Techniques for applying mathematical concepts in the real world: six rarely taught but crucial tools for analysis, research, and problem-solving. Many young graduates leave school with a solid knowledge of mathematical concepts but struggle to apply these concepts in practice. Real scientific and engineering problems are different from those found…

Korean secondary school students preparing for college learn about a simple algebraic formula for area bounded by a parabola and line. The approach does not seem well-known among American students. It is noted that, while the formula derivations rely on integration, algebra students could use the formulas without proofs. (MP)

Presents an alternate approach to teaching quadratics by fully integrating the study of quadratic equations and quadratic functions using graphs. Includes reproducible student worksheets. (MKR)

The usual methods for solving quadratic equations are noted to require either the use of numerical formula or curve plotting on graph paper. The method described here enables pupils to solve equations using only a 45 degree setsquare, graph paper, and a pencil for those which have both real roots and real coefficients. (Author/MP)

The game of Yahtzee is discussed in terms of the various outcomes of turns in the game and their point values and the probabilities associated with achieving specific combinations of dice values. Several tables and methods of table construction are noted, and several challenge exercises are included. (MP)

Most algebra textbooks use a trial-and-error method, but such a method is not necessary. A procedure is described which has been tested in basic and intermediate algebra classes for four semesters, with significant improvement found in pupil ability to handle trinomial factoring. (MP)

A program designed to plot three-dimensional graphs is described and presented. The program allows the user to select maximum and minimum ranges for X, Y, and Z, and can enlarge a graph on the screen or look at a portion away from the origin. It is in Applesoft BASIC. (MP)

Details of how observers on a moving ship can furnish an accurate report of wind velocity are provided. A method employing vector addition and some trigonometry is covered. Wind velocity is initially indicated through an anemometer and a wind vane. Ships are urged to radio weather data. (MP)

Details of an instructor's attempt to solve a problem in combinatorics taken from a textbook used by some of his students are presented. It is felt the material raises a number of significant points about problem solving and mathematics. Teachers are encouraged to put themselves in such situations. (MP)

Two examples are given of ways traffic engineers estimate traffic flow. The first, Floating Car Method, involves some basic ideas and the notion of relative velocity. The second, Maximum Traffic Flow, is viewed to involve simple applications of calculus. The material provides insight into specialized applications of mathematics. (MP)

This activity exposes beginning algebra students to the concepts of slope and intercept. Four worksheets pertain to the "electrician problem." (MNS)

The problems involved in making reservations for airline flights is discussed in creating a mathematical model designed to maximize an airline's income. One issue not considered in the model is any public relations problem the airline may have. The model does take into account the issue of denied boarding compensation. (MP)

Explorations of problems involving the zero power are presented as routes through which instructors can take their students to reduce pupil uneasiness with the concept. Initial examination begins with routines for calculators, and discussion proceeds to more formal mathematics to generate more support for the definition of zero power. (MP)

Presents an activity in which students draw a picture, analyze each line and curve, and write the symbolic equations represented by the graph. Includes reproducible student worksheets. (MKR)

Presents five lessons to demonstrate how graphing calculators can be used to teach the slope-intercept concept of linear equations and to establish more general principles about two-dimensional graphs. Contains a reproducible student quiz. (MKR)