Across Grade Coherence and Instructional Practice in ...€¦ · • Identify and reframe deficit...

February2019

AcrossGradeCoherenceandInstructionalPracticeinGrades6–8

ACROSSGRADECOHERENCEINGRADES6–8

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• Takeresponsibilityforyourselfasalearner.

• Honortimeframes(start,end,andactivity).

• Beanactiveandhands-onlearner.

• Usetechnologytoenhancelearning.

• Striveforequityofvoice.

• Contributetoalearningenvironmentinwhichitis“safetonotknow.”

• Identifyandreframedeficitthinkingandspeaking.

NormsThatSupportOurLearning

ThisWeekDay Ideas

Monday FocusandWithinGradeCoherence

Tuesday Rigorandthe MathematicalPractices

Wednesday Across Grade CoherenceandInstructionalPractice

Thursday Adaptation andCurriculumStudy

Friday AdaptationandPractice

“Dothemath”

Connecttoourpractice

Equityforall

• Morning:AcrossGradeCoherenceinGrades6–8

• Afternoon: InstructionalPracticeinGrades6–8

MorningObjectives• Participantswillunderstandandapplylearningprogressionstosupportstudentswhoarebelowgradelevel.

o Participantswillbeabletoidentifyasequenceofprerequisitestandardsnecessaryinmathunderstandingandlearning.

o Participantswillbeabletoidentifyonrampsforteachingmajorworktostudentswithunfinishedlearning.

o Participantswillbeabletoadaptalessonforstudentswithunfinishedlearningbyaddingjust-in-timescaffoldsbasedonlearningprogressions.

o ParticipantswillbeabletoexplainhowattendingtotheshiftofacrossgradecoherenceisanequitablepracticeinStandards-alignedmathinstruction.

MorningAgenda

I. AcrossGradeCoherence

II. VerticalCoherenceChallenge

III. MappingtheProgressions

IV. ToolsforUnderstandingtheProgressions

V. AdaptingLessonsforStudentswithUnfinishedLearning

UnpackingEquity

Equityexistswhenthebiasesderivedfromdominantculturalnormsandvaluesnolongerpredictorinfluencehowonefaresinsociety.

Equitysystematicallypromotesfairandimpartialaccesstorightsandopportunities.

Equitymaylooklikeaddingsupportsandscaffoldsthatresultinfairaccesstoopportunitiesorcreatingopportunitiesforallvoicestobeheard.

Educational Equityensuresthatallchildren—regardlessofcircumstances—arereceivinghigh-quality,grade-level,andstandards-alignedinstructionwithaccesstohigh-qualitymaterialsandresources.

Webecomechangeagentsforeducationalequitywhenweacknowledgethatwearepartofaneducationalsystemthatholdspoliciesandpracticesthatareinherentlyracistandthatwehaveparticipatedinthissystem.Wenowcommittoensuringthatallstudents,regardlessofhowwethinktheycometous,leaveushavinggrownagainstgrade-levelstandardsandconfidentintheirvalueandabilities.

I.AcrossGradeCoherence

Lenapaid$18.96for3poundsofcoffee.

Whatwouldstudentsneedtounderstandaboutproportionalrelationshipstographtherelationshipbetweenthenumberofpoundsofcoffeeandthetotalcost?

Grade6Useratioandratereasoningtosolvereal-worldandmathematicalproblems…bymakingtablesofequivalentratios,findingmissingvaluesintables,andplottingthepairsofvaluesonthecoordinateplane.

Grade8Graphproportionalrelationships,interpretingtheunitrateastheslopeofthegraph;comparedifferentproportionalrelationshipsindifferentways.

Grade7Explainwhatapoint(x,y)onthegraphofaproportionalrelationshipmeansintermsofthesituation,withspecialattentiontothepoints(0,0)and(1,r)wherer istheunitrate.

WhatIstheRightOrder?

“A focused, coherent progression of mathematics learning, with anemphasis on proficiency with key topics, should become the norm inelementary and middle school mathematics curricula. Any approach thatcontinually revisits topics year after year without closure is to be avoided. Bythe term focused, the Panel means that curriculum must include (and engagewith adequate depth) the most important topics underlying success in schoolalgebra. By the term coherent, the Panel means that the curriculum ismarked by effective, logical progressions from earlier, less sophisticatedtopics into later, more sophisticated ones. Improvements like thosesuggested in this report promise immediate positive results with minimaladditional cost.”

