The problem of determining the number of squares on a checkerboard is extended to finding the number of rectangles on an n x n board and finding the total numbers of cubes and rectangular solids in an n x n x n cube. (DT)

Some mathematical patterns are explored by visualizing and counting line segments, squares, cubes, and relationships between them. (JT)

Number sequence patterns for counting boundaries of familiar figures are extended to higher dimensions. (JP)

Using the two posters in this article, students are to search for patterns as a way of counting different types of squares and cubes obtained from a larger square or cube that is printed on the outside edge or surface. (MP)

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)

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

The number concepts of greatest common divisor and least common multiple are related to star patterns created through line designs. (JT)

Beginning with a set of design cards and a rectangular grid, students can generate interesting and colorful designs using rotations, reflections, and translations. (SD)

Patterns and relationships are shown between the Pythagorean theorem, Fibonacci sequences, and the golden ratio. Historical references also include the works of Euclid and Euler. These unexpected relationships can be used to motivate secondary students. (DC)

Patterns resulting from polygonal numbers are explored, with examples of triangular, square, pentagonal, rectangular, and other numbers. Tables and formulas to be developed are included. (MNS)

Patterns found in African art can be used in activities related to geometric concepts. (SD)

Observation of patterns constructed on geoboards can lead to discussions of properties of primes, number sequences, and complex numbers. (SD)

Described are: how teachers can use the computer language Logo, along with noncomputer activities, for teaching about linear and two-dimensional patterns and about combining shapes to create more complex shapes. Three computer program listings are included. (MNS)