Two Wheels and a Belt

This Two Wheels and a Belt activity & project also includes:

Geometry gets an engineering treatment in an exercise involving a belt wrapped around two wheels of different dimensions. Along with the wheels, this belt problem connects concepts of right triangles, tangent lines, arc length, and central angles. Roping in a helping of precision in calculation makes for a well-rounded problem, one that requires high-level thinking and synthesis from the class.

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CCSS: Designed
Instructional Ideas

  • Have learners bring in circular objects to recreate thw scenario with different dimensions, then cut belt to calculated measurement
  • Have one group use the calculated value of arccos and one wait until the end to show the value of the accumulated error
  • Bridge into a lesson on gear ratios and other engineering applications 
Classroom Considerations

  • Providing a physical model might help concrete learners develop the necessary triangles more easily
  • Shorten the lesson by having three different groups calculate the three different section lengths, then present and collaborate for a total length
Pros

  • Easily modeled but high-level problem bridges concrete and abstract geometric concepts
  • Combination of concepts from multiple lessons (circles, triangles, and trigonometry) makes for an excellent summative assessment
Cons

  • No clear separation between student problem and teaching notes / answer key