Understanding how learning environments productively mobilize children's ideas as resources for participation in joint activity is an ongoing focus of research on classroom instruction. We investigated whole-class mathematics conversations in which multiple students participated in ways previous research suggests are consequential for learning. We found that in such conversations, students rarely presented the entirety of their solutions before other students engaged. Rather, incomplete explanations and written representations that emerged over time created entry points for other students to contribute in mathematically substantive ways. These aspects of student participation operated in combination with teachers' in-the-moment responses to create opportunities for, and publicly recognize, different kinds of contributions as resources for collective work. Our findings suggest that, rather than challenges to communication that must be overcome, students' vague, unfinished, and ambiguous ideas present productive contributions that can be leveraged to support collective mathematical work.