The absence of discussions of identity that consider both subjective/personal and social aspects of identity is an important concern in mathematics education research. This paper proposes a framework to analyse the mathematical identities offered to and constructed by learners during peer interactions, by considering personal and social identities. To exemplify the framework, we discuss how two pairs of secondary school learners, who were engaged with similarly by their teachers and who performed similarly academically, interacted with each other and offered and constructed micro-identities during moments of a lesson, and macro-identities across lessons. We show that when learners were offered identities by a peer as higher, lower or equal status, they constructed their identities by affiliating with or resisting the identities offered by their peer. Their interactions and the identities that they constructed were informed by their personal identities, including their emotions when learning mathematics, and their social identities, including their choices to occupy certain roles in the classroom community.