by Jerald Murdock, Ellen Kamischke, and Eric Kamischke An Investigative Approach

Transcription

1 Number and Operations Understand numbers, ways of representing numbers, relationships among numbers, and number systems develop a deeper understanding of very large and very small numbers and of various representations of them; compare and contrast the properties of numbers and number systems, including the rational and real numbers, and understand complex numbers as solutions to quadratic equations that do not have real solutions; 3.1: Linear Equations 3.5: Residuals 5.6: The Logarithmic Function 7.1: Polynomial Degree and Finite Differences 7.4: The Quadratic Formula 9.7: Graphs of Rational Functions 9.8: Operations with Rational Expressions Chapter 11: Series 0.2: Symbolic Representation 1.1: Recursively Defined Sequences 1.2: Modeling Growth and Decay 4.2: Function Notation 4.4: Translations and the Quadratic Family 4.5: Reflections and the Square Root Family 4.6: Stretches and Shrinks, and the Absolute-Value Family 4.7: Transformations and the Circle Family 4.8: Compositions of Functions 5.2: Properties of Exponents and Power Functions 5.3: Rational Exponents and Roots 5.5: Building Inverses of Functions 5.6: The Logarithmic Function 5.7: Properties of Logarithms Key Curriculum Press 1 Ellen Kamischkee, ( 2004)

2 Understand numbers, ways of representing numbers, relationships among numbers, and number systems (cont.) Understand meanings of operations and how they relate to one another understand vectors and matrices as systems that have some of the properties of the real-number system; use number-theory arguments to justify relationships involving whole numbers. judge the effects of such operations as multiplication, division, and computing powers and roots on the magnitude of quantities; 7.5: Complex Numbers 7.8: More About Finding Solutions 10.2: Radian Measure and Arc Length Exploration: Polar Coordinates 6.1: Matrix Representations 6.2: Matrix Operations 6.3: Row Reduction Method 6.4: Solving Systems with Inverse Matrices 8.1: Graphing Parametric Equations 8.4: Using Trigonometry to Set a Course 8.5: Projectile Motion 0.2: Symbolic Representation 0.3: Organizing Information 1.1: Recursively Defined Sequences 1.2: Modeling Growth and Decay 1.3: A First Look at Limits 6.1: Matrix Representations 6.2: Matrix Operations 6.4: Solving Systems with Inverse Matrices 1.2: Modeling Growth and Decay 1.3: A First Look at Limits 1.4: Graphing Sequences Exploration: Refining the Growth Model 4.4: Translations and the Quadratic Family 4.5: Reflections and the Square Root Family Key Curriculum Press 2 Ellen Kamischkee, ( 2004)

3 Understand meanings of operations and how they relate to one another (cont.) Compare fluently and make reasonable estimates develop an understanding of properties of, and representations for, the addition and multiplication of vectors and matrices; develop an understanding of permutations and combinations as counting techniques. develop fluency in operations with real numbers, vectors, and matrices using mental computation or paper-and-pencil calculations for simple cases and technology for more-complicated cases; 5.2: Properties of Exponents and Power Functions 5.3: Rational Exponents and Roots 5.4: Applications of Exponential and Power Equations 6.1: Matrix Representations 6.2: Matrix Operations 6.3: Row Reduction Method 6.4: Solving Systems with Inverse Matrices 8.1: Graphing Parametric Equations 8.4: Using Trigonometry to Set a Course 8.5: Projectile Motion 12.5: Permutations and Probability 12.6: Combinations and Probability Chapter 2: Describing Data 4.5: Reflections and the Square Root Family 4.6: Stretches and Shrinks and the Absolute-Value Family 6.2: Matrix Operations 6.3: Row Reduction Method 6.6: Linear Programming Key Curriculum Press 3 Ellen Kamischkee, ( 2004)

