In this paper, we present an emerging set of learning conjectures and design principles to be used in the development of professional learning tasks that support elementary teachers' learning of mathematics learning trajectories. We outline our theoretical perspective on teacher knowledge of learning trajectories, review the literature concerning mathematics professional learning tasks, offer a set of initial conjectures about teacher learning of learning trajectories, and articulate a set of principles to guide the design of tasks. We conclude with an example of one learning trajectory professional learning task taken from our current research project. [This document was originally published as Wilson, P. H., Sztajn, P., & Edgington, C. (2012). Designing professional learning tasks for mathematics learning trajectories. In T.-Y. Tso (Ed.), "Proceedings of the 36th annual meeting of the International Group for the Psychology of Mathematics Education" (Vol. 4, pp. 227-233). Taipei, Taiwan: PME.]