Key Curriculum Press 1NCTM Correlation of Discovering Advanced Algebra by Jerald Murdock, Ellen Kamischkee, and Eric Kamischke (© 2004)
NCTM Standard
Number and OperationsUnderstand numbers, ways of representing numbers,relationships among numbers,and number systems
Expectations
• develop a deeper understanding of verylarge and very small numbers and ofvarious representations of them;
• compare and contrast the properties ofnumbers and number systems, includingthe rational and real numbers, andunderstand complex numbers assolutions to quadratic equations that donot have real solutions;
NCTM Correlation of Discovering Advanced Algebra
Chapter 1: Patterns and RecursionAll lessons
Chapter 3: Linear Models and Systems3.1: Linear Equations3.5: Residuals
Chapter 5: Exponential, Power, and Logarithmic Functions5.1: The Exponential Function5.6: The Logarithmic Function
Chapter 7: Quadratic and Other Polynomial Functions7.1: Polynomial Degree and Finite Differences7.4: The Quadratic Formula
Chapter 9: Conic Sections and Rational Functions9.7: Graphs of Rational Functions9.8: Operations with Rational Expressions
Chapter 11: SeriesAll lessons
Chapter 0: Problem Solving0.2: Symbolic Representation
Chapter 1: Patterns and Recursion1.1: Recursively Defined Sequences1.2: Modeling Growth and Decay
Chapter 4: Functions, Relations, and Transformations4.2: Function Notation4.4: Translations and the Quadratic Family4.5: Reflections and the Square Root Family4.6: Stretches and Shrinks, and the Absolute-Value Family4.7: Transformations and the Circle Family4.8: Compositions of Functions
Chapter 5: Exponential, Power, and Logarithmic Functions5.1: The Exponential Function5.2: Properties of Exponents and Power Functions5.3: Rational Exponents and Roots5.5: Building Inverses of Functions5.6: The Logarithmic Function5.7: Properties of Logarithms
Advanced AlgebraDiscovering
Advanced AlgebraAn Investigative Approach
by Jerald Murdock,Ellen Kamischke, and Eric Kamischke
Key Curriculum Press 2NCTM Correlation of Discovering Advanced Algebra by Jerald Murdock, Ellen Kamischkee, and Eric Kamischke (© 2004)
NCTM Standard
Understand numbers, ways of representing numbers,relationships among numbers,and number systems (cont.)
Understand meanings ofoperations and how they relateto one another
Expectations
• understand vectors and matrices assystems that have some of the propertiesof the real-number system;
• use number-theory arguments to justifyrelationships involving whole numbers.
• judge the effects of such operations asmultiplication, division, and computingpowers and roots on the magnitude ofquantities;
NCTM Correlation of Discovering Advanced Algebra
Chapter 7: Quadratic and Other Polynomial Functions7.5: Complex Numbers7.8: More About Finding Solutions
Chapter 10: Trigonometric Functions10.2: Radian Measure and Arc LengthExploration: Polar Coordinates
Chapter 6: Matrices and Linear Systems6.1: Matrix Representations6.2: Matrix Operations6.3: Row Reduction Method6.4: Solving Systems with Inverse Matrices
Chapter 8: Parametric Equations and Trigonometry8.1: Graphing Parametric Equations8.4: Using Trigonometry to Set a Course8.5: Projectile Motion
Chapter 0: Problem Solving0.2: Symbolic Representation0.3: Organizing Information
Chapter 1: Patterns and Recursion1.1: Recursively Defined Sequences1.2: Modeling Growth and Decay1.3: A First Look at Limits
Chapter 6: Matrices and Linear Systems6.1: Matrix Representations6.2: Matrix Operations6.4: Solving Systems with Inverse Matrices
Chapter 1: Patterns and Recursion1.2: Modeling Growth and Decay1.3: A First Look at Limits1.4: Graphing SequencesExploration: Refining the Growth Model
Chapter 4: Functions, Relations, and Transformations4.4: Translations and the Quadratic Family4.5: Reflections and the Square Root Family
Advanced AlgebraDiscovering
Advanced AlgebraAn Investigative Approach
by Jerald Murdock,Ellen Kamischke, and Eric Kamischke
Key Curriculum Press 3NCTM Correlation of Discovering Advanced Algebra by Jerald Murdock, Ellen Kamischkee, and Eric Kamischke (© 2004)
NCTM Standard
Understand meanings ofoperations and how they relateto one another (cont.)
Compare fluently and makereasonable estimates
Expectations
• develop an understanding of propertiesof, and representations for, the additionand multiplication of vectors andmatrices;
• develop an understanding ofpermutations and combinations ascounting techniques.
• develop fluency in operations with realnumbers, vectors, and matrices usingmental computation or paper-and-pencilcalculations for simple cases andtechnology for more-complicated cases;
NCTM Correlation of Discovering Advanced Algebra
Chapter 5: Exponential, Power, and Logarithmic Functions5.1: The Exponential Function5.2: Properties of Exponents and Power Functions5.3: Rational Exponents and Roots5.4: Applications of Exponential and Power Equations
Chapter 6: Matrices and Linear Systems6.1: Matrix Representations6.2: Matrix Operations6.3: Row Reduction Method6.4: Solving Systems with Inverse Matrices
Chapter 8: Parametric Equations and Trigonometry8.1: Graphing Parametric Equations8.4: Using Trigonometry to Set a Course8.5: Projectile Motion
Chapter 12: Probability12.5: Permutations and Probability12.6: Combinations and Probability
Chapter 1: Patterns and RecursionAll lessons
Chapter 2: Describing DataAll lessons
Chapter 3: Linear Models and SystemsAll lessons
Chapter 4: Functions, Relations, and Transformations4.5: Reflections and the Square Root Family4.6: Stretches and Shrinks and the Absolute-Value Family
Chapter 5: Exponential, Power, and Logarithmic FunctionsAll lessons
Chapter 6: Matrices and Linear Systems6.2: Matrix Operations6.3: Row Reduction Method6.6: Linear Programming
Advanced AlgebraDiscovering
Advanced AlgebraAn Investigative Approach
by Jerald Murdock,Ellen Kamischke, and Eric Kamischke
Key Curriculum Press 4NCTM Correlation of Discovering Advanced Algebra by Jerald Murdock, Ellen Kamischkee, and Eric Kamischke (© 2004)
NCTM Standard
Compare fluently and makereasonable estimates (cont.)
Expectations
• judge the reasonableness of numericalcomputation and their results.