4 Compare fluently and make reasonable estimates (cont.) judge the reasonableness of numerical computation and their results. 7.3: Completing the Square 7.4: The Quadratic Formula 7.8: More About Finding Solutions 8.4: Using Trigonometry to Set a Course 8.5: Projectile Motion 8.6: The Law of Sines 8.7: The Law of Cosines 9.1: Using the Distance Formula 9.8: Operations with Rational Expressions 10.2: Radian Measure and Arc Length 12.5: Permutations and Probability 12.6: Combinations and Probability 0.1: Pictures, Graphs, and Diagrams 1.3: A First Look at Limits 1.5: Loans and Investments Exploration: Recursion in Geometry 5.2: Properties of Exponents and Power Functions 5.8: Applications of Logarithms 7.2: Equivalent Quadratic Forms 8.6: The Law of Sines 9.1: Using the Distance Formula 13.4: The Central Limit Theorem Key Curriculum Press 4 Ellen Kamischkee, ( 2004)

5 Algebra Understand patterns, relations, and functions generalize patterns using explicitly defined and recursively defined functions; understand relations and functions and select, convert flexibly among, and use various representations of them; analyze functions of one variable by investigating rates of change, intercepts, zeros, asymptotes, and local and global behavior; 3.1: Linear Equations and Arithmetic Sequences Chapter 11: Series 4.2: Function Notation 4.3: Lines in Motion 4.4: Translations and the Quadratic Family 4.5: Reflections and the Square Root Family 4.6: Stretches and Shrinks, and the Absolute-Value Family 4.7: Transformations and the Circle Family 4.8: Compositions of Functions 7.1: Polynomial Degree and Finite Differences 7.7: Higher-Degree Polynomials 10.1: Defining the Circular Functions 10.3: Graphing Trigonometric Functions 3.1: Linear Equations and Arithmetic Sequences 3.2: Revisiting Slope 4.3: Lines in Motion 4.4: Translations and the Quadratic Family 5.4: Applications of Exponential and Power Equations Key Curriculum Press 5 Ellen Kamischkee, ( 2004)

6 Understand patterns, relations, and functions (cont.) understand and perform transformations such as arithmetically combining, composing, and inverting commonly used functions, using technology to perform such operations on morecomplicated symbolic expressions; 5.6: The Logarithmic Function 5.8: Applications of Logarithms 7.2: Equivalent Quadratic Forms 7.3: Completing the Square 7.4: The Quadratic Formula 7.5: Complex Numbers 7.6: Factored Polynomials 7.7: Higher-Degree Polynomials 7.8: More About Finding Solutions 9.6: Introduction to Rational Functions 9.7: Graphs of Rational Functions 10.3: Graphing Trigonometric Functions 4.3: Lines in Motion 4.4: Translations and the Quadratic Family 4.5: Reflections and the Square Root Family 4.6: Stretches and Shrinks, and the Absolute-Value Family 4.7: Transformations and the Circle Family 4.8: Compositions of Functions 5.5: Building Inverses of Functions 5.6: The Logarithmic Function 7.1: Polynomial Degree and Finite Differences 7.2: Equivalent Quadratic Forms 9.3: The Parabola 9.6: Introduction to Rational Functions 9.7: Graphs of Rational Functions 10.3: Graphing Trigonometric Functions 10.7: Combining Trigonometric Functions Key Curriculum Press 6 Ellen Kamischkee, ( 2004)

7 Understand patterns, relations, and functions (cont.) Represent and analyze mathematical situations and structures using algebraic symbols understand and compare the properties of classes of functions, including exponential, polynomial, rational, logarithmic, and periodic functions; interpret representations of functions of two variables. understand the equivalent forms of expressions, equations, inequalities, and relations; 9.6: Introduction to Rational Functions 9.7: Graphs of Rational Functions 10.1: Defining the Circular Functions 10.3: Graphing Trigonometric Functions 10.1: Defining the Circular Functions 10.3: Graphing Trigonometric Functions 0.2: Symbolic Representation 1.1: Recursively Defined Sequences 1.2: Modeling Growth and Decay 3.1: Linear Equations and Arithmetic Sequences 3.2: Revisiting Slope Key Curriculum Press 7 Ellen Kamischkee, ( 2004)

