Part of the power of algebra is that it provides students with tools that they can use to model a variety of problems and applications. Such modeling requires them to understand patterns and choose from a variety of representations--numeric, graphical, symbolic--to construct a model that accurately reflects the relationships found in the original problem or context. This article presents a student investigation which is built around a problem of interest to most students. This probability exploration built on shooting basketball free throws leads unexpectedly to the golden ratio. This exploration illustrates how a contextual problem can provide students with opportunities to use the mathematics they know to represent and model both the original problem and extensions that they themselves generate. In addition, student explorations such as this one have the potential to help students further develop their mathematical understanding, skills, and problem solving. (Contains 7 figures and 2 tables.)