Rich technological environments present many opportunities for guided inquiry in the mathematics classroom. In this paper we focus on the role of the teacher supporting the forming and proving of conjectures by the students, during a whole class discussion. We examine the practices of an expert teacher that conducts a classroom discussion based on students' conjectures formed while working in pairs with a dynamic geometry environment (DGE). Specifically, we analyse the way the teacher categorizes the different conjectures, and then addresses them during the whole class discussion. We suggest that this categorization could be offloaded onto a technological platform that would do it automatically, thus making this type of information accessible not only to teachers that could perform this categorization on the spot.