The Euclidean Discus Toss is an active and tactile learning activity that models the extended Euclidean algorithm with a frisbee relay. The extended Euclidean algorithm involves both iterative and recursive programming and is regularly taught throughout the mathematics and computer science curricula. The Euclidean Discus Toss invites students to toss and catch frisbees in a collaborative and hands-on effort designed to sharpen modular arithmetic skills, enhance familiarity with iterative and recursive algorithms, and strengthen classroom community. The activity is fun, low-stakes, and can be customized to meet a variety of pedagogical objectives.