Despite substantial research exploring multiplicative thinking and students' difficulty in the domain, the topic of multi-digit multiplication is under-researched. In this paper, I share a learning trajectory for multi-digit multiplication that combined social and cognitive perspectives of learning. Using Design Research methods and involving 45 Year 5 (9-11-year-olds) students from two different schools, an instructional sequence based on the trajectory was implemented. Findings led to the refinement of a trajectory that has implications for teaching practice.