Mathematics Grade 8

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Mathematics Grade 8Unit 1 Problem SolvingEstimatedTime Framefor UnitBig Ideas11 daysPatterns exhibitrelationships thatcan be extendeddescribed andgeneralized.Patterns exhibitrelationships thatcan be extendeddescribed andgeneralized.Patterns exhibitrelationships thatcan be extendeddescribed andgeneralized.EssentialQuestionHow do problemsolving strategiesandMathematicalpractices helpone becomemore successfulin math class?How do problemsolving strategiesandMathematicalpractices helpone becomemore successfulin math class?How do problemsolving strategiesandMathematicalpractices helpone becomemore successfulin math cticesMathematicalPracticesCompetenciesStudents should be ableto solve problems usingguess and checkstrategy.Students should be ableto persevere throughproblems.Students should be ableto use quantitativereasoning that entailscreating a coherentrepresentation ofquantities, not justcomputation.Students should be ableto find and expressregularity in repeatedreasoning.Students should be ableto describerelationships andextend terms inarithmetic sequences.Lesson Plans andSuggested ResourcesVocabularyStandards/EligibleContentGuess and CheckCCSS Mathematical Practice 1Math Connects Course2Section 1-5Problem solvingInvestigation(Pgs. 42-43)Eliminate PossibilitiesCCSS Mathematical Practice 2Math ConnectsSection 5-3Problem SolvingInvestigation(pgs. 248-249)PatternsSequencePreparation for:Glencoe Math Course2Problem SolvingInvestigation(pgs 225-227)TermCC.2.2.7.B.1 Apply properties ofoperations to generateequivalent expressions.Glencoe Math Course 2Section 5-2(pgs 357-364)Math ConnectsSection 1-9(Pgs. 57-62)Section 2-7Problem SolvingInvestigation (pgs. 112113)ArithmeticsequenceM07.B-E.1.1.1 Apply propertiesof operations to add, subtract,factor, and expand linearexpressions with rationalcoefficients.CCSS Mathematical Practice 8

Patterns exhibitrelationships thatcan be extendeddescribed andgeneralized.How do problemsolving strategiesandMathematicalpractices helpone becomemore successfulin math class?MathematicalPracticesStudents should be ableto understand and usestated assumptions,definitions andpreviously establishedresults in constructingarguments and findingsolutions.Word ProblemsPatterns exhibitrelationships thatcan be extendeddescribed andgeneralized.How do problemsolving strategiesandMathematicalpractices helpone becomemore successfulin math class?MathematicalPracticesStudents should be ableto estimate percentsusing fractions anddecimals.Estimate SolutionsStudents should be ableto use estimation tosolve problems anddetermine reasonabilityof solutions.Glencoe Math Course 2Section 2-2(pgs 111-118)Math Connects Course2Section 5-1(pgs. 230-235)Math Connects Course2Section 7-5Problem SolvingInvestigation(pgs. 366-367)CCSS Mathematical Practice1,3,4,6,7CC.2.2.7.B.1 Apply properties ofoperations to generateequivalent expressionsCC.2.2.7.B.3 Model and solvereal world and mathematicalproblems by using andconnecting numerical, algebraicand/or graphicalrepresentations.CC.2.1.8.E.4 Estimate irrationalnumbers by comparing them torational numbers.M07.B-E.2.1.1 Apply propertiesof operations to calculate withnumbers in any form; convertbetweenForms as appropriate,M07.B-E.2.3.1 Determine thereasonableness of answer(s) orinterpret the solution(s) in thecontext of the problem.M08.A-N.1.1.3 Estimate thevalue of irrational numberswithout a calculator (limit wholenumber radicand to led than144)CCSS Mathematical Practice 2Review Common Assessment Unit 1 Problem Solving 1 Day

