Open tasks are mathematical problems "that promote mathematical reasoning and problem solving and allow multiple entry points and varied solution strategies" (National Council of Teachers of Mathematics [NCTM], 2014, p. 17). Open tasks can have more than one right answer, solution, or outcome. Facilitation of open tasks offers learning situations for students from different ability levels, allowing them to choose the solution strategy that best fits their thinking (Van de Walle et al., 2014). In addition, open tasks provide opportunities for students to explain their reasoning to others and contrast their ways of thinking with other students' thinking. In turn, by giving and receiving explanations, students are able to discuss, argue, represent, hear, and compare one another's viewpoints (Cobb, 1995). This article focuses on how different types of open tasks can be used as a tool to promote the crucial practice of rigorous student mathematical discourse.