NCTM Correlation of Discovering Advanced Algebra
Chapter 7: Quadratic and Other Polynomial Functions7.3: Completing the Square7.4: The Quadratic Formula7.8: More About Finding Solutions
Chapter 8: Parametric Equations and Trigonometry8.4: Using Trigonometry to Set a Course8.5: Projectile Motion8.6: The Law of Sines8.7: The Law of Cosines
Chapter 9: Conic Sections and Rational Functions9.1: Using the Distance Formula9.8: Operations with Rational Expressions
Chapter 10: Trigonometric Functions 10.2: Radian Measure and Arc Length
Chapter 12: Probability12.5: Permutations and Probability12.6: Combinations and Probability
Chapter 0: Problem Solving0.1: Pictures, Graphs, and Diagrams
Chapter 1: Patterns and Recursion1.3: A First Look at Limits1.5: Loans and InvestmentsExploration: Recursion in Geometry
Chapter 5: Exponential, Power, and Logarithmic Functions5.2: Properties of Exponents and Power Functions5.8: Applications of Logarithms
Chapter 7: Quadratic and Other Polynomial Functions7.2: Equivalent Quadratic Forms
Chapter 8: Parametric Equations and Trigonometry8.6: The Law of Sines
Chapter 9: Conic Sections and Rational Functions9.1: Using the Distance Formula
Chapter 13: Applications of Statistics13.4: The Central Limit Theorem
Advanced AlgebraDiscovering
Advanced AlgebraAn Investigative Approach
by Jerald Murdock,Ellen Kamischke, and Eric Kamischke
Key Curriculum Press 5NCTM Correlation of Discovering Advanced Algebra by Jerald Murdock, Ellen Kamischkee, and Eric Kamischke (© 2004)
NCTM Standard
Algebra Understand patterns, relations,and functions
Expectations
• generalize patterns using explicitlydefined and recursively definedfunctions;
• understand relations and functions andselect, convert flexibly among, and usevarious representations of them;
• analyze functions of one variable byinvestigating rates of change, intercepts,zeros, asymptotes, and local and globalbehavior;
NCTM Correlation of Discovering Advanced Algebra
Chapter 1: Patterns and RecursionAll lessons
Chapter 3: Linear Models and Systems3.1: Linear Equations and Arithmetic Sequences
Chapter 5: Exponential, Power, and Logarithmic Functions5.1: The Exponential Function
Chapter 11: SeriesAll lessons
Chapter 4: Functions, Relations, and Transformations4.2: Function Notation4.3: Lines in Motion4.4: Translations and the Quadratic Family4.5: Reflections and the Square Root Family4.6: Stretches and Shrinks, and the Absolute-Value Family4.7: Transformations and the Circle Family4.8: Compositions of Functions
Chapter 5: Exponential, Power, and Logarithmic FunctionsAll lessons
Chapter 7: Quadratic and Other Polynomial Functions7.1: Polynomial Degree and Finite Differences7.7: Higher-Degree Polynomials
Chapter 10: Trigonometric Functions10.1: Defining the Circular Functions10.3: Graphing Trigonometric Functions
Chapter 3: Linear Models and Systems3.1: Linear Equations and Arithmetic Sequences3.2: Revisiting Slope
Chapter 4: Functions, Relations, and Transformations4.3: Lines in Motion4.4: Translations and the Quadratic Family
Chapter 5: Exponential, Power, and Logarithmic Functions5.1: The Exponential Function5.4: Applications of Exponential and Power Equations
Advanced AlgebraDiscovering
Advanced AlgebraAn Investigative Approach
by Jerald Murdock,Ellen Kamischke, and Eric Kamischke
Key Curriculum Press 6NCTM Correlation of Discovering Advanced Algebra by Jerald Murdock, Ellen Kamischkee, and Eric Kamischke (© 2004)
NCTM Standard
Understand patterns, relations,and functions (cont.)
Expectations
• understand and perform transformationssuch as arithmetically combining,composing, and inverting commonlyused functions, using technology toperform such operations on more-complicated symbolic expressions;
NCTM Correlation of Discovering Advanced Algebra
5.6: The Logarithmic Function5.8: Applications of Logarithms
Chapter 7: Quadratic and Other Polynomial Functions7.2: Equivalent Quadratic Forms7.3: Completing the Square7.4: The Quadratic Formula7.5: Complex Numbers7.6: Factored Polynomials7.7: Higher-Degree Polynomials7.8: More About Finding Solutions
Chapter 9: Conic Sections and Rational Functions9.6: Introduction to Rational Functions9.7: Graphs of Rational Functions
Chapter 10: Trigonometric Functions10.3: Graphing Trigonometric Functions
Chapter 4: Functions, Relations, and Transformations4.3: Lines in Motion4.4: Translations and the Quadratic Family4.5: Reflections and the Square Root Family4.6: Stretches and Shrinks, and the Absolute-Value Family4.7: Transformations and the Circle Family4.8: Compositions of Functions
Chapter 5: Exponential, Power, and Logarithmic Functions5.5: Building Inverses of Functions5.6: The Logarithmic Function
Chapter 7: Quadratic and Other Polynomial Functions7.1: Polynomial Degree and Finite Differences7.2: Equivalent Quadratic Forms
Chapter 9: Conic Sections and Rational Functions9.3: The Parabola9.6: Introduction to Rational Functions9.7: Graphs of Rational Functions
Chapter 10: Trigonometric Functions10.3: Graphing Trigonometric Functions10.7: Combining Trigonometric Functions
Advanced AlgebraDiscovering
Advanced AlgebraAn Investigative Approach
by Jerald Murdock,Ellen Kamischke, and Eric Kamischke
Key Curriculum Press 7NCTM Correlation of Discovering Advanced Algebra by Jerald Murdock, Ellen Kamischkee, and Eric Kamischke (© 2004)
NCTM Standard
Understand patterns, relations,and functions (cont.)
Represent and analyzemathematical situations andstructures using algebraicsymbols
Expectations
• understand and compare the properties ofclasses of functions, includingexponential, polynomial, rational,logarithmic, and periodic functions;
• interpret representations of functions oftwo variables.
• understand the equivalent forms ofexpressions, equations, inequalities, andrelations;
NCTM Correlation of Discovering Advanced Algebra
Chapter 5: Exponential, Power, and Logarithmic FunctionsAll lessons
Chapter 7: Quadratic and Other Polynomial FunctionsAll lessons
Chapter 9: Conic Sections and Rational Functions9.6: Introduction to Rational Functions9.7: Graphs of Rational Functions
Chapter 10: Trigonometric Functions10.1: Defining the Circular Functions10.3: Graphing Trigonometric Functions
Chapter 1: Patterns and RecursionAll lessons
Chapter 3: Linear Models and SystemsAll lessons
Chapter 5: Exponential, Power, and Logarithmic FunctionsAll lessons
Chapter 7: Quadratic and Other Polynomial FunctionsAll lessons
Chapter 10: Trigonometric Functions10.1: Defining the Circular Functions10.3: Graphing Trigonometric Functions
Chapter 0: Problem Solving0.2: Symbolic Representation
Chapter 1: Patterns and Recursion1.1: Recursively Defined Sequences1.2: Modeling Growth and Decay
Chapter 3: Linear Models and Systems3.1: Linear Equations and Arithmetic Sequences3.2: Revisiting Slope
Chapter 5: Exponential, Power, and Logarithmic Functions5.1: The Exponential Function
Advanced AlgebraDiscovering
Advanced AlgebraAn Investigative Approach
by Jerald Murdock,Ellen Kamischke, and Eric Kamischke
Key Curriculum Press 8NCTM Correlation of Discovering Advanced Algebra by Jerald Murdock, Ellen Kamischkee, and Eric Kamischke (© 2004)
NCTM Standard
Represent and analyzemathematical situations andstructures using algebraicsymbols (cont.)
