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.
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.
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.
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.
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).
|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|
|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|
|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|
|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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