The sample material is the fourth investigation of Lesson 2, "Simulating Linear and Nonlinear Motion." In this investigation, students model circular and elliptical motion parametrically. Students draw on their understanding of transformations of function graphs to modify graphs of parametric equations to fit problem situations.
Throughout the curriculum, interesting problem contexts serve as the foundation for instruction. As lessons unfold around these problem situations, classroom instruction tends to follow a common pattern as elaborated under Instructional Design.
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In Course 4, Unit 7, Functions and Symbolic Reasoning, students intending to pursue college majors in the mathematical, physical, and biological sciences, or engineering develop proficiency in reasoning with and manipulating symbolic representations of exponential, logarithmic, and trigonometric functions. They use trigonometric functions, identities, and polar coordinates to develop an understanding of the geometry of complex numbers. In Unit 8, Space Geometry, students extend their ability to visualize and represent three-dimensional surfaces using contours, cross sections, and reliefs and to visualize and sketch surfaces and conic sections defined by algebraic equations.
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