Open large-scale datasets (LSDS) and data visualization technologies are new cultural tools that have potential to inform public dialogue and learning about important socioeconomic and scientific matters, particularly if the data is used to consider both personal and shared experiences. This paper reports on a design study in which diverse middle and high school youth in a free summer workshop at an urban public library were asked to model their family geobiographies, or their personal family migration stories, with socioeconomic LSDS. Youth represented family decision-making and social conditions that might have motivated family movements with online, dynamic data modeling and mapping tools (Gapminder.org; SocialExplorer.com). The qualitative video analysis examined participants' experiences and learning in storytelling and modeling the family geobiography, focusing on multimodal talk-in-interaction to understand how the study design engaged learners' capacities, histories, and imagined futures in relation to the LSDS and supported learning about oneself and society. Grounded examples from two family cases are used to illustrate how participants placed their families and selves into data ontologies and the role of family members in composing storylines.