

Objectives
of the Unit

Sample Overview
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 publicdomain CPMPTools computer
software. You will notice reference to the "Light It Up!" custom tool.
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 fourphase cycle of classroom activities—Launch,
Explore, Share and Summarize, and Apply.
This instructional model is elaborated under Instructional
Design.
View the
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 14
descriptions.)
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