

It is preferred to illustrate spherical geometry on The Geometer's Sketchpad. (Nicholas Jackiw, designer. Windows and Macintosh versions. Berkeley, CA: Key Curriculum Press, 1995.) Using a computer with a remote LCD is preferred, however this illustration can also be accomplished by grouping students at computers.

This site provides links and valuable information for teacher and student resources in the mathematics of earth studies.


This site is where "exploring Earth From Space Lithograph Set and Instructional Materials can be found. These materials are used in the extensions of this unit. This set of materials provides sites for further exploration through links and books.

.materials/ nasa.educational.


Assessment can be in the form of portfolio entries about projects or unit quizzes and exams. The worksheets are a great place from which to model exam questions. You might also include specific questions from the video as well. Let the students know that taking notes during the video would be wise.

For additional lesson plans and ideas relating to this topic and many others try TeacherSource at PBS Online! You will find activities, lesson plans, teacher guides and links to other great educational web sites! Search the database by keyword, grade level or subject area! Mathline and Scienceline are also great resources for teachers seeking teaching tips, lesson plans, assessment methods, professional development, and much more!

The Idaho 2000 National Teacher Training Institute is made possible through the efforts of

Idaho Public Television