Conversations as moments for interpersonal and intimate turning round of ideas for the purpose of growth are well-defined within curriculum inquiry. Interactions among grade 12 students in this study demonstrate the possibility of learning to learn mathematics through conversation. Attending to opportunities for learning-based conversations, constructivist grounded theory supported developing a Model of Providing Opportunities for Learning-based Conversations. Four features of preparation, presence, mode, and pacing represent a space where students could improve their learning through connectedness among conversational moments. Understanding how conversational opportunities were offered could empower others to engage in learning-based conversations with their students.