Understanding the roles of random selection and random assignment in experimental design is a central learning objective in most introductory statistics courses. This article describes an activity, appropriate for a high school or introductory statistics course, designed to teach the concepts, values and pitfalls of random selection and assignment using the not-easily-forgotten Madagascar hissing cockroach. Evidence is summarized demonstrating conceptual gains for students performing the Randomizing Roaches activity, and follow-up activities are suggested.