The 1989 document, "Curriculum and Evaluation Standards for School Mathematics" (the "Standards"), provides a vision and a framework for revising and strengthening the K-12 mathematics curriculum in North American schools and for evaluating both the mathematics curriculum and students' progress. This book, one in a series designed to interpret and illustrate how the vision could be translated into classroom practice, addresses issues and concerns about teaching and learning geometry and spatial thinking in relation to implementing the Standards. Not intended as a geometry curriculum, the book presents different approaches to some geometry topics and provides a sample of 22 activities organized into four sections: Two- and Three-Dimensional Geometry Concepts; Relationships among Properties of Shapes Including Angle Sums; Transformation Geometry; and Enrichment Topics. An introduction provides the rationale for the book and describes how the van Hiele model of thinking in geometry is incorporated into the activities. Using an investigative approach, the activities encourage students to make conjectures and discover patterns. Each section, called a cluster, provides objectives for the cluster, teaching notes for each of the activities that indicate materials needed, teaching ideas, and answers to key questions, and evaluation notes for each activity. Reproducible worksheets accompany the activities. Nine computer software packages are listed. (Contains 26 references.) (MDH)