–NationalMathematicsAdvisoryPanel

CoherenceIsKey

TheProgressions

AcrossGradeCoherence:Learningiscarefullyconnectedacrossgradessothatstudentscanbuildnewunderstandingontofoundationsbuiltinpreviousyears.

• Inyourgroups,youhave13standardsonpiecesofpaper.MoststandardscomefromtheRatios&ProportionalRelationshipsdomaininGrades6–8.

• Thestandardsarenotlabeled!

• Determinewhichstandardsareprerequisitesforotherstandards.

• Note: Thereismorethanoneverticalstrand.

• Bonus: Canyoudeterminewhichstandardsbelonginwhichgrade?

II.VerticalCoherenceChallenge

Grades4and5

Grade6 Grade7 Grade8 HighSchool

J4.MD.2

B5.NF.3

G5.G.2

F6.RP.2

L6.RP.3a

D7.RP.1

K7.RP.2

M7.RP.3

H7.G.1

C8.F.2

A8.EE.6

I8.EE.8

EF-BF.1

APictureofCoherence

ProgressionsofContent

Howdoesunderstandingtheprogressionofcontentsupportourunderstandingofgrade-levelcontent?

Protocol:

• Identifythreeprerequisitestandards—thestandardsdonothavetobeinthreedifferentgrades.

• Identifytheaspectsofrigorforeachprerequisite.

• Discusswithapartner:1. Howdoeseachprerequisite

supportthestandard?2. Whyisitimportanttopay

attentiontotherigoroftheprerequisitestandard?

III.StandardsMapping

TheStandards:Grade6– 6.EE.B.7Grade7– 7.NS.A.2Grade8– 8.F.A.2

Solvereal-worldandmathematicalproblemsbywritingandsolvingequationsoftheformx +p =q andpx =q forcasesinwhichp,q,andx areallnonnegative rationalnumbers.

Grade6—6.EE.B.7

5.NF.B.4Applyandextendpreviousunderstandingsofmultiplicationtomultiplya fraction orwholenumber byafraction.

6.EE.B.5Understandsolvinganequationorinequalityasaprocessofansweringaquestion:whichvaluesfromaspecifiedset,ifany,maketheequationorinequalitytrue?Usesubstitutiontodeterminewhetheragivennumberinaspecifiedsetmakesanequationorinequalitytrue.

6.NS.A.1Interpretandcomputequotientsof fractions,andsolvewordproblemsinvolvingdivisionoffractionsbyfractions,e.g.,byusing visualfractionmodels andequationstorepresenttheproblem.

Applyandextendpreviousunderstandingsofmultiplicationanddivisionandoffractions tomultiplyanddivide rationalnumbers.

Grade7—7.NS.A.2

6.NS.A.1Interpretandcomputequotientsof fractions,andsolvewordproblemsinvolvingdivisionoffractionsbyfractions,e.g.,byusing visualfractionmodels andequationstorepresenttheproblem.

5.NF.B.3Interpreta fraction asdivisionofthenumeratorbythedenominator(a/b=a÷ b).Solvewordproblemsinvolvingdivisionof wholenumbers leadingtoanswersintheformoffractionsormixednumbers,e.g.,byusing visualfractionmodels orequationstorepresenttheproblem.

5.NF.B.4Applyandextendpreviousunderstandingsofmultiplicationtomultiplya fraction orwholenumber byafraction.

Comparepropertiesoftwofunctionseachrepresentedinadifferentway(algebraically,graphically,numericallyintables,orbyverbaldescriptions).Forexample,givenalinearfunctionrepresentedbyatableofvaluesandalinearfunctionrepresentedbyanalgebraicexpression,determinewhichfunctionhasthegreaterrateofchange.

Grade8—8.F.A.2

7.RP.A.2Recognizeandrepresentproportionalrelationshipsbetweenquantities.

8.F.A.1Understandthatafunctionisarulethatassignstoeachinputexactlyoneoutput.Thegraphofafunctionisthesetoforderedpairsconsistingofaninputandthecorrespondingoutput.

8.EE.B.5Graphproportionalrelationships,interpretingtheunitrateastheslopeofthegraph.Comparetwodifferentproportionalrelationshipsrepresentedindifferentways.Forexample,compareadistance-timegraphtoadistance-timeequationtodeterminewhichoftwomovingobjectshasgreaterspeed.

