Project-based curricula have the potential to engage students' interests. But how do students become interested in the goals of a project? This article documents how a group of 8th-grade students participated in an architectural design project called the Antarctica Project. The project is based on the imaginary premise that students need to design a research station in Antarctica. This premise is meant to provide a meaningful context for learning mathematics. Using ethnography and discourse analysis, the article investigates students' engagement with the imaginary premise and curricular tasks during the 7-week project. A case study consisting of scenes from main phases of the project shows how the students took on concerns and responsibilities associated with the figured world proposed by the Antarctica Project and how this shaped their approaches to mathematical tasks (Holland, Lachicotte, Skinner, & Cain, 1998). Participating in the figured world of Antarctica and evaluating situations within this world was important for how students used mathematics meaningfully to solve problems. Curricular tasks and classroom activities that facilitated students in assuming and shifting between roles relevant to multiple figured worlds (i.e., of the classroom, Antarctica, and mathematics) helped them engage in the diverse intentions of curricular activities.