Expectations
• write equivalent forms of equations,inequalities, and systems of equationsand solve them with fluency- mentally orwith paper and pencil in simple casesand using technology in all cases;
• use symbolic algebra to represent andexplain mathematical relationships;
NCTM Correlation of Discovering Advanced Algebra
Chapter 6: Matrices and Linear Systems6.5: Systems of Linear Inequalities6.6: Linear Programming
Chapter 7: Quadratic and Other Polynomial Functions7.2: Equivalent Quadratic Forms
Chapter 9: Conic Sections and Rational Functions9.8: Operations with Rational Expressions
Chapter 6: Matrices and Linear Systems6.2: Matrix Operations6.3: Row Reduction Method6.4: Solving Systems with Inverse Matrices6.5: Systems of Linear Inequalities6.6: Linear Programming
Chapter 1: Patterns and Recursion1.1: Recursively Defined Sequences1.2: Modeling Growth and Decay1.5: Loans and Investments
Chapter 3: Linear Models and Systems3.3: Fitting a Line to Data3.4: The Median-Median Line
Chapter 5: Exponential, Power, and Logarithmic Functions5.1: The Exponential Function5.4: Applications of Exponential and Power Equations5.6: The Logarithmic Function5.8: Applications of Logarithms
Chapter 7: Quadratic and Other Polynomial Functions7.1: Polynomial Degree and Finite Differences7.7: Higher-Degree Polynomials
Chapter 9: Conic Sections and Rational Functions9.3: The Parabola9.4: The Hyperbola9.5: The General Quadratic9.6: Introduction to Rational Functions
Advanced AlgebraDiscovering
Advanced AlgebraAn Investigative Approach
by Jerald Murdock,Ellen Kamischke, and Eric Kamischke
Key Curriculum Press 9NCTM Correlation of Discovering Advanced Algebra by Jerald Murdock, Ellen Kamischkee, and Eric Kamischke (© 2004)
NCTM Standard
Represent and analyzemathematical situations andstructures using algebraicsymbols (cont.)
Expectations
• use a variety of symbolic representations,including recursive and parametricequations, for functions and relations;
• judge the meaning, utility, andreasonableness of the results of symbolmanipulations, including those carriedout by technology.
NCTM Correlation of Discovering Advanced Algebra
Chapter 10: Trigonometric Functions10.3: Graphing Trigonometric Functions
Chapter 1: Patterns and RecursionAll lessons
Chapter 8: Parametric Equations and Trigonometry8.1: Graphing Parametric Equations8.2: Converting From Parametric to Non-parametric8.4: Using Trigonometry to Set a Course8.5: Projectile Motion
Chapter 11: SeriesAll lessons
Chapter 0: Problem Solving0.1: Pictures, Graphs, and Diagrams
Chapter 1: Patterns and Recursion1.5: Loans and Investments
Chapter 5: Exponential, Power, and Logarithmic Functions5.2: Properties of Exponents and Power Functions5.8: Applications of Logarithms
Chapter 7: Quadratic and Other Polynomial Functions7.2: Equivalent Quadratic Forms
Chapter 8: Parametric Equations and Trigonometry8.6: The Law of Sines
Chapter 9: Conic Sections and Rational Functions9.1: Using the Distance Formula
Chapter 13: Applications of Statistics13.4: The Central Limit Theorem
Advanced AlgebraDiscovering
Advanced AlgebraAn Investigative Approach
by Jerald Murdock,Ellen Kamischke, and Eric Kamischke
Key Curriculum Press 10NCTM Correlation of Discovering Advanced Algebra by Jerald Murdock, Ellen Kamischkee, and Eric Kamischke (© 2004)
NCTM Standard
Use mathematical models torepresent and understandquantitative relationshipsUsemathematical models torepresent and understandquantitative relationships
Expectations
• identify essential quantitativerelationships in a situation and determinethe class or classes of functions thatmight model the relationships;
• use symbolic expressions, includingiterative and recursive forms, to representrelationships arising from variouscontexts;
NCTM Correlation of Discovering Advanced Algebra
Chapter 1: Patterns and Recursion1.1: Recursively Defined Sequences1.2: Modeling Growth and Decay1.5: Loans and InvestmentsExploration: Refining the Growth Model
Chapter 3: Linear Models and Systems3.3: Fitting a Line to Data3.4: The Median-Median Line3.5: Residuals
Chapter 5: Exponential, Power, and Logarithmic Functions5.1: The Exponential Function5.4: Applications of Exponential and Power Equations5.8: Applications of Logarithms
Chapter 7: Quadratic and Other Polynomial Functions7.1: Polynomial Degree and Finite Differences7.7: Higher-Degree Polynomials7.8: More About Finding Solutions
Chapter 13: Applications of Statistics13.6: Least Squares Line
Chapter 1: Patterns and RecursionAll lessons
Chapter 3: Linear Models and Systems3.1: Linear Equations and Arithmetic Sequences3.2: Revisiting Slope3.3: Fitting a Line to Data
Chapter 5: Exponential, Power, and Logarithmic Functions5.1: The Exponential Function
Chapter 11: SeriesAll lessons
Advanced AlgebraDiscovering
Advanced AlgebraAn Investigative Approach
by Jerald Murdock,Ellen Kamischke, and Eric Kamischke
Key Curriculum Press 11NCTM Correlation of Discovering Advanced Algebra by Jerald Murdock, Ellen Kamischkee, and Eric Kamischke (© 2004)
NCTM Standard
Use mathematical models torepresent and understandquantitative relationshipsUsemathematical models torepresent and understandquantitative relationships (cont.)
Analyze change in variouscontexts
Geometry Analyze characteristics andproperties of two- and three-dimensional geometric shapesand develop mathematicalarguments about geometricrelationships
Expectations
• draw reasonable conclusions about asituation being modeled.
• approximate and interpret rates of changefrom graphical and numerical data.
• analyze properties and determineattributes of two- and three dimensionalobjects;
NCTM Correlation of Discovering Advanced Algebra
Chapter 1: Patterns and Recursion1.1: Recursively Defined Sequences1.2: Modeling Growth and Decay1.5: Loans and InvestmentsExploration: Refining the Growth Model
Chapter 3: Linear Models and Systems3.3: Fitting a Line to Data3.4: The Median-Median Line3.5: ResidualsExploration: Residual Plots and Least Squares
Chapter 5: Exponential, Power, and Logarithmic Functions5.1: The Exponential Function5.4: Applications of Exponential and Power Equations5.8: Applications of Logarithms
Chapter 7: Quadratic and Other Polynomial Functions7.1: Polynomial Degree and Finite Differences7.7: Higher-Degree Polynomials7.8: More About Finding Solutions
Chapter 13: Applications of Statistics13.6: Least Squares Line
Chapter 1: Patterns and Recursion1.1: Recursively Defined Sequences1.4: Graphing Sequences
Chapter 3: Linear Models and Systems3.1: Linear Equations and Arithmetic Sequences3.2: Revisiting Slope3.3: Fitting a Line to Data
Chapter 0: Problem Solving0.1: Pictures, Graphs, and Diagrams
Chapter 7: Quadratic and Other Polynomial Functions7.2: Equivalent Quadratic Forms7.3: Completing the Square7.6: Factored Polynomials
Advanced AlgebraDiscovering
Advanced AlgebraAn Investigative Approach
by Jerald Murdock,Ellen Kamischke, and Eric Kamischke
Key Curriculum Press 12NCTM Correlation of Discovering Advanced Algebra by Jerald Murdock, Ellen Kamischkee, and Eric Kamischke (© 2004)
NCTM Standard
Analyze characteristics andproperties of two- and three-dimensional geometric shapesand develop mathematicalarguments about geometricrelationships (cont.)
