Teaching teachers to participate in mathematical inquiry has the potential to both transform belief systems about mathematics and to transform teachers from consumers of mathematics to producers of mathematics. The focus of this paper is to describe the use of a problem, based on a non-traditional binary operation, to encourage and teach pre-service and in-service teachers inquiry and problem-posing. We present a brief mathematical solution for the problem and we then discuss problem-posing activities and discussions of connections to the Standards of Mathematical Practice from the Common Core State Standards. We discuss several key aspects of the problem that make it well-suited for the purposes of teaching inquiry and problem-posing.