Early word learning is contingent on linguistic input, but a child's linguistic experience is also embedded in the larger, natural structure of everyday life at home. We investigate the activity structure of life in the home of one young child, and link this structure to the child's early word learning. Our analysis is based on the dense, naturalistic, longitudinal corpus collected for the Human Speechome Project. To study activity structure, we apply probabilistic topic modeling techniques to the corpus. The emergent topics capture not only linguistic structure, but also spatial and temporal regularities indicative of coherent activity contexts. We consider the child's word learning with respect to caregiver word usage frequency and word distributions across activity contexts. We find that frequency and consistency of use across context are predictive of age of acquisition. Words that are used more frequently and in more contextually constrained settings are learned earlier, suggesting that activity contexts may be an important aspect of the child's natural learning environment and worthy of further study.