The purpose of this study was to identify and categorize in-the-moment teaching moves which support productive general social norms and sociomathematical norms during dialogic instruction by drawing on transcripts of classroom episodes. To understand how teachers construct in-the-moment teaching moves, this paper is grounded in a revised version of the Advancing Children's Thinking framework. In particular, the framework reveals three interconnected dimensions of teaching moves: (1) eliciting group strategies, (2) supporting conceptual understanding "and" group coordination, and (3) extending group mathematical thinking "and" coordination. Drawing on this framework, we use a novel self-study methodology to construct a sequence of in-the-moment teaching moves that support the development of productive social and sociomathematical norms in dialogic classrooms. These teaching moves include (1) inviting strategies and encouraging all members to actively listen; (2) exploring, clarifying, and questioning the mathematical details of all strategies as a group; (3) promoting understanding of differing strategies; (4) comparing and evaluating differing strategies as a group; and (5) connecting the group's thinking for making progress on the task/advancing current strategy to become viable. Implications for research and practice are offered.