Using a design-based research approach, we studied ways to advance opportunities for children and families to engage in engineering design practices in an informal educational setting. 213 families with 5–11-year-old children were observed as they visited a tinkering exhibit at a children’s museum during one of three iterations of a program posing an engineering design challenge. Children’s narrative reflections about their experience were recorded immediately after tinkering. Across iterations of the program, changes to the exhibit design and facilitation provided by museum staff corresponded to increased families’ engagement in key engineering practices. In the latter two cycles of the program, families engaged in the most testing, and in turn, redesigning. Further, in the latter cycles, the more children engaged in testing and retesting during tinkering, the more their narratives contained engineering-related content. The results advance understanding and the evidence base for educational practices that can promote engineering learning opportunities for children.