Expectations
• explore relationships (includingcongruence and similarity) amongclasses of two- and three dimensionalgeometric objects, make and testconjectures about them, and solveproblems involving them;
• establish the validity of geometricconjectures using deduction, provetheorems, and critique arguments madeby others;
NCTM Correlation of Discovering Advanced Algebra
Chapter 8: Parametric Equations and Trigonometry8.6: The Law of Sines8.7: The Law of Cosines
Chapter 9: Conic Sections and Rational Functions9.1: Using the Distance Formula
Chapter 13: Applications of Statistics13.1: Probability Distributions
Chapter 4: Functions, Relations, and TransformationsExploration: Rotation as a Composition of Transformations4.7: Transformations and the Circle Family
Chapter 4: Functions, Relations, and Transformations4.7: Transformations and the Circle FamilyExploration: Rotation as a Composition of Transformations
Chapter 7: Quadratic and Other Polynomial Functions7.4: The Quadratic Formula
Chapter 8: Parametric Equations and Trigonometry8.7: The Law of Cosines Exploration: Parametric Equations for a Circle
Chapter 9: Conic Sections and Rational Functions9.3: The Parabola9.4: The Hyperbola9.5: The General Quadratic
Chapter 10: Trigonometric Functions10.6: Fundamental Trigonometric Identities10.7: Combining Trigonometric Functions
Chapter 13: Applications of Statistics13.4: The Central Limit Theorem
Advanced AlgebraDiscovering
Advanced AlgebraAn Investigative Approach
by Jerald Murdock,Ellen Kamischke, and Eric Kamischke
Key Curriculum Press 13NCTM Correlation of Discovering Advanced Algebra by Jerald Murdock, Ellen Kamischkee, and Eric Kamischke (© 2004)
NCTM Standard
Analyze characteristics andproperties of two- and three-dimensional geometric shapesand develop mathematicalarguments about geometricrelationships (cont.)
Specify locations and describespatial relationships usingcoordinate geometry and otherrepresentational systems;
Expectations
• use trigonometric relationships todetermine lengths and angle measures.
• use Cartesian coordinates and othercoordinate systems, such as navigational,polar, or spherical systems, to analyzegeometric situations;
• investigate conjectures and solveproblems involving two- and three-dimensional objects represented withCartesian coordinates.
NCTM Correlation of Discovering Advanced Algebra
Chapter 8: Parametric Equations and Trigonometry8.3: Right Triangle Trigonometry8.6: The Law of Sines8.7: The Law of Cosines
Chapter 0: Problem Solving0.1: Pictures, Graphs, and Diagrams
Chapter 3: Linear Models and Systems3.1: Linear Equations3.2: Revisiting Slope3.4: The Median-Median Line3.6: Linear Systems3.7: Substitution and Elimination
Chapter 4: Functions, Relations, and Transformations4.3: Lines in Motion
Chapter 9: Conic Sections and Rational Functions9.1: Using the Distance Formula
Chapter 8: Parametric Equations and Trigonometry8.4: Using Trigonometry to Set a Course8.5: Projectile Motion
Chapter 10: Trigonometric FunctionsExploration: Polar Coordinates
Chapter 3: Linear Models and Systems3.1: Linear Equations and Arithmetic Sequences3.2: Revisiting Slope3.4: The Median-Median Line
Chapter 4: Functions, Relations, and Transformations4.3: Lines in Motion
Advanced AlgebraDiscovering
Advanced AlgebraAn Investigative Approach
by Jerald Murdock,Ellen Kamischke, and Eric Kamischke
Key Curriculum Press 14NCTM Correlation of Discovering Advanced Algebra by Jerald Murdock, Ellen Kamischkee, and Eric Kamischke (© 2004)
NCTM Standard
Apply transformations and use symmetry to analyzemathematical situations
Use visualization, spatialreasoning, and geometricmodeling to solve problems
Expectations
• understand and represent translations,reflections, rotations, and dilations ofobjects in the plane by using sketches,coordinates, vectors, function notation,and matrices;
• use various representations to helpunderstand the effects of simpletransformations and their compositions.
• draw and construct representations oftwo- and three-dimensional geometricobjects using a variety of tools;
NCTM Correlation of Discovering Advanced Algebra
Chapter 4: Functions, Relations, and Transformations4.3: Lines in Motion4.4: Translations and the Quadratic Family4.5: Reflections and the Square Root Family4.6: Stretches and Shrinks, and the Absolute-Value Family4.7: Transformations and the Circle Family4.8: Compositions of FunctionsExploration: Rotation as a Composition of Transformations
Chapter 5: Exponential, Power, and Logarithmic Functions5.5: Building Inverses of Functions
Chapter 6: Matrices and Linear Systems6.1: Matrix Representations6.2: Matrix Operations
Chapter 8: Parametric Equations and Trigonometry8.1: Graphing Parametric Equations8.4: Using Trigonometry to Set a Course
Chapter 4: Functions, Relations, and Transformations4.3: Lines in Motion4.4: Translations and the Quadratic Family4.5: Reflections and the Square Root Family4.6: Stretches and Shrinks, and the Absolute-Value Family4.7: Transformations and the Circle Family4.8: Compositions of Functions
Chapter 4: Functions, Relations, and Transformations4.7: Transformations and the Circle Family
Chapter 6: Matrices and Linear Systems6.6: Linear Programming
Chapter 9: Conic Sections and Rational Functions9.2: The Circle and the Ellipse9.3: The Parabola
Chapter 10: Trigonometric Functions10.1: Defining the Circular Functions
Advanced AlgebraDiscovering
Advanced AlgebraAn Investigative Approach
by Jerald Murdock,Ellen Kamischke, and Eric Kamischke
Key Curriculum Press 15NCTM Correlation of Discovering Advanced Algebra by Jerald Murdock, Ellen Kamischkee, and Eric Kamischke (© 2004)
NCTM Standard
Use visualization, spatialreasoning, and geometricmodeling to solve problems(cont.)
Expectations
• visualize three-dimensional objects fromdifferent perspectives and analyze theircross sections;
• use vertex-edge graphs to model andsolve problems;
• use geometric models to gain insightinto, and answer questions in, other areasof mathematics;
• use geometric ideas to solve problems in,and gain insights into, other disciplinesand other areas of interest such as art andarchitecture.
