Background: We explore how school-based mathematical experiences shape out-of-school mathematical experiences, developing the idea that learners hybridize norms and practices around authority and evaluation across these two contexts. To situate our study, we build on constructs of participatory identity and framing. Methods: Drawing from a large corpus of video records capturing children's point-of-view, we present a case study of hybridization with two purposively sampled 12-year-old friends--Aimee and Dia--interacting in an out-of-school mathematics playspace. We use interaction analysis to articulate grounded theories of hybridization. Findings: We present a thick description of how "children hybridize their activity in out-of-school spaces and how such hybridization is consequential for engagement." Dia's case illustrates how traditional norms and practices around authority and evaluation can lead to uncertainty and dissatisfaction, while Aimee's illustrates how playful norms and practices can lead to exploration and pleasure in making. We argue that their school-based mathematics experiences and identities influenced these differences. Contribution: This report strengthens theoretical and methodological tools for understanding how activity and identity development in one context become relevant and shape activity in another by connecting analytic constructs of identity, framing, and hybridizing.