Block: Guidance for teacher for a single block of ... · - Exploring ""Angle relationships,"" pp. 1-5, Block 1, SAS - Exploring "Angle relationships," Block 2, SAS - Exploring "Angle

2016-17STATEOFFLORIDAINSTRUCTIONALMATERIALSADOPTION,STANDARDSALIGNMENT,COURSESTANDARDS/BENCHMARKS(IM7)

M/JGRADE7MATH/AgileMindMathematics7 1of25

BIDID: 3575

SUBMISSIONTITLE: AgileMindMathematics7

GRADELEVEL: 6-8

COURSETITLE: M/JGRADE7MATH

COURSECODE: 1205040

ISBN: 978-1-948905-82-4

PUBLISHER: AgileMindEducationalHoldings,Inc.

PUBLISHERID: 27000820301

BENCHMARKCODE BENCHMARK

LESSONSWHERESTANDARD/BENCHMARKISDIRECTLYADDRESSEDINMAJORTOOL(MOSTIN-DEPTHCOVERAGELISTEDFIRST)(Includethestudenteditionandteachereditionwiththepagenumbersoflesson,alinktolesson,orotheridentifierforeasylookupbyreviewers.)

MAFS.7.EE.1.1: Applypropertiesofoperationsasstrategiestoadd,subtract,factor,andexpandlinearexpressionswithrationalcoefficients.

Topic8.Equationsandinequalities-Exploring""Modelingandsolvinglinearequations,""pp.8-13,Block3,SAS-Exploring"Linearexpressionsandequations,"pp.1-5,Block4,SAS-Exploring"Linearexpressionsandequations,"pp.6-9,Block5,SAS-Constructedresponse,Block6-Guidedpractice,Block7-Exploring"Solvingandgraphinginequalities,"pp.1-8,Block8,SAS-Exploring"Solvingandgraphinginequalities,"pp.9-12,Block9,SAS

MAFS.7.EE.1.2: Understandthatrewritinganexpressionindifferentformsinaproblemcontextcanshedlightontheproblemandhowthequantitiesinitarerelated.Forexample,a+0.05a=1.05ameansthat“increaseby5%”isthesameas“multiplyby1.05.”

Topic8.Equationsandinequalities-Overview,Block1,SAS-Exploring"Linearexpressionsandequations,"pp.1-5,Block4,SAS-Constructedresponse,Block6,SAS-Guidedpractice,Block7,SAS

SAS:StudentActivitySheet.TheSASthatarepartofthetopicmaterialsareavailableinprintformbutcanbeaccessedaspdfdownloadsfromtheStudentActivitySheetareainatopic.

Block:Guidanceforteacherforasingleblockofinstructionforatopic.TheguidanceisfoundinProfessionalsupport->AdviceforInstruction–>Deliverinstruction->Blockxyz



Solvemulti-stepreal-lifeandmathematicalproblemsposedwithpositiveandnegativerationalnumbersinanyform(wholenumbers,fractions,anddecimals),usingtoolsstrategically.Applypropertiesofoperationstocalculatewithnumbersinanyform;convertbetweenformsasappropriate;andassessthereasonablenessofanswersusingmentalcomputationandestimationstrategies.Forexample:Ifawomanmaking$25anhourgetsa10%raise,shewillmakeanadditional1/10ofhersalaryanhour,or$2.50,foranewsalaryof$27.50.Ifyouwanttoplaceatowelbar93/4incheslonginthecenterofadoorthatis271/2incheswide,youwillneedtoplacethebarabout9inchesfromeachedge;thisestimatecanbeusedasacheckontheexactcomputation.

Topic7.Rationalnumbers-Overview,Block1,SAS-Exploring"Operationswithpositiverationalnumbers,"pp.1-7,Block2-Exploring"Operationswithpositiverationalnumbers,"pp.8-11,Block3-Exploring"Understandingrationalnumberoperations,"pp.1-2,Block4-Exploring"Understandingrationalnumberoperations,"pp.3-7,Block5-Exploring"Understandingrationalnumberoperations,"pp.8-12,Block6-Exploring"Applyingrationalnumberoperations,"pp.1-8,Block7,SAS-Exploring"Applyingrationalnumberoperations,"pp.9-12,Block8,SAS

Topic13.Solvingproblemswith2-Dshapes-Exploring""Frompolygonstocircles,""pp.1-5,Block1,SAS-Exploring"Frompolygonstocircles,"pp.6-12,Block2,SAS-Exploring"Estimatingareas,"Block3,SAS-Exploring"Areaoftrianglesandquadrilaterals,"pp.1-8,Block4,SAS-Exploring"Areaoftrianglesandquadrilaterals,"pp.9-12,Block5,SAS-Exploring"Areaofpolygonsandcircles,"pp.1-3,Block6,SAS-Exploring"Areaofpolygonsandcircles,"pp.4-6,Block7,SAS

Remarks/Examples:

FluencyExpectationsorExamplesofCulminatingStandards

Studentssolvemultistepproblemsposedwithpositiveandnegativerationalnumbersinanyform(wholenumbers,fractions,anddecimals),usingtoolsstrategically.Thisworkistheculminationofmanyprogressionsoflearninginarithmetic,problemsolvingandmathematicalpractices.ExamplesofOpportunitiesforIn-DepthFocusThisisamajorcapstonestandardforarithmeticanditsapplications.Usevariablestorepresentquantitiesinareal-worldormathematicalproblem,andconstructsimpleequationsandinequalitiestosolveproblemsbyreasoningaboutthequantities.

MAFS.7.EE.2.3:

MAFS.7.EE.2.4:



a. Solvewordproblemsleadingtoequationsoftheformpx+q=randp(x+q)=r,wherep,q,andrarespecificrationalnumbers.Solveequationsoftheseformsfluently.Compareanalgebraicsolutiontoanarithmeticsolution,identifyingthesequenceoftheoperationsusedineachapproach.Forexample,theperimeterofarectangleis54cm.Itslengthis6cm.Whatisitswidth?

Topic3.Patternsinproportionalrelationships-Exploring""Proportionalandnon-proportionalrelationships,""pp.1-4,Block2,SAS-Exploring"Identifyingproportionalrelationships,"pp.1-4,Block5,SAS-MarsTask:Tilingsquares,Block8

Topic8.Equationsandinequalities-Overview,Block1,SAS-Exploring"Modelingandsolvinglinearequations,"pp.1-7,Block2,SAS-Exploring"Modelingandsolvinglinearequations,"pp.8-13,Block3,SAS-Exploring"Linearexpressionsandequations,"pp.1-5,Block4,SAS-Exploring"Linearexpressionsandequations,"pp.6-9,Block5,SAS-Constructedresponse,Block6,SAS-Guidedpractice,Block7,SAS

b. Solvewordproblemsleadingtoinequalitiesoftheformpx+q>rorpx+q<r,wherep,q,andrarespecificrationalnumbers.Graphthesolutionsetoftheinequalityandinterpretitinthecontextoftheproblem.Forexample:Asasalesperson,youarepaid$50perweekplus$3persale.Thisweekyouwantyourpaytobeatleast$100.Writeaninequalityforthenumberofsalesyouneedtomake,anddescribethesolutions.

