This article reports on a 4th-grade problem activity implemented as part of a 4-year longitudinal, design research study across grades 3-6. The activity integrated the four STEM disciplines through a focus on design. Following investigations of their feet measurements and shoes, two classes of 9-year-olds explored the roles of designers and engineers in shoe manufacture, experimented with materials, and then designed and constructed their own pairs of shoes. A conceptual framework, "towards informed design" (adapted from Crismond and Adams in J Eng Educ 101(4):738-797, 2012), is advanced for exploring students' learning while designing. Drawing on this framework, consideration is given to students' use of design strategies, including posing their own problems and design aims, sketching their shoe designs, testing and reflecting on their products, and redesigning and reconstructing. Although more students expressed a desired shoe than a design problem to be solved, they nevertheless were able to develop their own design aims and constraints. Designing a functional and aesthetically pleasing shoe was most common, together with comfort. Material properties typically less accessible to young students (water repellent, durable, insulated) were also considered in their designs. Students' attention to detail in their design sketches (e.g., style features, 2-D and 3-D perspectives, measurements, materials) suggested they had progressed beyond beginning designers. Likewise, students' increased satisfaction with their redesigns, displaying knowledge of material properties, measurement and spatial skills, and design processes indicated progress towards informed design.