Common Core State Standards For Mathematics Integrated .
A CORRELATION OFMathematics ITO THECommon Core State Standardsfor MathematicsIntegrated Pathway: Mathematics III
A Correlation of Pearson Integrated High School Mathematics - Mathematics IIIto the Common Core State Standards for Mathematics –Integrated Pathway: Mathematics IIITable of ContentsUnit 1: Inferences and Conclusions from Data . 1Unit 2: Polynomials, Rational, and Radical Relationships . 3Unit 3: Trigonometry of General Triangles and Trigonometric Functions . 9Unit 4: Mathematical Modeling . 11
A Correlation of Pearson Integrated High School Mathematics - Mathematics IIIto the Common Core State Standards for Mathematics –Integrated Pathway: Mathematics IIIClusters with InstructionalNotesCommon Core StateStandards for Mathematics,Integrated Pathway:Mathematics IIIUnit 1: Inferences and Conclusions from DataSummarize, represent, andS.ID.4 Use the mean andinterpret data on a single count standard deviation of a data setor measurement variable.to fit it to a normal distributionand to estimate populationWhile students may have heard percentages. Recognize thatof the normal distribution, it isthere are data sets for whichunlikely that they will havesuch a procedure is notprior experience using it toappropriate. Use calculators,make specific estimates. Buildspreadsheets, and tables toon students’ understanding ofestimate areas under thedata distributions to help themnormal curve.see how the normal distributionuses area to make estimates offrequencies (which can beexpressed as probabilities).Emphasize that only some dataare well described by a normaldistribution.Understand and evaluaterandom processes underlyingstatistical experiments.For S.IC.2, include comparingtheoretical and empirical resultsto evaluate the effectiveness ofa treatment. Modeling StandardPearson Integrated HighSchool Mathematics Mathematics IIIChapters-Lessons1-4: Normal DistributionsFor an additional opportunity tointroduce this standard, pleasesee:1-2: LESSON LAB 1-2: AnIntroduction to SummationNotationS.IC.1 Understand thatstatistics allows inferences tobe made about populationparameters based on a randomsample from that population.1-3: Samples and SurveysS.IC.2 Decide if a specifiedmodel is consistent with resultsfrom a given data-generatingprocess, e.g., using simulation.1-4: ACTIVITY LAB 1-4a:Probability Distributions1
A Correlation of Pearson Integrated High School Mathematics - Mathematics IIIto the Common Core State Standards for Mathematics –Integrated Pathway: Mathematics IIIClusters with InstructionalNotesMake inferences and justifyconclusions from samplesurveys, experiments, andobservational studies.In earlier grades, students areintroduced to different ways ofcollecting data and usegraphical displays andsummary statistics to makecomparisons., These ideas arerevisited with a focus on howthe way in which data iscollected determines the scopeand nature of the conclusionsthat can be drawn from thatdata. The concept of statisticalsignificance is developedinformally through simulationas meaning a result that isunlikely to have occurred solelyas a result of random selectionin sampling or randomassignment in an experiment.For S.IC.4 and 5, focus on thevariability of results fromexperiments—that is, focus onstatistics as a way of dealingwith, not eliminating, inherentrandomness. Modeling StandardCommon Core StateStandards for Mathematics,Integrated Pathway:Mathematics IIIPearson Integrated HighSchool Mathematics Mathematics IIIChapters-LessonsS.IC.3 Recognize the purposesof and differences amongsample surveys, experiments,and observational studies;explain how randomizationrelates to each.1-3: Samples and SurveysS.IC.4 Use data from a samplesurvey to estimate a populationmean or proportion; develop amargin of error through the useof simulation models forrandom sampling.1-4: ACTIVITY LAB 1-4b:Margin of ErrorS.IC.5 Use data from arandomized experiment tocompare two treatments; usesimulations to decide ifdifferences betweenparameters are significant.1-4: ACTIVITY LAB 1-4c:Drawing Conclusions FromSamplesS.IC.6 Evaluate reports basedon data.1-1: Analyzing Data1-2: Standard Deviation1-3: Samples and Surveys2
