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)

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)

Presents several examples of investigations which demonstrate the following: (1) algebra is connected to other mathematical topics; (2) algebra is an effective tool for representing patterns and relationships; and (3) algebra is an effective tool for analyzing patterns. (DDR)

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

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

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)

Presents three investigations related to the game Bulgarian Solitaire. Investigations ask students to find and represent optimal solutions to the problem, to identify cyclical solution patterns for different numbers, and to respond to questions involving the number and nature of the cyclical solutions. An appendix provides answers to questions.…

Presented are problem-solving experiences with area, volume, and algebraic expresssions resulting from data collection. Three worksheets are included for students in grades 7-12. (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)

Described is a learning activity that requires students to observe, read, and interpret graphs and organize and describe data. Included are the grade level, materials, objectives, prerequisites, directions, answers to questions, and copies of handouts. (KR)