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, functions, matrices, 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, inventing mathematics, 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 periodic functions. Each algebraic model is investigated in four linked representations - verbal, graphic, numeric, and symbolic - with the aid of technology. Attention is also given to modeling with systems of equations, both linear and nonlinear, and to symbolic reasoning and manipulation.
Geometry and Trigonometry
The primary goal of the geometry and trigonometry strand is to develop visual thinking and student ability to construct, reason with, interpret, and apply mathematical models of patterns in visual and physical contexts. 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 shapes under geometric 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 involving enumeration, sequential change, decision making in finite settings, and relationships among a finite number of elements. Topics include matrices, vertex-edge graphs, recursion, models of social decision making, and systematic counting methods. Key themes are discrete mathematical modeling, existence (Is there a solution?), optimization (What is the best solution?), and algorithmic problem solving (Can you efficiently construct a solution?).

View a Scope and Sequence (pdf - 548Kb) of mathematical topics typically taught in high school mathematics courses and their location in the CPMP four-year curriculum.

Correlations
Correlations of Core-Plus Mathematics to state mathematics frameworks/standards are available from Glencoe/McGraw-Hill (1-800-334-7344) for the following states:

Colorado
Florida
Illinois
Indiana
Kansas
Michigan
Mississippi
New York
Ohio
Oregon
Pennsylvania
Texas
Virginia
Washington
Wisconsin
West Virginia




Sequence of Units in the CPMP Three-year Core Program

(printable C1-3 Sequence Chart)
STRANDS
Algebra &
Functions
Statistics &
Probability
Geometry &
Trigonometry
Discrete
Mathematics
Course 1
Unit 1   Patterns in Data    
Unit 2 Patterns of Change      
Unit 3 Linear Models      
Unit 4       Graph Models
Unit 5     Patterns in Space
& Vizualization
 
Unit 6 Exponential Models      
Unit 7   Simulation Models    
Capstone Planning a
Benefits Carnival
Planning a
Benefits Carnival
Planning a
Benefits Carnival
Planning a
Benefits Carnival
Course 2
Unit 1 Matrix Models     Matrix Models
Unit 2 Patterns of Location,
Shape & Size
  Patterns of Location,
Shape & Size
 
Unit 3   Patterns of
Association
   
Unit 4 Power Models      
Unit 5       Network
Optimization
Unit 6     Geometric Form &
Its Function
 
Unit 7   Patterns in Chance    
Capstone Forests,
the Environment,
and Mathematics
Forests,
the Environment,
and Mathematics
Forests,
the Environment,
and Mathematics
Forests,
the Environment,
and Mathematics
Course 3
Unit 1 Multiple-Variable
Models
  Multiple-Variable
Models
 
Unit 2   Modeling Public
Opinion
  Modeling Public
Opinion
Unit 3 Symbol Sense and
Algebraic Reasoning
     
Unit 4     Shapes & Geometric
Reasoning
 
Unit 5   Patterns in
Variation
   
Unit 6 Families of
Functions
  Families of
Functions
 
Unit 7 Discrete Models
of Change
    Discrete Models
of Change
Capstone Making the Best
of It: Optimal Forms
and Strategies
Making the Best
of It: Optimal Forms
and Strategies
Making the Best
of It: Optimal Forms
and Strategies
Making the Best
of It: Optimal Forms
and Strategies



Sequence of Units in CPMP Course 4
Continuing the Preparation of Students for College Mathematics

(printable C4 Sequence Chart)
STRANDS
Algebra &
Functions
Statistics &
Probability
Geometry &
Trigonometry
Discrete
Mathematics
Course 4
Unit 1 Rates of Change   Rates of Change  
Unit 2 Modeling Motion   Modeling Motion  
Unit 3 Logarithmic Functions
and Data Models
Logarithmic Functions
and Data Models
   
Unit 4       Counting Models
Unit 5   Binomial Distributions
and Statistical Inference
   
Unit 6 Polynomial and
Rational Functions
     
Unit 7 Functions and
Symbolic Reasoning
  Functions and
Symbolic Reasoning
 
Unit 8     Space Geometry  
Unit 9       Informatics
Unit 10 Problem Solving,
Algorithms, and Spreadsheets
Problem Solving,
Algorithms, and Spreadsheets
   

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