Student-directed projects--projects in which students have individual control over what they create and how to create it--are a promising practice for supporting the development of conceptual understanding and personal interest in K-12 computer science classrooms. In this article, we explore a central (and perhaps counterintuitive) design principle identified by a group of K-12 computer science teachers who support student-directed projects in their classrooms: in order for students to develop their own ideas and determine how to pursue them, students must have opportunities to engage with other students' work. In this qualitative study, we investigated the instructional practices of 25 K-12 teachers using a series of in-depth, semi-structured interviews to develop understandings of how they used peer work to support student-directed projects in their classrooms. Teachers described supporting their students in navigating three stages of project development: generating ideas, pursuing ideas, and presenting ideas. For each of these three stages, teachers considered multiple factors to encourage engagement with peer work in their classrooms, including the quality and completeness of shared work and the modes of interaction with the work. We discuss how this pedagogical approach offers students new relationships to their own learning, to their peers, and to their teachers and communicates important messages to students about their own competence and agency, potentially contributing to aims within computer science for broadening participation.