IV.UnderstandingtheProgressions

TheProgressionsDocuments

WiringDiagram

ContentGuides

UnderstandingtheProgressions

Howdoesunderstandingtheprogressionssupportinstruction?

ACROSSGRADECOHERENCEINGRADESK-2

LeveragingtheProgressions

Howcanweleverageprogressionsofcontenttogiveall studentsaccesstograde-levelcontent?

V.AdaptingLessonsforStudentswithUnfinishedLearning

Protocol:• Review Lesson1andidentify thetargetedstandard.• Identify theprerequisitestandardsfrompriorgradesthatsupportthetargetedstandard.

o Whatistheaspectofrigorforeachprerequisite?• Discuss withapartner:

1. Howdoeseachprerequisitesupportthestandard?2. Howcouldyoustrategicallyusetheseprerequisitestandardsto

supportstudentswhoarenotongradelevel?o Annotate thelessonwithspecificsupports.

• Withyourtable:o Eachpairsharesoutthespecificadaptationsyouandyour

partnermade. Explainwhyyoumadetheseadaptations.

LessonAdaptations

Whattypesofadaptationscouldyouconsideratthelessonlevel?

• Addawarm-upactivitythatconnectstopriorlearning.

• Addasectiontothelessonportiontoaddressprerequisiteskills.

• Adjusttheexamplesand/orproblemsettofocusonprerequisiteskills.

Protocol: time• 10min:Individualworktime• 15min:Partnerwork• 10min:Tableshareout

AdaptingLessonsforStudentswithUnfinishedLearning

GoalsforThisActivity:I. ReviewLesson1andidentify

thetargetedstandard(s).II. Whataretheprerequisite

standardsfrompriorgradesthatsupportthisstandard(s)?

III. Whataspectsofrigorarehighlightedintheprerequisitestandards?

Protocol:• ReviewLesson1andidentifythetargetedstandard.• Identifytheprerequisitestandardsfrompriorgradesthatsupportthetargetedstandard.

o Whatistheaspectofrigorforeachprerequisite?• Discuss withapartner:

supportstudentswithunfinishedlearning?o Annotatethelessonwithspecificsupports.

partnermade.Explainwhyyoumadetheseadaptations.

TransitiontoPartnerTime!30

GoalsforThisActivity:I. Howdotheseprerequisite

standardssupportthegrade-levelstandard(s)?

II. Howcouldyoustrategicallyusetheseprerequisitestandardstosupportstudentswithunfinishedlearning?

o Annotatethelessonwithspecificsupports.

o Whatistheaspectofrigorforeachprerequisite?• Discusswithapartner:

partnermade. Explainwhyyoumadetheseadaptations.

TransitiontoTableShare!

GoalsforThisActivity:o Eachpairsharesoutthespecific

adaptationsmadeandexplainswhytheseadaptationsweremade.

o Whatistheaspectofrigorforeachprerequisite?• Discusswithapartner:

partnermade.Explainwhyyoumadetheseadaptations.

Whatgrade-levelstandarddoesthelessonaddress?Whatistheevidence ofalignmenttothisstandard?

What aretheprerequisitestandardsfrompriorgradesthatsupportthisstandard?

Brainstorm waysyoucouldusetheseprerequisitestosupportstudentswithunfinishedlearninginaccessingthecontentofthislesson.• Annotatethelessonwithspecific

supports.

Summary

• Whatistheshiftofcoherence?

• Howdoescoherencehelpussupportstudentswithunfinishedlearning?

• Howdoesrigorhelpussupportstudentswithunfinishedlearning?

• Howdoesthislearningapplytoyourspecificrole?

ACROSSGRADECOHERENCEINGRADESK-2

Lunch12:00-1:00

Lunch12:00–1:00

INSTRUCTIONALPRACTICEINGRADES6–8

• Morning:AcrossGradeCoherenceinGrades6–8

• Afternoon: InstructionalPracticeinGrades6–8

AfternoonObjectives• ParticipantswillbeabletousetheInstructionalPracticeGuide(IPG)asalessonplanningtoolandacoachingtool.

• Participantswillbeabletoidentifywhere,inlessonsandvideos,teachersengageinCoreActions.

• ParticipantswillbeabletoexplaintherelationshipbetweenCoreActionsandequitableinstructioninStandards-alignedmathinstruction.

