We address the challenge of creating intersections between children's everyday engagement and museum exhibitions. Specifically, we propose an approach to participatory design inquiry where children's everyday engagement is taken as the point of departure. We base our discussion on a design workshop -- Gaming the Museum -- where a primary school class was invited to participate in exploring future exhibition spaces for a museum, based on their everyday use of computer games and online communities. We reflect on the results of the workshop, and broadly discuss the everyday engagement of children as point of departure for designing interactive museum exhibitions.