Develops the formulas for the sum of the numbers from 1 to n and for the squares of the numbers from 1 to n geometrically by utilizing the formulas for the area of a triangle and the volume of a pyramid. (MDH)

Presents four related problems that provide examples of ways to include justifications of interesting mathematics in courses taught prior to a geometry course. (ASK)

Presents and discusses examples that can be used to develop the concept of slope as a rate of change through three modes of learning: (1) visualization, (2) verbalization, and (3) symbolization. (ASK)

Active involvement and infusion of mathematics into familiar, everyday experiences are essential elements in challenging students to engage in true thinking. Presents an investigation on graphing that touches on all representations including tables of values, graphs, and verbal descriptions. (ASK)

Describes an activity in which students are given a set of designs and are required to use their electronic grapher to reproduce the designs. The activity reinforces students' understanding of lines and of the formula for a linear function. (MKR)

How can a chain with 63 links be cut in 3 places so that you could hand a person any number of links from 1 to 63? Considers variations on the problem and derives a general formula. (TO)

Examines a root-approximation method using fixed points as a pedagogical tool for reinforcing and expanding students' conception of functions. (KHR)

Shows how the phenomenon of instability in the solution of a system of linear equations can be analyzed both algebraically and geometrically. (KHR)

Presents a real-life example of mathematical modeling in which a medical company asks for help in solving a warehouse-inventory problem. Uses charts, graphs, and computers. (MKR)

Presents a paper-folding method to develop a class repertoire of construction methods for the ellipse, hyperbola, and parabola using straws, rulers, dental floss, paper circles, and other household items. Uses the Geometer's Sketchpad software to complement the paper-folding process. (MKR)

Presents the Fibonacci sequence in a format that is readily implemented using the table and list features of the Texas Instruments TI-82 graphing calculator or a spreadsheet. Includes questions and investigations that can be explored using these tables and lists. (MKR)

Describes the effect, method, and mathematics of the following magic tricks which can be used in introducing mathematics lessons: the Ninth Card, Fibonacci Revealed, the Case of the Missing Area, I've Got Your Numbers, and the Card That Turns Inside Out. (MKR)

Presents a method for introducing students to broken-line functions with unbroken domains. Concludes that a unit on broken-line functions should enhance students' understanding of the function concept. (ASK)

Describes a method of effectively introducing the concept of radian measure that uses Cabri Geometry II software to construct a circle of arbitrary radius and to measure that radius. The goal is to determine how many of these radii fit around a circle. (DDR)

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)