Download pdf - ELED 533 LESSON PLAN FORMAT - Weeblyemilyvaughters.weebly.com/uploads/4/2/8/7/42874725/lesson_plan-_math... · ELED 533 LESSON PLAN FORMAT JMU Elementary Education Program A. TITLE/TYPE

ELED533LESSONPLANFORMATJMUElementaryEducationProgram

A. TITLE/TYPEOFLESSONPerimeterandArea

B. CONTEXTOFLESSONInthefourthgradethestudentworkedonSOL4.7theseemphasizedestimationandmeasurementsoflengthinmetricandU.S.Customaryunits.Thepreassessmentwillbeaworksheetwithproblemsthatexploremeasurementintheseareas.Therewillbefourproblemsonaworksheetforthestudentstofilloutquickly,theproblemswillemphasizebasicmeasurementconceptsinbothmetricandcustomaryunits.Weknowthatthisisaqualityassessmentforavarietyofreasons.Weknowthatqualityassessmentsarequick,andthissheetshouldtakestudentswiththeproperskillslessthanfiveminutes.Ifistakesthestudentsmorethanashortamountoftime,weknowthattheyneedarefresheronthecontentbecausetheywillnotthatthenecessarypriorknowledge.Thisassessmentisbuiltoncontentthattheyhavecoveredinthepast,whichalsomakesitaqualityassessmentbecauseitissomethingthatthestudentsshouldknowandbeabletosucceedon.AccordingtoPageKeeleywhowrote“ScienceFormativeAssessment”aformativeassessmentshouldfocusonactivatingpriorknowledgeandensuringreadinessfornewcontent.Ourassessmentdoesthisbyusingcontentthatthestudentswillknowfrompreviouslessons,butthatalsorelatestothecontentwewillbeteaching.Keeleyalsosaysthereshouldbeanaspectofself-assessmentandbyaskingthestudentstoexplaintheirthinking,wealsocreateaqualityassessmentthatincludesself-assessment.

• Thislessonisappropriatebecausethestudentshavebeenexploringmeasurementconcepts.Sincethestudentshavehadpriorexperiencewithmeasurementthroughouttheacademiccareerswebelievethattheyarereadytoexploreothertypesofmeasure.

• VerticalPlanning: AccordingtoVandeWalle,Lovin,KarpandBay-Williams,thestudentswillhavebeenworkingonmeasurementthroughouttheirelementaryschoolcareer.Ingradethree,theyestimatedandmeasureusingunitsoftimeandotherunitsaswellareworkingonareaandperimeter.Theyworkedinthefourthgradetoincreasetheirunderstandingofmeasurementbystudyingperimeterfurtherandmovingtowardsangles.Theyarenowinthefifthgradereadytoincreasetheirunderstandingofmeasurement.(313).TheVirginiaSOLsalsoemphasizemeasurementthroughouttheearlygrades:itbeginsasearlyaskindergartenwhenthestudentslearntorecognizethetoolsformeasurementandcomparesizedirectly.Instandard2.11thestudentsmeasurelength,weight/mass,andvolume.Thefourthgrademeasurementstandardshavethestudentsestimatinglength,usingthemetricsystemandworkingwithvolumeand

The following information should be included in the header of the lesson plan: • Emily Vaughters • Amanda Sawyer • 2 June 2015

length.Theireducationwithmeasurementisaconstantwithintheireducation,andwillcontinuewiththislesson.

• HorizontalPlanning:Thislessonisthebeginningofthemeasurementunit.Thereisalotoftimeandemphasisplacedonthestudyofmeasurementwithinthefifthgradecurriculum.Earlyintheyearthestudentworkedtousedecimalsandexpandedformtodeterminethesolutiontheproblemstheymustsolve(VASOLMathematics5.1and5.2).Theseskillslearnedearlierintheyearareessentialtosuccessfullyperformtheskillsoutlinedinthislessonaswellaslessonsthatwillbeperformedinthefuture.Theknowledgethatthestudentsbuildthroughouttheschoolyearbuildsonitselftoensuresuccess.