NCTM Correlation of Discovering Advanced Algebra
Chapter 6: Matrices and Linear Systems6.3: Row Reduction Method
Chapter 9: Conic Sections and Rational Functions9.2: The Circle and the Ellipse9.3: The Parabola9.4: The Hyperbola
Chapter 6: Matrices and Linear Systems6.1: Matrix Representations
Chapter 12: Probability12.2: Counting Outcomes and Tree Diagrams
Chapter 1: Patterns and RecursionExploration: Recursion in Geometry
Chapter 8: Parametric Equations and TrigonometryExploration: Parametric Equations for a Circle
Chapter 11: Series11.2: Infinite Geometric SeriesExploration: Seeing the Infinite Sum
Chapter 7: Quadratic and Other Polynomial Functions7.3: Completing the Square
Chapter 8: Parametric Equations and TrigonometryExploration: Parametric Equations for a Circle
Chapter 10: Trigonometric FunctionsExploration: Polar Coordinates
Chapter 11: Series11.2: Infinite Geometric Series
Advanced AlgebraDiscovering
Advanced AlgebraAn Investigative Approach
by Jerald Murdock,Ellen Kamischke, and Eric Kamischke
Key Curriculum Press 16NCTM Correlation of Discovering Advanced Algebra by Jerald Murdock, Ellen Kamischkee, and Eric Kamischke (© 2004)
NCTM Standard
Measurement Understand measurableattributes of objects and theunits, systems, and processes ofmeasurement
Expectations
• make decisions about units and scalesthat are appropriate for problemsituations involving measurement.
NCTM Correlation of Discovering Advanced Algebra
Chapter 0: Problem Solving0.3: Organizing Information
Chapter 1: Patterns and Recursion1.1: Recursively Defined Sequences1.4: Graphing Sequences
Chapter 3: Linear Models and Systems3.1: Linear Equations3.2: Revisiting Slope3.3: Fitting a Line to Data3.4: The Median-Median Line3.5: Residuals3.6: Linear Systems3.7: Substitution and Elimination
Chapter 4: Functions, Relations, and Transformations4.3: Lines in Motion
Chapter 6: Matrices and Linear Systems6.3: Row Reduction Method6.5: Systems of Linear Inequalities6.6: Linear Programming
Chapter 8: Parametric Equations and Trigonometry8.1: Graphing Parametric Equations8.2: Converting From Parametric to Non-parametric8.4: Using Trigonometry to Set a Course8.5: Projectile Motion
Chapter 9: Conic Sections and Rational Functions9.1: Using the Distance Formula
Chapter 11: Series11.1: Arithmetic Series
Chapter 13: Applications of Statistics13.6: The Least Squares Line
Advanced AlgebraDiscovering
Advanced AlgebraAn Investigative Approach
by Jerald Murdock,Ellen Kamischke, and Eric Kamischke
Key Curriculum Press 17NCTM Correlation of Discovering Advanced Algebra by Jerald Murdock, Ellen Kamischkee, and Eric Kamischke (© 2004)
NCTM Standard
Apply appropriate techniques,tools, and formulas to determinemeasurements
Expectations
• analyze precision, accuracy, andapproximate error in measurementsituations;
• understand and use formulas for the area,surface area, and volume of geometricfigures, including cones, spheres, andcylinders;
• apply informal concepts of successiveapproximation, upper and lower bounds,and limit in measurement situations;
• use unit analysis to check measurementcomputations.
NCTM Correlation of Discovering Advanced Algebra
Chapter 3: Linear Models and Systems3.3: Fitting a Line to Data3.4: The Median-Median Line3.5: ResidualsExploration: Residual Plots and Least Squares
Chapter 5: Exponential, Power, and Logarithmic Functions5.4: Applications of Exponential and Power Equations5.8: Applications of Logarithms
Chapter 0: Problem Solving0.1: Pictures, Graphs, and Diagrams
Chapter 7: Quadratic and Other Polynomial Functions7.2: Equivalent Quadratic Forms7.3: Completing the Square7.6: Factored Polynomials
Chapter 8: Parametric Equations and Trigonometry8.6: The Law of Sines8.7: The Law of Cosines
Chapter 9: Conic Sections and Rational Functions9.1: Using the Distance Formula
Chapter 13: Applications of Statistics13.1: Probability Distributions
Chapter 1: Patterns and Recursion1.3: A First Look at Limits
Chapter 11: Series11.1: Arithmetic Series11.2: Infinite Geometric Series
Chapter 0: Problem Solving0.3: Organizing Information
Advanced AlgebraDiscovering
Advanced AlgebraAn Investigative Approach
by Jerald Murdock,Ellen Kamischke, and Eric Kamischke
Key Curriculum Press 18NCTM Correlation of Discovering Advanced Algebra by Jerald Murdock, Ellen Kamischkee, and Eric Kamischke (© 2004)
NCTM Standard
Data Analysis and Probability Formulate questions that can beaddressed with data and collect,organize, and display relevantdata to answer them
Expectations
• understand the differences among variouskinds of studies and which types ofinferences can legitimately be drawnfrom each;
• know the characteristics of well-designedstudies, including the role ofrandomization in surveys andexperiments;
• understand the meaning of measurementdata and categorical data, of univariateand bivariate data, and of the termvariable;
• understand histograms, parallel boxplots, and scatterplots and use them todisplay data;
NCTM Correlation of Discovering Advanced Algebra
Chapter 12: Probability12.1: Randomness and Probability
Chapter 13: Applications of Statistics13.3: z-values and Confidence Intervals13.4: The Central Limit Theorem13.5: Bivariate Data and Correlation
Chapter 12: Probability12.1: Randomness and Probability
Chapter 13: Applications of Statistics13.3: z-values and Confidence Intervals13.5: Bivariate Data and Correlation
Chapter 0: Problem Solving0.3: Organizing Information
Chapter 2: Describing DataAll lessons
Chapter 12: Probability12.4: Random Variables and Expected Value
Chapter 13: Applications of Statistics13.1: Probability Distributions13.5: Bivariate Data and Correlation
Chapter 0: Problem Solving0.1: Pictures, Graphs, and Diagrams
Chapter 2: Describing Data2.1: Measures of Central Tendency and Box Plots2.3: Histograms and Percentile Ranks
Chapter 3: Linear Models and Systems3.3: Fitting a Line to Data
Advanced AlgebraDiscovering
Advanced AlgebraAn Investigative Approach
by Jerald Murdock,Ellen Kamischke, and Eric Kamischke
Key Curriculum Press 19NCTM Correlation of Discovering Advanced Algebra by Jerald Murdock, Ellen Kamischkee, and Eric Kamischke (© 2004)
NCTM Standard
Formulate questions that can beaddressed with data and collect,organize, and display relevantdata to answer them (cont.)
Select and use appropriatestatistical methods to analyzedata
Expectations
• compute basic statistics and understandthe distinction between a statistic and aparameter.
