This article describes a preservice teacher's imaginative exploration of completing the square through a process of reasoning and sense making. She recounts historical perspectives and her own discoveries in the process of completing the square. Through this process of sense making, she engaged with the content standard of completing the square to solve quadratic equations in a way different from what she had done before through symbolic study alone. Discovery led to excitement. She was no longer just a consumer of mathematics; she was a participant in making mathematics convey meaning and understanding to others.