### 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,