A familiar Christmas song described as a second-year algebra problem is presented in "The Twelve Days of Christmas". Five strategies for solving inequalities are discussed in "Solving Algebraic Inequalities". (JT)

A method for solving certain types of problems is illustrated by problems related to Fibonacci's triangle. The method involves pattern recognition, generalizing, algebraic manipulation, and mathematical induction. (MP)

Three games played with regular bridge decks of cards are described. By playing the games students gain practice in use of basic operations on integers and in the development of strategies. (SD)

This activity is designed to help students recognize and extend rectangular patterns and to use patterning to formulate rules for "nth" cases. Three worksheets are included. (MNS)

Curiosities offer an interesting alternative to traditional methods of attacking problems. An illustrative situation is given, with graphical, computer, and analytical methods used to solve the problem. (MNS)

The similarity between two apparently dissimilar problems is explored. Pascal's triangle is involved. (SD)

Information-processing students solving problems in the 1960s and 1970s accepted the tradition of early experimental psychology in concentrating primarily on the study of "knowledge-lean" tasks in which competence can usually be acquired over short periods of learning and experience. In recent years, experts have examined knowledge-rich…

An activity sequence is described. Several aspects of a population problem are developed using isoperimetric graph paper and symmetry principles to derive general rules. (SD)

Several games, which can be useful in the classroom for teaching problem solving strategies, are described. (SD)

Three worksheets provide exercises involving triangular arrays of numbers. (SD)

Describes an activity that utilizes four pattern blocks to help students understand and explain perimeter. Engages students in making and supporting conjectures about a scenario that involves trains composed of various shapes with different perimeters. (DDR)

Presents an extension of the hog game that satisfies the mathematical process activities of observing patterns; forming, testing and proving hypotheses; and applying and extending proved results. Discusses use of technology in the investigation of problems and in the process of devising and validating general rules. (ASK)

A computer program is presented for the billiard ball problem. It can be integrated into a lesson on inductive reasoning and suggests several ways to do so. (MNS)

Patterns resulting from polygonal numbers are explored, with examples of triangular, square, pentagonal, rectangular, and other numbers. Tables and formulas to be developed are included. (MNS)

Properties of the harmonic number triangle are listed, and ways of generating the elements of harmonic triangles are described. (MNS)