We leverage log data from an educational app and two-way text message records from over 3,500 students during the summers of 2019 and 2020, along with in-depth interviews in Spanish and English, to identify patterns of family engagement with educational technology. Based on the type and timing of technology use, we identify several distinct profiles of engagement, which we group into two categories: Independent Users who engage with technology-based educational software independently, and Interaction-Supported Users who use two-way communications to support their engagement. We also find that as the demands of families from schools increased during the COVID-19 pandemic, Spanish-speaking families were significantly more likely than English-speaking families to engage with educational technology across all categories of families, particularly as Interaction-Supported Users.