I. IntrototheInstructionalPracticeGuide(IPG)

II. CoreActionsinAction!

III. LessonPlanningwiththeIPG

IV. ConnecttoPractice

AfternoonAgenda

INSTRUCTIONALPRACTICEINGRADESK-2

InstructionalPractice...effectiveteachingisthenon-negotiablecorethatensuresthatallstudentslearnmathematicsathighlevels...

–PrinciplestoActions:EnsuringMathematicalSuccessforAll(NCTM)

I.InstructionalPracticeGuide(IPG)

TheInstructionalPracticeGuideincludescoaching andlessonplanning toolstohelpteachersandthosewhosupportteacherstomaketheKeyShiftsininstructionalpracticerequiredbytheStateStandards.

CoreActions

1. EnsuretheworkoftheenactedlessonreflectstheFocus,Coherence,andRigorrequiredbycollege- andcareer-readystandardsinmathematics.

2. Employinstructionalpracticesthatallowallstudentstolearnthecontentofthelesson.

3. Provideallstudentswithopportunitiestoexhibitmathematicalpracticeswhileengagingwiththecontentofthelesson.

CoreAction1

IndicatorsA. Theenactedlessonfocusesonthegrade-levelcluster(s),grade-levelcontent

standard(s),orpart(s)thereof.Mathematicallearninggoal:Standard(s)addressedinthislesson:

B. Theenactedlessonappropriatelyrelatesnewcontenttomathcontentwithinoracrossgrades.

C. Theenactedlessonintentionallytargetstheaspect(s)ofRigor(conceptualunderstanding,proceduralskillandfluency,application)calledforbythestandard(s)beingaddressed.

Circletheaspect(s)ofRigortargetedinthestandard(s)addressedinthislesson:Conceptualunderstanding/Proceduralskillandfluency/ApplicationCircletheaspect(s)ofRigortargetedinthislesson:Conceptualunderstanding/Proceduralskillandfluency/Application

EnsuretheworkoftheenactedlessonreflectstheFocus,Coherence,andRigorrequiredbycollege- andcareer-readystandardsinmathematics.

CoreAction2Employinstructionalpracticesthatallowallstudentstolearnthecontentofthelesson.

IndicatorsA. Theteachermakesthemathematicsofthelessonexplicitthroughthe

useofexplanations,representations,tasks,and/orexamples.B. Theteacherstrengthensallstudents’understandingofthecontentby

strategicallysharingstudents’representationsand/orsolutionmethods.

C. Theteacherdeliberatelychecksforunderstandingthroughoutthelessontosurfacemisconceptionsandopportunitiesforgrowth,andadaptsthelessonaccordingtostudentunderstanding.

D. Theteacherfacilitatesthesummaryofthemathematicswithreferencestostudentworkanddiscussioninordertoreinforcethepurposeofthelesson.

CoreAction3

IndicatorsA. Theteacherprovidesopportunitiesforallstudentstoworkwithandpracticegrade-level

problemsandexercises.Students workwithandpracticegrade-levelproblemsandexercises.

B. Theteachercultivatesreasoningandproblemsolvingbyallowingstudentstoproductivelystruggle.Students persevereinsolvingproblemsinthefaceofdifficulty.

C. Theteacherposesquestionsandproblemsthatpromptstudentstoexplaintheirthinkingaboutthecontentofthelesson.Students sharetheirthinkingaboutthecontentofthelessonbeyondjuststatinganswers.

D. Theteachercreatestheconditionsforstudentconversationswherestudentsareencouragedtotalkabouteachother’sthinking.Students talkandaskquestionsabouteachother’sthinking,inordertoclarifyorimprovetheirownmathematicalunderstanding.

E. Theteacherconnectsanddevelopsstudents’informallanguageandmathematicalideastoprecisemathematicallanguageandideas.Students useincreasinglyprecisemathematicallanguageandideas.

Provideallstudentswithopportunitiestoexhibitmathematicalpracticeswhileengagingwiththecontentofthelesson.

DeeperDivewiththeIPG

SmallGroupProtocol

• ReadtheindicatorsoftheCoreActionforyourgroup.

• Discussthefollowingwithyoursmallgroup:1. HowdoesthisCoreAction(includingthe

indicators)supportteachersandcoachesinbuildingunderstandingofStandards-alignedinstruction?