Topic8.Equationsandinequalities-Overview,Block1,SAS-Exploring"Solvingandgraphinginequalities,"pp.1-8,Block8,SAS-Exploring"Solvingandgraphinginequalities,"pp.9-12,Block9,SAS

Remarks/Examples:FluencyExpectationsorExamplesofCulminatingStandardsInsolvingwordproblemsleadingtoone-variableequationsoftheformpx+q=randp(x+q)=r,studentssolvetheequationsfluently.Thiswillrequirefluencywithrationalnumberarithmetic(7.NS.1.1–1.3),aswellasfluencytosomeextentwithapplyingpropertiesoperationstorewritelinearexpressionswithrationalcoefficients(7.EE.1.1).ExamplesofOpportunitiesforIn-DepthFocus

MAFS.7.EE.2.4:



Worktowardmeetingthisstandardbuildsontheworkthatledtomeeting6.EE.2.7andpreparesstudentsfortheworkthatwillleadtomeeting8.EE.3.7.

MAFS.7.G.1.1: Solveproblemsinvolvingscaledrawingsofgeometricfigures,includingcomputingactuallengthsandareasfromascaledrawingandreproducingascaledrawingatadifferentscale.

Topic1.Usingratios-Exploring""Scalingimages,""pp.1-6,Block2,SAS-Exploring"Scalingimages,"pp.7-11,Block3,SAS-Exploring"Scalingimages,"pp.12-14,,SAS4,Block4-MARStask:Mixingpaints,Block6,SAS-Exploring"Applyingproportionalreasoning,"pp.4-6,Block7,SAS-Constructedresponse,Block11,SAS

Topic2.Ratiosandrates-Overview,Block1,SAS-Exploring"Solvingproblemswithunitrates,"pp.1-6,Block6,SAS-Exploring"Solvingproblemswithunitrates,"pp.7-9,Block7,SAS-SummaryandSASBlock7,Block8,SAS

Topic15.Effectsofchange-Overview,Block1,SAS-Exploring"Changesin1-dimensionalmeasurements",Block2,SAS-Exploring"Changesin2-dimensionalmeasurements,"pp.1-7,Block4,SAS-Exploring"Changesin2-dimensionalmeasurements,"pp.8-11,Block5,

MAFS.7.G.1.2: Draw(freehand,withrulerandprotractor,andwithtechnology)geometricshapeswithgivenconditions.Focusonconstructingtrianglesfromthreemeasuresofanglesorsides,noticingwhentheconditionsdetermineauniquetriangle,morethanonetriangle,ornotriangle.

Topic12.Anglesandtriangles-Exploring""Drawingandconstructingtriangles,""pp.1-6,Block5,SAS-Exploring"Drawingandconstructingtriangles,"pp.7-12,Block6,SAS-Exploring"Drawingandconstructingtriangles,"Block7,SAS

MAFS.7.G.1.3: Describethetwo-dimensionalfiguresthatresultfromslicingthree-dimensionalfigures,asinplanesectionsofrightrectangularprismsandrightrectangularpyramids.

Topic14.Prisms,pyramids,andplanesections-Exploring""Planesections,""Block7,SAS

MAFS.7.EE.2.4:



MAFS.7.G.2.4: Knowtheformulasfortheareaandcircumferenceofacircleandusethemtosolveproblems;giveaninformalderivationoftherelationshipbetweenthecircumferenceandareaofacircle.

Topic13.Solvingproblemswith2-Dshapes-Exploring""Frompolygonstocircles,""pp.6-12,Block2,SAS-Exploring"Estimatingareas,"Block3,SAS-Exploring"Areaofpolygonsandcircles,"pp.1-3,Block6,SAS-Exploring"Areaofpolygonsandcircles,"pp.4-6,Block7,SAS

MAFS.7.G.2.5: Usefactsaboutsupplementary,complementary,vertical,andadjacentanglesinamulti-stepproblemtowriteandsolvesimpleequationsforanunknownangleinafigure.

Topic12.Anglesandtriangles-Exploring""Anglerelationships,""pp.1-5,Block1,SAS-Exploring"Anglerelationships,"Block2,SAS-Exploring"Anglerelationships,"pp.6-12,Block3,SAS-Exploring"Anglerelationships,"Block4,SAS

Solvereal-worldandmathematicalproblemsinvolvingarea,volumeandsurfaceareaoftwo-andthree-dimensionalobjectscomposedoftriangles,quadrilaterals,polygons,cubes,andrightprisms.

Topic13.Solvingproblemswith2-Dshapes-Exploring""Frompolygonstocircles,""pp.1-5,Block1,SAS-Exploring"Estimatingareas,"Block3,SAS-Exploring"Areaoftrianglesandquadrilaterals,"pp.1-8,Block4,SAS-Exploring"Areaoftrianglesandquadrilaterals,"pp.9-12,Block5,SAS-Exploring"Areaofpolygonsandcircles,"pp.1-3,Block6,SAS

Topic14.Prisms,pyramids,andplanesections-Exploring""Surfacearea,""pp.1–12,Block1,SAS-Exploring"Surfacearea,Block2,SAS-Exploring"Surfacearea,Block3,SAS-Exploring"Volume,Block4,SAS-Exploring"Volume,Block5,SAS-Constructedresponse,Block6-Exploring"Planesections,"Block7,SAS

Remarks/Examples:ExamplesofOpportunitiesforIn-DepthFocus

MAFS.7.G.2.6:



Worktowardmeetingthisstandarddrawstogethergrades3–6workwithgeometricmeasurement.Applyandextendpreviousunderstandingsofadditionandsubtractiontoaddandsubtractrationalnumbers;representadditionandsubtractiononahorizontalorverticalnumberlinediagram.a. Describesituationsinwhichoppositequantitiescombinetomake0.Forexample,ahydrogenatomhas0chargebecauseitstwoconstituentsareoppositelycharged.

Topic5.Addingandsubtractingintegers-Overview,Block1,SAS-Exploring"Modelingwithalgebratiles,"Block2,SAS-Exploring"Usinganumberline,"pp.1-7,Block3,SAS-Exploring"Usinganumberline,"pp.8-15,Block4,SAS-Exploring"Usingtheverticalnumberline,"pp.1-3,Block5,SAS-Exploring"Usingtheverticalnumberline,"pp.4-8,Block6,SAS

Topic7.Rationalnumbers-Overview,Block1,SAS-Exploring"Operationswithpositiverationalnumbers,"pp.1-7,Block2,-Exploring"Understandingrationalnumberoperations,"pp.1-2,Block4,-Exploring"Understandingrationalnumberoperations,"pp.3-7,Block5,-Exploring"Applyingrationalnumberoperations,"pp.1-8,Block7,SAS

b. Understandp+qasthenumberlocatedadistance|q|fromp,inthepositiveornegativedirectiondependingonwhetherqispositiveornegative.Showthatanumberanditsoppositehaveasumof0(areadditiveinverses).Interpretsumsofrationalnumbersbydescribingreal-worldcontexts.

