An activity project is described which encourages students to question and experiment. Appendices provide examples of student results. (MNS)

Some number investigations on the multiplication table are provided by a sequence of four activity sheets. Beginning with examples of triangular and square numbers, the activities lead to the generalization. (MNS)

Five activities involving an array of numbers called an even triangle are given. Properties of the triangle are listed and some generalizations are proven. (MP)

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)

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

Described are two examples involving recursive mathematical sequences designed to integrate a holistic approach to learning algebra. These examples promote pattern recognition with algebraic justification, full class participation, and mathematical values that can be transferred to other situations. (MDH)

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…

Three examples are given in which students create their own Logo software to explore the topics of number patterns and operations, fractions, and decimal parts in measurement. (MNS)

Activities to extend the core curriculum through the study of the periodicity of rational numbers to help students develop calculator and research skills are presented. Four worksheets are included, to be used as discovery activities. A computer program is listed, as well as examples of periodic pictures. (MNS)

Describes three activities using dominoes, playing cards, and the calendar to give students mathematical experiences reinforcing basic skills and problem-solving strategies that involve patterns, relationships, and functions. Students discover mathematical relationships underlying the magic tricks used in the activities. (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)

Discusses the use of computer visualization to motivate and support mathematical dialogues. Describes the "Scientific Visualization Software Suite," a set of public domain visualization tools from the National Center for Supercomputing Applications. (Author/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)

Chess experts remember meaningful knowledge in the form of networks or patterns. Applied to mathematics instruction, effective classroom approaches can use investigation to identify patterns or rules. Described are a class activity and a small-group activity to investigate addition of signed numbers and linear relationships. (MDH)

The "Curriculum and Evaluation Standards for School Mathematics" (1989) provides a vision and a framework for revising and strengthening the K-12 mathematics curriculum in North American schools and for evaluating both the mathematics curriculum and students' progress. The document not only addresses what mathematics students should…