Research has shown that the types of tasks assigned to students affect their learning. Studies have found that many mathematical tasks created for second and third level students promote instrumental rather than relational understanding, and imitative rather than creative reasoning. In this paper, we describe some frameworks that aim to guide teachers when writing tasks. From these frameworks a set of task types that are deemed appropriate for undergraduate students, and that foster mathematical habits of mind, have been selected: these are evaluating mathematical statements; example generation; analysing reasoning; conjecturing; generalising; visualisation; and using definitions. We report on an effort to design a set of tasks for an introductory calculus course using these principles and give examples of exercises on the topic of continuity. The teacher’s role in the implementation of such tasks is also discussed.