Topic5.Addingandsubtractingintegers-Overview,Block1,SAS-Exploring"Modelingwithalgebratiles,"Block2,SAS-Exploring"Usinganumberline,"pp.1-7,Block3,SAS-Exploring"Usinganumberline,"pp.8-15,Block4,SAS-Exploring"Usingtheverticalnumberline,"pp.1-3,Block5,SAS-Exploring"Usingtheverticalnumberline,"pp.4-8,Block6,SAS

Topic7.Rationalnumbers-Overview,Block1,SAS-Exploring"Operationswithpositiverationalnumbers,"pp.1-7,Block2,-Exploring"Understandingrationalnumberoperations,"pp.1-2,Block4,-Exploring"Understandingrationalnumberoperations,"pp.3-7,Block5,-Exploring"Applyingrationalnumberoperations,"pp.1-8,Block7,SAS-Exploring"Applyingrationalnumberoperations,"pp.9-12,Block8,SAS

MAFS.7.G.2.6:

MAFS.7.NS.1.1:



c. Understandsubtractionofrationalnumbersasaddingtheadditiveinverse,p–q=p+(–q).Showthatthedistancebetweentworationalnumbersonthenumberlineistheabsolutevalueoftheirdifference,andapplythisprincipleinreal-worldcontexts.

Topic5.Addingandsubtractingintegers-Exploring""Usinganumberline,""pp.8-15,Block4,SAS-Exploring"Usingtheverticalnumberline,"pp.1-3,Block5,SAS-Exploring"Usingtheverticalnumberline,"pp.4-8,Block6,SAS

Topic7.Rationalnumbers-Overview,Block1,SAS-Exploring"Understandingrationalnumberoperations,"pp.1-2,Block4,-Exploring"Understandingrationalnumberoperations,"pp.3-7,Block5,-Exploring"Applyingrationalnumberoperations,"pp.1-8,Block7,SAS-Exploring"Applyingrationalnumberoperations,"pp.9-12,Block8,SAS

d. Applypropertiesofoperationsasstrategiestoaddandsubtractrationalnumbers.

Topic5.Addingandsubtractingintegers-Exploring""Usinganumberline,""pp.8-15,Block4,SAS

Topic7.Rationalnumbers-Exploring""Understandingrationalnumberoperations,""pp.1-2,Block4,

Remarks/Examples:FluencyExpectationsorExamplesofCulminatingStandardsAdding,subtracting,multiplying,anddividingrationalnumbersistheculminationofnumericalworkwiththefourbasicoperations.Thenumbersystemwillcontinuetodevelopingrade8,expandingtobecometherealnumbersbytheintroductionofirrationalnumbers,andwilldevelopfurtherinhighschool,expandingtobecomethecomplexnumberswiththeintroductionofimaginarynumbers.Becausetherearenospecificstandardsforrationalnumberarithmeticinlatergradesandbecausesomuchotherworkingrade7dependsonrationalnumberarithmetic,fluencywithrationalnumberarithmeticshouldbethegoalingrade7.Applyandextendpreviousunderstandingsofmultiplicationanddivisionandoffractionstomultiplyanddividerationalnumbers.

MAFS.7.NS.1.1:

MAFS.7.NS.1.2:



a. Understandthatmultiplicationisextendedfromfractionstorationalnumbersbyrequiringthatoperationscontinuetosatisfythepropertiesofoperations,particularlythedistributiveproperty,leadingtoproductssuchas(–1)(–1)=1andtherulesformultiplyingsignednumbers.Interpretproductsofrationalnumbersbydescribingreal-worldcontexts.

Topic6.Multiplyinganddividingintegers-Exploring""Visualizingmultiplicationanddivisionofintegers,""pp.1-2,Block1,SAS-Exploring"Visualizingmultiplicationanddivisionofintegers,"pp.3-6,Block2,SAS-Exploring"Patternsofmultiplyinganddividingintegers,"pp.1-7,Block3,-Exploring"Patternsinoperationswithexponents,"pp.1-4,Block5,SAS

b. Understandthatintegerscanbedivided,providedthatthedivisorisnotzero,andeveryquotientofintegers(withnon-zerodivisor)isarationalnumber.Ifpandqareintegers,then–(p/q)=(–p)/q=p/(–q).Interpretquotientsofrationalnumbersbydescribingreal-worldcontexts.

Topic6.Multiplyinganddividingintegers-Exploring""Visualizingmultiplicationanddivisionofintegers,""pp.1-2,Block1,SAS-Exploring"Patternsofmultiplyinganddividingintegers,"pp.8-12,Block4,

c Applypropertiesofoperationsasstrategiestomultiplyanddividerationalnumbers.

Topic6.Multiplyinganddividingintegers-Exploring""Patternsofmultiplyinganddividingintegers,""pp.1-7,Block3,-Exploring"Patternsofmultiplyinganddividingintegers,"pp.8-12,Block4,

Topic7.Rationalnumbers-Exploring""Operationswithpositiverationalnumbers,""pp.8-11,Block3,-Exploring"Understandingrationalnumberoperations,"pp.1-2,Block4,-Exploring"Applyingrationalnumberoperations,"pp.1-8,Block7,SAS

d. Convertarationalnumbertoadecimalusinglongdivision;knowthatthedecimalformofarationalnumberterminatesin0soreventuallyrepeats.

Topic7.Rationalnumbers-Exploring""Operationswithpositiverationalnumbers,""pp.1-7,Block2,

Remarks/Examples:FluencyExpectationsorExamplesofCulminatingStandards

MAFS.7.NS.1.2:



Adding,subtracting,multiplying,anddividingrationalnumbersistheculminationofnumericalworkwiththefourbasicoperations.Thenumbersystemwillcontinuetodevelopingrade8,expandingtobecometherealnumbersbytheintroductionofirrationalnumbers,andwilldevelopfurtherinhighschool,expandingtobecomethecomplexnumberswiththeintroductionofimaginarynumbers.Becausetherearenospecificstandardsforrationalnumberarithmeticinlatergradesandbecausesomuchotherworkingrade7dependsonrationalnumberarithmetic,fluencywithrationalnumberarithmeticshouldbethegoalingrade7.Solvereal-worldandmathematicalproblemsinvolvingthefouroperationswithrationalnumbers.

Topic7.Rationalnumbers-Overview,Block1,SAS-Exploring"Operationswithpositiverationalnumbers,"pp.1-7,Block2,-Exploring"Operationswithpositiverationalnumbers,"pp.8-11,Block3,-Exploring"Understandingrationalnumberoperations,"pp.1-2,Block4,-Exploring"Understandingrationalnumberoperations,"pp.3-7,Block5,-Exploring"Understandingrationalnumberoperations,"pp.8-12,Block6,-Exploring"Applyingrationalnumberoperations,"pp.1-8,Block7,SAS-Exploring"Applyingrationalnumberoperations,"pp.9-12,Block8,SAS

Remarks/Examples:ExamplesofOpportunitiesforIn-DepthFocus

Whenstudentsworktowardmeetingthisstandard(whichiscloselyconnectedto7.NS.1.1and7.NS.1.2),theyconsolidatetheirskillandunderstandingofaddition,subtraction,multiplicationanddivisionofrationalnumbers.

