This paper addresses the ways in which teachers in whole-class discussions invite students to elaborate their previous turn. Our conversation analytic study uncovers that the teachers’ invitations are prompted by elicited as well as spontaneous student turns of both subjective and factual nature. While giving the students the space to expand on their previous turn, most invitations nevertheless steer towards a specific type of response, namely an account or explanation. Only incidentally, the invitations simply solicit a continuation. The fact that the invitations follow not only teacher-initiated, but also student-initiated contributions reflects the teachers’ attempts to foster an actual discussion framework in which they partly hand over control and in which the student contributions are taken up for further consideration.