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

This is part one of a three-part School Mathematics Study Group (SMSG) textbook. This part contains the first five chapters including: (1) Analytic Geometry, (2) Coordinates and the Line, (3) Vectors and Their Applications, (4) Proof by Analytic Methods, and (5) Graphs and Their Equations. (MK)

This is one in a series of manuals for teachers using SMSG high school supplementary materials. The pamphlet includes commentaries on the sections of the student's booklet, answers to the exercises, and sample test questions. Topics covered include definitions, parallel and perpendicular lines, distance formula, midpoint formula, linear equations,…

This is one in a series of SMSG supplementary and enrichment pamphlets for high school students. This series is designed to make material for the study of topics of special interest to students readily accessible in classroom quantity. Topics covered include graphs, slope, distance, mid-point, proof, equations, and circles. (MP)

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)

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…

Gives definitions of taxicab geometry and the MacDraw format for graphing. In the world of taxicab geometry, movement through the plane is along horizontal and vertical paths. Describes specific application to conic sections, including circle, ellipse, parabola, and hyperbola. Lists five references. (YP)

Presents a lesson in which students communicate verbally and in writing to create and describe geometric transformations, develop vocabulary, demonstrate ability to give unambiguous instructions to translate a triangle, form and test conjectures, and create extensions of problems. Includes reproducible student worksheets and questions for…

Graphing techniques are used to demonstrate the inverse function theorem and that the graph of the inverse function can be obtained by flipping the graph about the line y=x. (MP)

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

Topics covered are: a game to provide drill with linear equations; the relationship between area and perimeter in a triangle; a new form for factoring polynomials; and a technique for graphing inverse functions. (MP)

The simultaneous solution of equations in polar form does not always yield the points of intersection of their graphs. An explanation is given. (MP)

A geometric approach to the solution of quadratic equations and more general polynomials is based on finding points with minimum distance from the x-axis. The approach is useful in motivating the definition of complex numbers. (SD)

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)

Presents a secondary classroom investigation into mathematical modeling techniques with the graphing calculator using a match stick puzzle. Geometric models, through their corresponding area formulas, are constructed, tested, and analyzed graphically to fit specified problem conditions. (Author/MKR)