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

The relation between the area of a rectangle and its perimeter is clarified by looking at patterns. Several examples involving rectangles with integral sides are presented. (MNS)

A familiar procedure for generating magic squares is reviewed. A surprising pattern is noted. (MNS)

Simple patterns both in mathematics and music are discussed. Several activities using standard instruments and handmade devices are described. (MNS)

Several experiences with palindrome numbers are given, each leading to the "Law of 11." Conjectures for the reader to consider are included. (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)

Developing numerical relationships with calculators is emphasized. Calculators furnish some needed support for students as they investigate the value of fractions as the numerators or denominators change. An example with Logo programing for computers is also included. (MNS)

An activity project is described which encourages students to question and experiment. Appendices provide examples of student results. (MNS)

Three theorems for Pythagorean triples are presented, with discussion of how students can amend their ideas about such numbers. (MNS)

Deriving all Pythagorean triples from simple patterns within an addition table is presented, with formulas included. (MNS)

Lessons for first-grade students deal with the numbers five and six. How groups of five and six differ is the focus of the comparing and counting activities. (MNS)

A programing contest was designed to promote interest in mathematical randomness. Student-developed programs making clever uses of random numbers are presented. Modifications users might make are suggested. (MNS)

What is number sense, why it is important, how it is taught, and how it is measured are each discussed. Examples with concrete materials, calculators, and pattern recognition are included. (MNS)

Briefly presented are suggestions on using exercises in number patterns in second-year algebra and factoring quadratics in a 10th-grade enrichment class. (MNS)