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ArtsECOFellowsJoelleWorm,ArtsECODirector

UWMLessonPlanTemplate(adaptedfromPSOAArtEducationArea)

Name: OliviaPeterson Email: oap@uwm.eduLessonTitle: TransformationswithinComposition:AnArtisticApplicationtoGeometricTransformationsLevel/Grade/Age: 8thgradeGeometry

BIGIDEA(Describehowthebigideaisimportanttothisagegroupinrelationtostudentassetsandthecontentarea):Inthislessonongeometrictransformations,studentswillbeusethefourbasictypesoftransformationsandtheircorrespondencetoshapesonthecoordinateplanetocreateaworkofartutilizingeachofthedifferenttransformations.Priortotheprojectstudentswillbepresentedwithvariousexamplesofhowthisgeometricconceptisincorporatedintoart,especiallyinrelationtotheideaofrepetitionandperspectiveinartwork.Instructorswillinquireandexplorewhateachkindsoftransformationmaybeusedforincontemporaryartwork.Uponcompletionstudentswillhaveproficientcomprehensionandexecutionofgeometrictransformationsintheplane,createdaworkofartrepresentingtheseideasinart,andproducedawrittendescriptionoftheirartworkincludinghowtheyutilizedthedifferenttransformationsintheirartwork.Inaddition,studentswillbeaskedtofindaworkofartanddescribehowitutilizesthedifferentgeometrictranslationsinashort-writtenobservation.OBJECTIVESANDNATIONALSTANDARDS:http://www.nationalartsstandards.org/Art

CreatingAnchorStandard2:Organizeanddevelopartisticideasandwork.EnduringUnderstanding:Artistsanddesignersexperimentwithforms,structures,materials,concepts,media,andart-makingapproachesHowdoartistsanddesignerslearnfromtrialanderror?

- VA:Cr2.1.8aDemonstratewillingnesstoexperiment,innovate,andtakeriskstopursueideas,forms,andmeaningsthatemergeintheprocessofart-makingordesigning.

EnduringUnderstanding:Peoplecreateandinteractwithobjects,places,anddesignthatdefine,shape,enhance,andempowertheirlives.Howdoobjects,places,anddesignshapelivesandcommunities?Howdoartistsanddesignersdeterminegoalsfordesigningorredesigningobjects,places,orsystems?Howdoartistsanddesignerscreateworksofartordesignthateffectivelycommunicate?

- VA:Cr2.3.8aSelect,organize,anddesignimagesandwordstomakevisuallyclearandcompellingpresentations.

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PresentingAnchorStandard4:Select,analyze,andinterpretartisticworkforpresentation.�EnduringUnderstanding:Artistsandotherpresentersconsidervarioustechniques,methods,venues,andcriteriawhenanalyzing,selecting,andcuratingobjectsartifacts,andartworksforpreservationandpresentation.Whatcriteria,methods,andprocessesareusedtoselectworkforpreservationorpresentation?Whydopeoplevalueobjects,artifacts,andartworks,andselectthemforpresentation?

- VA:Pr4.1.7aCompareandcontrasthowtechnologieshavechangedthewayartworkispreserved,presented,andexperienced.

RespondingAnchorStandard8:Interpretintentandmeaninginartisticwork.EnduringUnderstanding:Peoplegaininsightsintomeaningsofartworksbyengagingintheprocessofartcriticism.Howdoesknowingandusingvisualartvocabularieshelpusunderstandandinterpretworksofart?

- VA:Re8.1.7aInterpretartbyanalyzingart-makingapproaches,thecharacteristicsofformandstructure,relevantcontextualinformation,subjectmatter,anduseofmediatoidentifyideasandmoodconveyed.

Connecting AnchorStandard10:Synthesizeandrelateknowledgeandpersonalexperiencestomakeart.EnduringUnderstanding:Throughart-making,peoplemakemeaningbyinvestigatinganddevelopingawarenessofperceptions,knowledge,andexperiences.Howdoesengagingincreatingartenrichpeople'slives?Howdoesmakingartattunepeopletotheirsurroundings?

- VA:Cn10.1.5aApplyformalandconceptualvocabulariesofartanddesigntoviewsurroundingsinnewwaysthroughart-making.

