In this exploratory study, we documented teachers' knowledge of children's mathematical thinking as they engaged in the task of anticipating children's strategies for an equal sharing fraction problem. To elicit an array of knowledge, 18 teachers were deliberately selected with a variety of numbers of years participating in professional development focused on children's mathematical thinking. We characterized the flexibility of teachers' knowledge by the number of valid and distinct strategies teachers anticipated and the degree to which these strategies reflected strategies research has shown children typically use. We argue that this flexibility is necessary for teachers to engage in instructional practices that are responsive to children's mathematical thinking. [For the complete proceedings, see ED583608.]