Research has shown that the types of tasks assigned to students affect their learning. Various authors have described desirable features of mathematical tasks or of the activity they initiate. Others have suggested task taxonomies that might be used in classifying mathematical tasks. Drawing on this literature, we propose a set of task types that are deemed appropriate for undergraduate students and which foster mathematical habits of mind. These are: generating examples; analyzing reasoning; evaluating mathematical statements; conjecturing and/or generalizing; visualizing; and using definitions. We give rationales for our choices and examples of each type of task suitable for use in an introductory calculus course.