A situation is presented that is intended to lead to open-ended mathematical discussions that allow students to conjecture, discover, and prove mathematical statements. (MP)

Complex numbers and trigonometry are used to prove that a given constructed line is equal to the length of one side of a regular pentagon inscribed in a unit circle. (MP)

The events surrounding the olympiad are discussed, test results are given, and the problems on the test are listed. (MP)

The author has selected a number of episodes that illustrate some of the successes and failures of humanity's attempt to find the area of the circle and presents them as problem studies. (MN)

An algorithm is given for the addition and subtraction of fractions based on dividing the sum of diagonal numerator and denominator products by the product of the denominators. As an explanation of the teaching method, activities used in teaching are demonstrated. (MN)

The idea of "complete permutations" of n distinct objects is explored in order to investigate an application of the concept that arises in Rex Stout's mystery novel, Too Many Cooks. (MN)

Answers to a list of twenty geometry-related questions are hidden in a matrix of letters. The answers can be read in eight different directions: vertically, horizontally, on both diagonals, forward, and backward. (MN)

Finding the sum of all n digit whole numbers that can be formed from an n digit whole number is proposed as a useful classroom activity. The problem leads from inductive method to deductive proof with the aid of pocket calculators, and provides an opportunity to introduce factorial notation and permutations. (MN)

A classroom activity is described where students divided circular regions into equal sections and reassembled them to determine the formula for the area of a circle. Using an odd number of sections (Instead of an even number) changes the shape of the reassembled pieces but still gives rise to the same formula. (MN)

The author describes and gives two illustrations of a method for solving a system of two linear equations. The ratio of left members is equated to the ratio of right members, the ratio of the two variables is solved for, and the resultant ratio is substituted into an original equation. (MN)

An activity is presented in which students use eight-place pocket calculators to demonstrate their knowledge of correct order of operations for mathematical expressions. After performing an indicated computation and getting a result, the student inverts the calculator to obtain a word or abbreviation to be entered in a crossword puzzle. (MN)

A mathematical model is developed for making population projections at five-year intervals from 1975 to 2000. The model starts with 1970 population figures, broken down by age and sex, and incorporates the change factors of birth, death, immigration, and emigration. A computer program is included along with projection outputs. (MN)

The author pinpoints those aspects of education where calculators seem sure to have an impact and quotes from several reports that outline some of the short-term and long-term things mathematics educators may need to do to bring about an orderly and fruitful adjustment to calculators. (MN)

A case is made against the major argument which implies that the use of a calculator for arithmetic problems that can be done by hand will prevent a student from being able to do arithmetic when the calculator is absent. (MN)

An account of student efforts to solve the problem of finding the equations for a pair of parabolas that intersect in exactly three points is given. The deceptively difficult problem leads to the rational root theorem and eventually to computer programs for locating roots and for approximating irrational roots. (MN)