We report a qualitative analysis of elementary school students engaged in collaborative problem solving involving mathematical equivalence tasks. We build on previous research showing that students often use strategies based on either operational or relational understandings of the equal sign. We closely analyze three cases and identify nuanced aspects of the social interaction that influence whether and how students develop and use operational or relational strategies toward a final solution. Students' demonstrated understandings of the equal sign during collaboration aligned with those identified in past research. We argue that a social-mathematical power dynamic was co-constructed in each of the dyads, and the ways students navigated that dynamic affected the quality of individual engagement and therefore learning. [For the complete proceedings, see ED583608.]