A Correlation of Pearson Integrated High School Mathematics - Mathematics IIIto the Common Core State Standards for Mathematics –Integrated Pathway: Mathematics IIIClusters with InstructionalNotesUse probability to evaluateoutcomes of decisions.Extend to more complexprobability models. Includesituations such as thoseinvolving quality control ordiagnostic tests that yields bothfalse positive and false negativeresults.Unit 2: Polynomials, Rational,Use complex numbers inpolynomial identities andequations.Common Core StateStandards for Mathematics,Integrated Pathway:Mathematics IIIS.MD.6 Use probabilities tomake fair decisions (e.g.,drawing by lots, using arandom number generator).1-4: ACTIVITY LAB 1-4a:Probability DistributionsS.MD.7 Analyze decisions andstrategies using probabilityconcepts (e.g., product testing,medical testing, pulling ahockey goalie at the end of agame).1-4: Normal Distributionsand Radical RelationshipsN.CN.8 Extend polynomialidentities to the complexnumbers.Build on work with quadraticsequations in Mathematics II.Limit to polynomials with realcoefficients.N.CN.9 Know the FundamentalTheorem of Algebra; show thatit is true for quadraticpolynomials. Modeling StandardPearson Integrated HighSchool Mathematics Mathematics IIIChapters-Lessons4-6: Theorems About Roots ofPolynomial Equations4-6: LESSON LAB 4-6: UsingPolynomial Identities4-7: The Fundamental Theoremof Algebra4-7: The Fundamental Theoremof Algebra3
A Correlation of Pearson Integrated High School Mathematics - Mathematics IIIto the Common Core State Standards for Mathematics –Integrated Pathway: Mathematics IIIClusters with InstructionalNotesInterpret the structure ofexpressions.Extend to polynomial andrational expressions. Modeling StandardCommon Core StateStandards for Mathematics,Integrated Pathway:Mathematics IIIPearson Integrated HighSchool Mathematics Mathematics IIIChapters-LessonsA.SSE.1 Interpret expressionsthat represent a quantity interms of its context. 4-3: Polynomials, LinearFactors, and Zerosa. Interpret parts of anexpression, such as terms,factors, and coefficients.3-3: Factoring QuadraticExpressions3-4: Quadratic Equations4-1: Polynomial Functions4-3: Polynomials, LinearFactors, and Zerosb. Interpret complicatedexpressions by viewing one ormore of their parts as a singleentity.4-4: Solving PolynomialEquations5-1: Simplifying RationalExpressions5-5: The Reciprocal FunctionFamily5-6: Rational Functions andTheir Graphs7-1: Exploring ExponentialModels7-2: Properties of ExponentialFunctions7-3: Logarithmic Functions asInverses4
A Correlation of Pearson Integrated High School Mathematics - Mathematics IIIto the Common Core State Standards for Mathematics –Integrated Pathway: Mathematics IIIClusters with InstructionalNotes(Continued)Interpret the structure ofexpressions.Common Core StateStandards for Mathematics,Integrated Pathway:Mathematics IIIPearson Integrated HighSchool Mathematics Mathematics IIIChapters-LessonsA.SSE.2 Use the structure of anexpression to identify ways torewrite it.3-3: Factoring QuadraticExpressions3-5: Completing the Square4-2: Adding, Subtracting, andMultiplying Polynomials4-3: Polynomials, LinearFactors, and Zeros4-4: Solving PolynomialEquations4-6: Theorems About Roots ofPolynomial Equations4-6: LESSON LAB 4-6: UsingPolynomial Identities4-7: The Fundamental Theoremof Algebra4-8: The Binomial Theorem5-1: Simplifying RationalExpressions5-2: Multiplying and DividingRational Expressions5-3: Adding and SubtractingRational Expressions5-6: Rational Functions andTheir Graphs5-6: TECHNOLOGY LAB 5-6:Oblique Asymptotes5-7: Solving Rational Equations6-1: Roots and RadicalExpressions6-2: Multiplying and DividingRadical Expressions6-3: Binomial RadicalExpressions6-4: Rational Exponents7-4: Properties of LogarithmsA.SSE.4 Derive the formula forthe sum of a geometric series(when the common ratio is not1), and use the formula tosolve problems. 9-5: ACTIVITY LAB 9-5:Geometry and Infinite Series9-5: Geometric SeriesExtend to polynomial andrational expressions.Write expressions in equivalentforms to solve problems.Consider extending A.SSE.4 toinfinite geometric series incurricular implementations ofthis course description. Modeling Standard5
