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)

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)

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 Historical references also include the works of Euclid and Euler.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

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)

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)

This booklet offers teacher instructions and student worksheets on number activities for gifted primary grade students. Three sections are included: (1) "moving numbers" which asks students to supply the missing member or members of addition and subtraction equations; (2) "number trails," which involve the completion of number…

Activities are described that reinforce knowledge of multiplication facts and also give students practice in making generalizations that improve problem-solving skills and provide a foundation for work with fractions. (MNS)

A visual model of fractions, the tower of bars, is used to discover patterns. Examples include equalities, inequalities, sums of unit fractions, sums of differences, symmetry, and differences and products. Infinite sequences of numbers, infinite series, and concepts of limits can be introduced. (DC)

Explores algebraic thinking as children search for patterns while collecting, organizing, and graphing data and as they derive equations describing relationships found in the data. (ASK)

Presents a brief definition and examples of residue designs while sharing some of the algebraic thought that a student used to form generalizations about the patterns discovered during the investigations of residue designs. (ASK)