It is critical for mathematics tasks to provide students with the opportunity to engage actively in reasoning, sense making, and problem solving so that they develop a deep understanding of mathematics. Learning mathematics while solving a problem can be like entering a dark room with a single small light. The objects are in the shadows, difficult to make out, but as students' eyes adjust and more lights go on, the objects and how they sit in relation to one another become sharper. Learning through problem solving occurs from grappling with some idea that students do not completely understand. In search of reasons and connections, they work to clarify, and the objects, ideas, and their relation to one another become clearer. Teachers can choose problems that allow students to bring some knowledge to apply to the situation and that challenge them to grapple with new ideas. The Rectangle Border problem yields many challenges through an accessible context. These challenges generate occasions for students to understand more fully how the mathematics models the problem situation. This article describes challenges that students have encountered while solving the Rectangle Border problem and discusses how those challenges helped them make sense of ideas that were new to them.