MAFS.7.NS.1.3:

MAFS.7.NS.1.2:



MAFS.7.RP.1.1: Computeunitratesassociatedwithratiosoffractions,includingratiosoflengths,areasandotherquantitiesmeasuredinlikeordifferentunits.Forexample,ifapersonwalks1/2mileineach1/4hour,computetheunitrateasthecomplexfraction1/2/1/4milesperhour,equivalently2milesperhour.

Topic2.Ratiosandrates-Overview,Block1,SAS-Exploring"Unitrates,"pp.1-6,Block2,SAS-Constructedresponse1,Block3-Exploring"Unitrates,"pp.7-11,Block4,SAS-Exploring"Unitrates"(reviewofkeyideas),Block5-Exploring"Solvingproblemswithunitrates,"pp.1-6,Block6,SAS-Exploring"Solvingproblemswithunitrates,"pp.7-9,Block7,SAS-Summary,Block7SAS,Block8,SAS

Topic7.Rationalnumbers-Exploring"Operationswithpositiverationalnumbers,"pp.1-7,Block2,-Exploring"Operationswithpositiverationalnumbers,"pp.8-11,Block3,-Exploring"Understandingrationalnumberoperations,"pp.8-12,Block6,-Exploring"Applyingrationalnumberoperations,"pp.1-8,Block7,SAS-Exploring"Applyingrationalnumberoperations,"pp.9-12,Block8,SAS

Recognizeandrepresentproportionalrelationshipsbetweenquantities.a. Decidewhethertwoquantitiesareinaproportionalrelationship,e.g.,bytestingforequivalentratiosinatableorgraphingonacoordinateplaneandobservingwhetherthegraphisastraightlinethroughtheorigin.

Topic3.Patternsinproportionalrelationships-Overview,Block1,SAS-Exploring"Proportionalandnon-proportionalrelationships,"pp.1-4,Block2,SAS-Exploring"Proportionalandnon-proportionalrelationships,"pp.5-9,Block3,SAS-Exploring"Proportionalandnon-proportionalrelationships,"pp.10-12,Block4,SAS-Exploring"Identifyingproportionalrelationships,"pp.1-4,Block5,SAS-Exploring"Identifyingproportionalrelationships,"pp.5-8,Block6,SAS-Summary/Reinforcementactivities,Block7,SAS-LiteracyTask,Block9

MAFS.7.RP.1.2:



b. Identifytheconstantofproportionality(unitrate)intables,graphs,equations,diagrams,andverbaldescriptionsofproportionalrelationships.

Topic2.Ratiosandrates-Overview,Block1,SAS-Exploring"Solvingproblemswithunitrates,"pp.1-6,Block6,SAS-Exploring"Solvingproblemswithunitrates,"pp.7-9,Block7,SAS-SummaryandSASBlock7,,SAS8,Block8

Topic3.Patternsinproportionalrelationships-Overview,Block1,SAS-Exploring"Proportionalandnon-proportionalrelationships,"pp.1-4,Block2,SAS-Exploring"Proportionalandnon-proportionalrelationships,"pp.5-9,Block3,SAS-Exploring"Proportionalandnon-proportionalrelationships,"pp.10-12,Block4,SASExploring"Identifyingproportionalrelationships,"pp.1-4,Block5,SAS-Exploring"Identifyingproportionalrelationships,"pp.5-8,Block6,SAS-Summary/Reinforcementactivities,Block7,SAS-MarsTask:Tilingsquares,Block8-LiteracyTask,Block9,SAS

c. Representproportionalrelationshipsbyequations.Forexample,iftotalcosttisproportionaltothenumbernofitemspurchasedataconstantpricep,therelationshipbetweenthetotalcostandthenumberofitemscanbeexpressedast=pn.

Topic2.Ratiosandrates-Overview,Block1,SAS-Exploring"Solvingproblemswithunitrates,"pp.1-6,Block6,SAS-Exploring"Solvingproblemswithunitrates,"pp.7-9,Block7,SAS-SummaryandSASBlock7,Block8,SAS

Topic3.Patternsinproportionalrelationships-Exploring""Proportionalandnon-proportionalrelationships,""pp.1-4,Block2,SAS-Exploring"Proportionalandnon-proportionalrelationships,"pp.5-9,Block3,SAS-Exploring"Proportionalandnon-proportionalrelationships,"pp.10-12,Block4,SAS-Exploring"Identifyingproportionalrelationships,"pp.1-4,Block5,SAS-Exploring"Identifyingproportionalrelationships,"pp.5-8,Block6,SAS-Summary/Reinforcementactivities,Block7,SAS

MAFS.7.RP.1.2:



d. Explainwhatapoint(x,y)onthegraphofaproportionalrelationshipmeansintermsofthesituation,withspecialattentiontothepoints(0,0)and(1,r)whereristheunitrate.

Topic3.Patternsinproportionalrelationships-Overview,Block1,SAS-Exploring"Proportionalandnon-proportionalrelationships,"pp.1-4,Block2,SAS-Exploring"Proportionalandnon-proportionalrelationships,"pp.5-9,Block3,SAS-Exploring"Identifyingproportionalrelationships,"pp.5-9,Block6,SAS-Summary/Reinforcementactivities,Block7,SAS-LiteracyTask,Block9

Remarks/Examples:ExamplesofOpportunitiesforIn-DepthFocusStudentsingrade7growintheirabilitytorecognize,represent,andanalyzeproportionalrelationshipsinvariousways,includingbyusingtables,graphs,andequations.

MAFS.7.RP.1.2:



MAFS.7.RP.1.3: Useproportionalrelationshipstosolvemultistepratioandpercentproblems.Examples:simpleinterest,tax,markupsandmarkdowns,gratuitiesandcommissions,fees,percentincreaseanddecrease,percenterror.