• ThislessonfitsintowhatIknowaboutchilddevelopmentbecauseitallowsthestudentstobuilduponpriorknowledge,demonstratetheirskills,andcommunicatetheirprocesseswhiledevelopingmathematicalproficiency.Sincelearningmathematicalprocessestakestimethestudentsareencouragedandsupportedastheypracticetheirmathematicalskillsandconcepts.

• AccordingtoTheNationalCouncilofTeachersofMathematics(NCTM)whenlearningproceduralfluencyandconceptualunderstandingstudentsshouldengageinproblemsolving,reasoningandproofing,representation,andcommunication,bymakingconnections.Studentswillusetheseskillsasawayofdevelopingadeepunderstandingofmathematics.Sinceitisourresponsibilitiesasteacherstohelpstudentsdeveloptheseskillswebuildonstudentexperiencesandknowledgewhileprovidingappropriatetoolsforsolvingmathematicalprocedure.

B. STANDARDS-VASOLsand/orCCSSContentStandards:Math:5.8Thestudentwilla)findperimeter,area,andvolumeinstandardunitsofmeasure;b)differentiateamongperimeter,area,andvolumeandidentifywhethertheapplicationoftheconceptofperimeter,area,orvolumeisappropriateforagivensituation;c)identifyequivalentmeasurementswithinthemetricsystem;d)estimateandthenmeasuretosolveproblems,usingU.S.Customaryandmetricunits;ande)chooseanappropriateunitofmeasureforagivensituationinvolvingmeasurementusingU.S.Customaryandmetricunits.Science:5.1:Thestudentwilldemonstrateanunderstandingofscientificreasoning,logic,andthenatureofsciencebyplanningandconductinginvestigationsinwhichb)estimatesaremadeandaccuratemeasurementsoflength,mass,volume,andtemperaturearemadeinmetricunitsusingpropertools;

g)dataarecollected,recorded,analyzed,andcommunicatedusingpropergraphicalrepresentationsandmetricmeasurements;History:USI.1Thestudentwilldemonstrateskillsforhistoricalandgeographicalanalysisandresponsiblecitizenship,includingtheabilitytoe)evaluateanddiscussissuesorallyandinwriting;

LanguageArts:

5.1Thestudentwilllisten,drawconclusions,andshareresponsesinsubject-relatedgrouplearningactivities.a)Participateinandcontributetodiscussionsacrosscontentareas.b)Organizeinformationtopresentinreportsofgroupactivities.c)Summarizeinformationgatheredingroupactivities.d)Communicatenewideastoothers.e)Demonstratetheabilitytocollaboratewithdiverseteams.f)Demonstratetheabilitytoworkindependently.

ProcessStandard:

• Representation:o Thestudentswilluseavarietyofmathematicalskillssuchasrepresentationtoorganize,

record,andcommunicatemathematicalideas.Theywilltheseskillsinordertomodeldivisionbyselecting,applying,andtranslatingamongdifferentmathematicalrepresentationstosolveproblems.Studentswillsolveavarietyofdivisionproblemsthroughrepresentation.

C. LEARNINGOBJECTIVESUnderstand–whatarethebroadgeneralizations/conceptsthestudentsshouldbegintodevelop?(Thesearetypicallydifficulttoassessinonelesson.)

Know–whatarethetools,vocabulary,symbols,etc.thestudentswillgainthroughthislesson?(These“knows”mustbeassessedinyourlesson.)

Do–whatarethespecificthinkingbehaviors/proceduresstudentswillbeabletodothroughthislesson?(Thesewillalsobeassessedinyourlesson.)

Thestudentswillunderstand…U1:theconceptsofperimeter,area,andvolume

Thestudentswillknow…K1:themeaningofperimeter;isthedistancearoundatwo-dimensionalregion.K2:themeaningofarea;isthetwo-dimensionalspaceinsidearegionK3:themeaningofvolume;isthecapacityofthecontainer.