MathCommonCoreStateStandards:Grade8Geometry

Understandcongruenceandsimilarityusingphysicalmodels,transparencies,orgeometrysoftware.

CCSS.MATH.CONTENT.8.G.A.1Verifyexperimentallythepropertiesofrotations,reflections,andtranslations:

CCSS.MATH.CONTENT.8.G.A.1.ALinesaretakentolines,andlinesegmentstolinesegmentsofthesamelength.

CCSS.MATH.CONTENT.8.G.A.1.BAnglesaretakentoanglesofthesamemeasure.

CCSS.MATH.CONTENT.8.G.A.1.CParallellinesaretakentoparallellines.

CCSS.MATH.CONTENT.8.G.A.2Understandthatatwo-dimensionalfigureiscongruenttoanotherifthesecondcanbeobtainedfromthefirstbyasequenceofrotations,reflections,andtranslations;giventwocongruentfigures,describeasequencethatexhibitsthecongruencebetweenthem.

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CCSS.MATH.CONTENT.8.G.A.3Describetheeffectofdilations,translations,rotations,andreflectionsontwo-dimensionalfiguresusingcoordinates.

CCSS.MATH.CONTENT.8.G.A.4Understandthatatwo-dimensionalfigureissimilartoanotherifthesecondcanbeobtainedfromthefirstbyasequenceofrotations,reflections,translations,anddilations;giventwosimilartwo-dimensionalfigures,describeasequencethatexhibitsthesimilaritybetweenthem.

LANGUAGEFUNCTIONUSEDTHROUGHOUTLESSON:Typeoflanguagefunction:http://www.eldstrategies.com/languagefunctions.html

Describingspecialrelations,askquestions,classifyingandidentifying,analyzing,summarizing

Emphasisoflanguagefunction(describethemainpurposeofusingthislanguagefunctionforyourlesson):

Bydescribingthespecialrelationsthatarepresentingeometrictransformationsstudentswillbeabletobetterrelaytheirknowledgeonthisconceptanditsrelatedideassuchascongruenceandsimilarityandwillalsobeabletomoreaccuratelyrepresenttheseconceptsonthecoordinateplane

Studentswillbeencouragedtoaskquestionstodispelmisconceptionsandtofurthertheirknowledgeandcuriosity.

Classifyingandidentifyingisthemainfunctionbeingaskedofstudentsinthislesson.Bytheendofthisprojectstudentsshouldbeabletoclassifyandidentifythedifferenttransformationsnotonlyinartworkandimages,butalsoonthegeometricplaneandintherealworld.

Studentswillbeaskedtoanalyzedifferentworksofartinordertopickoutdifferenttransformationswithintheimage.Thiswillhelpenhancestudentscriticalthinking,reasoningandobservationskills.Thisisalsoimportantbecauseitgivesstudentsachangetoobserveandanalyzetheseoccurrenceintherealworld,givingmathapracticalapplication.

Summarizingtheirfindingwillhelpstudentssolidifytheinformationandrelationshipstheyhavebeenworkingonfinding.

Wherelanguagefunctionwillbepracticed(i.e.,throughwriting,speaking,artmaking):

Describing,classifying,andidentifyingwillbedoneinclassroomdiscussionaboutthedifferenttransformations.Thisiswhereitisimportanttoshowstudentsvariousworksofartinorderforthemtoidentifythetransformationsaloudthemselves.Theywillalsobeanalyzingandsummarizingintheirtwowrittenworkstobeturnedinuponcompletionoftheirimage.

UNITorLESSONDETAIL(provideforeachlessonsession):Motivation/introduction:

Anintroductorylessonwillbegivenpriortointroduceandfamiliarizestudentswithtransformationssuchastranslations,rotations,reflections,anddilations.Examplesofeachcanbedrawnonboardorshowninapowerpoint.Referencetothecoordinateplanecanalsobehelpfulaswellasconsiderablementionanddiscussionofthefirstthreebeforementionofdilations.Askstudentstoobservehowthelengthoflinesandsegments,aswellasanglemeasure,ispreservedinthefirstthreetransformations.Useoftransparentpapercanbedemonstratedtoshowhowitcaneasilypreservethecongruenceofshapeswhenperformingtransformationsonpaper,specificallywithreflections.

