Some patterns resulting from certain operations on numbers are discussed, analyzed, and explained. A method for predicting the outcome of these operations for any number is developed.

Playing with number patterns can lead students to discover some divisibility tests. (JT)

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)

A learning activity relating modular arithmetic to patterns of figures determined by points equally spaced around a circle is described. (SD)

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

A game involving operations on whole numbers, observing patterns in the relationships between operands and results, and seeking problems yielding various numerical solutions is described. (SD)

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)

The observations of a fifth-grade student concerning number patterns are recorded and discussed. (SD)

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

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 Historical references also include the works of Euclid and Euler.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

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)

Completing these worksheets leads students to discover patterns in the distribution of even numbers and numbers obtained by successive additions of 9 (primary grades). Worksheets for intermediate grades involve counting the number of factorizations for integers, and addition of the first nine whole numbers. (SD)

Using these worksheets students explore patterns in numerical and geometric processes, and predict the outcomes when the processes are iterated further. (SD)