Many teachers have designed lessons for students who will be working in groups to discuss and solve a problem. After investing time in constructing an interesting problem, creating strategically designed groups, and introducing the problem carefully, teachers may be left wondering how to help students collaborate to make sense of mathematical ideas. Group work in which students labor together on open-ended problems has become a regular feature of many mathematics classrooms. This format allows students to communicate their mathematical thinking as well as listen carefully and respond to the ideas of their peers. Teachers can find it difficult to facilitate productive interactions in several groups of students simultaneously. The authors present excerpts from student conversations during a middle school mathematics lesson in which students worked in small groups on a problem about rates of change and linear relationships. The teacher had used group work previously, and the students had already experienced working in groups on an open-ended problem. Some students in the class used strategies for maintaining productive mathematical discussions within their groups. These strategies included: (1) asking questions about the problem; (2) sharing the mathematical authority within the group; and (3) challenging one another's mathematical ideas.