This handbook, and the VITAL Mathematics Series videotapes, contain 12 lessons that model effective use of active learning strategies in elementary mathematics instruction. The lessons are designed for preservice and inservice teacher development programs through courses or individual study. The videotapes that are available separately demonstrate the use of a variety of instructional materials and present alternative means to achieve teaching objectives. Each lesson has the following organization: (1) introduction to the activity; (2) background to the lesson; (3) questions to guide the study of the lesson; (4) further suggestions; (5) materials needed for the lesson; and (6) reference materials. (RH)