Properties of a given array of numbers are discussed and some sample activity cards involving discovery of number patterns are presented. (MP)

Three examples are given illustrating the use of the calculator in problems where determining patterns and making conjectures are stressed. (MP)

Presents a mathematics investigation in which students discover number patterns in physical structures and express their generalizations algebraically. (MKR)

The construction of tables of numbers is discussed as a learning activity that involves work in such things as reciprocals, calculators, formulas, patterns, discovery, prime numbers, and other types of numbers. (MP)

Students use a series of isosceles right triangles constructed on a geoboard to discover patterns and form generalizations. (MP)

This discussion of cyclic patterns that appear in repeating decimals includes the use of the calculator in discovering the patterns. (MP)

Activities that allow students to represent patterns concretely before showing the patterns in color on paper are presented. Three basic activities are described, with suggestions made for extensions that allow further pupil exploration of multiples. Student discovery of relationships not found by the teacher is expected. (MP)

An investigation of patterns in magic triangles leads to a number of discoveries concerning the sums of sides and corners. (MP)

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)

The focus of this article is patterns and pattern making using geometric figures. Included are sequentially planned activities for K-8 students that help them first to discover the attributes of various figures and later how to combine these figures into patterns. Finally, this information is applied to real world activities such as quilting and…

Presents a hands-on mathematics task that can be investigated experimentally to produce a sequence of numbers. Describes ways to extrapolate values of the table of numbers by formulating and verifying a conjecture related to the pattern in the numbers. (MDH)

Illustrates where several unexpected patterns of antiderivatives can be realized during calculus instruction via the application of integration by parts to the exploration of particular members of families of functions. (JJK)

Presents two worksheets that ask students to count and classify the triangles that can be formed with a given total number of toothpicks or a given number of toothpicks for one side of the triangle. A third worksheet asks students to identify patterns observed during the investigations. Provides reproducible worksheets. (MDH)

Presents activities that use visual-geometric models to help students develop their understanding of exponents and division of powers with the same base. Presents opportunities for students to discover patterns for themselves and communicate these findings to others. (MDH)

Presented is an activity that explores the relationship between the size of a rectangle and the number of squares intersected by a diagonal. Students incorporate pattern recognition and the concept of the greatest common divisor in solving the problem. A sample worksheet is provided. (MDH)