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Studentscanbeshownimagessimilartothebicycleimagetoseethatthisconcepthasrelevantapplicationsindesign.Importantemphasiscanbemadeontherelationshipbetweenrepetitionandperspectiveandthegeometrictransformations.Moreartworkorexamplesofeverydayobjectscanbeshowntobridgetheconnectionofthisconceptinart.AspecificexamplecouldincludeworkbyAlanKenny,firstgivingspecificexamplesofthetransformationsusedinartandthenmorebroadpictures,givingstudentstheopportunitytopickoutthetransformationsthemselves.

Examplesthatcanbeusedasbasicexamplesofreflection(left)andtranslations(right)

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Exampleofrotation(indancingfiguredtorightandleft)

Exampleofreflectioninthewater

Dilationandtranslationintheballoons.(evenreflectioninthemusicnotes)

ArtMaking: Supplies:Studentscanusetransparentpapertoexperimentwithdrawingthedifferenttransformations.Willrequiregraphpaper(orprinterpaper)forthefinalimageaswellascoloredpencils,markers,orcrayonsthatcanbeutilizedaswellastraditionalpensandpencilsforthefinalimage.Accesstocomputersmaybenecessaryforfindingreferenceimagesaswellasanimagetowriteafinalobservationon.Teacherinstruction:Givestudentstheoptiontouseeithergraphpaperorprinterpapertocreateaworkofartthatincorporatesoneofeachofthefourtransformations.Eachtransformationshouldbeutilizedandspecificallyidentifiable,exceptintheinstanceofatranslationwherestudentsmaypairadifferenttransformationalongwithatranslation.

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Objective:Createanimageoneithergraphpaperorprinterpaperthatincorporatesatleastoneelementofeachgeometrictransformation,translations,reflections,rotations,anddilations.Specificattentionshouldbepaidtothewayinwhichthetransformationslendthemselvestothecomposition.Studentsatwork:Studentsmaywanttoexperimentwithtransparentpaperanddrawpreliminarysketchesbeforestartingontheirfinalimage,instructorsmaysetupachecktoensurealltransformationsareusedbeforebeginningonthefinalimage.Studentswillbeaskedtorecordandreflectonhoweachtransformationisbeingused,itshouldbenotedthattransformationsdonotneedtobelimitedtosingleobject,asinreflectionscanbeusedinawaterreflectionlikeinexamplesshown.Theirworkcanbeabstractorrepresentational.Instructorsmayaidandprovideexamplesofadditionalartworkorartistssothatstudentshaveresourcestofindimagestowritetheirfinalobservationon.Possiblyatriptothelibraryorneighboringartmuseummaybeawayofexposingstudentstodifferentartworks.Studentsshouldbealloweddesignatedresearchtimetofindimagesandconsultwiththeinstructor.Closure:Uponcompletionstudentswillturnintheirfinalimagealongwithawrittenexplanationoftheirartworkincludinghowandwherethedifferenttransformationswereutilized.Studentsmaywishtocommentontheeffectivenessofthetransformationsandhowtheylentthemselvestothecompositionoftheimage.Studentswillalsoturninanadditionalwrittenobservationmadeonaseparateartworkwheretheyidentifywhereandhowcertaintransformationswereused,notalltransformationsarenecessary,butandeffectiveuseofatleasttwo(atranslationplusonemore)shouldbepresentintheartwork.

ComponentsEmbeddedintheLessonProcedureOpening/Stimulus:Aslideshowwillbeshownthatintroducestheideaofthegeometrictransformationsinrelationtodesign.Havinganopeningactivitythatletsstudentsanalyzeartworks,identifythetransformationswithinapiece,andexperiencethedifferentusesofeachtransformationwillgetthestudentsengagedandreadytocreateworkoftheirown.Students'Misconceptions:Whataresomepossiblemisconceptionsordifficultiesthatstudentswillhavewith/aboutthematerial.

- Studentsmaylookatthisassignmentastwodifferentparts,onebeingthemathematicalpartandonebeingtheartisticpart–andtreatthemseparately–wheninrealityeachaspectshouldbehelpingthestudentcompletetheother

- Inordertosucceedinthedesignprocessstudentswillhavetohaveproficientknowledgeinthegeometrictransformation,particularlytherelatedequationsforeachtransformation.Useofgraphpaperintheirfinalprojectwouldbeabletohelpstudentsaccuratelyapplythisknowledge.