• for univariate measurement data, be ableto display the distribution, describe itsshape, and select and calculate summarystatistics;
• for bivariate measurement data, be ableto display scatterplot, describe the shape,and determine regression coefficients,regression equations, and correlationcoefficients using technological tools;
• display and discuss bivariate data whereat least one variable is categorical;
NCTM Correlation of Discovering Advanced Algebra
Chapter 2: Describing DataAll lessons
Chapter 3: Linear Models and Systems3.3: Fitting a Line to Data3.4: The Median-Median Line
Chapter 13: Applications of Statistics13.1: Probability Distributions13.3: z-values and Confidence Intervals13.6: Least Squares Line
Chapter 2: Describing DataAll lessons
Chapter 13: Applications of Statistics13.1: Probability Distributions13.2: Normal Distributions
Chapter 0: Problem Solving0.1: Pictures, Graphs, and Diagrams
Chapter 1: Patterns and Recursion1.4: Graphing Sequences
Chapter 3: Linear Models and Systems3.3: Fitting a Line to Data3.4: The Median-Median Line3.5: ResidualsExploration: Residual Plots and Least Squares
Chapter 5: Exponential, Power, and Logarithmic Functions5.1: The Exponential Function
Chapter 13: Applications of Statistics13.5: Bivariate Data and Correlation13.6: Least Squares Line13.7: Nonlinear Regression
Not covered
Advanced AlgebraDiscovering
Advanced AlgebraAn Investigative Approach
by Jerald Murdock,Ellen Kamischke, and Eric Kamischke
Key Curriculum Press 20NCTM Correlation of Discovering Advanced Algebra by Jerald Murdock, Ellen Kamischkee, and Eric Kamischke (© 2004)
NCTM Standard
Select and use appropriatestatistical methods to analyzedata (cont.)
Develop and evaluate inferencesand predictions that are basedon data
Expectations
• recognize how linear transformations ofunivariate data affect shape, center, andspread;
• identify trends in bivariate data and findfunctions that model the data ortransform the data so that they can bemodeled.
• use simulations to explore the variabilityof sample statistics from a knownpopulation and to construct samplingdistributions;
• understand how sample statistics reflectthe values of population parameters anduse sampling distributions as the basisfor informal inferences;
NCTM Correlation of Discovering Advanced Algebra
Chapter 2: Describing Data2.1: Measures of Central Tendency and Box Plots2.2: Measures of Spread
Chapter 13: Applications of Statistics13.1: Probability Distributions
Chapter 1: Patterns and Recursion1.1: Recursively Defined Sequences1.2: Modeling Growth and Decay
Chapter 3: Linear Models and Systems3.3: Fitting a Line to Data3.4: The Median-Median Line
Chapter 5: Exponential, Power, and Logarithmic Functions5.1: The Exponential Function5.4: Applications of Exponential and Power Equations5.6: The Logarithmic Function5.8: Applications of Logarithms
Chapter 7: Quadratic and Other Polynomial Functions7.1: Polynomial Degree and Finite Differences7.7: Higher-Degree Polynomials7.8: More About Finding Solutions
Chapter 9: Conic Sections and Rational Functions9.6: Introduction to Rational Functions
Chapter 12: Probability12.1: Randomness and Probability
Chapter 13: Applications of Statistics13.1: Probability Distributions13.2: Normal Distributions13.3: z-values and Confidence Intervals13.4: The Central Limit Theorem
Chapter 13: Applications of Statistics13.1: Probability Distributions13.3: z-values and Confidence Intervals
Advanced AlgebraDiscovering
Advanced AlgebraAn Investigative Approach
by Jerald Murdock,Ellen Kamischke, and Eric Kamischke
Key Curriculum Press 21NCTM Correlation of Discovering Advanced Algebra by Jerald Murdock, Ellen Kamischkee, and Eric Kamischke (© 2004)
NCTM Standard
Develop and evaluate inferencesand predictions that are basedon data (cont.)
Understand and apply basicconcepts of probability
Expectations
• evaluate published reports that are basedon data by examining the design of thestudy, the appropriateness of the dataanalysis, and the validity of conclusions;
• understand how basic statisticaltechniques are used to monitor processcharacteristics in the workplace.
• understand the concepts of sample spacesand distributions in simple cases;
• use simulations to construct empiricalprobability distributions;
• compute and interpret the expected valueof random variables in simple cases;
• understand the concepts of conditionalprobability and independent events;
• understand how to compute theprobability of a compound event.
NCTM Correlation of Discovering Advanced Algebra
Chapter 2: Describing DataExploration: Census Microdata
Chapter 13: Applications of Statistics13.1: Probability Distributions13.2: Normal Distributions13.3: z-values and Confidence Intervals13.4: The Central Limit Theorem
Chapter 12: Probability12.1: Randomness and Probability12.2: Counting Outcomes and Tree Diagrams
Chapter 13: Applications of Statistics13.1: Probability Distributions
Chapter 12: Probability12.1: Randomness and Probability
Chapter 13: Applications of Statistics13.1: Probability Distributions
Chapter 12: Probability12.4: Random Variables and Expected Value
Chapter 12: Probability12.2: Counting Outcomes and Tree Diagrams12.3: Mutually Exclusive Events and Venn Diagrams
Chapter 12: Probability12.2: Counting Outcomes and Tree Diagrams12.3: Mutually Exclusive Events and Venn Diagrams12.4: Random Variables and Expected Value
Advanced AlgebraDiscovering
Advanced AlgebraAn Investigative Approach
by Jerald Murdock,Ellen Kamischke, and Eric Kamischke
Key Curriculum Press 22NCTM Correlation of Discovering Advanced Algebra by Jerald Murdock, Ellen Kamischkee, and Eric Kamischke (© 2004)
NCTM Standard
Problem Solving
Expectations
• Build new mathematical knowledgethrough problem solving
• Solve problems that arise inmathematical and in other contexts
NCTM Correlation of Discovering Advanced Algebra
Chapter 1: Patterns and RecursionAll lessons
Chapter 2: Describing DataAll lessons
Chapter 3: Linear Models and SystemsAll lessons
Chapter 5: Exponential, Power, and Logarithmic FunctionsAll lessons
Chapter 11: SeriesAll lessons
Chapter 0: Problem SolvingAll lessons
Chapter 1: Patterns and RecursionAll lessons
Chapter 3: Linear Models and SystemsAll lessons
Chapter 4: Functions, Relations, and TransformationsAll lessons
Chapter 5: Exponential, Power, and Logarithmic Functions5.1: The Exponential Function5.2: Properties of Exponents and Power Functions5.3: Rational Exponents and Roots5.4: Applications of Exponential and Power Equations5.8: Applications of Logarithms
Chapter 6: Matrices and Linear Systems6.1: Matrix Representations6.3: Row Reduction Method6.5: Systems of Linear Inequalities6.6: Linear Programming
Chapter 7: Quadratic and Other Polynomial Functions7.1: Polynomial Degree and Finite Differences7.7: Higher-Degree Polynomials7.8: More About Finding Solutions
Advanced AlgebraDiscovering
Advanced AlgebraAn Investigative Approach
by Jerald Murdock,Ellen Kamischke, and Eric Kamischke
Key Curriculum Press 23NCTM Correlation of Discovering Advanced Algebra by Jerald Murdock, Ellen Kamischkee, and Eric Kamischke (© 2004)
NCTM Standard
Problem Solving (cont.)