A Correlation of Pearson Integrated High School Mathematics - Mathematics IIIto the Common Core State Standards for Mathematics –Integrated Pathway: Mathematics IIIClusters with InstructionalNotesPerform arithmetic operationson polynomials.Extend beyond the quadraticpolynomials found inMathematics II.Understand the relationshipbetween zeros and factors ofpolynomials.Use polynomial identities tosolve problems.This cluster has manypossibilities for optionalenrichment, such as relatingthe example in A.APR.4 to thesolution of the systemu2 v2 1, v t(u 1), relatingthe Pascal triangle property ofbinomial coefficients to(x y)n 1 (x y)(x y)n,deriving explicit formulas forthe coefficients, or proving thebinomial theorem by induction. Modeling StandardCommon Core StateStandards for Mathematics,Integrated Pathway:Mathematics IIIPearson Integrated HighSchool Mathematics Mathematics IIIChapters-LessonsA.APR.1 Understand thatpolynomials form a systemanalogous to the integers,namely, they are closed underthe operations of addition,subtraction, and multiplication;add, subtract, and multiplypolynomials.4-2: Adding, Subtracting, andMultiplying PolynomialsA.APR.2 Know and apply theRemainder Theorem: For apolynomial p(x) and a numbera, the remainder on division byx – a is p(a), so p(a) 0 if andonly if (x – a) is a factor ofp(x).4-3: Polynomials, LinearFactors, and Zeros4-5: Dividing PolynomialsA.APR.3 Identify zeros ofpolynomials when suitablefactorizations are available, anduse the zeros to construct arough graph of the functiondefined by the polynomial.3-4: Quadratic Equations4-3: Polynomials, LinearFactors, and Zeros4-6: Theorems About Roots ofPolynomial Equations4-7: The Fundamental Theoremof Algebra4-7: ACTIVITY LAB 4-7:Graphing Polynomials UsingZerosA.APR.4 Prove polynomialidentities and use them todescribe numericalrelationships.4-6: LESSON LAB 4-6: UsingPolynomial Identities4-8: LESSON LAB 4-8:Mathematical InductionA.APR.5 Know and apply theBinomial Theorem for theexpansion of (x y)n inpowers of x and y for a positiveinteger n, where x and y areany numbers, with coefficientsdetermined for example byPascal’s Triangle.4-8: The Binomial Theorem4-8: LESSON LAB 4-8:Mathematical Induction6
A Correlation of Pearson Integrated High School Mathematics - Mathematics IIIto the Common Core State Standards for Mathematics –Integrated Pathway: Mathematics IIIClusters with InstructionalNotesRewrite rational expressionsThe limitations on rationalfunctions apply to the rationalexpressions in A.APR.6.A.APR.7 requires the generadivision algorithm forpolynomials.Understand solving equationsas a process of reasoning andexplain the reasoning.Extend to simple rational andradical equations.Represent and solve equationsand inequalities graphically.Include combinations of linear,polynomial, rational, radical,absolute value, and exponentialfunctions. Modeling StandardCommon Core StateStandards for Mathematics,Integrated Pathway:Mathematics IIIPearson Integrated HighSchool Mathematics Mathematics IIIChapters-LessonsA.APR.6 Rewrite simple rationalexpressions in different forms;write a(x)/b(x) in the form q(x) r(x)/b(x), where a(x), b(x),q(x), and r(x) are polynomialswith the degree of r(x) lessthan the degree of b(x), usinginspection, long division, or, forthe more complicatedexamples, a computer algebrasystem.4-5: Dividing Polynomials5-1: Simplifying RationalExpressionsA.APR.7 Understand thatrational expressions form asystem analogous to therational numbers, closed underaddition, subtraction,multiplication, and division by anonzero rational