Thestudentswill…D1:determinetheperimeterofapolygon,withoutwithoutdiagrams,when

• Thelengthsofallsidesofapolygonthatisnotarectangleorsquarearegiven

• Thelengthandwidthofa

rectanglearegiven• Thelengthofasideofa

squareisgiven.D2:estimateanddeterminetheperimeterofapolygon,andareaofasquare,rectangle,andrighttriangle,usingonlywholenumbermeasurementsgiveninmetricorU.S.Customaryunits,andrecordthesolutionwiththeappropriateunitofmeasureD3:Estimateanddeterminetheareaofasquare,rectangle,andrighttrianglewithourwithoutdiagrams

• Square:whenthelengthofthesidesaregiven

• Rectangle:whenthelengthandwidtharegiven

• RightTriangle:whenthebaseandheightaregiven.

D4:differentiateamongconceptsofarea,perimeter,andvolumeD5:developaprocedureoffindingvolumeusingmanipulativesD6:determinethevolumeinstandardunitsD7:describepracticalsituationswherearea,perimeter,andvolumeareappropriatemeasurestouse,andjustifytheirchoicesorallyorinwriting.D8:identifywhethertheapplicationoftheconceptsofperimeter,area,orvolumeisappropriateforagivensituation.D9:identifyequivalentmeasurementswithinthemetricsystemforthefollowing:

• Length:millimeters,

centimeters,meters,andkilometers

• Mass:gramsandkilograms

• Liquidvolume:milliliters,andliters.

D10:SolveproblemsinvolvingmeasurementsbyselectinganappropriatemeasuringdeviceandaU.S.customaryormetricunitofmeasureforthefollowing

• Length:partofaninch,inches,feet,yards,millimeters,centimeters,meters,andkilometers;

• Weight:ounces,pounds,andtons,

• Mass:gramsandkilograms

• Liquidvolume:cups,pints,quarts,gallons,milliliters,andliters

• Area:squareunits• Temperature:Celsiusand

FahrenheitunitsD11:howtoappropriatelyrepresentperimeter,area,andvolumeD12:howtouseappropriateunitsofmeasureforperimeter,area,andvolume.D13:howtoselectappropriatemeasuringdevicesandunitofmeasuretosolveproblemsinvolvingmeasurement.

D. ASSESSINGLEARNING

• Howwillyouassessstudentlearningoftheobjectives?Whattypeofassessmentwillyouuseandwhy?

• Remember–everyobjectivemustbeassessedforeverystudent!

Objective Assessment Tool Whatdocumentationwillyou

haveforeachstudent?

Data Collected Whatwillyourstudentsdoandsay,specifically,thatindicate

eachstudenthasachievedyourobjectives?

U1:theconceptsofperimeter,area,andvolume

Iwillbeusingdiscussionasmydocumentation.WhileobservingandcommunicatingwithstudentsIamlookingforstudenttobeusinglanguagethatrepresentstheirunderstandingofperimeter,area,andvolume.

Iwillknowstudentshaveachievedmyobjectiveswhentheyareabletoexpressthatareaandperimeteraregeometricmeasurementsusedtomeasureplanefiguresandvolumeisameasureofcapacityincubicunits.

K1:themeaningofperimeter;isthedistancearoundatwo-dimensionalregion.

Iwillbeusingdiscussionandstudentworkasmydocumentation.Whilereviewingwork,discussion,oractionsIamlookingforevidencethatstudentscancorrectlyrepresentthemeaningofperimeterthroughtheirrepresentations,actions,andwords.

Iwillknowstudentshaveachievedmyobjectiveswhentheyareabletoexpressthatperimeteristhedistancearoundatwo-dimensionalobject.Studentswillindicatetomethroughverbalexchangeorwrittenworkusingstatementslike:“Iaddedallthesidestogether”

K2:themeaningofarea;isthetwo-dimensionalspaceinsidearegion

Iwillbeusingdiscussionandstudentworkasmydocumentation.Whilereviewingwork,discussion,oractionsIamlookingforevidencethatstudentscancorrectlyrepresentthemeaningofareathroughtheirrepresentations,actions,andwords.

