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When and how do students engage in play when working on mathematical tasks? This proposal reports on the case of Pattakoby from a larger study. In this study, participants played digital puzzle games and worked on mathematical tasks in a series of clinical interviews. Pattakoby’s interactions with some of the mathematical tasks were playful, while other interactions he had with the tasks were not; this proposal describes and contrasts one playful and one not-so-playful interaction. These interactions illustrate that the relationship between computational complexity, task difficulty, and potential for play is not straightforward. Taken alongside other findings from the larger study, they suggest that design of the larger environment is as important as task design in designing for play.