CPMP Course 1 Units

Unit 1  (sample material)
Patterns of Change
Develops student ability to recognize and describe important patterns that relate quantitative variables, to use data tables, graphs, words, and symbols to represent the relationships, and to use reasoning and calculating tools to answer questions and solve problems.
Topics include:
Variables and functions, algebraic expressions and recurrence relations, coordinate graphs, data tables and spreadsheets, and equations and inequalities.
Unit 2  (sample material)
Patterns in Data
Develops student ability to make sense of real-world data through use of graphical displays, measures of center, and measures of variability.
Topics include:
Distributions of data and their shapes, as displayed in dot plots, histograms, and box plots; measures of center including mean and median, and their properties; measures of variability including interquartile range and standard deviation, and their properties; and percentiles and outliers.
Unit 3
Linear Functions
Develops student ability to recognize and represent linear relationships between variables and to use tables, graphs, and algebraic expressions for linear functions to solve problems in situations that involve constant rate of change or slope.
Topics include:
Linear functions, slope of a line, rate of change, modeling linear data patterns, solving linear equations and inequalities, equivalent linear expressions.
Unit 4
Vertex-Edge Graphs
Develops student understanding of vertex-edge graphs and ability to use these graphs to represent and solve problems involving paths, networks, and relationships among a finite number of elements, including finding efficient routes and avoiding conflicts.
Topics include:
Vertex-edge graphs, mathematical modeling, optimization, algorithmic problem solving, Euler circuits and paths, matrix representation of graphs, vertex coloring and chromatic number.
Unit 5  (sample material)
Exponential Functions
Develops student ability to recognize and represent exponential growth and decay patterns, to express those patterns in symbolic forms, to solve problems that involve exponential change, and to use properties of exponents to write expressions in equivalent forms.
Topics include:
Exponential growth and decay functions, data modeling, growth and decay rates, half-life and doubling time, compound interest, and properties of exponents.
Unit 6  (sample material)
Patterns in Shape
Develops student ability to visualize and describe two- and three-dimensional shapes, to represent them with drawings, to examine shape properties through both experimentation and careful reasoning, and to use those properties to solve problems.
Topics include:
Triangle Inequality, congruence conditions for triangles, special quadrilaterals and quadrilateral linkages, Pythagorean Theorem, properties of polygons, tilings of the plane, properties of polyhedra, and the Platonic solids.
Unit 7  (sample material)
Quadratic Functions
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.
Topics include:
Quadratic functions and their graphs, applications to projectile motion and economic problems, expanding and factoring quadratic expressions, and solving quadratic equations by the quadratic formula and calculator approximation.
Unit 8
Patterns in Chance
Develops student ability to solve problems involving chance by constructing sample spaces of equally-likely outcomes or geometric models and to approximate solutions to more complex probability problems by using simulation.
Topics include:
Sample spaces, equally-likely outcomes, probability distributions, mutually exclusive (disjoint) events, Addition Rule, simulation, random digits, discrete and continuous random variables, Law of Large Numbers, and geometric probability.

CPMP Courses 1–4 Unit Descriptions (206 KB)
Courses 1–3 and Course 4: Preparation for Calculus Unit and Lesson Objectives (1.58 MB)
Scope and Sequence (1.14 MB) of topics across Courses 1–4

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