"What do you do with the remainder when you divide?" Mrs. Thompson asked her third-grade students. They replied with such comments as, "You can't share that, because they won't be equal!" and "It's not going to come out even because you can't do that!" These answers were consistent with third- and fourth-grade student performance in a pretest and a posttest administered as part of a math professional development project conducted by author Teruni Lamberg. In this test, most students successfully solved the division problem involving whole numbers but were unable to solve 27/4, which made the authors wonder why children have difficulty with remainders. This article explores a lesson Thompson conducted with her third graders that involved using concrete materials to reason informally about division with remainders. The purpose of this lesson was to have students explore the meaning of division using their own informal problem-solving methods. (Contains 4 figures.)