Background: Groupwork is a desirable activity in mathematics classrooms for the opportunity it creates for collaborative reasoning and interdependence. Correlations between group-level processes and outcomes have helped characterize the features of more successful groups, but group-level constructs can obscure how students negotiate ideas. This study investigated how students' interactions, and the written work they produced, reflected their negotiations of authority and mathematics content during groupwork. Methods: I used techniques from systemic functional linguistics to analyze transcripts from groups of 7th-grade students during work on an open-ended mathematics task, to document connections between groups' interpersonal processes and their mathematical products. Findings: Two groups who produced similar products did so through different processes. In one group students' written work reflected consensus, evidenced by students' verbal contributions. In the other group, the written product reflected two distinct lines of reasoning that were both verbalized but never integrated in conversation. Contribution: While previous studies have documented differences in interactional patterns between more and, respectively, less successful groups, this study extends that line of research by describing differences between similarly successful groups. The use of SFL helps explain the path from group-level patterns and group outputs through individual students' participation.