Microcomputer programs that help students calculate permutations and combinations are developed. Listings of five programs are included. (MNS)

Three approaches for teaching students to solve inequalities involving absolute values, quadratic expressions, and rational expressions are illustrated. Then one technique that can be used with all of these problems is presented. (MNS)

Can the sum of the edges, the surface area, and the volume of a three-dimensional object be numerically equal? Solutions to this challenging problem are discussed. (MNS)

Rules from an old mathematics textbook are discussed. Suggested are approaches to using the materials with students, challenging them to come up with explanations of why the rules work. (MNS)

Presents an example of mathematics from an algorithmic point of view, with emphasis on the design and verification of this algorithm. The program involves finding roots for algebraic equations using the half-interval search algorithm. The program listing is included. (JN)

Computation errors that may occur by expanded use of calculators are discussed. Potential errors with five exact arithmetic examples are described as they are translated into approximate processes. (MNS)

Two mathematical topics are interpreted from the viewpoints of traditional (performing algorithms) and contemporary (creating algorithms and thinking in terms of them for solving problems and developing theory) algorithmic mathematics. The two topics are Horner's method for evaluating polynomials and Gauss's method for solving systems of linear…

Presents a personal account of some mathematical work undertaken by the authors during a workshop session on the use of short microcomputer programs as starting points for mathematical investigations. Factors in their work (in solving equations) which may have implications for investigational work with students are addressed. (JN)

Provides examples which illustrate a graphical approach to solving inequalities. Advantages of using this strategy with high school students are noted. (JN)

Discusses the meaning of calculation errors, describing two error types (truncation and roundoff errors). Examples of calculator calculations are given to illustrate the importance of an awareness of significant digits and the effects of errors that may lead user to a mistaken interpretation of calculated results or to faulty conclusions.…

Presents three problems, each with a computer solution in BASIC programming language: (1) finding sum equals product for three-digit numbers; (2) finding cases of improper cancellation that give a correct answer; and (3) finding perfect numbers. Some suggestions for further investigation are included. (JN)

Discusses: (1) use of matrix techniques to write secret codes (includes ready-to-duplicate worksheets); (2) a method of multiplication and division of polynomials in one variable that is not tedius, time-consuming, or dependent on guesswork; and (3) adding and subtracting rational expressions and solving rational equations. (JN)

Background information, list of materials needed, instructional strategies, two student worksheets (with answers), and three overhead transparency masters are provided for a lesson designed to help students develop estimating skills when multiplying or dividing numbers near a power of 10. The lesson is teacher-directed and initiated with overhead…

Presents historical comments related to these terms: absolute value, add, algebra, algorithm, calculus, ellipse, fraction, hyperbola, logarithm, mantissa, multiply, operations, parabola, radian, root, sine, and trigonometry. Suggests that students become involved in mathematics history projects. (JN)

How to take an existing magic square and surround it with a magic border is described, with a number of examples. (MNS)