expression;add, subtract, multiply, anddivide rational expressions.5-2: Multiplying and DividingRational Expressions5-3: Adding and SubtractingRational ExpressionsA.REI.2 Solve simple rationaland radical equations in onevariable, and give examplesshowing how extraneoussolutions may arise.5-7: Solving Rational Equations6-5: Solving Square Root andOther Radical EquationsA.REI.11 Explain why the xcoordinates of the points wherethe graphs of the equations y f(x) and y g(x) intersect arethe solutions of the equationf(x) g(x); find the solutionsapproximately, e.g., usingtechnology to graph thefunctions, make tables ofvalues, or find successiveapproximations. Include caseswhere f(x) and/or g(x) arelinear, polynomial, rational,absolute value, exponential,and logarithmic functions. 3-7: Quadratic Systems4-4: Solving PolynomialEquations5-7: Solving Rational Equations5-7: ACTIVITY LAB 5-7a:Systems With RationalEquations6-5: Solving Square Root andOther Radical Equations7-5: Exponential andLogarithmic Equations7-6: LESSON LAB 7-6:Exponential and LogarithmicInequalities7
A Correlation of Pearson Integrated High School Mathematics - Mathematics IIIto the Common Core State Standards for Mathematics –Integrated Pathway: Mathematics IIIClusters with InstructionalNotesAnalyze functions usingdifferent representations.Relate F.IF.7c to therelationship between zeros ofquadratic functions and theirfactored forms. Modeling StandardCommon Core StateStandards for Mathematics,Integrated Pathway:Mathematics IIIPearson Integrated HighSchool Mathematics Mathematics IIIChapters-LessonsF.IF.7 Graph functionsexpressed symbolically andshow key features of the graph,by hand in simple cases andusing technology for morecomplicated cases. 2-3: Linear Functions andSlope-Intercept Form2-4: Families of Functions2-5: Absolute Value Functionsand Graphs2-5: LESSON LAB 2-5:Piecewise Functions3-1: Quadratic Functions andTransformations3-2: Standard Form of aQuadratic Function4-1: Polynomial Functions4-3: Polynomials, LinearFactors, and Zeros4-9: Polynomial Models in theReal World5-4: Inverse Variation5-5: TECHNOLOGY LAB 5-5:Graphing Rational Functions5-5: The Reciprocal FunctionFamily5-6: Rational Functions andTheir Graphs6-8: Graphing RadicalFunctions7-1: Exploring ExponentialModels7-2: Properties of ExponentialFunctions7-3: Logarithmic Functions asInverses7-5: Exponential andLogarithmic Equations8-4: The Sine Function8-4: TECHNOLOGY LAB 8-4:Graphing TrigonometricFunctions8-5: The Cosine Function8-6: The Tangent Function8-7: Translating Sine andCosine Functions8-8: Reciprocal TrigonometricFunctions8
A Correlation of Pearson Integrated High School Mathematics - Mathematics IIIto the Common Core State Standards for Mathematics –Integrated Pathway: Mathematics IIIClusters with InstructionalNotes(Continued)Analyze functions usingdifferent representations.Relate F.IF.7c to therelationship between zeros ofquadratic functions and theirfactored forms.Common Core StateStandards for Mathematics,Integrated Pathway:Mathematics IIIPearson Integrated HighSchool Mathematics Mathematics IIIChapters-Lessonsc. Graph polynomial functions,identifying zeros when suitablefactorizations are available, andshowing end behavior.4-1: Polynomial Functions4-3: Polynomials, LinearFactors, and Zeros4-7: ACTIVITY LAB 4-7:Graphing Polynomials UsingZeros4-9: Polynomial Models in theReal World4-10: Transforming PolynomialFunctionsUnit 3: Trigonometry of General Triangles and Trigonometric FunctionsApply trigonometry to generalG.SRT.9 Derive the formula A8-10: Area and the Law oftriangles. 1/2 ab sin(C) for the area ofSinesa triangle by drawing anWith respect to the generalauxiliary line from a vertexcase of the Laws of Sines andperpendicular to the oppositeCosines, the definitions of sineside.and cosine must be extended toobtuse angles. Modeling StandardG.SRT.10 Prove the Laws ofSines and Cosines and usethem to solve problems.8-10: Area and the Law ofSines8-11: The Law of CosinesG.SRT.11 Understand andapply the Law of Sines and theLaw of Cosines to find unknownmeasurements in right andnon-right triangles (e.g.,surveying problems, resultantforces).8-10: Area and the Law ofSines8-10: LESSON LAB 8-10: TheAmbiguous Case8-11: The Law of Cosines9
