Computer gaming is a key component of the rapidly growing entertainment industry. While building computer games has typically been a commercial endeavor, we believe that designing and constructing a computer game is also a useful activity for educating students about geometric modeling and computer graphics. In particular, students are exposed to the practical issues surrounding topics such as geometric modeling, rendering, collision detection, character animation and graphical design. Moreover, building an advanced game provides students exposure to the real-world side of software engineering that they are typically shielded from in the standard computer class. In this paper, we describe our experiences with teaching a computer science class that focuses on designing and building the best game possible in the course of a semester. The paper breaks down a typical game into various components that are suited for individual student projects and discusses the use of modern graphical design tools such as Maya in building art for the game. We conclude with a rough timeline for developing a game during the course of a semester and review some of the lessons learned during the three years we have taught the class.