Activities with triangular, square, pentagonal, hexagonal, and octagonal numbers are briefly discussed. (MNS)

Advocated is developing intuitive ideas of limits whenever the opportunity arises in elementary mathematics. Examples are given for geometry, fractions, sequences and series, areas, probability, graphing, and the golden section. (MNS)

Activity questions based on the prime factorization of numbers can be answered by reference to the lattice structure of factors. (SD)

An activity sequence is described. Several aspects of a population problem are developed using isoperimetric graph paper and symmetry principles to derive general rules. (SD)

Described are a discrete group of isometries that fix a line but do not stabilize a point. Each type is accompanied by an example of their representation in concrete form which served as material on which young children could operate. Pupil responses to each situation are provided. (CW)

Mathematical concepts occur spontaneously from many topics and can be developed in the framework of cross-curricular schoolwork. Consequently, students can gain knowledge of where mathematics arises and insight about its purposes. (Included are activities dealing with the reflectional and rotational symmetries of automobile hubcaps evolved from…

Experiences with tessellations used with a group of preservice elementary teachers are described. Specific illustrations of patterns are included, with details on how these are analyzed. (MNS)

Describes an activity that utilizes four pattern blocks to help students understand and explain perimeter. Engages students in making and supporting conjectures about a scenario that involves trains composed of various shapes with different perimeters. (DDR)

Describes two activities involving sorting, counting, and determining relationships that use sameness and difference, spatial skills, pattern identification, number bonds, and generalization. (DDR)

A game involving operations on whole numbers, observing patterns in the relationships between operands and results, and seeking problems yielding various numerical solutions is described. (SD)

A method for helping students to find formulas involving symmetry under various conditions is explained. Necklace symmetries, orbit counting, tetrahedra and cubes, relationship patterns, and finding patterns are discussed. (CW)

Activities which may be used to investigate a variety of woven patterns are presented. Pattern predicting and analysis of different patterns are discussed. A Basic computer program for the weaving code is given. (CW)

Discussed are ways in which students can generalize both quadratic or cubic situations. Generalizations are produced using the factor method, repeated linear generalizations, means of the mean, and through the use of differences. (KR)