By working through well-designed tasks, students can expand their thinking about mathematical ideas and their approaches to solving mathematical problems. They can come to see the value of looking at tasks from different perspectives and of using different representations. This article discusses four tasks that encourage high school students and preservice secondary school mathematics teachers to think flexibly about mathematical concepts and problems. Appropriate use of these tasks challenges learners' intuitions while broadening and deepening their knowledge of mathematical concepts through the linking of multiple representations. (Contains 5 figures.)