Mathematics lessons can take a variety of formats. In this article, the authors discuss lessons organized around complex mathematical tasks. These lessons usually unfold in three phases. First, the task is introduced to students. Second, students work on solving the task. Third, the teacher "orchestrates" a concluding whole-class discussion in which students are supported to make mathematical connections between solutions and to develop conceptual understanding of significant mathematical ideas. Complex tasks invite students to generate multiple solutions and justify their reasoning. Such tasks live up to their potential only if students engage productively in the task. Therefore, the first phase, the task introduction, is crucial. The authors describe how teachers can set up, or "launch," complex tasks by leading introductory whole-class discussions in which they help students engage in the task and learn significant math. (Contains 2 figures.)