Discusses a method of graphing polar equations using information from the Cartesian graphs of trigonometric functions. (MKR)

A mathematical derivation is given, developing the cardioid as an epicycloid locus. Curve-stitched designs are given for a family of epicycloids. (MP)

Presents a strategy for graphing conic sections on the polar plane without using a table of values by beginning with information gained from the graphs of circular functions. (MKR)

Discusses activities to teach Cartesian graphing to young children in a conceptual way. Activities are organized around the concepts of finding one's way around in a plane and using the plane to represent variables in two dimensions by graphing equations in the usual way. (25 references) (MKR)

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)

Presented are activities concerning the method of graphing the equation y=kx in the Cartesian and other coordinate systems. Students progress from the graph of a straight line to the investigation of conceptually related geometric loci in non-Cartesian coordinate systems. (MDH)

This document contains detailed directions for constructing a device that mechanically produces the three-dimensional shape resulting from the rotation of any algebraic line or curve around either axis on the coordinate plant. The device was developed in response to student difficulty in visualizing, and thus grasping the mathematical principles…

This document argues that qualitative graphing is an effective introduction to mathematics as a construction for communication of ideas involving quantitative relationships. It is suggested that with little or no prior knowledge of Cartesian coordinates or analytic descriptions of graphs using equations students can successfully grasp concepts of…

Includes materials in reproducible format designed to help students read and draw distance-time graphs and use the slopes of these graphs to draw conclusions about car speed. (PK)

Entering a value into a calculator and repeatedly performing a function f(x) on the calculator can lead to the solution of the equation f(x)=x. Explores the outcomes of performing this iterative process on the calculator. Discusses how patterns of the resulting sequences converge, diverge, become cyclic, or display chaotic behavior. (MDH)

Offers practical tips on teaching secondary mathematics topics. The ideas are classroom-tested approaches that offer new slants on familiar subjects. The topics discussed include the interpretation of mathematical symbolism in concrete terms, ellipses, and vectors. (PK)

These materials are intended to provide meaningful mathematical experiences for pre-algebra students. These experiences emphasize the development of computational skills, mathematical concepts, and problem-solving techniques. This bulletin may be used as the basis for the second term of a one-year course, or for the second year of a two-year…

Presented are student activities that involve two standard problems from geometry and calculus--the volume of a box and the bank shot on a pool table. Problem solving is emphasized as a method of inquiry and application with descriptions of the results using graphical, numerical, and physical models. (JJK)

Presents an easy-to-use Applesoft BASIC program that graphs rational functions and any asymptotes that the functions might have. Discusses the nature of rational functions, graphing them manually, employing a computer to graph rational functions, and describes how the program works. (TW)

Explores the concept of extraneous roots in radical equations using an alternative to traditional algebraic methods. Using calculator- or computer-based graphs, accounts for extraneous roots by examining the four possible cases of systems of equations that can produce the solution to the radical equation. (MDH)