The activities in this monograph are self-contained explorations into mathematical topics not often included in regular classroom work in grades 3-8. They were selected because of their intriguing enjoyment and because they deal with honest mathematics; they also strengthen skills, especially problem-solving skills. Included are activities with geoboards, pentominoes, probability, solid shapes, symmetry, tangrams, tiling, topology, triangles, and dot paper. Introductory comments to the teacher precede each topic; each investigation is presented, then followed by worksheets. (MNS)