8 Represent and analyze mathematical situations and structures using algebraic symbols (cont.) write equivalent forms of equations, inequalities, and systems of equations and solve them with fluency- mentally or with paper and pencil in simple cases and using technology in all cases; use symbolic algebra to represent and explain mathematical relationships; 6.5: Systems of Linear Inequalities 6.6: Linear Programming 7.2: Equivalent Quadratic Forms 9.8: Operations with Rational Expressions 6.2: Matrix Operations 6.3: Row Reduction Method 6.4: Solving Systems with Inverse Matrices 6.5: Systems of Linear Inequalities 6.6: Linear Programming 1.1: Recursively Defined Sequences 1.2: Modeling Growth and Decay 1.5: Loans and Investments 3.3: Fitting a Line to Data 3.4: The Median-Median Line 5.4: Applications of Exponential and Power Equations 5.6: The Logarithmic Function 5.8: Applications of Logarithms 7.1: Polynomial Degree and Finite Differences 7.7: Higher-Degree Polynomials 9.3: The Parabola 9.4: The Hyperbola 9.5: The General Quadratic 9.6: Introduction to Rational Functions Key Curriculum Press 8 Ellen Kamischkee, ( 2004)

9 Represent and analyze mathematical situations and structures using algebraic symbols (cont.) use a variety of symbolic representations, including recursive and parametric equations, for functions and relations; judge the meaning, utility, and reasonableness of the results of symbol manipulations, including those carried out by technology. 10.3: Graphing Trigonometric Functions 8.1: Graphing Parametric Equations 8.2: Converting From Parametric to Non-parametric 8.4: Using Trigonometry to Set a Course 8.5: Projectile Motion Chapter 11: Series 0.1: Pictures, Graphs, and Diagrams 1.5: Loans and Investments 5.2: Properties of Exponents and Power Functions 5.8: Applications of Logarithms 7.2: Equivalent Quadratic Forms 8.6: The Law of Sines 9.1: Using the Distance Formula 13.4: The Central Limit Theorem Key Curriculum Press 9 Ellen Kamischkee, ( 2004)

10 Use mathematical models to represent and understand quantitative relationshipsuse mathematical models to represent and understand quantitative relationships identify essential quantitative relationships in a situation and determine the class or classes of functions that might model the relationships; use symbolic expressions, including iterative and recursive forms, to represent relationships arising from various contexts; 1.1: Recursively Defined Sequences 1.2: Modeling Growth and Decay 1.5: Loans and Investments Exploration: Refining the Growth Model 3.3: Fitting a Line to Data 3.4: The Median-Median Line 3.5: Residuals 5.4: Applications of Exponential and Power Equations 5.8: Applications of Logarithms 7.1: Polynomial Degree and Finite Differences 7.7: Higher-Degree Polynomials 7.8: More About Finding Solutions 13.6: Least Squares Line 3.1: Linear Equations and Arithmetic Sequences 3.2: Revisiting Slope 3.3: Fitting a Line to Data Chapter 11: Series Key Curriculum Press 10 Ellen Kamischkee, ( 2004)

11 Use mathematical models to represent and understand quantitative relationshipsuse mathematical models to represent and understand quantitative relationships (cont.) Analyze change in various contexts Geometry Analyze characteristics and properties of two- and threedimensional geometric shapes and develop mathematical arguments about geometric relationships draw reasonable conclusions about a situation being modeled. approximate and interpret rates of change from graphical and numerical data. analyze properties and determine attributes of two- and three dimensional objects; 1.1: Recursively Defined Sequences 1.2: Modeling Growth and Decay 1.5: Loans and Investments Exploration: Refining the Growth Model 3.3: Fitting a Line to Data 3.4: The Median-Median Line 3.5: Residuals Exploration: Residual Plots and Least Squares 5.4: Applications of Exponential and Power Equations 5.8: Applications of Logarithms 7.1: Polynomial Degree and Finite Differences 7.7: Higher-Degree Polynomials 7.8: More About Finding Solutions 13.6: Least Squares Line 1.1: Recursively Defined Sequences 1.4: Graphing Sequences 3.1: Linear Equations and Arithmetic Sequences 3.2: Revisiting Slope 3.3: Fitting a Line to Data 0.1: Pictures, Graphs, and Diagrams 7.2: Equivalent Quadratic Forms 7.3: Completing the Square 7.6: Factored Polynomials Key Curriculum Press 11 Ellen Kamischkee, ( 2004)

