CPMP Course 3 Units

Unit 1
Reasoning and Proof
Develops student understanding of formal reasoning in geometric, algebraic, and statistical contexts and of basic principles that underlie those reasoning strategies.
Topics include:
Inductive and deductive reasoning strategies; principles of logical reasoning—Affirming the Hypothesis and Chaining Implications; properties of line reflections; relation among angles formed by two intersecting lines or by two parallel lines and a transversal; rules for transforming algebraic expressions and equations; design of experiments; use of data from a randomized experiment to compare two treatments, sampling distribution constructed using simulation, randomization test, and statistical significance; inference from sample surveys, experiments, and observational studies and how randomization relates to each.
Unit 2
Inequalities and Linear Programming
Develops student ability to reason both algebraically and graphically to solve inequalities in one and two variables, introduces systems of inequalities in two variables, and develops a strategy for optimizing a linear function in two variables within a system of linear constraints on those variables.
Topics include:
Inequalities in one and two variables, number line graphs, interval notation, systems of linear inequalities, and linear programming.
Unit 3
Similarity and Congruence
Extends student understanding of similarity and congruence and their ability to use those relations to solve problems and to prove geometric assertions with and without the use of coordinates.
Topics include:
Connections between Law of Cosines, Law of Sines, and sufficient conditions for similarity and congruence of triangles; connections between transformations and sufficient conditions for congruence and similarity of triangles; centers of triangles, applications of similarity and congruence in real-world contexts; necessary and sufficient conditions for parallelograms, sufficient conditions for congruence of parallelograms, and midpoint connector theorems.
Unit 4
Samples and Variation
Develops student ability to use the normal distribution as a model of variation, introduces students to the binomial distribution and its use in making inferences about population parameters based on a random sample, and introduces students to the probability and statistical inference used in industry for statistical process control.
Topics include:
Normal distribution, standardized scores and estimating population percentages, binomial distributions (shape, expected value, standard deviation), normal approximation to a binomial distribution, odds, statistical process control, and the Central Limit Theorem.
Unit 5
Polynomial and Rational Functions
Extends student ability to represent and draw inferences about polynomial and rational functions using symbolic expressions and manipulations.
Topics include:
Definition and properties of polynomials, operations on polynomials; completing the square, proof of the quadratic formula, solving quadratic equations (including complex number solutions), vertex form of quadratic functions; definition and properties of rational functions, operations on rational expressions.
Unit 6
Circles and Circular Functions
Develops student understanding of properties of special lines, segments, angles, and arcs in circles and the ability to use those properties to solve problems; develops student understanding of circular functions and the ability to use those functions to model periodic change; and extends student ability to reason deductively in geometric settings.
Topics include:
Properties of chords, tangent lines, and central and inscribed angles and their intercepted arcs; linear and angular velocity; radian measure of angles; and circular functions as models of periodic change.
Unit 7
Recursion and Iteration
Extends student ability to model, analyze, and solve problems in situations involving sequential and recursive change.
Topics include:
Iteration and recursion as tools to model and solve problems about sequential change in real-world settings, including compound interest and population growth; arithmetic, geometric, and other sequences together with their connections to linear, exponential, and polynomial functions; arithmetic and geometric series; finite differences; linear and nonlinear recurrence relations; and function iteration, including graphical iteration and fixed points.
Unit 8
Inverse Functions
Develops student understanding of inverses of functions with a focus on logarithmic functions and their use in modeling and analyzing problem situations and data patterns.
Topics include:
Inverses of functions; logarithmic functions and their relation to exponential functions, properties of logarithms, equation solving with logarithms; and inverse trigonometric functions and their applications to solving trigonometric equations.

CPMP Courses 1–4 Unit Descriptions (284 KB)
Courses 1–3 and Course 4: Preparation for Calculus Unit and Lesson Objectives (395 KB)

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