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)

Presents responses to the pattern problem that appeared in the November 1998 "Problem Solvers" section of this journal. (ASK)

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)

Presents an extension of the hog game that satisfies the mathematical process activities of observing patterns; forming, testing and proving hypotheses; and applying and extending proved results. Discusses use of technology in the investigation of problems and in the process of devising and validating general rules. (ASK)

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)

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.…

Presents a problem that requires solving a card problem by exploring patterns that will lead to a logical solution. Involves students in developing and analyzing their own algorithms as well as discussing their reasoning with peers. (ASK)

Provided are follow-up activities for having students explore the concept of line symmetry. Using a mirror to move a pattern; finding patterns with one, two, or four lines of symmetry; finding asymmetrical patterns; deciding if patterns are different; and solving the problem of finding all patterns possible are discussed. (MNS)

Presents a problem suggested for students in grades one through six concerning the concepts of grouping, reasoning, and pattern finding. Discusses the student problem-solving process. (ASK)

This collection of activities resulted from a visit by the Polish author to the Teachers' Center Project at Southern Illinois University at Edwardsville in 1980. The set of 30 activity sheets involve blocks with various types of patterns depicted. Directions for using each sheet and questions to be answered are then given. Elementary school…

Activities and problems are interspersed with commentary in this book on the learning and teaching of mathematics. The emphasis is on helping students to enjoy mathematics through an awareness of structure and patterns. The chapter titles are as follows: (1) "My Three Sons--A Game"; (2) "The Tower Game"; (3) "Mathematical Games on a Different…

The problem-solving strategy "look for a pattern" is explored. The staircase problem and the region problem are discussed in detail, with varying solution procedures, and three other problem activities are outlined. (MNS)

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)

Quilt-making is presented as an activity that helps elementary school children recognize and appreciate geometry in their world while developing their problem-solving skills. Students choose an appropriate pattern and cooperatively make the quilt. Related measurement questions and problems are provided. (MDH)