Illustrated are the discovery and verification of new patterns in Pascal's Triangle. Discovery activities appropriate for students when they are learning to expand binomials are provided. (JP)

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

Presented are a series of conjectures and proofs resulting from an examination of patterns and relationships among natural numbers. (JP)

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)

Worksheets are provided for an activity involving the use of the calculator in discovering patterns when a number is divided by 9, 99, or 999. (DT)

Suggests that by using elementary concepts and arithmetic methods it is possible to find many interesting aspects of mathematics. The activities could be used to allow students to make individual discoveries about mathematics. (PK)

Discusses the distribution of primes and focuses directly on one particular recurring pattern among them. (Author/NB)

Characterizes those numbers that are the sum of consecutive natural numbers and counts how many such representations a given number has. (Author/NB)

The authors define an unusual partitioning or division" operation and explore number patterns and divisibility properties which result. The topic is suggested as enrichment material. (CT)

Provides some examples of mathematics problems that have solutions involving triangular numbers. Illustrates the observation of number patterns from which conjectures and generalizations can be made. Suggests other extensions for further investigation. (ASK)

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)

Patterns that appear in the repeating digits of a decimal are used to help convince students that any infinite repeating decimal can be written in the form of a rational number. (JT)

Patterns in modular arithmetic are discussed: (1) multiplication tables, and (2) diagrams obtained by joining points on the circumference of a circle. (MM)

Suggests guided discovery techniques to help students find the rule by which an arrival sequence of consecutively numbered school buses is considered a "success," and presents arguments by Honsberger for a formula to calculate the number of successful patterns for a given number of buses. (SEW)

Describes generalized Fibonacci sequences that satisfy many elegant identities and possess curious properties. Provides physical applications and connections to various branches of mathematics. (KHR)