Seven Circles III

This Seven Circles III activities & project also includes:

A basic set-up leads to a surprisingly complex analysis in this variation on the question of surrounding a central circle with a ring of touching circles. Useful for putting trigonometric functions in a physical context, as well as linking the trig of triangles with that of circles. A great bridge into the higher-level thinking that upper-level mathematics requires of motivated learners.

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CCSS: Designed
Instructional Ideas

  • A variety of geometric manipulatives or modeling programs are available to demonstrate the outer circles surrounding the central circle
  • Use to introduce double- and half-angle formulas
  • Consider the spacing and quantity of outside spheres needed on a central spere in 3-D
Classroom Considerations

  • If not used in sequence with Seven Circles I or II the class might need some help setting up the triangles and ratios needed for the calculations
  • Use as a refresher lesson on triangle trigonometry before introducing unit circle trigonometry, to help strengthen links between the two

  • Clear set-up and step-by-step answer key leads the class through analysis
  • Diagrams provided throughout add key information and insight
  • General application of answers emphasized, rather than specific values

  • Teaching notes and answer key not clearly separated from the class activity part