We started with a classic research question ("How do teachers motivate and engage middle year students in mathematics?") that is solidly underpinned and guided by an integration of two theoretical and multidimensional models. In particular, the current study illustrates how theory is important for guiding qualitative analytical approaches to motivation and engagement in mathematics. With little research on how teachers of mathematics are able to maintain high levels of student motivation and engagement, we focused on developing a qualitative framework that highlights the influence of teacher-student interactions. Participants were six teachers (upper primary and secondary) that taught students with higher-than-average levels of motivation and engagement in mathematics. Data sources included one video-recorded lesson and associated transcripts from pre- and post-lesson interviews with each teacher. Overall, effective classroom organisation stood out as a priority when promoting motivation and engagement in mathematics. Results on classroom organisation revealed four key indicators within teacher-student interactions deemed important for motivation and engagement in mathematics--confidence, climate, contact, and connection. Since much of the effect of teachers on student learning relies on interactions, and given the universal trend of declining mathematical performance during the middle years of schooling, future research and intervention studies might be assisted by our qualitative framework.