Iwillknowstudentshaveachievedmyobjectiveswhentheyareabletoexpressthatareaisthespaceinsideatwo-dimensionalregion.Studentswillindicatetomethroughverbalexchangeorwrittenworkusingstatementslike:“Ifoundtheareabymultiplylengthtimeswidth.”

K3:themeaningofvolume;isthecapacityofthecontainer.

Iwillbeusingdiscussionandstudentworkasmydocumentation.Whilereviewingwork,discussion,oractionsIamlookingforevidencethatstudentscancorrectlyrepresentthemeaningofvolumethroughtheirrepresentations,actions,andwords.

Iwillknowstudentshaveachievedmyobjectiveswhentheyareabletoexpressthatvolumeisthecapacityofacontainer.Studentswillindicatetomethroughverbalexchangeorwrittenworkusingstatementslike:“It’stheamountaspaceasubstanceuses”

D1:Determinetheperimeterofapolygon,withoutwithoutdiagrams,when

• Thelengthsofallsidesofa

Iwillbeusingstudentworkasmydocumentation.ThroughstudentworkIamobservingifstudentsareusingavarietyofstrategies

Studentneedstobeusingorattemptingdifferentstrategiestoindicatetomethattheyareachievingorworkingtowardsmy

polygonthatisnotarectangleorsquarearegiven

• Thelengthandwidthofarectanglearegiven

• Thelengthofasideofasquareisgiven.

dependingonthesituationtodeterminetheperimeterofapolygon.

objective.Iftheyhaveachievedthisgoaltheywillbeabletousedifferentstrategiescorrectlyandflexiblywhileworking.Strategiescanbeexpressedverbally,throughindividualwork,orwithpartners.

D2:Estimateanddeterminetheperimeterofapolygon,andareaofasquare,rectangle,andrighttriangle,usingonlywholenumbermeasurementsgiveninmetricorU.S.Customaryunits,andrecordthesolutionwiththeappropriateunitofmeasure

Iwillbeusingstudentworkasmydocumentation.ThroughstudentworkIamobservingifstudentsareusingavarietyofstrategiesdependingonthesituationtodeterminetheperimeterofapolygon.AlsoIwillbefocusingoniftheystudentsarecorrectlyusingandrecordinginU.S.Customaryandmetricunits.

Studentneedstobeusingorattemptingdifferentstrategiestoindicatetomethattheyareachievingorworkingtowardsmyobjective.Iftheyhaveachievedthisgoaltheywillbeabletousedifferentstrategiescorrectlyandflexiblywhileworking.Strategiescanbeexpressedverbally,throughindividualwork,orwithpartners.

D3:Estimateanddeterminetheareaofasquare,rectangle,andrighttrianglewithourwithoutdiagrams




Iwillbeusingstudentworkasmydocumentation.ThroughstudentworkIamobservingifstudentsareusingavarietyofstrategiesdependingonthesituationtodeterminetheareaofasquare,rectangle,andrighttriangle.

Studentneedstobeusingorattemptingdifferentstrategiestoindicatetomethattheyareachievingorworkingtowardsmyobjective.Iftheyhaveachievedthisgoaltheywillbeabletousedifferentstrategiescorrectlyandflexiblywhileworking.Strategiescanbeexpressedverbally,throughindividualwork,orwithpartners.

D4:differentiateamongconceptsofarea,perimeter,andvolume

Iwillbeusingdiscussionasmydocumentation.WhileobservingandcommunicatingwithstudentsIamlookingforstudenttobeusinglanguagethatrepresentstheirunderstandingofthedifferencesamongtheconceptsofarea,perimeter,andvolumeastheyexplaintheirreasoningorstrategytosolvetheproblem.

Iwillknowstudentshaveachievedmyobjectiveswhentheyareabletoexpressthatareaandperimeteraregeometricmeasurementsusedtomeasureplanefiguresandvolumeisameasureofcapacityincubicunits.Studentswillalsobeabletoexpresswhatmakeseachmeasurement.