Test Common Assessment Unit 1 Problem Solving 1 DayUnit 2EstimatedTime Framefor UnitBig Ideas18 daysNumbers,measures,expressions,equations, andinequalities canrepresentmathematicalsituations andstructures inmany equivalentforms.EssentialQuestionWhy is it helpfulto write numbersin different ways?ConceptsApply concepts ofRational Numbersand IrrationalNumbersNumbers and OperationsCompetenciesDistinguish betweenRational and IrrationalNumbers using theirproperties.Students should be ableto write rationalnumbers as decimalsand decimals asfractionsLesson Plans andSuggested ResourcesVocabularyNumber SystemsRational NumberGlencoe Math Course 3Section 2-1(pgs 84 - 89 )Irrational NumberGlencoe Math Course 2Section 1-1(pgs 7 - 14)TerminatingDecimalRepeating DecimalStandards/EligibleContentCC.2.1.8.E.1 Distinguish betweenRational and Irrational Numbersusing their properties.CC.2.1.8.E.4 Estimate irrationalnumbers by comparing them torational numbers.M08.A-N.1.1.1 Determinewhether a number is rational orirrational. For rational numbers,show that the decimal expansionterminates or repeats(limitrepeating decimals tothousandths)Students should be ableto comparemathematicalexpressionsM08.A-N.1.1.2 Convert aterminating or repeating decimalto a rational number (limitrepeating decimals tothousandths)M08.A-N.1.1.3 Estimate thevalue of irrational numberswithout a calculator. (Limit theradicand to less than 144)M08.A-N.1.1.4 Use rationalapproximations of irrationalnumbers to compare and orderirrational numbers.Numbers,measures,expressions,Why is it helpfulto write numbersin different ways?Apply concepts ofRational Numbersand IrrationalDistinguish betweenRational and IrrationalNumbers using theirRational OperationsFractionsGlencoe MathMultiplicativeM08.A-N.1.1.5 Locate/identifyrational and irrational numbersat their locations on a numberline.In preparation of:M08.B-E.3.1.2 Solve linear

equations, andinequalities canrepresentmathematicalsituations andstructures inmany equivalentforms.NumberspropertiesStudents should be ableto apply properties ofoperations to add andsubtract, multiply anddivide rationalnumbers, includingreal-world contextsAcceleratedSection 3-3(Pgs. 107-112)inverseReciprocalGlencoe MathAcceleratedSection 3-4(Pgs. 114-119)equations that have rationalcoefficients, including equationswhose solutions requireexpanding expressions usingdistributive property andcollecting like terms.Glencoe MathAcceleratedSection 3-5(Pgs. 120-125)Glencoe MathAcceleratedSection 3-6(Pgs. 126-131)Numbers,measures,expressions,equations, andinequalities canrepresentmathematicalsituations andstructures inmany equivalentforms.Why is it helpfulto write numbersin different ways?Apply concepts ofRational Numbersand IrrationalNumbersApply concepts ofradical and integerexponents to generateequivalent expressions.Estimate irrationalnumbers by comparingthem to rationalnumbers.Students should be ableto use powers andexponents to writelarge and smallnumbersStudents will write andevaluate expressionsusing negativeexponents.Students will findsquare roots of perfectsquares.Students will estimatesquare roots of nonperfect squaresExponents and RootsPowerGlencoe Math Course 3Section 1-2(pgs 15 - 22)BaseGlencoe Math Course 3Section 1-5(pgs. 43 – 50)Glencoe Math Course 3Section 1-8(pgs. 71 – 78)Negative ExponentExponentZero exponentSquare rootPerfect squareGlencoe Math Course 3Section 1-9(Pgs.79 – 88)Radical signNon-perfectsquaresCC.2.2.8.B.1 Apply concepts ofradical and integer exponents togenerate equivalent expressions.CC.2.1.8.E.4 Estimate irrationalnumbers by comparing them torational numbers.M08.B-E.1.1.1 Apply one or moreproperties of integer exponentsto generate equivalent numericalexpressions without a calculator.(with final answers expressed inexponential form with positiveexponents)M08.B-E. 1.1.2 Use square rootand cube root symbols torepresent solutions to equationsof the form x 2 p and x 3 p,where p is a positive rationalnumber. Evaluate square roots ofperfect squares (up to andincluding 12 2) and cube roots ofperfect cubes (up to andincluding 5 3) without acalculator.

