Presents an activity to involve students in mathematical communication and creative thinking. The activity is similar to the "pass it along" gossip game in which each person in a chain adds a piece of information. The class analyzes the resulting mathematics problem using George Polya's problem-solving techniques. (MKR)

How can a chain with 63 links be cut in 3 places so that you could hand a person any number of links from 1 to 63? Considers variations on the problem and derives a general formula. (TO)

The author uses Stella the Spider as the main character in a number of three-dimensional geometry problems. Eight of these problems are discussed, with solutions. (MNS)

Motivational classroom materials that provide direct instruction on problem-solving skills are given. The activity highlights and provides opportunities for practice with two problem-solving skills, make a drawing and work backward. (MNS)

Some uncomplicated illustrations of how probability yields results that seem in conflict with traditional intuition are given. (MNS)

Involving students in generating and solving their own problems is proposed. A method for generating problems by using a number puzzle is presented. Ideas for using the "what if not" technique are also given. (MNS)

The use of trial-and-error strategies to solve problems is endorsed. Types of problems with which trial and error is effective are discussed, with examples of how it is used, and teaching considerations are briefly considered. A computer program for one problem is included. (MNS)

The mathematical content involved in self-teaching enrichment models for students in grades 8-12, the pedagogy employed in a summer institute for such students, and the results obtained are presented. (MNS)

Given are several examples of seemingly unrelated problems that nevertheless can be solved with a single mathematical idea--the proportion. It is hoped that as students see how a variety of problem contexts can be modeled by a proportion, they will use proportions more frequently in problem solving. (MNS)

Presents 14 distinct methods to determine the sine of the angle formed by the line segments joining one vertex of a square to the midpoints of the nonadjacent sides. Nine methods were developed by mathematics club participants preparing for mathematics competitions and the remaining five by faculty members. (MDH)

Presented is the problem of determining alternative schedules for major league baseball. Equations of the schedule, conditions on the solutions, and solutions are discussed. (CW)

Outlines an instructional approach that can be used to teach students to apply a strategy known as subgoal generation to multistep problems. (PK)

Four teaching ideas are discussed: a "giant" math problem designed to motivate students to use library sources, calculators, computers, and textbooks; a different way of finding fractional equivalents; a task-card project designed to encourage mathematics students to use libraries; and journal writing in a mathematics class. (MP)

A problem-solving approach is developed for secondary or college students to estimate the number of piano tuners in a large city. The answer and method are analyzed for appropriateness. Four similar problems are suggested. (DC)

Presents four investigations involving geometric sequences and series: folding a sheet of paper in half 8 times, stacking pieces of paper cut in half 50 times, snapping your fingers at intervals doubled in length for 1 year, and summing time intervals continuously cut in half. (MDH)