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…

Imagine two classfuls of American high school students, separated by 1,500 miles and profound differences in local cultures (East Coast urban and Midwestern rural) as they correspond and collaborate in writing between their geometry classes. Reading the students' observations, one sees authentic voice, specific detail, precise language, what…

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)

Several activities that can be used to give children more experience with triangles are submitted. By handling triangular shapes and building triangles with strips, pupils can experience a diversity of triangles in a very concrete way. Examination of triangles and nontriangles can help develop understandings of some inequalities. (MP)

Presented is a method of reorganizing a high school geometry course to integrate coordinate geometry together with Euclidean geometry at an earlier stage in the course, thus enabling students to prove subsequent theorems from either perspective. Several examples contrasting different proofs from both perspectives are provided. (MDH)

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

A sequence of ellipses and a sequence of hyperbolas, both graphically approaching some parabola, are expressed algebraically and then shown to approach the parabola. (MN)

The 1989 document, "Curriculum and Evaluation Standards for School Mathematics" 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. When completed, it is expected that the Addenda Series will…

Introduces four activities on forming rectangles according to specific directions. Critical reading, experimentation, logical reasoning, and validation of given directions are necessary for accuracy. Provides objectives, directions, extensions, answers, and a worksheet for each activity. (YP)

Directions are given for seven activities involving the folding of paper strips to illustrate geometric concepts. Properties of pentagons, triangles, hexagons, and Mobius bands resulting from the various foldings are discussed. (DT)

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)

Presents the Morris Loe Angle Trisection Approximation Method to introduce students to areas of mathematics where approximations are used when exact answers are difficult or impossible to obtain. Examines the accuracy of the method using the laws of sines and cosines and a BASIC computer program that is provided. (MDH)