Young geometers become pool sharks in this analysis of the angles and lengths of a trick shot. By using angles of incidence and reflection to develop similar triangles, learners plan the exact placement of balls to make the shot. Alternative solution methods extend the problem, quite literally, outside the box, while fractional solutions give practice in some of the messiness of real-life measurements.

Concepts

similar triangles, angle of incidence, angle of refraction, math modeling

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Additional Tags

math

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Instructional Ideas

• After this activity, have the class create similar problems for one another to solve
• Link with a physics or physical science unit on inelastic / elastic collisions and the relationships of force, momentum, and distance in pool
• Have learners diagram and analyze trick shots from videos of professional pool players

Classroom Considerations

• If references to pool or billiards are controversial, activity might need rewording. Pupils unfamiliar with the language of billiards might need help with some of the problem's terms
• The activity-mentioned consideration points out that learners without a strong physical science background might need supports for developing the equality of the angle of incidence and angle of reflection

Pros

• Real-world problem with multiple attack methods and worked-out solutions
• Specific application of similar triangle theorems and properties
• Synthesis of algebraic equation writing and geometric relationships to solve the problem

Cons

• Class problems are not separated from the teaching notes and answer key

Common Core

HSG-SRT.B.5