In the context of a three-year professional development program in mathematics, practicing elementary teachers persistently engaged in collaborative inquiry and reflection to build connected meanings for slope. One teacher invented a compelling representation for slope as a process of repeated addition, using Cuisenaire rods, based on teachers' shared experiences developing recursively defined linear equations. The presence of and tension between different representations of slope, brought forth by the teachers, catalyzed productive cycles of choice and inquiry for the entire class. Personal agency, purposeful choice, and performance provide a valuable lens for fine-grained analysis of mathematical learning.