A Correlation of Pearson Integrated High School Mathematics - Mathematics IIIto the Common Core State Standards for Mathematics –Integrated Pathway: Mathematics IIIClusters with InstructionalNotesExtend the domain oftrigonometric functions usingthe unit circle.Model periodic phenomena withtrigonometric functions. Modeling StandardCommon Core StateStandards for Mathematics,Integrated Pathway:Mathematics IIIPearson Integrated HighSchool Mathematics Mathematics IIIChapters-LessonsF.TF.1 Understand radianmeasure of an angle as thelength of the arc on the unitcircle subtended by the angle.8-3: Radian MeasureF.TF.2 Explain how the unitcircle in the coordinate planeenables the extension oftrigonometric functions to allreal numbers, interpreted asradian measures of anglestraversed counterclockwisearound the unit circle.8-4: The Sine Function8-5: The Cosine Function8-6: The Tangent Function8-8: Reciprocal TrigonometricFunctionsF.TF.5 Choose trigonometricfunctions to model periodicphenomena with specifiedamplitude, frequency, andmidline. 8-4: The Sine Function8-5: The Cosine Function8-6: The Tangent Function8-7: Translating Sine andCosine Functions8-8: Reciprocal TrigonometricFunctionsFor an additional opportunity tointroduce this standard, pleasesee:8-2: Angles and the Unit CircleFor an additional opportunity tointroduce this standard, pleasesee:8-2: Angles and the Unit Circle8-3: Radian Measure10
A Correlation of Pearson Integrated High School Mathematics - Mathematics IIIto the Common Core State Standards for Mathematics –Integrated Pathway: Mathematics IIIClusters with InstructionalNotesCommon Core StateStandards for Mathematics,Integrated Pathway:Mathematics IIIUnit 4: Mathematical ModelingCreate equations that describeA.CED.1 Create equations andnumbers or relationships.inequalities in one variable anduse them to solve problems.For A.CED.1, use all availableInclude equations arising fromtypes of functions to createlinear and quadraticfunctions, and simple rationalsuch equations, including rootand exponential functions.functions, but constrain tosimple cases. While functionsused in A.CED.2, 3, and 4 willoften be linear, exponential, orquadratic the types of problemsshould draw from morecomplex situations than thoseaddressed in Mathematics I.For example, finding theequation of a line through agiven point perpendicular toanother line allows one to findthe distance from a point to aline. Note that the exampleA.CED.2 Create equations ingiven for A.CED.4 applies totwo or more variables toearlier instances of thisrepresent relationships betweenstandard, not to the currentquantities; graph equations oncourse.coordinate axes with labels andscales. Modeling StandardPearson Integrated HighSchool Mathematics Mathematics IIIChapters-Lessons2-1: Solving Equations2-2: Solving Inequalities3-4: Quadratic Equations3-5: Completing the Square3-6: The Quadratic Formula5-7: Solving Rational Equations5-7: TECHNOLOGY LAB 5-7b:Rational Inequalities6-5: Solving Square Root andOther Radical Equations7-5: Exponential andLogarithmic Equations7-6: LESSON LAB 7-6:Exponential and LogarithmicInequalities2-3: Linear Functions andSlope-Intercept Form2-7: Solving Systems ofEquations3-1: Quadratic Functions andTransformations3-2: Standard Form of aQuadratic Function4-3: Polynomials, LinearFactors, and Zeros4-9: Polynomial Models in theReal World5-4: Inverse Variation5-5: The Reciprocal FunctionFamily5-6: Rational Functions andTheir Graphs6-8: Graphing RadicalFunctions7-1: Exploring ExponentialModels7-2: Prop
A Correlation of Pearson Integrated High School Mathematics - Mathematics III to the Common Core State Standards for Mathematics – Integrated Pathway: Mathematics III
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