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.

Concepts

gps, spheres, 3-d figures, geometric, linear modeling

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Additional Tags

math

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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

HSG-GMD.B.4 HSG-MG.A.1 MP4