Topic1.Usingratios-Overview,Block1,SAS-Exploring"Scalingimages,"pp.1-6,Block2,SAS-Exploring"Scalingimages,"pp.7-11,Block3,SAS-Exploring"Scalingimages,"pp.12-14,Block4,SAS-Exploring"Applyingproportionalreasoning,"p.1-3,Block5-MARStask:Mixingpaints,Block6,SAS-Exploring"Applyingproportionalreasoning,"pp.4-6,Block7,SAS-Exploring"Applyingproportionalreasoning,"pp.7-8,Block8,SAS-Guidedpractice,Block9,SAS-Exploring"Applyingproportionalreasoning,"p.9,Block10,SAS-Constructedresponse,Block11,SAS

Topic2.Ratiosandrates-Overview,Block1,SAS-Exploring"Unitrates,"pp.1-6,Block2,SAS-Constructedresponse1,Block3-Exploring"Unitrates,"pp.7-11,Block4,SAS-Exploring"Unitrates"(reviewofkeyideas),Block5-Exploring"Solvingproblemswithunitrates,"pp.1-6,Block6,SAS-Exploring"Solvingproblemswithunitrates,"pp.7-9,Block7,SAS-SummaryandSASBlock7,Block8,SAS

Topic4.Applicationsofpercents-Exploring""Percentofanumber,""p.1,Block1,SAS-Exploring"Percentofanumber,"pp.2-7,Block2,SAS-Exploring"Percentofanumber,"pp.8-9,Block3,SAS-Exploring"Applyingpercentstobusinesssituations,"pp.1-3,Block4,SAS-Exploring"Applyingpercentstobusinesssituations,"pp.4-6,Block5,SAS-Exploring"Applyingpercentstobusinesssituations,"pp.7-10,Block6,SAS-Exploring"Applyingpercentstoconsumersituations,"pp.1-4,Block7,SAS-MarsTask:25%Sale,Block8-Exploring"Applyingpercentstoconsumersituations,"pp.5-7,Block9,SAS-MarsTask:Fudge,Block10-Exploring"Applyingpercentstoconsumersituations,"pp.8-10,Block11,



MAFS.7.SP.1.1: Understandthatstatisticscanbeusedtogaininformationaboutapopulationbyexaminingasampleofthepopulation;generalizationsaboutapopulationfromasamplearevalidonlyifthesampleisrepresentativeofthatpopulation.Understandthatrandomsamplingtendstoproducerepresentativesamplesandsupportvalidinferences.

Topic10.Representingandinterpretingdata-Exploring""Representingdata,""pp.1-3,Block1,SAS-Exploring"Representingdata,"pp.4-6,Block2,SAS-Constructedresponse,Block6,SAS-Exploring"Misleadinggraphs,"pp.8-12,,SAS10,Block10-Writtenreport,Block11-Writtenreport,Block12

MAFS.7.SP.1.2: Usedatafromarandomsampletodrawinferencesaboutapopulationwithanunknowncharacteristicofinterest.Generatemultiplesamples(orsimulatedsamples)ofthesamesizetogaugethevariationinestimatesorpredictions.Forexample,estimatethemeanwordlengthinabookbyrandomlysamplingwordsfromthebook;predictthewinnerofaschoolelectionbasedonrandomlysampledsurveydata.Gaugehowfarofftheestimateorpredictionmightbe.

Topic10.Representingandinterpretingdata-Exploring""Representingdata,""pp.1-3,Block1,SAS-Constructedresponse,Block6,SAS-Writtenreport,Block11-Writtenreport,Block12

MAFS.7.SP.2.3: Informallyassessthedegreeofvisualoverlapoftwonumericaldatadistributionswithsimilarvariabilities,measuringthedifferencebetweenthecentersbyexpressingitasamultipleofameasureofvariability.Forexample,themeanheightofplayersonthebasketballteamis10cmgreaterthanthemeanheightofplayersonthesoccerteam,abouttwicethevariability(meanabsolutedeviation)oneitherteam;onadotplot,theseparationbetweenthetwodistributionsofheightsisnoticeable.

Topic10.Representingandinterpretingdata-Exploring""Representingdata,""pp.1-3,Block1,SAS-Exploring"Representingdata,"pp.7-9,Block3,SAS-Exploring"Representingdata,"pp.10-11,Block4,SAS-Exploring"Interpretinggraphs,"pp.1-4,Block5,SAS-Constructedresponse,Block6,SAS-Exploring"Interpretinggraphs,"pp.5-10,Block7,SAS-MARStask:BestGuess,Block8-Writtenreport,Block11-Writtenreport,Block12

MAFS.7.SP.2.4: Usemeasuresofcenterandmeasuresofvariabilityfornumericaldatafromrandomsamplestodrawinformalcomparativeinferencesabouttwopopulations.Forexample,decidewhetherthewordsinachapterofaseventh-gradesciencebookaregenerallylongerthanthewordsinachapterofafourth-gradesciencebook.

Topic10.Representingandinterpretingdata-Exploring""Representingdata,""pp.7-9,Block3,SAS-Exploring"Interpretinggraphs,"pp.1-4,Block5,SAS-MARStask:BestGuess,Block8-Exploring"Misleadinggraphs,"pp.8-12,Block10,SAS-Writtenreport,Block11



MAFS.7.SP.3.5: Understandthattheprobabilityofachanceeventisanumberbetween0and1thatexpressesthelikelihoodoftheeventoccurring.Largernumbersindicategreaterlikelihood.Aprobabilitynear0indicatesanunlikelyevent,aprobabilityaround1/2indicatesaneventthatisneitherunlikelynorlikely,andaprobabilitynear1indicatesalikelyevent.

Topic9.Probability-Overview,Block1,SAS-Exploring"Definingprobability,"pp.1-2,Block2,SAS-Exploring"Definingprobability,"pp.3-5,Block3,SAS-Exploring"Definingprobability,"pp.6-10,Block4,SAS-MARStask:Counters,Block6-Exploring"Probabilityofcompoundevents,"pp.9-10,Block10,SAS

Topic11.Designingexperiments-Exploring""Cerealboxprize,""Block3,SAS-Exploring"Simulatingbaseballseasons,"Summary,Block4,SAS

MAFS.7.SP.3.6: Approximatetheprobabilityofachanceeventbycollectingdataonthechanceprocessthatproducesitandobservingitslong-runrelativefrequency,andpredicttheapproximaterelativefrequencygiventheprobability.Forexample,whenrollinganumbercube600times,predictthata3or6wouldberolledroughly200times,butprobablynotexactly200times.

Topic9.Probability-Overview,Block1,SAS-Exploring"Definingprobability,"pp.3-5,Block3,SAS-Exploring"Probabilityofcompoundevents,"pp.1-4,Block7,SAS-Exploring"Probabilityofcompoundevents,"pp.5-8,Block8,SAS-Exploring"Probabilityofcompoundevents,"pp.9-10,Block10,SAS-Exploring"Probabilityofcompoundevents,"pp.11-13,Block11,SAS

Topic11.Designingexperiments-Exploring""Simulations,""pp.1-2,Block1,SAS-Exploring"Simulations,"pp.3-7,Block2,SAS-Exploring"Cerealboxprize,"Block3,SAS

Developaprobabilitymodelanduseittofindprobabilitiesofevents.Compareprobabilitiesfromamodeltoobservedfrequencies;iftheagreementisnotgood,explainpossiblesourcesofthediscrepancy.

MAFS.7.SP.3.7:



a. Developauniformprobabilitymodelbyassigningequalprobabilitytoalloutcomes,andusethemodeltodetermineprobabilitiesofevents.Forexample,ifastudentisselectedatrandomfromaclass,findtheprobabilitythatJanewillbeselectedandtheprobabilitythatagirlwillbeselected.