12 Analyze characteristics and properties of two- and threedimensional geometric shapes and develop mathematical arguments about geometric relationships (cont.) explore relationships (including congruence and similarity) among classes of two- and three dimensional geometric objects, make and test conjectures about them, and solve problems involving them; establish the validity of geometric conjectures using deduction, prove theorems, and critique arguments made by others; 8.6: The Law of Sines 8.7: The Law of Cosines 9.1: Using the Distance Formula 13.1: Probability Distributions Exploration: Rotation as a Composition of Transformations 4.7: Transformations and the Circle Family 4.7: Transformations and the Circle Family Exploration: Rotation as a Composition of Transformations 7.4: The Quadratic Formula 8.7: The Law of Cosines Exploration: Parametric Equations for a Circle 9.3: The Parabola 9.4: The Hyperbola 9.5: The General Quadratic 10.6: Fundamental Trigonometric Identities 10.7: Combining Trigonometric Functions 13.4: The Central Limit Theorem Key Curriculum Press 12 Ellen Kamischkee, ( 2004)

13 Analyze characteristics and properties of two- and threedimensional geometric shapes and develop mathematical arguments about geometric relationships (cont.) Specify locations and describe spatial relationships using coordinate geometry and other representational systems; use trigonometric relationships to determine lengths and angle measures. use Cartesian coordinates and other coordinate systems, such as navigational, polar, or spherical systems, to analyze geometric situations; investigate conjectures and solve problems involving two- and threedimensional objects represented with Cartesian coordinates. 8.3: Right Triangle Trigonometry 8.6: The Law of Sines 8.7: The Law of Cosines 0.1: Pictures, Graphs, and Diagrams 3.1: Linear Equations 3.2: Revisiting Slope 3.4: The Median-Median Line 3.6: Linear Systems 3.7: Substitution and Elimination 4.3: Lines in Motion 9.1: Using the Distance Formula 8.4: Using Trigonometry to Set a Course 8.5: Projectile Motion Exploration: Polar Coordinates 3.1: Linear Equations and Arithmetic Sequences 3.2: Revisiting Slope 3.4: The Median-Median Line 4.3: Lines in Motion Key Curriculum Press 13 Ellen Kamischkee, ( 2004)

14 Apply transformations and use symmetry to analyze mathematical situations Use visualization, spatial reasoning, and geometric modeling to solve problems understand and represent translations, reflections, rotations, and dilations of objects in the plane by using sketches, coordinates, vectors, function notation, and matrices; use various representations to help understand the effects of simple transformations and their compositions. draw and construct representations of two- and three-dimensional geometric objects using a variety of tools; 4.3: Lines in Motion 4.4: Translations and the Quadratic Family 4.5: Reflections and the Square Root Family 4.6: Stretches and Shrinks, and the Absolute-Value Family 4.7: Transformations and the Circle Family 4.8: Compositions of Functions Exploration: Rotation as a Composition of Transformations 5.5: Building Inverses of Functions 6.1: Matrix Representations 6.2: Matrix Operations 8.1: Graphing Parametric Equations 8.4: Using Trigonometry to Set a Course 4.3: Lines in Motion 4.4: Translations and the Quadratic Family 4.5: Reflections and the Square Root Family 4.6: Stretches and Shrinks, and the Absolute-Value Family 4.7: Transformations and the Circle Family 4.8: Compositions of Functions 4.7: Transformations and the Circle Family 6.6: Linear Programming 9.2: The Circle and the Ellipse 9.3: The Parabola 10.1: Defining the Circular Functions Key Curriculum Press 14 Ellen Kamischkee, ( 2004)

