Some unconventional word problems containing excessive, inconsistent, or inadequate data and their possible limitations and benefits in a mathematics classroom are discussed. (JT)

A problem from number theory is used to illustrate the use of the computer and programable calculators in solving problems. Programs are included. (MP)

The importance of teaching mathematics as a body of strategies and methods of inquiry is stressed; examples of situations which emphasize skills in classification, generalization, using symbols, and proof are given. (DT)

Modular arithmetic is used to show that there is at least one Friday the 13th in every year. A case-by-case proof is outlined and a proof of the general case is given. (DT)

Student errors led to this exploration of the conditions under which log of x base a = x. The discussion requires only techniques contained in a first-year calculus course. (MP)

Discussed is the problem of finding the volume common to two intersecting right circular cylinders. (MP)

A technique is given for solving problems involving a balance scale and a number of coins which are to be sorted in a certain number of weighings. (MP)

Methods are suggested for encouraging high school students to write mathematics research papers. Sources for information are discussed, a general outline for the paper is given, grading procedures are described, and several topics for reports are listed. (DT)