Topic9.Probability-Exploring"Definingprobability,"pp.1-2,Block2,SAS-Exploring"Definingprobability,"pp.3-5,Block3,SAS-Exploring"Definingprobability,"pp.6-10,Block4,SAS-Exploring"Definingprobability,"pp.11-13,Block5,SAS-MARStask:Counters,Block6,SAS-Exploring"Probabilityofcompoundevents,"pp.1-4,Block7,SAS-Exploring"Probabilityofcompoundevents,"pp.5-8,Block8,SAS-Exploring"Probabilityofcompoundevents,"pp.9-10,Block10,SAS-ExploringProbabilityofcompoundevents,"pp.11-13,Block11,SAS-Exploring""Dependentevents,""Block12,SAS

b. Developaprobabilitymodel(whichmaynotbeuniform)byobservingfrequenciesindatageneratedfromachanceprocess.Forexample,findtheapproximateprobabilitythataspinningpennywilllandheadsuporthatatossedpapercupwilllandopen-enddown.Dotheoutcomesforthespinningpennyappeartobeequallylikelybasedontheobservedfrequencies?

Topic9.Probability-Overview,Block1,SAS-Exploring"Definingprobability,"pp.1-2,Block2,SAS-Exploring"Definingprobability,"pp.3-5,Block3,SAS-Exploring"Definingprobability,"pp.6-10,Block4,SAS-Exploring"Probabilityofcompoundevents,""pp.5-8,Block8,SAS-Exploring"Probabilityofcompoundevents,""pp.9-10,Block10,SAS-Exploring"Probabilityofcompoundevents,""pp.11-13,Block11,SAS-Exploring"Dependentevents,""Block12,SAS

Findprobabilitiesofcompoundeventsusingorganizedlists,tables,treediagrams,andsimulation.a. Understandthat,justaswithsimpleevents,theprobabilityofacompoundeventisthefractionofoutcomesinthesamplespaceforwhichthecompoundeventoccurs.

Topic9.Probability-Exploring""Probabilityofcompoundevents,""pp.5-8,Block8,SAS-Exploring"Probabilityofcompoundevents,"pp.9-10,Block10,SAS-Exploring"Probabilityofcompoundevents,"pp.11-13,Block11,SAS-Exploring"Dependentevents,"Block12,SAS

b. Representsamplespacesforcompoundeventsusingmethodssuchasorganizedlists,tablesandtreediagrams.Foraneventdescribedineverydaylanguage(e.g.,“rollingdoublesixes”),identifytheoutcomesinthesamplespacewhichcomposetheevent.

Topic9.Probability-Exploring""Probabilityofcompoundevents,""pp.1-4,Block7,SAS-Exploring"Probabilityofcompoundevents,"pp.5-8,Block8,SAS-MARStask:Duckgame,Block9-Exploring"Probabilityofcompoundevents,"pp.9-10,Block10,SAS-Exploring"Probabilityofcompoundevents,"pp.11-13,Block11,SAS-Exploring"Dependentevents,"Block12,SAS

MAFS.7.SP.3.7:

MAFS.7.SP.3.8:



c. Designanduseasimulationtogeneratefrequenciesforcompoundevents.Forexample,userandomdigitsasasimulationtooltoapproximatetheanswertothequestion:If40%ofdonorshavetypeAblood,whatistheprobabilitythatitwilltakeatleast4donorstofindonewithtypeAblood?

Topic11.Designingexperiments-Exploring""Simulations,""pp.1-2,Block1,SAS-Exploring"Simulations,"pp.3-7,Block2,SAS-Exploring"Cerealboxprize,"Block3,SAS-Exploring"Simulatingbaseballseasons,"Summary,Block4,SAS

Makesenseofproblemsandpersevereinsolvingthem.

Mathematicallyproficientstudentsstartbyexplainingtothemselvesthemeaningofaproblemandlookingforentrypointstoitssolution.Theyanalyzegivens,constraints,relationships,andgoals.Theymakeconjecturesabouttheformandmeaningofthesolutionandplanasolutionpathwayratherthansimplyjumpingintoasolutionattempt.Theyconsideranalogousproblems,andtryspecialcasesandsimplerformsoftheoriginalprobleminordertogaininsightintoitssolution.Theymonitorandevaluatetheirprogressandchangecourseifnecessary.Olderstudentsmight,dependingonthecontextoftheproblem,transformalgebraicexpressionsorchangetheviewingwindowontheirgraphingcalculatortogettheinformationtheyneed.Mathematicallyproficientstudentscanexplaincorrespondencesbetweenequations,verbaldescriptions,tables,andgraphsordrawdiagramsofimportantfeaturesandrelationships,graphdata,andsearchforregularityortrends.Youngerstudentsmightrelyonusingconcreteobjectsorpicturestohelpconceptualizeandsolveaproblem.Mathematicallyproficientstudentschecktheiranswerstoproblemsusingadifferentmethod,andtheycontinuallyaskthemselves,“Doesthismakesense?”Theycanunderstandtheapproachesofotherstosolvingcomplexproblemsandidentifycorrespondencesbetweendifferentapproaches.

Topic1.Usingratios-MARStask:Mixingpaints,Block5-MARStask:Cereal,Block7

Topic2.Ratiosandrates-Exploring“Unitrates”page7,Block4,SAS

Topic9.Probability-MARStask:Duckgame,Block9

Topic10.Representingandinterpretingdata-MARStask:Animals,Block3

Topic11.Designingexperiments-Constructedresponse

MAFS.7.SP.3.8:

MAFS.K12.MP.1.1:



Reasonabstractlyandquantitatively.Mathematicallyproficientstudentsmakesenseofquantitiesandtheirrelationshipsinproblemsituations.Theybringtwocomplementaryabilitiestobearonproblemsinvolvingquantitativerelationships:theabilitytodecontextualize—toabstractagivensituationandrepresentitsymbolicallyandmanipulatetherepresentingsymbolsasiftheyhavealifeoftheirown,withoutnecessarilyattendingtotheirreferents—andtheabilitytocontextualize,topauseasneededduringthemanipulationprocessinordertoprobeintothereferentsforthesymbolsinvolved.Quantitativereasoningentailshabitsofcreatingacoherentrepresentationoftheproblemathand;consideringtheunitsinvolved;attendingtothemeaningofquantities,notjusthowtocomputethem;andknowingandflexiblyusingdifferentpropertiesofoperationsandobjects.

Topic1.Usingratios-Exploring“Proportionalreasoningindifferentsituations”page6-Exploring“Applyingproportionalreasoning”pages1,6

Topic3.Patternsinproportionalrelationships-Exploring“Proportionalandnon-proportionalrelationships”page5,Block3,SAS

Topic9.Probability-Exploring“Definingprobability”page3,Block3,SAS

Topic8.Equationsandinequalities-Exploring“Modelingandsolvinglinearequations”page1,Block2,SAS

Topic12.Anglesandtriangles-Exploring“Anglerelationships”pages7-8,Block3,SAS

MAFS.K12.MP.2.1:



Constructviableargumentsandcritiquethereasoningofothers.