15 Use visualization, spatial reasoning, and geometric modeling to solve problems (cont.) visualize three-dimensional objects from different perspectives and analyze their cross sections; use vertex-edge graphs to model and solve problems; use geometric models to gain insight into, and answer questions in, other areas of mathematics; use geometric ideas to solve problems in, and gain insights into, other disciplines and other areas of interest such as art and architecture. 6.3: Row Reduction Method 9.2: The Circle and the Ellipse 9.3: The Parabola 9.4: The Hyperbola 6.1: Matrix Representations 12.2: Counting Outcomes and Tree Diagrams Exploration: Recursion in Geometry Exploration: Parametric Equations for a Circle Chapter 11: Series 11.2: Infinite Geometric Series Exploration: Seeing the Infinite Sum 7.3: Completing the Square Exploration: Parametric Equations for a Circle Exploration: Polar Coordinates Chapter 11: Series 11.2: Infinite Geometric Series Key Curriculum Press 15 Ellen Kamischkee, ( 2004)

16 Measurement Understand measurable attributes of objects and the units, systems, and processes of measurement make decisions about units and scales that are appropriate for problem situations involving measurement. 0.3: Organizing Information 1.1: Recursively Defined Sequences 1.4: Graphing Sequences 3.1: Linear Equations 3.2: Revisiting Slope 3.3: Fitting a Line to Data 3.4: The Median-Median Line 3.5: Residuals 3.6: Linear Systems 3.7: Substitution and Elimination 4.3: Lines in Motion 6.3: Row Reduction Method 6.5: Systems of Linear Inequalities 6.6: Linear Programming 8.1: Graphing Parametric Equations 8.2: Converting From Parametric to Non-parametric 8.4: Using Trigonometry to Set a Course 8.5: Projectile Motion 9.1: Using the Distance Formula Chapter 11: Series 11.1: Arithmetic Series 13.6: The Least Squares Line Key Curriculum Press 16 Ellen Kamischkee, ( 2004)

17 Apply appropriate techniques, tools, and formulas to determine measurements analyze precision, accuracy, and approximate error in measurement situations; understand and use formulas for the area, surface area, and volume of geometric figures, including cones, spheres, and cylinders; apply informal concepts of successive approximation, upper and lower bounds, and limit in measurement situations; use unit analysis to check measurement computations. 3.3: Fitting a Line to Data 3.4: The Median-Median Line 3.5: Residuals Exploration: Residual Plots and Least Squares 5.4: Applications of Exponential and Power Equations 5.8: Applications of Logarithms 0.1: Pictures, Graphs, and Diagrams 7.2: Equivalent Quadratic Forms 7.3: Completing the Square 7.6: Factored Polynomials 8.6: The Law of Sines 8.7: The Law of Cosines 9.1: Using the Distance Formula 13.1: Probability Distributions 1.3: A First Look at Limits Chapter 11: Series 11.1: Arithmetic Series 11.2: Infinite Geometric Series 0.3: Organizing Information Key Curriculum Press 17 Ellen Kamischkee, ( 2004)

