This book is one in a series of teacher resource books developed to: (1) rescue students from the clutches of computers that drill and control; and (2) supply teachers with computer activities compatible with a mathematics program that emphasizes investigation, problem solving, creativity, and hypothesis making and testing. This is not a book about Logo, but about mathematics and thinking mathematically. Many chapters require no Logo skills. Each chapter may include as many as seven sections: summary box, getting started, instructions, examples, activities, key summary, and worksheets and includes appropriate grade-level designations. The chapters in this book are: (1) Stamp Designs, (2) Designs from Color Patterns, (3) Sticker Designs, (4) Circular Fraction Paths, (5) Design Master, (6) Tartan Design, (7) Making Tracks, (8) Instant Logo, (9) Lotsalists, (10) Fractal Designs, (11) Translation Designs, and (12) Designs from Overlapping Arrays. Appendices include a summary of LogoWriter keys (Apple IIe/IIc, IBM, and Macintosh), a quick reference (LogoWriter Primitives and Special Words), and additional primitives for the Macintosh. (MKR)