Distributing opportunities to participate in talk-in-interaction during whole-class mathematics discussions is an important equity issue, with multiple studies reporting pervasive inequitable participation patterns in mathematics classrooms. Less attention, however, has been given to the underlying interactional practices that can initiate and support minoritized students' participation. This article examines how and what kinds of opportunities for participation are interactionally generated for minoritized students in whole-class mathematics discussions in two US high school classrooms. Through the lenses of turn-taking organizations and epistemic dimensions from conversation analysis, this study details the interactional features of turn-taking by three Black students in predominantly White classrooms. The analysis shows the importance of establishing epistemic congruence about the nature of students' knowledge before inviting them to take up the conversational floor. The findings imply that locally achieved, mutual understanding of what minoritized students know in the moment-by-moment classroom interaction is an important interactional feature for making minoritized students' brilliance more visible during whole-class discussions.