18 Data Analysis and Probability Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them understand the differences among various kinds of studies and which types of inferences can legitimately be drawn from each; know the characteristics of well-designed studies, including the role of randomization in surveys and experiments; understand the meaning of measurement data and categorical data, of univariate and bivariate data, and of the term variable; understand histograms, parallel box plots, and scatterplots and use them to display data; 12.1: Randomness and Probability 13.3: z-values and Confidence Intervals 13.4: The Central Limit Theorem 13.5: Bivariate Data and Correlation 12.1: Randomness and Probability 13.3: z-values and Confidence Intervals 13.5: Bivariate Data and Correlation 0.3: Organizing Information Chapter 2: Describing Data 12.4: Random Variables and Expected Value 13.1: Probability Distributions 13.5: Bivariate Data and Correlation 0.1: Pictures, Graphs, and Diagrams Chapter 2: Describing Data 2.1: Measures of Central Tendency and Box Plots 2.3: Histograms and Percentile Ranks 3.3: Fitting a Line to Data Key Curriculum Press 18 Ellen Kamischkee, ( 2004)

19 Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them (cont.) Select and use appropriate statistical methods to analyze data compute basic statistics and understand the distinction between a statistic and a parameter. for univariate measurement data, be able to display the distribution, describe its shape, and select and calculate summary statistics; for bivariate measurement data, be able to display scatterplot, describe the shape, and determine regression coefficients, regression equations, and correlation coefficients using technological tools; display and discuss bivariate data where at least one variable is categorical; Chapter 2: Describing Data 3.3: Fitting a Line to Data 3.4: The Median-Median Line 13.1: Probability Distributions 13.3: z-values and Confidence Intervals 13.6: Least Squares Line Chapter 2: Describing Data 13.1: Probability Distributions 13.2: Normal Distributions 0.1: Pictures, Graphs, and Diagrams 1.4: Graphing Sequences 3.3: Fitting a Line to Data 3.4: The Median-Median Line 3.5: Residuals Exploration: Residual Plots and Least Squares 13.5: Bivariate Data and Correlation 13.6: Least Squares Line 13.7: Nonlinear Regression Not covered Key Curriculum Press 19 Ellen Kamischkee, ( 2004)

20 Select and use appropriate statistical methods to analyze data (cont.) Develop and evaluate inferences and predictions that are based on data recognize how linear transformations of univariate data affect shape, center, and spread; identify trends in bivariate data and find functions that model the data or transform the data so that they can be modeled. use simulations to explore the variability of sample statistics from a known population and to construct sampling distributions; understand how sample statistics reflect the values of population parameters and use sampling distributions as the basis for informal inferences; Chapter 2: Describing Data 2.1: Measures of Central Tendency and Box Plots 2.2: Measures of Spread 13.1: Probability Distributions 1.1: Recursively Defined Sequences 1.2: Modeling Growth and Decay 3.3: Fitting a Line to Data 3.4: The Median-Median Line 5.4: Applications of Exponential and Power Equations 5.6: The Logarithmic Function 5.8: Applications of Logarithms 7.1: Polynomial Degree and Finite Differences 7.7: Higher-Degree Polynomials 7.8: More About Finding Solutions 9.6: Introduction to Rational Functions 12.1: Randomness and Probability 13.1: Probability Distributions 13.2: Normal Distributions 13.3: z-values and Confidence Intervals 13.4: The Central Limit Theorem 13.1: Probability Distributions 13.3: z-values and Confidence Intervals Key Curriculum Press 20 Ellen Kamischkee, ( 2004)

21 Develop and evaluate inferences and predictions that are based on data (cont.) Understand and apply basic concepts of probability evaluate published reports that are based on data by examining the design of the study, the appropriateness of the data analysis, and the validity of conclusions; understand how basic statistical techniques are used to monitor process characteristics in the workplace. understand the concepts of sample spaces and distributions in simple cases; use simulations to construct empirical probability distributions; compute and interpret the expected value of random variables in simple cases; understand the concepts of conditional probability and independent events; understand how to compute the probability of a compound event. Chapter 2: Describing Data Exploration: Census Microdata 13.1: Probability Distributions 13.2: Normal Distributions 13.3: z-values and Confidence Intervals 13.4: The Central Limit Theorem 12.1: Randomness and Probability 12.2: Counting Outcomes and Tree Diagrams 13.1: Probability Distributions 12.1: Randomness and Probability 13.1: Probability Distributions 12.4: Random Variables and Expected Value 12.2: Counting Outcomes and Tree Diagrams 12.3: Mutually Exclusive Events and Venn Diagrams 12.2: Counting Outcomes and Tree Diagrams 12.3: Mutually Exclusive Events and Venn Diagrams 12.4: Random Variables and Expected Value Key Curriculum Press 21 Ellen Kamischkee, ( 2004)