M08.A-N.1.1.3 Estimate thevalue of irrational numberswithout a calculator. (Limit theradicand to less than 144)M08.A-N.1.1.4 Use rationalapproximations of irrationalnumbers to compare and orderirrational numbers.Numbers,measures,expressions,equations, andinequalities canrepresentmathematicalsituations andstructures inmany equivalentforms.Why is it helpfulto write numbersin different ways?Apply concepts ofRational Numbersand IrrationalNumbersDistinguish betweenRational and IrrationalNumbers using theirpropertiesStudents will usescientific notation towrite large and smallnumbersStudents will computewith numbers inScientific NotationStudents will interpretscientific notation usingtechnology.Scientific NotationGlencoe Math Course 3Section 1-6(pgs. 51 – 58)Glencoe Math Course 3Section 1-7(Pgs.59 – 70)Scientific NotationM08.A-N.1.1.5 Locate/identifyrational and irrational numbersat their locations on a numberline.CC.2.2.8.1.B.1 1 Apply conceptsof radical and integer exponentsto generate equivalentexpressions.M08.B-E.1.1.1 Apply one or moreproperties of integer exponentsto generate equivalent numericalexpressions without a calculator.(with final answers expressed inexponential form with positiveexponents)M08.B-E.1.1.3 Estimate verylarge or very small quantities byusing numbers expressed in theform of a single digit times aninteger power of 10 and expresshow many times larger orsmaller one number is thananother.M08.B-E.1.1.4 Performoperations with numbersexpressed in scientific notation,including problems where bothdecimal and scientific notationsare used. Express answers inscientific notation and chooseunits of appropriate size formeasurements of very large orvery small quantities (e.g., usemillimeters per year for seafloorspreading). Interpret scientific

notation that has beengenerated by technology (e.g.,interpret 4.7EE9 displayed on acalculator as 4.7 x 10 9)Review Unit 2Assessment Unit 2Numbers and OperationsNumbers and OperationsUnit 3 Pre-Algebra ConceptsEstimatedTime Framefor UnitBig Ideas28 daysMathematicalrelationshipscam berepresented asexpressions,equations, andinequalities inmathematicalsituations.EssentialQuestionHow canexpressions andequations beused toquantify, solvemodel sions andEquationsCompetenciesStudents should be ableto evaluate expressionsusing order ofoperations.Lesson Plans andSuggested ResourcesVocabularyStandards/EligibleContentOrder of OperationsEvaluatePreparation for:Math Connects Course3Section 1-2(Pgs.29 – 34)Order ofOperationsCC.2.2.8.B.3 Analyze and solvelinear equations and pairs ofsimultaneous linear equations.M08.B-E.3.1.1 Write and identifylinear equations in one variablewith one solution, infinitelymany solutions, or no solutions.Show that these possibilities isthe case by successfullytransforming the given equationinto a simpler form until anequivalent form x a, a a, or a b results (where a and b aredifferent numbers).M08.B-E.3.1.2 Solve linearequations that have rationalcoefficients, including equationswhose solutions requireexpanding using the distributiveproperty or collecting like terms.Mathematicalrelationships cambe representedas expressions,How canexpressions,equations, andInequalities beExpressions andEquationsStudents should be ableto evaluate expressionsby combining liketerms.Combining TermsMath ConnectsCourse 3EquivalentexpressionsTermPreparation for:CC.2.2.8.B.3 Analyze and solvelinear equations and pairs of

