Tasks play a central role in the mathematics classroom. Especially when teaching in a heterogeneous mathematics class, teachers should be able to find, select, modify, and assign tasks adequately. The focus in this paper is on adaptivity to cognitively activate all learners at the individual level, and on teachers' abilities to allow for such adaptivity by means of selecting appropriate tasks. More specifically, when planning lesson phases for practice and consolidation, teachers may consider which tasks have differentiation potential and can thus be completed by all students at the same time but at different levels. In order to analyse teachers' strategies in this regard, we investigated the task features that teachers may consider when assessing the differentiation potential of exercise tasks. We first deductively constructed rating categories based on the literature on instructionally relevant features of adaptive tasks. Then, we inductively extended and refined the constructed categories by analysing teachers' reasoning based on a sample of 78 in-service teachers at secondary schools. We validated the resulting 22 categories by determining interrater reliability. Our findings indicate that teachers consider a broad spectrum of task features when analysing the differentiation potential of tasks. However, only some of these features are directly relevant with regard to using adaptive tasks as a differentiation strategy. Our results also show that many teachers arrived at conclusions about the differentiation potential of tasks that were different from task-design experts. Based on our findings regarding teachers' perspectives on the differentiation potential of tasks and on certain task features, we discuss how these findings may have arisen and how important the knowledge about the deep structure of adaptive tasks is for teachers' professional development.