An analysis of the rabbit problem reveals some of the fascinating properties of the Fibonacci numbers. (MP)

Conjecture and proof, as opposed to numerical calculation, are presented as being the primary focus for teaching mathematics. (MP)

Designs and arrangements of pentominoes are examined. (SD)

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)

Stresses that powers are all based on geometric progressions which start at unity. Various patterns are discussed. (MNS)

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

Mathematical investigations pursued by two gifted students are presented. One is written by a boy age 9 with his follow-up at 11; he studied patterns to derive the factors for the difference of two squares. Another boy of 11 discovered formulas for slopes of tangent lines and areas under curves. (LS)

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…

The use of paper folding to demonstrate polygons which give plane tessellations, conic sections, and the solutions to several problems is described. (SD)

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)