Expectations
• Apply and adapt a variety of appropriatestrategies to solve problems
NCTM Correlation of Discovering Advanced Algebra
Chapter 9: Conic Sections and Rational Functions9.1: Using the Distance Formula9.2: The Circle and the Ellipse9.3: The Parabola9.4: The Hyperbola9.5: The General Quadratic9.6: Introduction to Rational Functions
Chapter 10: Trigonometric FunctionsAll lessons
Chapter 11: SeriesAll lessons
Chapter 1: Patterns and RecursionAll lessons
Chapter 2: Describing DataAll lessons
Chapter 3: Linear Models and SystemsAll lessons
Chapter 4: Functions, Relations, and Transformations4.6: Stretches and Shrinks and the Absolute-Value Family
Chapter 5: Exponential, Power, and Logarithmic Functions5.1: The Exponential Function5.4: Applications of Exponential and Power Equations5.5: Building Inverses of Functions5.8: Applications of Logarithms
Chapter 6: Matrices and Linear Systems6.6: Linear Programming
Chapter 7: Quadratic and Other Polynomial Functions7.1: Polynomial Degree and Finite Differences7.2: Equivalent Quadratic Forms7.3: Completing the Square7.4: The Quadratic Formula7.6: Factored Polynomials7.7: Higher-Degree Polynomials
Advanced AlgebraDiscovering
Advanced AlgebraAn Investigative Approach
by Jerald Murdock,Ellen Kamischke, and Eric Kamischke
Key Curriculum Press 24NCTM Correlation of Discovering Advanced Algebra by Jerald Murdock, Ellen Kamischkee, and Eric Kamischke (© 2004)
NCTM Standard
Problem Solving (cont.)
Expectations
• Monitor and reflect on the process ofmathematical problem solving
NCTM Correlation of Discovering Advanced Algebra
Chapter 9: Conic Sections and Rational Functions9.1: Using the Distance Formula9.2: The Circle and the Ellipse9.4: The Hyperbola9.6: Introduction to Rational Functions
Chapter 10: Trigonometric Functions 10.1: Defining the Circular Function10.2: Radian Measure and Arc Length10.3: Graphing Trigonometric Functions
Chapter 11: SeriesAll lessons
Chapter 13: Applications of Statistics13.1: Probability Distributions
Chapter 3: Linear Models and Systems3.3: Fitting a Line to Data3.4: The Median-Median Line3.5: ResidualsExploration: Residual Plots and Least Squares
Chapter 4: Functions, Relations, and Transformations4.6: Stretches and Shrinks and the Absolute-Value Family
Chapter 5: Exponential, Power, and Logarithmic Functions5.1: The Exponential Function5.4: Applications of Exponential and Power Equations5.8: Applications of Logarithms
Chapter 7: Quadratic and Other Polynomial Functions7.1: Polynomial Degree and Finite Differences7.7: Higher-Degree Polynomials
Chapter 10: Trigonometric Functions10.1 Defining the Circular Function
Chapter 13: Applications of Statistics13.5: Bivariate Data and Correlation13.6: The Least Squares Line
Advanced AlgebraDiscovering
Advanced AlgebraAn Investigative Approach
by Jerald Murdock,Ellen Kamischke, and Eric Kamischke
Key Curriculum Press 25NCTM Correlation of Discovering Advanced Algebra by Jerald Murdock, Ellen Kamischkee, and Eric Kamischke (© 2004)
NCTM Standard
Reasoning and Proof
Expectations
• Recognize reasoning and proof asfundamental aspects of mathematics
• Develop and evaluate mathematicalarguments and proofs
• Select and use various types of reasoningand methods of proof
NCTM Correlation of Discovering Advanced Algebra
Chapter 0: Problem Solving0.3: Organizing Information
Chapter 7: Quadratic and Other Polynomial Functions7.4: The Quadratic Formula
Chapter 8: Parametric Equations and Trigonometry8.7: The Law of Cosines
Chapter 10: Trigonometric Functions10.6: Fundamental Trigonometric Identities10.7: Combining Trigonometric Functions
Chapter 0: Problem Solving0.3: Organizing Information
Chapter 7: Quadratic and Other Polynomial Functions7.4: The Quadratic Formula
Chapter 8: Parametric Equations and Trigonometry8.6: The Law of Sines
Chapter 9: Conic Sections and Rational Functions9.3: The Parabola9.4: The Hyperbola9.5: The General Quadratic
Chapter 0: Problem Solving0.3: Organizing Information
Chapter 7: Quadratic and Other Polynomial Functions7.4: The Quadratic Formula
Chapter 8: Parametric Equations and Trigonometry8.6: The Law of Sines8.7: The Law of Cosines
Chapter 9: Conic Sections and Rational Functions9.3: The Parabola9.4: The Hyperbola9.5: The General Quadratic
Chapter 10: Trigonometric Functions10.6: Fundamental Trigonometric Identities10.7: Combining Trigonometric Functions
Chapter 13: Applications of Statistics13.4: The Central Limit Theorem
Advanced AlgebraDiscovering
Advanced AlgebraAn Investigative Approach
by Jerald Murdock,Ellen Kamischke, and Eric Kamischke
Key Curriculum Press 26NCTM Correlation of Discovering Advanced Algebra by Jerald Murdock, Ellen Kamischkee, and Eric Kamischke (© 2004)
NCTM Standard
Communication
Expectations
• Organize and consolidate theirmathematical thinking throughcommunication
• Communicate their mathematicalthinking coherently and clearly to peers,teachers, and others
• Analyze and evaluate the mathematicalthinking and strategies of others
• Use the language of mathematics toexpress mathematical ideas precisely
NCTM Correlation of Discovering Advanced Algebra
Chapter 2: Describing DataExploration: Census Microdata
Chapter 3: Linear Models and SystemsAll lessons
Chapter 4: Functions, Relations, and Transformations4.1: Interpreting Graphs
Chapter 7: Quadratic and Other Polynomial Functions7.8: More About Finding Solutions
Chapter 13: Applications of Statistics13.3: z-values and Confidence Intervals13.4: The Central Limit Theorem
Chapter 2: Describing DataExploration: Census Microdata
Chapter 3: Linear Models and Systems3.2: Revisiting Slope
Chapter 4: Functions, Relations, and Transformations4.1: Interpreting Graphs4.7: Transformations and the Circle Family
Chapter 12: Probability12.1: Randomness and Probability
Chapter 13: Applications of Statistics13.3: z-values and Confidence Intervals13.4: The Central Limit Theorem
Chapter 4: Functions, Relations, and Transformations4.1: Interpreting Graphs
Chapter 5: Exponential, Power, and Logarithmic Functions5.1: The Exponential Function5.4: Applications of Exponential and Power Equations5.8: Applications of Logarithms
Chapter 0: Problem Solving0.3: Organizing Information
Advanced AlgebraDiscovering
Advanced AlgebraAn Investigative Approach
by Jerald Murdock,Ellen Kamischke, and Eric Kamischke
Key Curriculum Press 27NCTM Correlation of Discovering Advanced Algebra by Jerald Murdock, Ellen Kamischkee, and Eric Kamischke (© 2004)
NCTM Standard
Communication (cont.)