Mathematicallyproficientstudentsunderstandandusestatedassumptions,definitions,andpreviouslyestablishedresultsinconstructingarguments.Theymakeconjecturesandbuildalogicalprogressionofstatementstoexplorethetruthoftheirconjectures.Theyareabletoanalyzesituationsbybreakingthemintocases,andcanrecognizeandusecounterexamples.Theyjustifytheirconclusions,communicatethemtoothers,andrespondtotheargumentsofothers.Theyreasoninductivelyaboutdata,makingplausibleargumentsthattakeintoaccountthecontextfromwhichthedataarose.Mathematicallyproficientstudentsarealsoabletocomparetheeffectivenessoftwoplausiblearguments,distinguishcorrectlogicorreasoningfromthatwhichisflawed,and—ifthereisaflawinanargument—explainwhatitis.Elementarystudentscanconstructargumentsusingconcretereferentssuchasobjects,drawings,diagrams,andactions.Suchargumentscanmakesenseandbecorrect,eventhoughtheyarenotgeneralizedormadeformaluntillatergrades.Later,studentslearntodeterminedomainstowhichanargumentapplies.Studentsatallgradescanlistenorreadtheargumentsofothers,decidewhethertheymakesense,andaskusefulquestionstoclarifyorimprovethearguments.

Topic1.Usingratios-MARStask:Mixingpaints,Block5-MARStask:Cereal,Block7

Topic2.Ratiosandrates-Exploring“Unitrates”page7,Block4

Topic3.PatternsInproportionalrelationships-Exploring“Proportionalandnon-proportionalrelationships”page6,Block3,SAS

Topic8.Equationsandinequalities-Constructedresponse1,Block6

Topic12.Anglesandtriangles-Block7,StudentActivitySheet

Topic10.Representingandinterpretingdata-MARStask:BestGuess,Block8

MAFS.K12.MP.3.1:



Modelwithmathematics.Mathematicallyproficientstudentscanapplythemathematicstheyknowtosolveproblemsarisingineverydaylife,society,andtheworkplace.Inearlygrades,thismightbeassimpleaswritinganadditionequationtodescribeasituation.Inmiddlegrades,astudentmightapplyproportionalreasoningtoplanaschooleventoranalyzeaprobleminthecommunity.Byhighschool,astudentmightusegeometrytosolveadesignproblemoruseafunctiontodescribehowonequantityofinterestdependsonanother.Mathematicallyproficientstudentswhocanapplywhattheyknowarecomfortablemakingassumptionsandapproximationstosimplifyacomplicatedsituation,realizingthatthesemayneedrevisionlater.Theyareabletoidentifyimportantquantitiesinapracticalsituationandmaptheirrelationshipsusingsuchtoolsasdiagrams,two-waytables,graphs,flowchartsandformulas.Theycananalyzethoserelationshipsmathematicallytodrawconclusions.Theyroutinelyinterprettheirmathematicalresultsinthecontextofthesituationandreflectonwhethertheresultsmakesense,possiblyimprovingthemodelifithasnotserveditspurpose.

Topic1.Usingratios-Exploring“Applyingproportionalreasoning”page1-MARStask:Cereal,Block7

Topic3.Patternsinproportionalrelationships-MARStask:TilingSquares,Block8

Topic5.Addingandsubtractingintegers-Exploring“Usingthenumberline”pages1-4-Exploring“Usingtheverticalnumberline”page1

Topic9.Probability-MARStask:Counters,Block6

Topic12.Anglesandtriangles-Block2,StudentActivitySheet

Topic13.Solvingproblemswith2-Dshapes-Exploring“Estimatingareas”page4,Block3,SAS

MAFS.K12.MP.4.1:



Useappropriatetoolsstrategically.

Mathematicallyproficientstudentsconsidertheavailabletoolswhensolvingamathematicalproblem.Thesetoolsmightincludepencilandpaper,concretemodels,aruler,aprotractor,acalculator,aspreadsheet,acomputeralgebrasystem,astatisticalpackage,ordynamicgeometrysoftware.Proficientstudentsaresufficientlyfamiliarwithtoolsappropriatefortheirgradeorcoursetomakesounddecisionsaboutwheneachofthesetoolsmightbehelpful,recognizingboththeinsighttobegainedandtheirlimitations.Forexample,mathematicallyproficienthighschoolstudentsanalyzegraphsoffunctionsandsolutionsgeneratedusingagraphingcalculator.Theydetectpossibleerrorsbystrategicallyusingestimationandothermathematicalknowledge.Whenmakingmathematicalmodels,theyknowthattechnologycanenablethemtovisualizetheresultsofvaryingassumptions,exploreconsequences,andcomparepredictionswithdata.Mathematicallyproficientstudentsatvariousgradelevelsareabletoidentifyrelevantexternalmathematicalresources,suchasdigitalcontentlocatedonawebsite,andusethemtoposeorsolveproblems.Theyareabletousetechnologicaltoolstoexploreanddeepentheirunderstandingofconcepts.

Topic8.Equationsandinequalities-Exploring“Solvingandgraphinginequalities”page11,Block9,SAS

Topic10.Representingandinterpretingdata-Exploring“Representingdata”page9,Block3,SAS

Topic12.Anglesandtriangles-Exploring“Anglerelationships”page3,panels5and7-Block7,StudentActivitySheet

MAFS.K12.MP.5.1:



Attendtoprecision.

Mathematicallyproficientstudentstrytocommunicatepreciselytoothers.Theytrytousecleardefinitionsindiscussionwithothersandintheirownreasoning.Theystatethemeaningofthesymbolstheychoose,includingusingtheequalsignconsistentlyandappropriately.Theyarecarefulaboutspecifyingunitsofmeasure,andlabelingaxestoclarifythecorrespondencewithquantitiesinaproblem.Theycalculateaccuratelyandefficiently,expressnumericalanswerswithadegreeofprecisionappropriatefortheproblemcontext.Intheelementarygrades,studentsgivecarefullyformulatedexplanationstoeachother.Bythetimetheyreachhighschooltheyhavelearnedtoexamineclaimsandmakeexplicituseofdefinitions.

Topic1.Usingratios-Exploring“Proportionalreasoningindifferentsituations”page4,Block2,SAS-MARStask:Cereal,Block7Topic4.Applicationsofpercents-Exploring“Applyingpercentstobusinesssituations”pages4-6,Block5,SAS-MARStask:25%Sale,Block8

Topic7.Rationalnumbers-Exploring“Applyingrationalnumberoperations”page6,Block7,SAS

Topic13.Solvingproblemswith2-Dshapes-Constructedresponse1-3

Lookforandmakeuseofstructure.

Mathematicallyproficientstudentslookcloselytodiscernapatternorstructure.Youngstudents,forexample,mightnoticethatthreeandsevenmoreisthesameamountassevenandthreemore,ortheymaysortacollectionofshapesaccordingtohowmanysidestheshapeshave.Later,studentswillsee7×8equalsthewellremembered7×5+7×3,inpreparationforlearningaboutthedistributiveproperty.Intheexpressionx²+9x+14,olderstudentscanseethe14as2×7andthe9as2+7.Theyrecognizethesignificanceofanexistinglineinageometricfigureandcanusethestrategyofdrawinganauxiliarylineforsolvingproblems.Theyalsocanstepbackforanoverviewandshiftperspective.Theycanseecomplicatedthings,suchassomealgebraicexpressions,assingleobjectsorasbeingcomposedofseveralobjects.Forexample,theycansee5–3(x–y)²as5minusapositivenumbertimesasquareandusethattorealizethatitsvaluecannotbemorethan5foranyrealnumbersxandy.

