This chapter, addressing the fine art of preparing and presenting a topic at a math circle meeting, is the final one within this part of the handbook because the author has reasonably chosen to present issues more or less in the order in which a coordinator must handle them. Planning how to use the time during which the students are actually assembled is one of the last considerations on an organizer’s checklist, coming to the fore only a day or two before the math circle convenes. But if the chapters were arranged in order of importance, this one would be the first. One instinctively recognizes this as fact: a math circle exists to captivate and inspire the kids, and from their point of view it is defined by what transpires while they are present. So the time has come, belatedly, to discuss the finer points of leading a math circle.