Student engagement in classroom activities is usually described as a function of factors such as human needs, affect, intention, motivation, interests, identity, and others. We take a different approach and develop a framework that models classroom engagement as a function of students' "conceptual competence" in the "specific content" (e.g., the mathematics of motion) of an activity. The framework uses a spatial metaphor--i.e., the classroom "activity as a territory" through which students move--as a way to both capture common engagement-related dynamics and as a communicative device. In this formulation, then, students' engaged participation can be understood in terms of the nature of the "regions" and overall "topography" of the activity territory, and how much student "movement" such a territory affords. We offer the framework not in competition with other instructional design approaches, but rather as an additional tool to aid in the analysis and conduct of engaging classroom activities. (Contains 14 figures.)