Overview of the Mathematical Strands

Each year the CPMP curriculum features interwoven strands of algebra and functions, statistics and probability, geometry and trigonometry, and discrete mathematics. Each of these strands is developed within focused units connected by fundamental ideas such as symmetry, matrices, functions, and data analysis and curve-fitting. The strands are also connected across units by mathematical habits of mind such as visual thinking, recursive thinking, searching for and explaining patterns, making and checking conjectures, reasoning with multiple representations, describing and using algorithms, and providing convincing arguments and proofs. The strands are further linked by fundamental themes of data, representation, shape, and change. By encountering each strand each year from a more mathematically sophisticated point of view, students' understanding of mathematics and its connections deepens across the four-year curriculum.

Algebra and Functions
The Algebra and Functions strand develops student ability to recognize, represent, and solve problems involving relations among quantitative variables. Central to the development is the use of functions as mathematical models. The key algebraic models in the curriculum are linear, exponential, power, polynomial, logarithmic, rational, and circular functions. Each algebraic model is investigated in at least four linked representations—verbal, graphic, numeric, and symbolic—with the aid of technology. Modeling with systems of equations, both linear and nonlinear, is developed. Attention is also given to symbolic reasoning and manipulation.
  Geometry and Trigonometry
The primary goal of the Geometry and Trigonometry strand is to develop visualization skills and reasoning and the ability to build, interpret, and apply mathematical models involving shape and motion. The focus is on describing patterns with regard to shape, size, and location; representing patterns with drawings, coordinates, or vectors; predicting changes and invariants in figures under transformations; and organizing geometric facts and relationships through deductive reasoning.
 
Statistics and Probability
The primary role of the Statistics and Probability strand is to develop student ability to analyze data intelligently, to recognize and measure variation, and to understand the patterns that underlie probabilistic situations. The ultimate goal is for students to understand how inferences can be made about a population by looking at a sample from that population. Graphical methods of data analysis, simulations, sampling, and experience with the collection and interpretation of real data are featured.
  Discrete Mathematics
The Discrete Mathematics strand develops student ability to model and solve problems using recursion, matrices, vertex-edge graphs, and systematic counting methods (combinatorics). Key themes are discrete mathematical modeling, optimization, and algorithmic problem solving.

Download Courses 1–3 and Course 4: Preparation for Calculus Unit and Lesson Objectives (395 KB).

Correlations
A correlation between the Common Core State Standards (CCSS) and Core-Plus Mathematics Courses 1–3 and Course 4: Preparation for Calculus is available from McGraw-Hill Education (ISBN 978-0-07-665814-5).




Sequence of Units in the CPMP Three-year Core Program

(printable C1–C3 Sequence Chart)
STRANDS
Algebra &
Functions
Geometry &
Trigonometry
Statistics &
Probability
Discrete
Mathematics
Course 1
Unit 1 Patterns of Change  Patterns of Change Patterns of Change  
Unit 2     Patterns in Data  
Unit 3 Linear Functions      
Unit 4       Discrete Mathematical Modeling
Unit 5 Exponential Functions      
Unit 6   Patterns in Shape    
Unit 7 Quadratic Functions      
Unit 8     Patterns in Chance  
Course 2
Unit 1 Functions, Equations, and Systems      
Unit 2 Matrix Methods     Matrix Methods
Unit 3 Coordinate Methods Coordinate Methods    
Unit 4     Regression and Correlation  
Unit 5 Nonlinear Functions and Equations      
Unit 6       Modeling and Optimization
Unit 7   Trigonometric Methods    
Unit 8     Probability Distributions  
Course 3
Unit 1 Reasoning and Proof Reasoning and Proof Reasoning and Proof  
Unit 2 Inequalities and Linear Programming      
Unit 3   Similarity and Congruence    
Unit 4     Samples and Variation  
Unit 5 Polynomial and Rational Functions      
Unit 6   Circles and Circular Functions    
Unit 7 Recursion and Iteration     Recursion and Iteration
Unit 8 Inverse Functions      



Sequence of Units in CPMP Course 4
Preparation for Calculus

(printable C4 Sequence Chart)
STRANDS
Algebra &
Functions
Geometry &
Trigonometry
Statistics &
Probability
Discrete
Mathematics
Course 4
Unit 1 Families of Functions Families of Functions    
Unit 2   Vectors and Motion    
Unit 3 Algebraic Functions and Equations      
Unit 4   Trigonometric Functions and Equations    
Unit 5 Exponential Functions, Logarithms, and Data Modeling   Exponential Functions, Logarithms, and Data Modeling  
Unit 6   Surfaces and Cross Sections    
Unit 7 Concepts of Calculus      
Unit 8       Counting Methods and Induction

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