Global Positioning System II

Intricate details of a modern technology that many of us take for granted in our phones, computers (and some cars) are laid bare in a short but deeply investigative activity. The math behind a seemingly simple GPS device is explored here, specifically through the use of intersecting spheres to demonstrate how a device is so precisely located. Open-ended questions are given thorough geometric and algebraic treatment in the answer key, along with teacher notes where more information is available.

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CCSS: Designed
Instructional Ideas

  • Could be an extension project for an advanced level class or a choice for a student-led project
  • Possible co-curricular links with a science unit on radio signals, satellites or orbiting bodies.
Classroom Considerations

  • The more information link for Global Positioning Systems takes the reader to Wikipedia (which may be blocked in the classroom, or a forbidden source for research).
  • Algebraic reasoning section requires knowledge of conic sections and spheres, possibly not introduced until Algebra 2.
  • Student worksheet is not separated from background considerations or answer key.
  • Explanations reference color-coded spheres, might need adaptation for grayscale copies
Pros

  • High degree of relevance and complexity
  • Open-ended questions lend themselves to higher orders of thinking 
  • Strong development of links between geometry and algebra
Cons

  • On page 2 diagram, satellite 3 is matched with distance d2 while satellite 2 is matched with distance d3.
  • Page 11 "c. Any location of satellite 3 which will is not equidistant" typo
  • Second diagram of intersecting spheres (top of page 6) does not contain the purple sphere.
  • Pupil directions are not very clear on expected response—whether it is just the counterexample, the geometric justification and diagrams, the algebraic proof, or some combination of the three.
Common Core