Fifty-seven 30-minute programs, 54 of them with accompanying student workbooks, make use of a variety of learning approaches and problem-solving strategies to teach senior high math. A 15-minute introduction of the series demonstrates how to use the video and print components. The final two programs present a variety of strategies that help students prepare for and write a final exam. The student workbooks are included free when the complete series is purchased.
Subjects: Quadratic Relations
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Physical Properties of Conic Sections
Explores the topology of the double-napped cone and, through computer technology and graphics, demonstrates conditions necessary to produce the conic sections and their degenerates.
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General Quadratic Relation: An Introduction
Discusses the difference between a relation and a function, and focuses on developing the general quadratic relation and the conic sections that it defines.
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General Quadratic Relation: Circles and Ellipses
Physical characteristics of the circle and ellipse are identified and related to the parameters of the general quadratic relation. The connection between A and C and the effects of changing D, E and F are determined.
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General Quadratic Relations: Parabola and Hyperbolas
Provides an understanding of the general quadratic relation, Ax2 + Bxy + Cy2 + Dx + Ey + F = 0, where B = 0 with respect to parabolas and hyperbolas.
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Locus and Eccentricity of the Parabola
Presents several approaches that can be used to investigate the shape of the parabola. Locus and eccentricity are explained and then used to solve problems that involve determining and analysing equations of various parabolas.
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Eccentricity of the Ellipse
Orbits and sewers are just two of the examples used in this study of the eccentricity definition of ellipses. Eccentricity is defined, the shape of an ellipse as e approaches 0 and 1 is observed, and problems are solved using the eccentricity.
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Alternate Locus Definitions: Ellipse and Circle
String and tacks are used to redefine the circle and ellipse using the concept of locus. Also shown: how to find the equation of a conic, use double-concentric graph paper, and solve problems that require an understanding of the concept of locus.
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Locus and Eccentricity of the Hyperbolas
Investigates several approaches used to study the hyperbola’s shape: locus involving two fixed points; double concentric circles; the focus-directrix (eccentricity) definition; and computer graphing programs.
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Identification, Connections and Applications of Quadratic Relations
Shows how to identify the type of conic given a description based on any of the four forms, connect the various conics to their definitions and solve a variety of problems.