The properties of the cube are explored. A set of activities is given that forms the basis of a class project on discovery. (MNS)

Several kinds of special dice are displayed and the various winning probabilities in games that could be played with them are discussed. Patterns for dice construction are provided. (MP)

Geometric construction problems are recommended as sources of stimulating exercises for mathematics classes. (MP)

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

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)

A problem involving the search for an equivalence class of triangles is viewed to provide several exciting and satisfying moments of insight. After solving the original problem, there is a brief discussion of a slight variation and several notes regarding related theorems and ideas. References for additional exploration are provided. (MP)

Presented is a method for finding two triangles that have five pairs of congruent parts, yet fail to be congruent. The solution is thought to involve some creative insights that should challenge both the teacher and students to recall and analyze all the congruence axioms and theorems. (MP)

The problem of finding the maximum number of right angles a polygon can have, given the number of sides, is discussed in detail. (MP)

A rationale is provided for the notion that mathematical games can be a valuable resource for the stimulation and support of student collaboration and cooperative classroom mathematical discussion. Included are examples of tangram games, people games, and board strategy games. (JJK)

Student research projects are open-ended questions or sets of questions intended to give undergraduate students experience doing introductory mathematical research. Proposed is an investigation of a Faro shuffle that is performed by cutting the deck exactly in half and then perfectly interleaving the cards of the two halves. (Author/JJK)

The roles and uses of symbols in mathematical thinking are discussed. The thinking process is further subdivided into specialization, generalization, and reasoning. (MP)

Much constructive computer and programable calculator activity can be stimulated by BASIC programs that are only three or four lines in length. This article illustrates several ideas with accompanying BASIC program, particularly related to the learning of algebraic concepts, that can be explored with both elementary and secondary mathematics…

Students are given a computational rule to follow for the first set of problems and must then discover the rule for the second set. Four worksheets for grades 1-8 are included. (MNS)

A set of three worksheets is provided, along with a guide for the teacher. Using manipulative materials, students investigate the difference between the consecutive sums of the numbers along the three sides of a triangle. (MNS)

Computational environments that provide integrated numeric, symbolic, and graphical capabilities provide new opportunities for laboratories in Numerical Analysis. Hermite interpolation is one topic that can benefit from such an environment. Describes a laboratory session using Mathematica that allows students to actively experience Hermite…