Cognitive demand is a crucial dimension of instructional quality. Its heterogenous operationalizations call for refined investigations, with respect to discursive richness (generic conceptualizations) and conceptual richness (subject-related conceptualizations). Considering not only teachers’ intended cognitive activation (operationalized, e.g., by tasks), but also the enacted activation and individual students’ participation as realized in the interaction, raises the question of how far the interaction quality is associated with students’ prerequisites, school context, and class composition. In this paper, we present a video study of leader-led small-group instruction (in 49 groups of 3–6 middle school students each) with the same fraction tasks, so that differences in interaction quality can be scrutinized in generic and subject-related conceptualizations. In spite of equal task quality, large differences occurred in interaction quality across heterogenous class compositions. The regression analyses revealed that the enacted activation and individual participation were significantly associated with the school context (of higher-tracked and lower-tracked schools), but much less with individual learning prerequisites. These findings reveal the need to capture students’ collective and individual engagement in cognitive demands in the interaction and in generic and subject-related conceptualizations and to systematically investigate their association with class composition.