equations, andinequalities inmathematicalsituations.used to quantify,solve modeland/or analyzemathematicalsituations?Section 8-1(Pgs.416 – 412)simultaneous linear equations.CoefficientLike termsConstantSimplest formSimplifying theexpressionM08.B-E.3.1.1 Write and identifylinear equations in one variablewith one solution, infinitelymany solutions, or no solutions.Show that these possibilities isthe case by successfullytransforming the given equationinto a simpler form until anequivalent form x a, a a, or a b results (where a and b aredifferent numbers).M08.B-E.3.1.2 Solve linearequations that have rationalcoefficients, including equationswhose solutions requireexpanding using the distributiveproperty or collecting like terms.Mathematicalrelationships cambe representedas expressions,equations, andinequalities inmathematicalsituations.How canexpressions andequations beused to quantify,solve modeland/or analyzemathematicalsituations?Expressions andEquationsStudents should be ableto use the DistributiveProperty to simplifyalgebraic expressions.Distributive PropertyMath ConnectsCourse 2Section 1-8(Pgs.53 - 56)EquivalentexpressionsPropertiesPreparation for:CC.2.2.8.B.3 Analyze and solvelinear equations and pairs ofsimultaneous linear equations.M08.B-E.3.1.1 Write and identifylinear equations in one variablewith one solution, infinitelymany solutions, or no solutions.Show that these possibilities isthe case by successfullytransforming the given equationinto a simpler form until anequivalent form x a, a a, or a b results (where a and b aredifferent numbers).Math ConnectsCourse 3Section 1-2(Pgs.29 – 34)M08.B-E.3.1.2 Solve linearequations that have rationalcoefficients, including equationswhose solutions requireexpanding using the distributiveproperty or collecting like terms.Mathematicalrelationships camHow canexpressions andExpressions andEquationsStudent should be ableto analyze, model andOne Step EquationsMultiplicativeInverseCC.2.2.8.B.3 Analyze and solvelinear equations and pairs of

be representedas expressions,equations, andinequalities inmathematicalsituations.Mathematicalrelationships cambe representedas expressions,equations, andinequalities inmathematicalsituations.Mathematicalrelationships cambe representedas expressions,equations, andinequalities inequations beused to quantify,solve modeland/or analyzemathematicalsituations?How canexpressions andequations beused to quantify,solve modeland/or analyzemathematicalsituations?How canexpressions andequations beused to quantify,solve modeland/or analyzesolve linear equations.Students will solve onestep-equation withrational coefficients.Expressions andEquationsStudent should be ableto analyze, model andsolve linear equations.Students should be ableto solve two stepequations.Expressions andEquationsStudent should be ableto analyze, model andsolve linear equations.Students will solveequations withGlencoe Math Course 3Section 2-1(Pgs.107 – 118)simultaneous linear equations.coefficientM08.B-E.3.1.1 Write and identifylinear equations in one variablewith one solution, infinitelymany solutions, or no solutions.Show that these possibilities isthe case by successfullytransforming the given equationinto a simpler form until anequivalent form x a, a a, or a b results (where a and b aredifferent numbers).Two Step EquationsPropertiesGlencoe Math Course 3Section 2-2(Pgs.121 – 128)Two StepEquationsM08.B-E.3.1.2 Solve linearequations that have rationalcoefficients, including equationswhose solutions requireexpanding using the distributiveproperty or collecting like terms.CC.2.2.8.B.3 Analyze and solvelinear equations and pairs ofsimultaneous linear equations.M08.B-E.3.1.1 Write and identifylinear equations in one variablewith one solution, infinitelymany solutions, or no solutions.Show that these possibilities isthe case by successfullytransforming the given equationinto a simpler form until anequivalent form x a, a a, or a b results (where a and b aredifferent numbers).Multi-Step EquationNull setGlencoe Math Course 3Section 2-4 and 2-5(Pgs.145 – 160)IdentityM08.B-E.3.1.2 Solve linearequations that have rationalcoefficients, including equationswhose solutions requireexpanding using the distributiveproperty or collecting like terms.CC.2.2.8.B.3 Analyze and solvelinear equations and pairs ofsimultaneous linear equations.M08.B-E.3.1.1 Write and identifylinear equations in one variable

