Uses colored cube combinations to investigate surface area, volume, and axes of symmetry. (ASK)

Presents activities that emphasize engaging students in proportional reasoning. Introduces students to the rules involved in recognizing proportions and invites students to discover how the numbers in an ordered pair are related. (JRH)

Argues that mathematics is, to a large extent, the study of patterns. Presents an activity in which students search for patterns in the Fibonacci sequence and Pascal's Triangle. (ASK)

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

Reviews an alternative patterning approach and highlights the difficulties it can present when students lack the requisite skills and knowledge of processes. Describes how this approach can be used to introduce elementary algebraic ideas and offers recommendations for establishing these important understandings. (ASK)

Three activities and patterns involving the addition table are described, each involving pentagons. (MNS)

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)

Four worksheets for levels one-eight are included. Practice on addition, multiplication, fractions and decimals, and integers is provided through activities involving puzzling patterns. (MNS)

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 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 Historical references also include the works of Euclid and Euler.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)

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)

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)

A useful approach for developing insights and discovering patterns is to examine numbers in relation to the number of their divisors. A teaching procedure for this approach is presented, with questions, answers, and homework suggestions. (MNS)

Describes a card trick that provides opportunities for students to discover patterns, work with variables, create tables, and ponder mathematics. Students at various levels of ability are able to enjoy the trick, and mathematical discourse is promoted within the classroom. (AIM)

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.…