Large-scale data and data visualizations are ubiquitous now in the stories that shape our society. In particular, these stories influence youth and families' communication and understanding of scientific, social, and personal issues. Consequently, we need to better understand how youth and families can engage and learn with the tools that generate such narratives. This study reports on a qualitative analysis of 13 data discussions with families that used data visualization tools to explore georeferenced data connected to their family migration histories. We developed the Co-Construct, Situate, Advance a Theory (CSAT) model, from family cases, which details the discursive and interactional processes by which families tell personal stories grounded in data displays. Extending earlier studies of storytelling as theory-building in family conversations, our model provides an understanding of families' discursive practices around data exploration. We discuss implications for family learning with data technologies.