Ways of finding the sums of some interesting sequences of numbers are discussed. Finding the patterns creates a challenge, but the patterns are not too difficult for average pupils to discover. Mathematical induction can then be used to prove the formulas. (LS)

Elementary School Teachers were instructed on finding number patterns in a figure in one of three groups: individual discovery, group discovery, and expository. They were tested for recall, retention, and transfer. The expository groups did better on recall, but group discovery was more effective for retention and recall. (SD)

Patterns emerging when two-digit numbers in various bases are operated on by squaring and summing the digits. (SD)

The author organizes some of the information known about the problem of dividing space by five planes in general position along with its extensions, and consolidates it to highlight some interesting patterns in both methods of solving analogous problems and their results. (MN)

A learning activity relating modular arithmetic to patterns of figures determined by points equally spaced around a circle 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)

Details of an investigation into polygonal numbers are given. From a study of the tabled series, patterns are discovered both within and between the various polygonal series. From a study of these results and the corresponding figures, formulas are developed. (LS)

The observations of a fifth-grade student concerning number patterns are recorded and discussed. (SD)

Students examined patterns emerging when numbers placed at vertices in a braided pattern were summed. (SD)

Describes an activity in which students, grades 7-12, explore patterns and properties of repunits, an integer written as a string of ones. Includes extensions for exploring algebraic justifications. (MKR)

Completing these worksheets leads students to discover patterns in the distribution of even numbers and numbers obtained by successive additions of 9 (primary grades). Worksheets for intermediate grades involve counting the number of factorizations for integers, and addition of the first nine whole numbers. (SD)

Using these worksheets students explore patterns in numerical and geometric processes, and predict the outcomes when the processes are iterated further. (SD)

Paper squares, each divided into eight congruent triangles, can be used in a variety of activities introducing ideas related to symmetry, pattern, and geometric transformations. (SD)

Presents three investigations related to the game Bulgarian Solitaire. Investigations ask students to find and represent optimal solutions to the problem, to identify cyclical solution patterns for different numbers, and to respond to questions involving the number and nature of the cyclical solutions. An appendix provides answers to questions.…