In this article, we analyze the complexity of using instructional dialogues in the teaching of mathematics. We trace a 10-lesson unit on functions and their graphs taught by Magdalene Lampert to a 5th-grade classroom. We use this trace to help analyze and systematize the complexity of the classroom discourse. Analysis shows that Lampert's instructional dialogues served 2 purposes: They developed coconstructed instructional explanations of the key mathematical concepts, and they allowed the class to navigate a meaningful path through the relevant mathematics. In creating an instructional explanation, the class as a group flagged the central questions, coordinated and differentiated between the central ideas, and anticipated and made public potential errors. Although misconceptions were often raised as part of the public knowledge space, students individually and collectively resolved these misconceptions publicly through the dialogues. The path through the mathematics was supported through the careful use of agendas, sets of conditions under which an aside was taken from the agendas, and the careful problematizing of the mathematics. Routines, metatalk, and the crafting and maintenance of the intellectual climate played important roles in supporting the instructional dialogues. In the cases of routines and metatalk, we make comparisons to other instances of expert teaching. We also show evidence of student engagement and significant student learning that transcended individual participation patterns. We explore implications for teacher education.