Course 1 Unit 5 - Exponential Functions

This is the third unit from the algebra and functions strand in Course 1. Exponential functions are useful in solving problems involving change in populations, pollution, temperature, bank savings, drugs in the blood stream, and radioactive materials. Their usefulness as well as the fact that the difference equation for exponential growth, NEXT = NOW x b, is a natural counterpoint to the difference equation for linear change, NEXT = NOW + b, are strong reasons for introducing exponential functions prior to quadratic functions in Course 1.

Unit Overview
See the sample Teacher's Guide pages below.

Objectives of the Unit
  • Recognize and give examples of growth and decay situations in which exponential functions are likely to match the patterns of change that are observed or expected. This function-recognition skill should apply to information given in data tables, graphs, or verbal descriptions of related changing variables.
  • Develop ability to use reasoning, estimation, and curve-fitting utilities to find exponential functions to match patterns of change in exponential growth and decay situations. This should include rules in the "y = ..." and NOW-NEXT forms.
  • Use exponential rules to produce tables and graphs to answer questions about exponential change of variables.
  • Interpret an exponential function rule in order to sketch or predict the shape of its graph and the pattern of change in tables of values.
  • Describe major similarities and differences between linear and exponential patterns of change.
  • Develop skill in rewriting exponential and radical expressions in equivalent forms.

Sample Overview
The sample material is the first lesson of Unit 5. This material provides an example of how one unit begins. The sample Teacher's Guide material shows the features of the Teacher's Guide including the Unit Planning Guide, instructional notes, solutions, collaboration skills and prompts, and a Promoting Mathematical Discourse scenario. In the margin, you will see reduced-size pictures of the Unit Resource Masters for the investigation. See Implementing Core-Plus Mathematics for information on features of the Teacher's Guide.

Instructional Design
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 four-phase cycle of classroom activities—Launch, Explore, Share and Summarize, and Apply. This instructional model is elaborated under Instructional Design.

View Sample Material
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How the Algebra and Functions Strand Continues
The final algebra and functions strand unit in Course 1, Unit 7, develops student ability to recognize and represent quadratic relations between variables using data tables, graphs, and symbolic formulas; to solve problems involving quadratic functions; and to express quadratic polynomials in equivalent factored and expanded forms.
     In Course 2, students review and extend their ability to recognize, describe, and use functional relationships among quantitative variables, with special emphasis on relationships that involve two or more independent variables. They also develop matrix and linear combination methods for solving systems of two linear equations. They are introduced to function notation, review and extend their ability to construct and reason with functions that model parabolic shapes and other quadratic relationships in science and economics, with special emphasis on formal symbolic reasoning methods, and are introduced to common logarithms and algebraic methods for solving exponential equations.
     In Course 3, students extend their understanding of formal reasoning in contexts, study linear inequalities and linear programming, polynomial and rational functions, sequences and series, and inverse functions.
     Course 4: Preparation for Calculus extends student algebraic skills and understandings in equations and functions in algebra units but also in geometry units such as Unit 2, Vectors and Motion, and Unit 6, Surfaces and Cross Sections. (See the CPMP Courses 1-4 descriptions.)

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