This book is based on the underlying philosophy that mathematics learning at the elementary level should be active. Children should learn through meaningful hands-on activities with manipulative materials, pictures and technology. More than 400 pupil activities and suggestions for designing more activities are described. Because mathematics is to be used in real world problem solving, mental arithmetic, estimation and the ability to use technology, the technological activities presented include the use of: (1) calculators for developing understanding of mathematics; (2) programming activities for developing mathematical understandings; (3) application programs such as spread sheets and data base programs for problem solving; (4) calculators and computers in problem solving activities; and (5) tape recorders, overhead projectors, and other devices in the classroom. Standard topics such as whole number computation, fractions, measurement and geometry are also considered. (PK)