Cover -- Title Page -- Copyright Page -- Table of Contents -- Acknowledgments -- Introduction -- Chapter 1: About the Common Core Mathematics Standards for High School -- The Standards for Mathematical Content -- The Standards for Mathematical Practice -- Implications of the Standards' Structure on Teaching and Learning -- How to Begin Implementation -- Focus on the mathematical practice standards -- Focus on critical areas -- Focus on connections -- Chapter 2: Number and Quantity -- The Real Number System -- Extend the properties of exponents to rational exponents -- Use properties of rational and irrational numbers -- Quantities -- Reason quantitatively and use units to solve problems -- The Complex Number System -- Perform arithmetic operations with complex numbers -- Represent complex numbers and their operations on the complex plane -- Use complex numbers in polynomial identities and equations -- Vector and Matrix Quantities -- Represent and model with vector quantities -- Perform operations on vectors -- Perform operations on matrices and use matrices inapplications -- Chapter 3: Algebra -- Seeing Structure in Expressions -- Interpret the structure of expressions -- Write expressions in equivalent forms to solve problems -- Arithmetic with Polynomials and Rational Expressions -- Perform arithmetic operations on polynomials -- Understand the relationship between zeros and factors of polynomials -- Use polynomial identities to solve problems -- Rewrite rational expressions -- Creating Equations -- Create equations that describe numbers or relationships -- Reasoning with Equations and Inequalities -- Understand solving equations as a process of reasoning and explain the reasoning -- Solve equations and inequalities in one variable -- Solve systems of equations -- Represent and solve equations and inequalities graphically.

Chapter 4: Functions -- Interpreting Functions -- Understand the concept of a function and use function notation -- Interpret functions that arise in applications in terms of the context -- Analyze functions using different representations -- Building Functions -- Build a function that models a relationship between two quantities -- Build new functions from existing functions -- Linear, Quadratic, and Exponential Models -- Construct and compare linear, quadratic, and exponential models and solve problems -- Interpret expressions for functions in terms of the situation they model -- Trigonometric Functions -- Extend the domain of trigonometric functions using the unit circle -- Model periodic phenomena with trigonometric functions -- Prove and apply trigonometric identities -- Chapter 5: Geometry -- Congruence -- Experiment with transformations in the plane -- Understand congruence in terms of rigid motions -- Prove geometric theorems -- Make geometric constructions -- Similarity, Right Triangles, and Trigonometry -- Understand similarity in terms of similarity transformations -- Prove theorems involving similarity -- Define trigonometric ratios and solve problems involving right triangles -- Apply trigonometry to general triangles -- Circles -- Understand and apply theorems about circles -- Find arc lengths and areas of sectors of circles -- Expressing Geometric Properties with Equations -- Translate between the geometric description and the equation for a conic section -- Use coordinates to prove simple geometric theorems algebraically -- Geometric Measurement and Dimension -- Explain volume formulas and use them to solve problems -- Visualize relationships between two-dimensional and three-dimensional objects -- Modeling with Geometry -- Apply geometric concepts in modeling situations -- Chapter 6: Statistics and Probability.

Interpreting Categorical and Quantitative Data -- Summarize, represent, and interpret data on a single count or measurement variable -- Summarize, represent, and interpret data on two categorical and quantitative variables -- Interpret linear models -- Making Inferences and Justifying Conclusions -- Understand and evaluate random processes underlying statistical experiments -- Make inferences and justify conclusions from sample surveys, experiments, and observational studies -- Conditional Probability and the Rules of Probability -- Understand independence and conditional probability and use them to interpret data -- Use the rules of probability to compute probabilities of compound events in a uniform probability model -- Using Probability to Make Decisions -- Calculate expected values and use them to solve problems -- Use probability to evaluate outcomes of decisions -- Chapter 7: Guidance for Instructional Planning -- The Framework for Instructional Planning -- Creating the environment for learning -- Helping students develop understanding -- Helping students extend and apply knowledge -- Lesson Development, Step by Step -- Step 1: Identify the focus for the lesson -- Step 2: Determine how learning will be assessed -- Step 3: Determine the activities that will start the lesson -- Step 4: Determine the activities that will engage students in learning the content -- Step 5: Determine the activities that will close the lesson -- Sample Lesson 1: Growth Models-Connecting Linear and Exponential Functions -- Sample Lesson 2: Understanding Conditional Probability -- Sample Lesson 3: The Unit Circle and Trigonometric Functions -- References -- About the Authors -- About McREL -- ASCD and Common Core State Standards Resources.