This article shows how to use six parameters describing the International Space Station's orbit to predict when and in what part of the sky observers can look for the station as it passes over their location. The method requires only a good background in trigonometry and some familiarity with elementary vector and matrix operations. An included set of exercises leads the reader step-by-step through the computations. Specific instructions are included for implementation of the method using a spreadsheet tool such as Excel. This article gives students the rare opportunity to use classroom mathematics to solve a complicated real-world problem, and to observe the results of their solution in real time.