Teachers who participated in a recent summer institute focused on implementing the Common Core State Standards for Mathematics (CCSSM). Throughout the summer institute, teachers had many in-depth discussions about the meanings they attributed to the Standards for Mathematical Practice (SMPs). In this article, the authors share some of the thoughts, concerns, and questions that fifty-seven participating teachers of grades 3-6 raised. In particular, the authors share ideas related to those SMPs that provoked the most discussion (i.e., SMP 2, 4, 7, and 8). The goal is threefold: (1) To describe the interpretation issues that were prominent for our teachers; (2) To offer potentially clarifying examples aligned with the constructed meanings of our teachers; and (3) To catalyze discussions about interpretation of SMPs among mathematics teachers across the United States.