Math walks, where participants explore physical spaces and make connections to mathematics, have been implemented in a wide variety of ways in different learning settings. Math walks connect place-based learning, the development of interest in STEM fields, and opportunities for students to exercise agency over their STEM learning. However, many enactments of math walks have been highly structured and directive in both the mathematics they promote and in the physical movements students are permitted to engage in as they walk. In the present exploratory, qualitative-dominant, mixed-methods bounded case study, we examine eight secondary students engaging in math walk activities as they participate in a STEM summer camp. We examine the nature and types of mathematical questions they ask during math walks, the ways in which they describe the spatial and epistemic agency they have during the experience, and their attitudes toward mathematics. We found that student-led math walks expose a consequential design problem: how to facilitate spatial and epistemic agency while retaining enough mathematical coherence to support depth and continued learning. The article enumerates implications for researchers, educators, and learning designers.