The roles that families can play in children’s mathematics learning is not well documented. In this paper, a negotiation about reproducing a block construction from a picture between a grandmother and her two grandsons as part of a game is analyzed. During the interaction analysis, the theory of negotiation types was further elaborated. To this end, considerations of recipient design and participation in production design—both understood as components of interaction theory—were systematically integrated into the analytical process. The result demonstrates that the social space of the block play provides different learning opportunities for all. During this interaction, different negotiation types emerge, while family members co-construct mathematical meanings.