D5:developaprocedureoffindingvolumeusingmanipulatives

Iwillbeusingstudentworkasmydocumentation.ThroughstudentworkIamobservingifstudentsareusingavarietyofstrategies

Iwillknowstudentshaveachievedmygoalthroughtheirrepresentationofmodelscreatedtoexpressvolume

dependingonthesituationtodevelopproceduresforfindingthevolumeofanobject.

problems.Specificallystudentswillsetupmodelscorrectly,usemodelsasatooltohelpmakesenseofaproblem,andkeeptrackofnumbersandwhatthosenumbersrepresent.

D6:determinethevolumeinstandardunits

Iwillbeusingstudentworkasmydocumentation.ThroughstudentworkIamobservingifstudentsareusingavarietyofstrategiesdependingonthesituationtodeterminethevolumeofafigure.

I will know that students have achieved my goal through their correct usage of the proper standard unit. Students will be able to express which unit is the proper unit for volume as well as be able to determine the volume through a variety of strategies of their choice.

D7:describepracticalsituationswherearea,perimeter,andvolumeareappropriatemeasurestouse,andjustifytheirchoicesorallyorinwriting.

Iwillbeusingdiscussionandstudentworkasmydocumentation.WhileobservingandcommunicatingwithstudentsIamlookingforstudenttodescribepracticalreasonswhenthemightseeperimeter,area,andvolumebeingusedintherealworld.

Studentsneedtobeabletogiveexamplesofwhereperimeter,area,andvolumeareusedintherealworldtoindicatetomethattheyhaveachievedmygoal.Theywilldescribesituationslikeconstructionworkerneedsitfortheirjob.

D8:identifywhethertheapplicationoftheconceptsofperimeter,area,orvolumeisappropriateforagivensituation.

Iwillbeusingstudentwork,discussions,andactionsasmydocumentation.Whenreviewwork,discussion,oractionsIamlookingforevidencethatstudentscanidentifybetweenperimeter,area,andvolume;aswellasusethecorrectapplicationwhensolvingaproblem.

Iwillknowstudentshaveachievedmyobjectivewhentheyareabletoavoidguessingandexpresstomehowtheymightsolveaproblem.ThroughverbalandwrittenworkIamlookingforstudentstatementslike:(area)“I’mfindtheareabecauseIamlookingforhowmuchspaceisbeingusedintheobject.”(Perimeter)“IwanttoknowthedistancearoundtheobjectsoI’msolvingforperimeter.”(Volume)“IwanttoknowhowmuchliquidcangointomyshapesoI’mlookingforthevolume.”

D9:identifyequivalentmeasurementswithinthemetricsystemforthefollowing:

• Length:millimeters,centimeters,meters,and

Iwillbeusingstudentworkasmydocumentation.ThroughstudentworkIamobservingifstudentsarecorrectlyidentifyingequivalentmeasurementswhen

I will know students have achieved my objective when they are able to correctly identify equivalent measurement when using the metric system. I will be

kilometers• Mass:gramsandkilograms• Liquidvolume:milliliters,

andliters.

usingthemetricsystem.

looking for statements that show understanding such as: “I know these measurements are equivalent because I measured them and they are the same length” or “I know they are equivalent because I converted meters into kilometers and I got the same answer.”

D10:SolveproblemsinvolvingmeasurementsbyselectinganappropriatemeasuringdeviceandaU.S.customaryormetricunitofmeasureforthefollowing

• Length:partofaninch,inches,feet,yards,millimeters,centimeters,meters,andkilometers;

• Weight:ounces,pounds,andtons,

• Mass:gramsandkilograms• Liquidvolume:cups,pints,

quarts,gallons,milliliters,andliters

• Area:squareunits• Temperature:Celsiusand

Fahrenheitunits

Iwillbeusingstudentworkasmydocumentation.WhilelookingthroughstudentsworkIamlookingtoseeifstudentsareselectingappropriatemeasuringtools.Iamalsofocusingoniftheycanusethosetoolstohelpthemunderstandwhatishappeningtheproblem,andiftheyarekeepingtrackofthevariablesinawaythatrepresentstheirmeaning.

