Designers in out-of-school spaces often negotiate the meaning of mathematics as part of the design process, determining what to include in classes and exhibits both implicitly and explicitly. This analysis suggests that instead of keeping these conversations behind the scenes, we should foreground them for participants. In doing so, we may actually be helping to expand their sense of what counts as mathematics as they participate in legitimate communal activity. The focal analysis examines the case of one participant in a knitting summer camp as she encounters the mathematics that the facilitator deemed necessary to move the knitting project forward. Together they negotiate whether their work counts as knitting or as mathematics, and what the consequences for that designation are for how they make sense of the activity. I argue that this kind of encounter has the potential to build bridges between everyday and school mathematics and thus to broaden participation.