NCTM DAA correlation - Prek 12math.kendallhunt.com/Documents/correlations/NCTM_DAA_corr.pdf ·...

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


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;


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





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;


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 12: Probability12.5: Permutations and Probability12.6: Combinations and Probability


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





NCTM Standard

Compare fluently and makereasonable estimates (cont.)

Expectations

• judge the reasonableness of numericalcomputation and their results.


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





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;



Chapter 3: Linear Models and Systems3.1: Linear Equations and Arithmetic Sequences

Chapter 5: Exponential, Power, and Logarithmic Functions5.1: The Exponential Function


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 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





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;


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





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;



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 0: Problem Solving0.2: Symbolic Representation


Chapter 3: Linear Models and Systems3.1: Linear Equations and Arithmetic Sequences3.2: Revisiting Slope






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;


Chapter 6: Matrices and Linear Systems6.5: Systems of Linear Inequalities6.6: Linear Programming


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 9: Conic Sections and Rational Functions9.3: The Parabola9.4: The Hyperbola9.5: The General Quadratic9.6: Introduction to Rational Functions





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.


Chapter 10: Trigonometric Functions10.3: Graphing Trigonometric Functions


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 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









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;


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 3: Linear Models and Systems3.1: Linear Equations and Arithmetic Sequences3.2: Revisiting Slope3.3: Fitting a Line to Data







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;


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 13: Applications of Statistics13.6: Least Squares Line

Chapter 1: Patterns and Recursion1.1: Recursively Defined Sequences1.4: Graphing Sequences



Chapter 7: Quadratic and Other Polynomial Functions7.2: Equivalent Quadratic Forms7.3: Completing the Square7.6: Factored Polynomials





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;


Chapter 8: Parametric Equations and Trigonometry8.6: The Law of Sines8.7: The Law of Cosines


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






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.


Chapter 8: Parametric Equations and Trigonometry8.3: Right Triangle Trigonometry8.6: The Law of Sines8.7: The Law of Cosines


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 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






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;


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





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.


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





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.


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 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 11: Series11.1: Arithmetic Series

Chapter 13: Applications of Statistics13.6: The Least Squares Line





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.



Chapter 5: Exponential, Power, and Logarithmic Functions5.4: Applications of Exponential and Power Equations5.8: Applications of Logarithms


Chapter 7: Quadratic and Other Polynomial Functions7.2: Equivalent Quadratic Forms7.3: Completing the Square7.6: Factored Polynomials




Chapter 1: Patterns and Recursion1.3: A First Look at Limits

Chapter 11: Series11.1: Arithmetic Series11.2: Infinite Geometric Series






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;


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 13: Applications of Statistics13.3: z-values and Confidence Intervals13.5: Bivariate Data and Correlation



Chapter 12: Probability12.4: Random Variables and Expected Value

Chapter 13: Applications of Statistics13.1: Probability Distributions13.5: Bivariate Data and Correlation


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





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;




Chapter 13: Applications of Statistics13.1: Probability Distributions13.3: z-values and Confidence Intervals13.6: Least Squares Line


Chapter 13: Applications of Statistics13.1: Probability Distributions13.2: Normal Distributions


Chapter 1: Patterns and Recursion1.4: Graphing Sequences



Chapter 13: Applications of Statistics13.5: Bivariate Data and Correlation13.6: Least Squares Line13.7: Nonlinear Regression

Not covered





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;


Chapter 2: Describing Data2.1: Measures of Central Tendency and Box Plots2.2: Measures of Spread




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 9: Conic Sections and Rational Functions9.6: Introduction to Rational Functions


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





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.


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 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





NCTM Standard

Problem Solving

Expectations

• Build new mathematical knowledgethrough problem solving

• Solve problems that arise inmathematical and in other contexts







Chapter 0: Problem SolvingAll 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






NCTM Standard

Problem Solving (cont.)

Expectations

• Apply and adapt a variety of appropriatestrategies to solve problems


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 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





NCTM Standard

Problem Solving (cont.)

Expectations

• Monitor and reflect on the process ofmathematical problem solving


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 4: Functions, Relations, and Transformations4.6: Stretches and Shrinks and the Absolute-Value Family



Chapter 10: Trigonometric Functions10.1 Defining the Circular Function

Chapter 13: Applications of Statistics13.5: Bivariate Data and Correlation13.6: The Least Squares Line





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




Chapter 8: Parametric Equations and Trigonometry8.7: The Law of Cosines
















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




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 3: Linear Models and Systems3.2: Revisiting Slope

Chapter 4: Functions, Relations, and Transformations4.1: Interpreting Graphs4.7: Transformations and the Circle Family


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







NCTM Standard

Communication (cont.)

Connections

Expectations

• mathematical ideas precisely

• Recognize and use connections amongmathematical ideas


Chapter 1: Patterns and Recursion1.5: Loans and Investments


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 12: ProbabilityAll lessons


Chapter 3: Linear Models and Systems3.1: Linear Equations and Arithmetic Sequences



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






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





Chapter 9: Conic Sections and Rational FunctionsAll lessons

Chapter 1: Patterns and Recursion1.5: Loans and InvestmentsExploration: Refining the Growth Model


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 9: Conic Sections and Rational Functions9.6: Introduction to Rational Functions


Chapter 12: ProbabilityAll lessons

Chapter 13: Applications of StatisticsAll lessons





NCTM Standard

Representations

Expectations

• Create and use representations toorganize, record, and communicatemathematical ideas

• Select, apply, and translate amongmathematical representations to solveproblems


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 4: Functions, Relations, and Transformations4.2: Function Notation



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 13: Applications of Statistics13.3: z-values and Confidence Intervals







NCTM Standard

Representations (cont.)

Expectations

• Use representations to model andinterpret physical, social, andmathematical phenomena










Chapter 6: Matrices and Linear Systems6.1: Matrix Representations6.6: Linear Programming



Chapter 12: Probability12.1: Randomness and Probability12.4: Random Variables and Expected Value

Chapter 13: Applications of StatisticsAll lessons




NCTM DAA correlation - Prek 12math.kendallhunt.com/Documents/correlations/NCTM_DAA_corr.pdf ·...

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Transcript of NCTM DAA correlation - Prek 12math.kendallhunt.com/Documents/correlations/NCTM_DAA_corr.pdf ·...