The 2018 International Computer and Information Literacy Study (ICILS) provides a comprehensive dataset with contextual information on German school environments. The data comes from responses by eighth-grade teachers and principals to a questionnaire about Information and Communication Technology (ICT) for teaching. We performed an exploratory re-analysis examining what influences teachers' adoption and use of ICT by employing six factors -- Social Influence, Effort Expectancy, Performance Expectancy, Facilitating Conditions, Behavioural Intention, and Use Behaviour -- from the Unified Theory of Acceptance and Use of Technology (UTAUT). We measured relationships between these constructs with a Structural Equation Model (SEM) consisting of 15 indicators provided by the ICILS study. The goodness of fit measures indicated confirmation of the model (RMSEA = 0.05, SRMR = 0.05, CFI = 0.93, TLI = 0.91). Our findings show that teachers' attitudes toward ICT and the school administration's support affected how ICT was applied in the classroom.