Studentsneedtobeusingameasuringdevicecorrectlytoindicatetomethattheyareachievingmyobjective.ThroughstudentworkIamlookingforstudentstocorrectlyuseU.S.Customaryandmetricunitsofmeasurebyidentifyingappropriatetoolsandunitsofmeasureinagivensituation.Forexampletheywouldusearuler,yardstick,ormetersticktofindtheperimeterofthedesk;notmilesorkilometers.

D11:howtoappropriatelyrepresentperimeter,area,andvolume

Iwillbeusingstudentworkasmydocumentation.WhilelookingthroughstudentsworkIamlookingtoseeifstudentsareselectingappropriatestrategiesandformulaswhensolvingforperimeter,area,andvolume.

Iwillknowstudentshaveachievedmyobjectivewhentheyareabletoavoidguessingandexpresstomehowtheymightsolveaproblem.ThroughwrittenworkIamlookingforstudenttocorrectlysolveforperimeter,area,andvolumeandusethecorrectunitsofmeasure;(perimeter)cm,(area)cm2,(volume)cm3.

D12:howtouseappropriateunitsofmeasureforperimeter,area,andvolume.

Iwillbeusingstudentworkasmydocumentation.WhilelookingthroughstudentsworkIamlookingtoseeifstudentsareselectingappropriateunitsofmeasure.Iamalsofocusingon

Iwillknowthatstudentshaveachievedthisobjectivewhentheyareabletocorrectlyidentifywhatunittousewhentakingameasurement.Iwilllookforstudentstatementsthatshow

howtheyusethoseunitswhenrepresenttheirunderstandingoftheproblem.

understandingoftheconceptsuchas:“Iknowthisshouldbemeasuredinlitersbecauseitisvolume”

D13:howtoselectappropriatemeasuringdevicesandunitofmeasuretosolveproblemsinvolvingmeasurement.

Iwillbeusingstudentworkasmydocumentation.WhilelookingthroughstudentsworkIamlookingtoseeifstudentsareselectingappropriatemeasuringdevicesandunitswhensolvingaproblem.Iamalsofocusingoniftheycanusethosetoolsandunitsofmeasuretohelpthemunderstandwhatishappeningtheproblem,andiftheyarekeepingtrackofthevariablesinawaythatrepresentstheirmeaning.

Inordertoachievemyobjectivesstudentswillindicatetomethattheyunderstandthedifferentlengtheachmeasuringdevicerepresents.Throughtheirworktheywillcorrectlyidentifywhentouseinchesversemiles.

E. MATERIALSNEEDED

• Ruler(withunitsremoved)• Pencil• Geo-boards• Rubberbands• Whiteboard• MathJournals• GridPaper• 20dice• Recordingsheet

G1ANTICIPATIONOFSTUDENTS’MATHEMATICALRESPONSESTOTHETASK(S)POSEDINTHEPROCEDURE

PORTIONOFTHELESSON

Selectthemathematicaltask(s)fortheselessons.Whattask(s)willstudentscompleteonDay1andDay2?Includetheactualproblem(s),center(s),game(s),etc.Anticipatestudents’strategiesandmistakesastheyworkonthetask(s)inthelessons.Whatvalidstrategiesmightstudentsuse?Whatmistakeswouldmakesenseandindicateamisconception?Bespecific.Actuallydoingthetask(s)yourselfisthebestwaytoanticipate.Thissectionisoneofthepracticesfororchestratingproductivemathematicsdiscussions:Anticipating.

Anticipate Strategies:

• The students are likely to use the tools given to solve the problems, such as the ruler. • Some students may make an estimate, and then measure to check. • Some students may use their prior knowledge of addition, subtraction and measurement

to solve the problems • Some students are likely to use finger counting as a strategy for some of the arithmetic. • Students are likely to use their prior knowledge of measurement to choose the proper

units and tools. Anticipate Mistakes:

• The students are likely to confuse area, perimeter and volume. • Some students may mix up units and measure in the incorrect unit. • Some students may have the misconception that an inch in a meaningful length, and thus

have difficulty understanding units of measure and how they apply to area, perimeter and volume.

