Teachers play a critical role in supporting students' mathematical engagement. There is evidence that meaningful student engagement occurs more often in student-centered classrooms, in which the teacher and the students mutually share mathematical authority. However, teacher-centered instruction continues to dominate classroom discourse, and teachers struggle to effectively support student inquiry. This paper presents a framework of teacher moves specific to inquiry-oriented instruction, the "Teacher Moves for Supporting Student Reasoning" (TMSSR) framework. Based on the analysis of four instructors' implementations of a middle grades (ages 12-14) research-based unit on ratio and linear functions, the TMSSR framework organizes pedagogical moves into four categories, "eliciting," "responding," "facilitating," and "extending," and then places individual moves within each category on a continuum according to their potential for supporting student reasoning. In this manner, the TMSSR framework characterizes how multiple teacher moves can work together to foster an inquiry-oriented environment. We detail the framework with data examples and then present a classroom episode exemplifying the framework's operation.