Educational psychology usually focuses on explaining phenomena. As a result, researchers seldom explore how well their models predict the outcomes they care about using best-practice approaches to predictive statistics. In this paper, we focus less on explanation and more on prediction, showing how both are important for advancing the field. We apply predictive models to the role of teachers on student engagement, i.e. the thoughts, attitudes, and behaviours, that translate motivation into progress. We integrate the suggestions from four prominent motivational theories (self-determination theory, achievement goal theory, growth mindset theory, and transformational leadership theory), and aim to identify those most critical behaviours for predicting changes in students’ engagement in physical education. Students (N = 1324 all from year 7, 52% girls) from 17 low socio-economic status schools rated their teacher’s demonstration of 71 behaviours in the middle of the school year. We also assessed students’ engagement at the beginning and end of the year. We trained elastic-net regression models on 70% of the data and then assessed their predictive validity on the held-out data (30%). The models showed that teacher behaviours predicted 4.39% of the variance in students’ change in engagement. Some behaviours that were most consistently associated with a positive change in engagement were being good role models (β = 0.046), taking interest in students’ lives outside of class (β = 0.033), and allowing students to make choices (β = 0.029). The influential behaviours did not neatly fit within any single motivational theory. These findings support arguments for integrating different theoretical approaches, and suggest practitioners may want to consider multiple theories when designing interventions. More generally, we argue that researchers in educational psychology should more frequently test how well their models not just explain, but predict the outcomes they care about.