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.

Concepts

circles, right triangles, trigonometric functions, arc length, tangent lines

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Additional Tags

math

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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

Common Core

HSG-SRT.C.8 HSG-C.A.1 HSG-C.A.2 HSG-C.A.3 HSG-C.A.4 HSG-C.B.5