Many research studies have documented the positive benefits of an active learning environment compared to the traditional lecture format. The activities contain a variety of exercises including drill sets, applications of prior knowledge, previews of upcoming concepts, and investigations using technology. Solutions appear in Appendix D.

Almost every activity begins with one or more "For Discussion" questions. If your teacher decides to implement this section of the activity, then be prepared to contribute to the class discussion. This may be a good time to ask a question that you wrote down the night before.

The main body of the activity consists of a problem set intended to help you transition from the basic questions asked in the quiz to the more challenging questions asked in the homework assignment. This is a great time to assess your understanding and to get help if you need it. Sections marked "Optional" are intended for those students who have finished the required problems and who are interested in some of the more theoretical and deeper aspects of calculus. Most lessons have optional supplemental exercises for extra practice, and these can be found in Appendix E.