In the process of reforming physics education over the last several decades, a tension has developed between engaging students with the content in more conceptually challenging ways and helping them identify with physics so they are personally motivated in their learning. Through comparative case studies of four high school physics teachers, we used a teacher positioning lens to understand an emergent theme around differences in students' level of engagement, including behavioral, affective, and cognitive engagement, and physics identity development. In each classroom, data were collected over the course of one week by two observers in multiple formats, including student and teacher interviews and surveys, video recordings, and field notes. We used a constant comparative approach with the qualitative data and regression with the quantitative data to compare across the four teachers. Our findings suggest that teachers' physical, structural, contextual, and social cues may influence the extent to which students engage with their physics class. The teachers' social cues appeared to be the most important for affective and cognitive engagement, and subsequently physics identity development. Contextual cues were less prominent, which may indicate the difficulty in making physics content contextually meaningful for students. Finally, physical/structural cues appeared to be important for behavioral engagement but this engagement was not sufficient for physics identity development. In sum, the way that physics teachers position themselves can moderate students' level and type of engagement with the class and ultimately their physics identity development.