of the Unit
In Lesson 1 of this unit, students investigate and model exponential growth using both explicit and recursive rules. (For the initial development of recursive rules for linear models, see page 112-115; for recursive exponential rules see page 422.) The sample material consists of the three short investigations from Lesson 2, "Exponential Decay." Students determine and explore exponential models of the form y = a(bx), where 0 < b < 1, through tables, graphs, and algebraic rules. They then compare these models to exponential growth and linear models.
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 early units in Course 2, students develop matrix and linear combination methods for solving systems of two linear equations. In Unit 4, Power Models, students develop the ability to recognize and model data patterns and problem conditions that involve direct or inverse power variation and quadratic models. They also study their applications.
Course 3 contains three units devoted to extending students' ability to represent and solve problems using algebraic methods. Students develop the ability to construct, reason with, and solve equations involving several variables and constraints in Unit 1, Multiple-Variable Models. Unit 3, Symbol Sense and Algebraic Reasoning, formalizes the function concept, introduces polynomial and rational functions, extends the solution of equations and inequalities by methods including factoring and the quadratic formula, and develops student ability in algebraic proof. The final algebra and functions unit, Families of Functions, reviews and extends student understanding of the basic function families and develops student ability to adjust these basic functions to match patterns in tables, graphs, and problem conditions.
Four units in Course 4 extend student understanding of algebra and function concepts in preparation for post-secondary education. Students develop understanding of the fundamental concepts underlying calculus, develop understanding of logarithmic functions and their use in modeling and analyzing problem situations, extend their ability to use polynomial and rational functions to solve problems, and extend their ability to manipulate symbolic representations of exponential, logarithmic, and trigonometric functions.
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 programs in social, management, and some of the health sciences or humanities.
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