• Some students may have the misconception that the base is the bottom of the figure. G2 PROCEDURE

IncludeaDETAILEDdescriptionofeachstep,includinghowyouwillgetthestudents’attention,yourintroductionoftheactivity,thedirectionsyouwillgivestudents,thequestionsyouwillask,andappropriateclosure.WriteexactlywhatyouwillSAYandDO.Thinkofthisasascript.

DAY1

BEFORE:Engagement-Howwillyoupreparestudentstobereadytoengagewiththemaintask/activity?(seepp.25ofyour3-5text).Inyourprocedure,besuretoaddressthe3BeforePhaseTeacherActions:

ü Activatepriorknowledge.ü Besurethetaskisunderstood.ü Establishclearexpectations.

Beginwithasimpleversionofthetask:

• Toactivatepriorknowledgeabouttheconceptsofareahaveadiscussionwiththestudentsaboutthemeaningofarea.Ask,“Whatdoyoumeanbyarea?Howdowemeasurearea?”afterhelpingstudentsdefineareaanddescribehowitismeasure,askstudentsforformulastheyalreadyknow.Askingprobingquestionslike:“howmanydifferentformulascanyouthinkoftofindtheareaofashape?”

• Writeallformulasthatthestudentscomeupwithontheboard.

Presentthefocustasktotheclass:• Canyouexplainwhytheareasofatriangle=½baseXheight• Determineandrecordthehowtofindtheareaforanyparallelogram.

Provideclearexpectations:

• Writethefollowingdirectionsontheboard

o Usingthegeoboardexplainwhytheformulaforanareaofatriangleis½basexheight.Dothisfora

§ Isosceles§ Equilateral§ Scalene

DURING:Implementation–thisisthetimewhenstudentsareeitherworkingindependentlyorinsmallgroupsandyouareconferringwithstudents.(seepp.25ofyour3-5text)Inyourprocedure,besuretoaddressthe4DuringPhaseTeacherActions:

ü Letgo!ü Noticechildren’smathematicalthinking.ü Provideappropriatesupport.ü Provideworthwhileextensions.

Noticingchildren’smathematicalthinkingisanotherwaytodescribeoneofthepracticesfororchestratingproductivemathematicsdiscussions:Monitoring.Inyourprocedure,explainhowyouwillmonitor(anddocument)studentstrategiestopreparefortheAfterphase.Initially:

• Questionthestudentstobesuretheyunderstandthetaskandthemeaningofarea.Alsomakesurestudentsunderstandthemeaningofanisosceles,equilateral,andscalenetriangle.Lookforstudentswhoareconfusedabouttheseterms.Ifmanystudentsseemedconfusedbringtheclasstogetherforaquickreview.

• Besurestudentsarecreatingideasandconceptsaboutwhytheareaofatriangleis½baseXheight.

Provideworthwhileextensions:

• Askingprobingquestionslike:o “Iseethatyou[makingacommentabouttheirgeoboard]howdoesthis

provetoyouwhytheareais½basexheight?o Whataboutthescalenetriangle?Whathaveyoutriedtodoinordertofind

whytheareais½baseXheight?o Whatothershapescanyoupossiblymakeatriangleinto?

§ Directinglanguagetowardstheuseofparallelogramo Whydidyou…?o Wouldthesameideasworkforascalenetriangle?Whyorwhynot?o You’reontherighttrackbuthaveyouthoughtaboutitlikethis…?o Isthereanywaythiscouldbemadeintoaparallelogram?(oncetheylearned

aboutthatitcanbemadeintoaparallelogram)Manipulativeswillbeprovidedtoensureforavarietyofwaystosolvetheproblemsandtohelpthestudentsbasedontheirdevelopmentallevel.AFTER:Engagethefullclassindiscussion;encouragestudentstoevaluatetheideas;lookforopportunitiestohighlightsignificantideasinstudents’worktomakethesemathematical

ideasmoreexplicittoallstudents.(seepp.25ofyour3-5text).Inyourprocedure,besuretoaddressthe3AfterPhaseTeacherActions:

ü Promoteacommunityoflearners.ü Listenactivelywithoutevaluation.ü Summarizemainideasandidentifyfutureproblems.

