Provides an activity as an example of how matrices can be introduced from finite graphs and how finite graphs can be analyzed by examining their matrix representations. Presents the materials, objectives, prerequisites, directions, extension activities, answers, and worksheets. (YP)

Discusses figurate number learning activities using patterns and manipulative models. Provides examples of square numbers, triangular numbers, pentagonal numbers, hexagonal numbers, and oblong numbers. (YP)

Presents an example from the combinatorial theory of partially ordered sets. Discusses algorithms of on-line antichain partitioning problems, a topic in discrete optimization. (YP)

Two problem-solving posters with a Halloween theme are included. These activity sheets are designed to be easily reproduced for classroom use. (MP)

Explored are various aspects of drawing graphs on surfaces. The Euler's formula, Kuratowski's theorem and the drawing of graphs in the plane with as few crossings as possible are discussed. Some applications including embedding of graphs and coloring of maps are included. (YP)

Discusses geometric construction problems. Presents four ways to construct a regular octagon using different conditions. Provides drawings showing the constructions. (YP)

The method used at airports in determining the cloud height at night is presented. Several problems, the equation used, and a simple design of an alidade (an instrument that shows cloud heights directly) are also included. (MP)

Discussed is the benefit of the inclusion of historical material in a student's text. Several geometry problems are used as examples. A suggested list of problem sources is provided in the appendix. (YP)

Describes the use of calculators for the teaching of mathematics in grade 1. (YP)

Illustrates some learning encounters for facilitating first graders' understanding of geometry. Describes some of children's approaches using Cuisenaire rods and teacher's intervening. Presents six problems involving various combinations of Cuisenaire rods and cubes. (YP)

Presents problems focusing on multiple representations of a function to develop students' ability to translate tabular, symbolic, and graphical representations. Indicates needed materials, objectives, prerequisites, directions, and answers. (YP)

Presents two practice-discovery activities to furnish computational review in a nonroutine setting. Provides a worksheet for the activities. (YP)

Presents four examples on arithmetic mean and harmonic mean. Provides solution of each of the examples and instructional activities related to the examples. Lists eight references on mathematical problem solving. (YP)

Presented is a lesson in which the patterns that occur within and between sequences of polygonal numbers present an opportunity for students to analyze, represent, and generalize relationships. Materials, objectives, levels, and directions for this activity are discussed. Worksheets to accompany the activities are provided. (CW)

Discusses making tessellations by using a polyomino. Illustrates the various ways for various shapes of polyomino. Provides several diagrams and instructional guides. (YP)