There are two different samples from Polynomial and Rational Functions. The first sample is the first two investigations of Lesson 2 of the unit. In these investigations, students examine nested, standard, and factored forms of polynomials, the effects of the symbolic form on computational efficiency, and the information provided by each form. Students develop skill in factoring polynomials. This work builds the necessary knowledge to introduce complex numbers in the third investigation.
The second sample material is the "Looking Back" lesson for this unit. This lesson is intended to provide students with tasks that will encourage them to look back at the unit as a whole. Students review, synthesize, and apply the knowledge gained during the study of the unit.
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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The next unit in Course 4, Functions and Symbolic Reasoning, extends student ability to manipulate symbolic representations of exponential, common and natural logarithmic, and trigonometric functions and to solve exponential, logarithmic, and trigonometric equations. Trigonometric identities are developed and proved or disproved. Geometric representations of complex numbers are used to reason about and to find roots of complex numbers. Algebraic representations of surfaces and conic sections are introduced in Unit 8, Space Geometry.
A unit that develops understanding and skill in the use of standard spreadsheet operations while reviewing and extending many of the basic algebra topics from Courses 1-3 is included for students intending to pursue college programs in social, management, and some of the health sciences or humanities.
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