This paper reports on a teaching experiment in which a hypothetical learning trajectory was enacted. The aim of this learning trajectory was to support children to develop efficient strategies for calculating multi-digit division computations in ways that made sense to them. This paper analyses the strategies that they used and how these changed over the course of the teaching experiment. Findings indicate that the teaching approach, which emphasised trialling multiple solution strategies and selecting and justifying computation methods, allowed children to develop efficient, meaningful solution strategies.