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This Seven Circles III lesson plan also includes:
- Activity
- Answer Key
- Teacher Reference
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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 students.
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CCSS:
Designed
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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
Pros
- 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
Cons
- Teaching notes and answer key not clearly separated from the class activity part