Flipped classrooms and inquiry-based learning (IBL) have each become popular in their own right, leading to a natural question: Why not combine these two great ideas? Although flipping a class usually involves students reading or watching videos before class, and IBL focuses on allowing and encouraging students to develop material on their own, both styles emphasize active learning and critical thinking through activities such as group work and presentations while minimizing lectures. In this article, I discuss ways that the two teaching styles can complement each other and be implemented concurrently, with some examples from my flipped calculus II course. Throughout this discussion the focus remains on ways to keep students engaged and how to instill deep content knowledge.