Our particular flavor of inquiry-based learning (IBL) uses mathematical discourse, conversations, and discussions to empower students to deepen their mathematical thinking, building on strengths of students in the humanities. We present an organized catalog of powerful questions, discussion prompts, and talk moves that can help faculty facilitate a classroom focused on mathematical discourse. The paper brings this discourse alive through classroom vignettes and explores various teacher moves and their impacts. The mathematical theme of the classroom investigations, Maypole dance patterns, stems from the learning guide "Discovering the Art of Mathematics: Dance." Both authors are part of the NSF-funded project "Discovering the Art of Mathematics," which provides IBL materials for mathematics for liberal arts courses, see www.artofmathematics.org.