Connections
Expectations
• mathematical ideas precisely
• Recognize and use connections amongmathematical ideas
NCTM Correlation of Discovering Advanced Algebra
Chapter 1: Patterns and Recursion1.5: Loans and Investments
Chapter 3: Linear Models and Systems3.2: Revisiting Slope
Chapter 4: Functions, Relations, and Transformations4.2: Function Notation4.3: Lines in Motion4.4: Translations and the Quadratic Family4.5: Reflections and the Square Root Family4.6: Stretches and Shrinks, and the Absolute-Value Family4.7: Transformations and the Circle Family
Chapter 7: Quadratic and Other Polynomial FunctionsAll lessons
Chapter 12: ProbabilityAll lessons
Chapter 1: Patterns and RecursionAll lessons
Chapter 3: Linear Models and Systems3.1: Linear Equations and Arithmetic Sequences
Chapter 4: Functions, Relations, and TransformationsAll lessons
Chapter 5: Exponential, Power, and Logarithmic Functions5.1: The Exponential Function
Chapter 6: Matrices and Linear Systems6.1: Matrix Representations6.4: Solving Systems with Inverse Matrices
Chapter 9: Conic Sections and Rational Functions9.2: The Circle and the Ellipse9.3: The Parabola9.4: The Hyperbola9.5: The General Quadratic
Chapter 11: SeriesAll lessons
Advanced AlgebraDiscovering
Advanced AlgebraAn Investigative Approach
by Jerald Murdock,Ellen Kamischke, and Eric Kamischke
Key Curriculum Press 28NCTM Correlation of Discovering Advanced Algebra by Jerald Murdock, Ellen Kamischkee, and Eric Kamischke (© 2004)
NCTM Standard
Connections (cont.)
Expectations
• Understand how mathematical ideasinterconnect and build on one another toproduce a coherent whole
• Recognize and apply mathematics incontexts outside of mathematics
NCTM Correlation of Discovering Advanced Algebra
Chapter 3: Linear Models and SystemsAll lessons
Chapter 5: Exponential, Power, and Logarithmic FunctionsAll lessons
Chapter 7: Quadratic and Other Polynomial FunctionsAll lessons
Chapter 9: Conic Sections and Rational FunctionsAll lessons
Chapter 1: Patterns and Recursion1.5: Loans and InvestmentsExploration: Refining the Growth Model
Chapter 2: Describing DataAll lessons
Chapter 3: Linear Models and Systems3.3: Fitting a Line to Data3.5: Residuals
Chapter 6: Matrices and Linear Systems6.1: Matrix Representations6.4: Solving Systems with Inverse Matrices6.6: Linear Programming
Chapter 7: Quadratic and Other Polynomial Functions7.1: Polynomial Degree and Finite Differences
Chapter 8: Parametric Equations and Trigonometry8.1: Graphing Parametric Equations8.4: Using Trigonometry to Set a Course8.5: Projectile Motion
Chapter 9: Conic Sections and Rational Functions9.6: Introduction to Rational Functions
Chapter 11: SeriesAll lessons
Chapter 12: ProbabilityAll lessons
Chapter 13: Applications of StatisticsAll lessons
Advanced AlgebraDiscovering
Advanced AlgebraAn Investigative Approach
by Jerald Murdock,Ellen Kamischke, and Eric Kamischke
Key Curriculum Press 29NCTM Correlation of Discovering Advanced Algebra by Jerald Murdock, Ellen Kamischkee, and Eric Kamischke (© 2004)
NCTM Standard
Representations
Expectations
• Create and use representations toorganize, record, and communicatemathematical ideas
• Select, apply, and translate amongmathematical representations to solveproblems
NCTM Correlation of Discovering Advanced Algebra
Chapter 0: Problem Solving0.1: Pictures, Graphs, and Diagrams0.3: Organizing Information
Chapter 1: Patterns and Recursion1.1: Recursively Defined Sequences1.2: Modeling Growth and Decay1.3: A First Look at Limits
Chapter 2: Describing Data2.1: Measures of Central Tendency and Box Plots
Chapter 3: Linear Models and Systems3.1: Linear Equations and Arithmetic Sequences3.2: Revisiting Slope3.3: Fitting a Line to Data
Chapter 4: Functions, Relations, and Transformations4.2: Function Notation
Chapter 5: Exponential, Power, and Logarithmic Functions5.1: The Exponential Function
Chapter 7: Quadratic and Other Polynomial Functions7.1: Polynomial Degree and Finite Differences
Chapter 10: Trigonometric Functions10.1: Defining the Circular Functions10.5: Modeling with Trigonometric Equations
Chapter 11: Series11.1: Arithmetic Series11.2: Infinite Geometric Series
Chapter 12: Probability12.4: Random Variables and Expected Value
Chapter 13: Applications of Statistics13.3: z-values and Confidence Intervals
Chapter 1: Patterns and RecursionAll lessons
Chapter 2: Describing DataAll lessons
Advanced AlgebraDiscovering
Advanced AlgebraAn Investigative Approach
by Jerald Murdock,Ellen Kamischke, and Eric Kamischke
Key Curriculum Press 30NCTM Correlation of Discovering Advanced Algebra by Jerald Murdock, Ellen Kamischkee, and Eric Kamischke (© 2004)
NCTM Standard
Representations (cont.)
Expectations
• Use representations to model andinterpret physical, social, andmathematical phenomena
NCTM Correlation of Discovering Advanced Algebra
Chapter 3: Linear Models and SystemsAll lessons
Chapter 4: Functions, Relations, and TransformationsAll lessons
Chapter 7: Quadratic and Other Polynomial FunctionsAll lessons
Chapter 11: SeriesAll lessons
Chapter 1: Patterns and Recursion1.1: Recursively Defined Sequences1.2: Modeling Growth and Decay
Chapter 3: Linear Models and Systems3.2: Revisiting Slope
Chapter 4: Functions, Relations, and Transformations4.3: Lines in Motion
Chapter 5: Exponential, Power, and Logarithmic Functions5.1: The Exponential Function
Chapter 6: Matrices and Linear Systems6.1: Matrix Representations6.6: Linear Programming
Chapter 7: Quadratic and Other Polynomial Functions7.1: Polynomial Degree and Finite Differences
Chapter 8: Parametric Equations and Trigonometry8.1: Graphing Parametric Equations8.4: Using Trigonometry to Set a Course8.5: Projectile Motion
Chapter 12: Probability12.1: Randomness and Probability12.4: Random Variables and Expected Value
Chapter 13: Applications of StatisticsAll lessons
Advanced AlgebraDiscovering
Advanced AlgebraAn Investigative Approach
by Jerald Murdock,Ellen Kamischke, and Eric Kamischke
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