of the Unit
The sample investigation below is the first investigation in Lesson 2. In this investigation, students are asked to think about the relationship of current to voltage and resistance in simple circuits as an example of a multivariable function that combines direct and inverse variation. Then they revisit the inclined plane experiment data (from Lesson 1) and work on a model of the combined effect of ramp length and platform height on roll time. Finally, they are asked to generalize these function ideas to consider general patterns in relationships of the form z = xy and z = x/y.
This investigation makes use of the public-domain CPMP-Tools computer software. You will notice reference to the "Light It Up!" custom tool.
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.
Unit Table of Contents and Sample Lesson Material
You will need the free Adobe Acrobat Reader software to view and print the sample material.
How the Algebra
and Functions Strand Continues
In Course 2 Unit 2 and Unit 5, students 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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