22 Problem Solving Build new mathematical knowledge through problem solving Solve problems that arise in mathematical and in other contexts Chapter 2: Describing Data Chapter 11: Series 5.2: Properties of Exponents and Power Functions 5.3: Rational Exponents and Roots 5.4: Applications of Exponential and Power Equations 5.8: Applications of Logarithms 6.1: Matrix Representations 6.3: Row Reduction Method 6.5: Systems of Linear Inequalities 6.6: Linear Programming 7.1: Polynomial Degree and Finite Differences 7.7: Higher-Degree Polynomials 7.8: More About Finding Solutions Key Curriculum Press 22 Ellen Kamischkee, ( 2004)

23 Problem Solving (cont.) Apply and adapt a variety of appropriate strategies to solve problems 9.1: Using the Distance Formula 9.2: The Circle and the Ellipse 9.3: The Parabola 9.4: The Hyperbola 9.5: The General Quadratic 9.6: Introduction to Rational Functions Chapter 11: Series Chapter 2: Describing Data 4.6: Stretches and Shrinks and the Absolute-Value Family 5.4: Applications of Exponential and Power Equations 5.5: Building Inverses of Functions 5.8: Applications of Logarithms 6.6: Linear Programming 7.1: Polynomial Degree and Finite Differences 7.2: Equivalent Quadratic Forms 7.3: Completing the Square 7.4: The Quadratic Formula 7.6: Factored Polynomials 7.7: Higher-Degree Polynomials Key Curriculum Press 23 Ellen Kamischkee, ( 2004)

24 Problem Solving (cont.) Monitor and reflect on the process of mathematical problem solving 9.1: Using the Distance Formula 9.2: The Circle and the Ellipse 9.4: The Hyperbola 9.6: Introduction to Rational Functions 10.1: Defining the Circular Function 10.2: Radian Measure and Arc Length 10.3: Graphing Trigonometric Functions Chapter 11: Series 13.1: Probability Distributions 3.3: Fitting a Line to Data 3.4: The Median-Median Line 3.5: Residuals Exploration: Residual Plots and Least Squares 4.6: Stretches and Shrinks and the Absolute-Value Family 5.4: Applications of Exponential and Power Equations 5.8: Applications of Logarithms 7.1: Polynomial Degree and Finite Differences 7.7: Higher-Degree Polynomials 10.1 Defining the Circular Function 13.5: Bivariate Data and Correlation 13.6: The Least Squares Line Key Curriculum Press 24 Ellen Kamischkee, ( 2004)

25 Reasoning and Proof Recognize reasoning and proof as fundamental aspects of mathematics Develop and evaluate mathematical arguments and proofs Select and use various types of reasoning and methods of proof 0.3: Organizing Information 7.4: The Quadratic Formula 8.7: The Law of Cosines 10.6: Fundamental Trigonometric Identities 10.7: Combining Trigonometric Functions 0.3: Organizing Information 7.4: The Quadratic Formula 8.6: The Law of Sines 9.3: The Parabola 9.4: The Hyperbola 9.5: The General Quadratic 0.3: Organizing Information 7.4: The Quadratic Formula 8.6: The Law of Sines 8.7: The Law of Cosines 9.3: The Parabola 9.4: The Hyperbola 9.5: The General Quadratic 10.6: Fundamental Trigonometric Identities 10.7: Combining Trigonometric Functions 13.4: The Central Limit Theorem Key Curriculum Press 25 Ellen Kamischkee, ( 2004)