- Studentsmayhavedifficultyfindingimagesandartiststoutilizefortheiradditionalwrittenobservation.

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- Itisimportantforstudentstoknowthatincreatingtheirimagedifferentusesofthetransformationscanbeutilized,itdoesn’tsimplyhavetobeanimagerepeated,reflected,orrotated.Pushstudentstodevelopacomposition.

Questionstoask:Providekeythoughtprovokingquestionsthatmightrelatetostudent’smisconceptionsorkeyquestionstogetstudentstofocusoncriticalaspectsoftheactivity. (FromNationalArtStandardsAbove)

- Howdoeslearningaboutartimpacthowweperceivetheworld(andourthoughtsongeometry)?Whatcanwelearnfromourresponsestoart?Areyoulearningmoreaboutthistopicbyhearingotherpeopletalkaboutandpresenttheirexperiencesofthisproject?

- Howdoesknowingandusingvisualartvocabularieshelpusunderstandandinterpretworksofart(ormathematicalconcepts)?

- Howdoesknowingandusingvisualartvocabularieshelpusunderstandandinterpretworksofart?***

- Howdoartistsanddesignerscreateworksofartordesignthateffectivelycommunicate(dotheyutilizethesegeometryconcepts)?

Objectives/Assessment:Whatevidencewillyoubelookingforthatwilltellyouhowthestudentshavemettheobjectivesofthelesson?Manyaspectsofthisprojectcanbeconsideredwhenlookingforevidenceofproficientunderstandingofthetopicsusedinthelesson.Thefirstisinthetransformationidentificationactivityduringtheopeningslideshow.Ifstudentsareabletoaccuratelyidentifydifferenttransformationsincomplexcompositionsthestudentmayhaveaneasiertimeutilizingthesesametechniquesintheirownartwork.Ifstudentsareabletodothisitwillalsolendtoadeeperunderstandingofhowdifferentmathematicalconceptscanbeutilizedindesignandlaterintherealworld.Uponcompletionofthefinalimage,ifstudentsareaskedorchoosetousegraphpaperthedifferentpointstransformedwithreflections,rotations,translations,anddilationscanbeproperlyassessedforaccuracy.Ifstudentshaveproperlyplacedpointsafteratransformationitshowsagreaterunderstandingofhowpointsaretransformedintheplane,thisinformationcanbelaterutilizedontestsandfollowinglessonsonmorecomplexgeometrymaterial.Inthefinalimageagreatersenseofcompositioncanbelookedfor.Ifstudentshavebeenabletosuccessfullycreateacompositionusingthetransformationitshowsthattheynotonlyhavemasteroftransformationsbutalsohowtheycanlendthemselvestoagreaterstylisticorinterpretivemeaningwithinalargercomposition.Checkforthisversesasimpleimagemovedacrossthepage–howeverinthiscaseapatternmaybetheobjectiveandthatcanalsoshowgreaterunderstandingofhowthesemathematicalconceptsrelatetotheideasofrepetition,pattern,andpossiblyperspectiveinart.Thelastaspectofthisprojecttocheckforunderstandingisofcoursethetwowrittenreflections.Theobjectiveofthetworeflectionsistoassessthestudentsunderstandingofthewaystheretransformationsareusedinart,andmoreimportantly,whatthesetransformationsdofortheimage.Inthefirstreflectionitisfirstlyimportanttocheckifeachtransformationhasbeenusedproperlyandalsowhatitwasusedfor.Doesthetransformationlenditselftotheimageorcompositioninanymeaningfulway?Hasthestudentrecognizedthatintheirownwork?Additionally,itisimportantinthesecondreflectiontoseehowthestudenthaspickeduponthesetransformationsoutsideoftheirownwork.Thissecondreflectioncanbeseenasanextensiontothefirstactivitywherestudentspickedouttransformationsinartwork.Whatkindofimagehasthestudentchosen?Howdotheythinkthetransformationslendthemselvestotheworkofothers?Didtheyseeatrendintheirresearch?