Topic4.Applicationsofpercents-Overviewpage3,Block1,SAS

Topic8.Equationsandinequalities-Exploring“Linearexpressionsandequations”page1,Block4,SAS-Constructedresponse1,Block6-Exploring“Solvingandgraphinginequalities”page5,Block8,SAS

Topic12.Anglesandtriangles-Exploring“Anglerelationships”pages7-8,Block3,SAS

Topic13.Solvingproblemswith2-Dshapes-Exploring“Frompolygonstocircles”pages6-12,Block2,SAS

MAFS.K12.MP.6.1:

MAFS.K12.MP.7.1:



Lookforandexpressregularityinrepeatedreasoning.Mathematicallyproficientstudentsnoticeifcalculationsarerepeated,andlookbothforgeneralmethodsandforshortcuts.Upperelementarystudentsmightnoticewhendividing25by11thattheyarerepeatingthesamecalculationsoverandoveragain,andconcludetheyhavearepeatingdecimal.Bypayingattentiontothecalculationofslopeastheyrepeatedlycheckwhetherpointsareonthelinethrough(1,2)withslope3,middleschoolstudentsmightabstracttheequation(y–2)/(x–1)=3.Noticingtheregularityinthewaytermscancelwhenexpanding(x–1)(x+1),(x–1)(x²+x+1),and(x–1)(x³+x²+x+1)mightleadthemtothegeneralformulaforthesumofageometricseries.Astheyworktosolveaproblem,mathematicallyproficientstudentsmaintainoversightoftheprocess,whileattendingtothedetails.Theycontinuallyevaluatethereasonablenessoftheirintermediateresults.

Topic3.Patternsinproportionalrelationships-MARStask:TilingSquares,Block8

Topic8.Equationsandinequalities-Exploring“Modelingandsolvinglinearequations”pages1-8

Topic13.Solvingproblemswith2-Dshapes-Exploring“Frompolygonstocircles”pages6-12,Block2,SAS

LAFS.68.RST.1.3: Followpreciselyamultistepprocedurewhencarryingoutexperiments,takingmeasurements,orperformingtechnicaltasks.

Topic11:Representingandinterpretingdata-Exploring"Representingdata,"page6

LAFS.68.RST.2.4: Determinethemeaningofsymbols,keyterms,andotherdomain-specificwordsandphrasesastheyareusedinaspecificscientificortechnicalcontextrelevanttogrades6–8textsandtopics.

Topic16:Anglesandtriangles-Overview,pp.1-3,SAS,Block1

LAFS.68.RST.3.7: Integratequantitativeortechnicalinformationexpressedinwordsinatextwithaversionofthatinformationexpressedvisually(e.g.,inaflowchart,diagram,model,graph,ortable).

Topic11:Representingandinterpretingdata-Exploring"Interpretinggraphs,"pp.1-4

Writeargumentsfocusedondiscipline-specificcontent.a. Introduceclaim(s)aboutatopicorissue,acknowledgeanddistinguishtheclaim(s)fromalternateoropposingclaims,andorganizethereasonsandevidencelogically.

Topic4.Applicationsofpercents-MARSTask"25%Sale"-MARSTask"Fudge"

MAFS.K12.MP.8.1:

LAFS.68.WHST.1.1:



b. Supportclaim(s)withlogicalreasoningandrelevant,accuratedataandevidencethatdemonstrateanunderstandingofthetopicortext,usingcrediblesources.

c. Usewords,phrases,andclausestocreatecohesionandclarifytherelationshipsamongclaim(s),counterclaims,reasons,andevidence.d. Establishandmaintainaformalstyle.e. Provideaconcludingstatementorsectionthatfollowsfromandsupportstheargumentpresented.

LAFS.68.WHST.2.4: Produceclearandcoherentwritinginwhichthedevelopment,organization,andstyleareappropriatetotask,purpose,andaudience.


Engageeffectivelyinarangeofcollaborativediscussions(one-on-one,ingroups,andteacher-led)withdiversepartnersongrade7topics,texts,andissues,buildingonothers’ideasandexpressingtheirownclearly.a. Cometodiscussionsprepared,havingreadorresearchedmaterialunderstudy;explicitlydrawonthatpreparationbyreferringtoevidenceonthetopic,text,orissuetoprobeandreflectonideasunderdiscussion.b. Followrulesforcollegialdiscussions,trackprogresstowardspecificgoalsanddeadlines,anddefineindividualrolesasneeded.c. Posequestionsthatelicitelaborationandrespondtoothers’questionsandcommentswithrelevantobservationsandideasthatbringthediscussionbackontopicasneeded.d. Acknowledgenewinformationexpressedbyothersand,whenwarranted,modifytheirownviews.

LAFS.7.SL.1.2: Analyzethemainideasandsupportingdetailspresentedindiversemediaandformats(e.g.,visually,quantitatively,orally)andexplainhowtheideasclarifyatopic,text,orissueunderstudy.

Topic15:Effectsofchange-Constructedresponse,page1

LAFS.7.SL.1.3: Delineateaspeaker’sargumentandspecificclaims,evaluatingthesoundnessofthereasoningandtherelevanceandsufficiencyoftheevidence.

Topic5:Applicationofpercent-Constructedresponse,page1


Topic1:Usingratios-MARStask:Mixingpaint,Block5

LAFS.7.SL.1.1:

LAFS.68.WHST.1.1:



LAFS.7.SL.2.4: Presentclaimsandfindings,emphasizingsalientpointsinafocused,coherentmannerwithpertinentdescriptions,facts,details,andexamples;useappropriateeyecontact,adequatevolume,andclearpronunciation.

Topic10:Representingandinterpretingdata-MARStask"BestGuess;"Block8

ELD.K12.ELL.MA.1: Englishlanguagelearnerscommunicateinformation,ideasandconceptsnecessaryforacademicsuccessinthecontentareaofMathematics.

Topic1:Usingratios-MARStask:Mixingpaint,Block6

ELD.K12.ELL.SI.1: Englishlanguagelearnerscommunicateforsocialandinstructionalpurposeswithintheschoolsetting.

Topic9.Probability-MarsTask"Counters,"Block6

Block: Guidance for teacher for a single block of ... · - Exploring ""Angle relationships,"" pp. 1-5, Block 1, SAS - Exploring "Angle relationships," Block 2, SAS - Exploring "Angle

Documents

Block: Guidance for teacher for a single block of ... · - Exploring ""Angle relationships,"" pp. 1-5, Block 1, SAS - Exploring "Angle relationships," Block 2, SAS - Exploring "Angle