When students work with a non-Euclidean distance formula, geometric objects such as circles and segment bisectors can look very different from their Euclidean counterparts. Students and even teachers can experience the thrill of creative discovery when investigating these differences among geometric worlds. In this article, the author describes a…

An enrichment activity used in sixth and seventh grade mathematics classes to develop geometric concepts is presented. (JG)

Discussed are techniques of presentation and solution of the Classical Cake Problem. A frosted cake with a square base is to be cut into n pieces with the volume of cake and frosting the same for each piece. Needed are minimal geometric concepts and the formula for the volume of a prism. (JP)

On a triangular grid of equilateral triangles an analytical procedure is presented for solving puzzles that require one to measure out a specified amount of liquid from containers of various volumes. (JP)

Mathematics in nature and in the technological world is discussed. Outdoor activities with mathematical content are listed. (JP)

Outlines a guided discovery activity for ascertaining the conditions which allow for the correct tracing of networks. (JP)

A formula comparable to Pick's formula for area of a polygonal region on a geoboard is presented for the situation in which the standard unit is an equilateral triangle instead of a square. (JP)

Brief articles are included on creating in first-year algebra, making a Moebius hat, and graphing cubics. (MNS)

Cones as containers and envelopes are discussed with appropriate activities for middle grade children provided. (MP)

This section concerns pattern recognition activities related to the properties of cubes and is suitable for reproduction in worksheet and transparency form for classroom use. (JP)

Some geometric activities are described that teachers can use to give their students experiences that will influence their spatial abilities. It is noted that the goal is to improve spatial abilities, not to increase knowledge, so individual pupil responses should not be used to judge student achievement. (MP)