26 Communication Organize and consolidate their mathematical thinking through communication Communicate their mathematical thinking coherently and clearly to peers, teachers, and others Analyze and evaluate the mathematical thinking and strategies of others Use the language of mathematics to express mathematical ideas precisely Chapter 2: Describing Data Exploration: Census Microdata 4.1: Interpreting Graphs 7.8: More About Finding Solutions 13.3: z-values and Confidence Intervals 13.4: The Central Limit Theorem Chapter 2: Describing Data Exploration: Census Microdata 3.2: Revisiting Slope 4.1: Interpreting Graphs 4.7: Transformations and the Circle Family 12.1: Randomness and Probability 13.3: z-values and Confidence Intervals 13.4: The Central Limit Theorem 4.1: Interpreting Graphs 5.4: Applications of Exponential and Power Equations 5.8: Applications of Logarithms 0.3: Organizing Information Key Curriculum Press 26 Ellen Kamischkee, ( 2004)

27 Communication (cont.) Connections mathematical ideas precisely Recognize and use connections among mathematical ideas 1.5: Loans and Investments 3.2: Revisiting Slope 4.2: Function Notation 4.3: Lines in Motion 4.4: Translations and the Quadratic Family 4.5: Reflections and the Square Root Family 4.6: Stretches and Shrinks, and the Absolute-Value Family 4.7: Transformations and the Circle Family 3.1: Linear Equations and Arithmetic Sequences 6.1: Matrix Representations 6.4: Solving Systems with Inverse Matrices 9.2: The Circle and the Ellipse 9.3: The Parabola 9.4: The Hyperbola 9.5: The General Quadratic Chapter 11: Series Key Curriculum Press 27 Ellen Kamischkee, ( 2004)

28 Connections (cont.) Understand how mathematical ideas interconnect and build on one another to produce a coherent whole Recognize and apply mathematics in contexts outside of mathematics 1.5: Loans and Investments Exploration: Refining the Growth Model Chapter 2: Describing Data 3.3: Fitting a Line to Data 3.5: Residuals 6.1: Matrix Representations 6.4: Solving Systems with Inverse Matrices 6.6: Linear Programming 7.1: Polynomial Degree and Finite Differences 8.1: Graphing Parametric Equations 8.4: Using Trigonometry to Set a Course 8.5: Projectile Motion 9.6: Introduction to Rational Functions Chapter 11: Series Key Curriculum Press 28 Ellen Kamischkee, ( 2004)

29 Representations Create and use representations to organize, record, and communicate mathematical ideas Select, apply, and translate among mathematical representations to solve problems 0.1: Pictures, Graphs, and Diagrams 0.3: Organizing Information 1.1: Recursively Defined Sequences 1.2: Modeling Growth and Decay 1.3: A First Look at Limits Chapter 2: Describing Data 2.1: Measures of Central Tendency and Box Plots 3.1: Linear Equations and Arithmetic Sequences 3.2: Revisiting Slope 3.3: Fitting a Line to Data 4.2: Function Notation 7.1: Polynomial Degree and Finite Differences 10.1: Defining the Circular Functions 10.5: Modeling with Trigonometric Equations Chapter 11: Series 11.1: Arithmetic Series 11.2: Infinite Geometric Series 12.4: Random Variables and Expected Value 13.3: z-values and Confidence Intervals Chapter 2: Describing Data Key Curriculum Press 29 Ellen Kamischkee, ( 2004)

30 Representations (cont.) Use representations to model and interpret physical, social, and mathematical phenomena Chapter 11: Series 1.1: Recursively Defined Sequences 1.2: Modeling Growth and Decay 3.2: Revisiting Slope 4.3: Lines in Motion 6.1: Matrix Representations 6.6: Linear Programming 7.1: Polynomial Degree and Finite Differences 8.1: Graphing Parametric Equations 8.4: Using Trigonometry to Set a Course 8.5: Projectile Motion 12.1: Randomness and Probability 12.4: Random Variables and Expected Value Key Curriculum Press 30 Ellen Kamischkee, ( 2004)