ables on each side.with one solution, infinitelymany solutions, or no solutions.Show that these possibilities isthe case by successfullytransforming the given equationinto a simpler form until anequivalent form x a, a a, or a b results (where a and b aredifferent numbers).Students will solvemulti-step equations.Mathematicalrelationships cambe representedas expressions,equations, andinequalities inmathematicalsituations.How canexpressions andequations beused to quantify,solve modeland/or analyzemathematicalsituations?Expressions andEquationsStudent should be ableto analyze, model andsolve linear equationsStudents will Writealgebraic equationsfrom verbal sentencesand problem situation.Writing EquationsGlencoe Math Course 3Section 2-3(Pgs.145 – 160)Math ConnectsCourse 3Section 8-3(Pgs.427 – 431)M08.B-E.3.1.2 Solve linearequations that have rationalcoefficients, including equationswhose solutions requireexpanding using the distributiveproperty or collecting like terms.CC.2.2.8.B.3 Analyze and solvelinear equations and pairs ofsimultaneous linear equations.M08.B-E.3.1.1 Write and identifylinear equations in one variablewith one solution, infinitelymany solutions, or no solutions.Show that these possibilities isthe case by successfullytransforming the given equationinto a simpler form until anequivalent form x a, a a, or a b results (where a and b aredifferent numbers).M08.B-E.3.1.2 Solve linearequations that have rationalcoefficients, including equationswhose solutions requireexpanding using the distributiveproperty or collecting like terms.Review Unit 3 Pre-Algebra ConceptsAssessment Unit 3 Pre-Algebra ConceptsUnit 4 Algebra Concepts

EstimatedTime Framefor UnitBig IdeasEssentialQuestionConceptsCompetencies27 daysMathematicalrelations andfunctions can bemodeled throughmultiplerepresentationsand analyzed toraise and answerquestions.How arerelationshipsrepresentedmathematically?Linear Equationsand FunctionsStudent will be able toplot points on acoordinate planemanually and usingtechnology.Lesson Plans andSuggested nate SystemCoordinate planePreparation for:Math ConnectsCourse 3Section 3-7(Pgs.173 – 178)OriginCC.2.2.8.B.2 Understand theconnections betweenproportional relationships, lines,and linear equationsy-axisx-axisGlencoe Math Course 3Section 4-2(Pgs.277 – 284)QuadrantsOrdered pairsx-coordinateM08.B-E.2.1.1 Graphproportional relationships,interpreting the unit rate as theslope of the graph. Compare twodifferent proportionalrelationships represented indifferent ions andfunctions can bemodeled throughmultiplerepresentationsand analyzed toraise and answerquestions.How icalrelations andfunctions can bemodeled throughmultiplerepresentationsand analyzed toraise and answerquestions.How arerelationshipsrepresentedmathematically?Linear Equationsand FunctionsLinear Equationsand FunctionsStudent will be able torepresent a data set viatable, chart, graph, &map.Students Should beable to use directvariation to solveproblems.Students should be ableto write an equation ofa line given a point anda slope, the slope andthe y-intercept, from agraph, from two pointsand from a table inRelationsLinear FunctionsGlencoe Math Course 3Section 4-1(Pgs.277 – 284)Math ConnectsCourse 3Section 9-3(Pgs.475 – 480)Linear EquationsGlencoe Math Course 3Section 3-3(Pgs.189 – 198)Glencoe Math Course 3Section 3-6(Pgs.221 – 228)Glencoe Math Course 3Section 4-1Preparation for:CC.2.2.8.C.1 Define, evaluate andcompare functions.M08.B-F.1.1.1 Determinewhether a relation is a function.Direct variationConstant ofVariationConstant ofproportionalityCC.2.2.8.B.2 Understand theconnections betweenproportional relationships, lines,and linear equationsCC.2.2.8.B.3 analyze and solvelinear equations and pairs ofsimultaneous linear equations.Point-slope formLinear equationCC.2.2.8.C.1 Define, evaluate andcompare functions

both point-slope formand slope-interceptform.Students should be ableto translate tables andgraphs into linearequations.Students should be ableto determine andinterpret the rate ofchange and initial valueof a functionStudents should be ableto determine whether afunction is linear ornonlinear.Students should be ableto construct andinterpret two waytable

Accelerated Section 3-3 (Pgs. 107-112) Glencoe Math Accelerated Section 3-4 (Pgs. 114-119) Glencoe Math Accelerated Section 3-5 (Pgs. 120-125) Glencoe Math Accelerated Section 3-6 (Pgs. 126-131) inverse Reciprocal equations that have rational coefficients, including equations whose solutions require expanding expressions using

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