2. Whataretheessentialteacherpracticesthatsupporttheindicators?

3. HowdoesthisCoreActionsupportequitableinstructionforall students?

TableDiscussionProtocol

• Turnandteach.• Discussthefollowingwithyourtablegroup:

1. HowdoesthistoolsupportteachersandcoachesinbuildingunderstandingofStandards-alignedinstruction?

2. WhatareessentialteacherpracticesthatsupporteachCoreAction?

3. WheredoeseachoftheStandardsforMathematicalPracticeshowupintheIPG?

4. HowdoesthisCoreActionsupportequitableinstructionforall students?

WholeGroupDiscussionProtocol

1. HowdoesthistoolsupportteachersandcoachesinbuildingunderstandingofStandards-alignedinstruction?

2. WheredoeseachoftheStandardsforMathematicalPracticeshowupintheIPG?

3. WhatconnectionsdidyoumakebetweentheCoreActionsandequitableinstructionforall students?

• Usefulinbothplanningandcoaching.

• Evidencefortheindicatorscancomefromlessonmaterials,teacheractions,studentdiscussion,andstudentwork.

• Whenusingasacoachingtool,notallindicatorsmaybeevidentinasingleclassperiod.

• Not tobeusedasanevaluationinstrument.

IPGSummary

WhatCoreActionsarevisible?

II.CoreActionsinAction!

III.LessonPlanningwiththeIPG

HowcanweusetheCoreActionsandindicators?• Planning• Evaluating• Reflecting

LessonPlanningTheCoreActionsshouldbeevidentinplanningandobservableininstruction.

• Whatpartsofthelessonplanarevital toshowevidenceofCoreAction1?Annotatethelessontoshowthese.

• WhataresomeofthethingsyoucoulddotoensurealignmentwiththeindicatorsforCoreActions2and3?

WhattoReview:Grade6,Module1,Lesson2Grade7,Module1,Lesson2Grade8,Module5,Lesson2

Example:Grade7,Module1,Lesson1

LessonPlanning

Protocol: time• 15min:Individualworktime• 10min:Smallgroupcollaboration• 15min:Tableshareout

GoalsforThisActivity:1. Readthelesson.2. AnnotatethelessonforyourCore

Action.• Whatpartsofthelessonplanare

vital toshowevidenceofCoreAction1?

• WhataresomeofthethingsyoucoulddotoensurealignmentwiththeindicatorsforCoreActions2and3?

TransitiontoSmallGroupTime!58

LessonPlanning

GoalsforThisActivity:1. Sharehowyouannotatedthetask

withyourgroup.

TransitiontoTableShare!

LessonPlanning

Goalsforthisactivity:1. Shareyourannotationswiththe

peopleatyourtable.2. Discussandrecord:

• WhatkindsofevidencesupportedtheindicatorsforCA1?

• WhatkindsofactionsdidyouaddtosupportCA2?

• WhatkindsofactionsdidyouaddtosupportCA3?

IV.LessonPlanning

Protocol:

AnnotateyourlessonforeachCoreAction:1. WhatistheevidenceofalignmenttoCoreAction1?Howcanyou

improvealignmenttoCoreAction1?2. Whataresomeofthethingsyoucoulddotoensurealignment

withtheindicatorsforCoreAction2?3. Whataresomeofthethingsyoucoulddotoensurealignment

withtheindicatorsforCoreAction3?

Summary

• HowwilltheCoreActionsimpactyourworkwith creatingand/orcoachingaroundlessonplans,andensuringequitableinstructionforallstudents?

• Howhasyourthinkingchangedaboutlessonplanning?

• HowhavetheShiftsimpactedyourapproachtoinstruction?

HomeworkTopreparefortheworkwewilldotomorrowandFriday:• Read UnderstandingLanguage- PrinciplesfortheDesignofMathematicsCurricula:PromotingLanguageandContentDevelopment.– LocatedinmaterialsforThursday,ontheStandardsInstituteswebsite:standardsinstitutes.org

• Thinkaboutapossibleproblemofpracticethatyouarestrugglingwithrelatedtothecontentwehavecoveredthisweek,thatyouwouldwanttoproblemsolveonFriday.Share thisproblemofpracticewithmetodaybeforeyouleave.– TheProblemofPracticeQ&AwilltakeplaceFridayafternoon.

FeedbackPleasefilloutthesurveylocatedhere:www.standardsinstitutes.org.

• Click“Winter2019”onthetopofthepage.• Click“Details”onthecenterofthepage.

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