CPMP Course 3 1st Edition Units

Unit 1
Multiple-Variable Models
Develops student ability to construct and reason with linked quantitative variables and relations involving several variables and several constraints.
Topics include:
Formulas, including the Law of Sines and the Law of Cosines, relating several variables by a single equation; systems of equations with several dependent variables or constraints; patterns of change in one or more variables in response to changes in others; solution of systems of equations and inequalities; and linear programming.
Unit 2
Modeling Public Opinion
Develops student understanding of how public opinion can be measured. The situations analyzed include elections (where there are more than two choices) and sample surveys, including political polling.
Topics include:
Preferential voting, vote-analysis methods, Arrow's theorem, fairness in social decision making; surveys, sampling, sampling distributions, relationship between a sample and a population, confidence intervals, margin of error; and critical analysis of elections and surveys.
Unit 3  (sample material)
Symbol Sense and Algebraic Reasoning
Develops student ability to represent and draw inferences about algebraic relations and functions using symbolic expressions and manipulations.
Topics include:
Formalization of function concept, notation, domain, and range; use of polynomial, exponential, and rational expressions to model relations among quantitative variables; field properties of real numbers and their application to expression of algebraic relations in equivalent forms and to solution of equations and inequalities by methods including factoring and the quadratic formula, and algebraic proof.
Unit 4  (sample material)
Shapes and Geometric Reasoning
Introduces students to formal reasoning and deduction in geometric settings.
Topics include:
Inductive and deductive reasoning, counterexamples, the role of assumptions in proof; conclusions concerning supplementary and vertical angles and the angles formed by parallel lines and transversals; conditions insuring similarity and congruence of triangles and their application to quadrilaterals and other shapes; and necessary and sufficient conditions for parallelograms.
Unit 5  (sample material)
Patterns in Variation
Extends student understanding of the measurement of variation, develops student ability to use the normal distribution as a model of variation, and introduces students to the probability and statistical inference involved in the control charts used in industry for statistical process control.
Topics include:
Standard deviation and its properties, normal distribution and its relation to standard deviation, statistical process control, control charts, control limits, mutually exclusive events, and the Addition Rule of Probability.
Unit 6  (sample material)
Families of Functions
Reviews and extends student ability to recognize different function patterns in numerical and graphical data and to interpret and construct appropriate symbolic representations modeling those data patterns.
Topics include:
Review of linear, polynomial, exponential, rational, and trigonometric functions (including effects of parameters on numeric and graphic patterns) and construction of function rules for function tables and graphs that are transformations of basic types (translation, reflection, stretch).
Unit 7  (sample material)
Discrete Models of Change
Extends student ability to represent, analyze, and solve problems in situations involving sequential and recursive change.
Topics include:
Iteration and recursion as tools to model and analyze sequential change in real-world contexts; arithmetic, geometric, and other sequences; arithmetic and geometric series; finite differences; linear and nonlinear recurrence relations; and function iteration, including graphical iteration and fixed points.
Capstone
Making the Best of It: Optimal Forms and Strategies
A thematic, two-week, project-oriented activity that enables students to pull together and apply the important mathematical concepts and methods developed throughout the course.

Reference and Practice (RAP) (sample material)
The Course 3 Reference and Practice book provides Core-Plus students with summaries of previously learned concepts and methods; distributed practice to review and polish previously learned concepts and skills; and test-taking practice for standardized tests and for college admission tests.
Scope and Sequence (pdf - 548Kb) of topics across Courses 1-4

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