Creatingacommunityoflearnersintheafterphaseinvolves3practicesfororchestratingproductivemathematicsdiscussions:Selecting&Sequencing&Connecting.Inyourprocedure,explainhowyouwilluseyouranticipatingandmonitoringofstudentstrategiestoselect,sequence,andconnectstudentstrategies.Bespecificandnamethestrategiesyouwillselectandinwhatsequence,andthequestionsyouwillasktohelpstudentsconnectstrategies.Bringtheclasstogether:

• Asthestudentswhattheyfoundoutaboutareaofatriangle.o “Howdidyoufindtheformulafortheareaofaequilateraltriangleo “Howdidyoufindtheformulafortheareaofaisoscelestriangle?”o “Howdidyoufindtheformulafortheareaofascalenetriangle?”

• Askthestudentstodescribehowtheymighttransformanytriangleintoaparallelogram

• Havethestudenthelpexplainwhytheformulaforaparallelogramisbasexheighto Thestudentshouldbewritingtheinformalproofsintheirnotebooks

• Usingtheexplanationfortheareaofaparallelogramhasthestudentshelpexplainwhytheareaofanytriangleis½basexheight.

• Providetimeforpair-shareideasandstrategies.

BEFORE:Beginwithasimpleversionofthetask

Wewillbeginwithaquickareviewofwhatperimeterandareaare.Thisknowledgeshouldbefreshfromthedayoneactivitiesandotherpastlessons.Wewillaskthestudents:• Whatisarea?Howdoyoudescribeit?• Whatisperimeter?Howdoyoudescribeit?

Presentthefocustasktotheclass

Nextwewillexplainthetask.ThestudentswillbeplayingagamethatrelatedtoperimeterandareacalledBattleBoxes.Wewillexplaintheinstructions,whilemodelingthetask:• Youwillworkingroupsoftwoorthree.• Player1willgofirst,andtheywillbeginbyrollingthedice.Thenumbersthatcomeup

onthedicerepresenttheperimeteroftherectangletheywilldrawontheirgridpaper.Theywillalsorecordtheperimeterstheyroll,andthecorrespondingareaofthefigure.Theywillmarkthefigurewiththeirinitial.

• Thenthesecondplayerwilldothesameactions,rollinganddrawingtheirfiguresandrecordingthemonthesheet,andmakingthesquaretheydrewwiththeirinitials.

• Ifthereisathirdplayerinthegroup,theydothesamething.

• Theseinstructionswillbeontherecordingsheettoprovideforrefresherswhenneeded.

• Ifyourunoutofspaceonthesheet,youcangetanothersheetfromtheinstructor.Thesecondsheetwillhaveslightlydifferentinstructions.Forthisone,theyrollthediceandreceivethebaseandheight,butinsteadofcreatingarectangle,theywillcreateatriangle.Theywilljustconnectthebaseandheightwithahypotenuse.Theywillfollowthesameinstructionsfromhere,findingandrecordingtheareaandperimeterofthetrianglethistime.

ProvideClearExpectations:

• Theinstructorwillmodeldoingonerollforrectanglesandonefortriangles:o Iwillrollthedice“Oh,Igot3and4.Thismeansthatmyperimeteris3squares

by4squares.ThismeansthatIwilldrawarectanglethathasabaseof3andaheightof4,likethis.NowIhavetofigureoutmyarea.Weknowthattheformulafortheareaofarectangleisa=bxh,sotheareais12.WhataresomeotherwaysthatIcouldfindtheareaofthisrectangle?

o Iwillrollthedice.“Oh,Igota2andafour.Thismeansthatmybaseis2andmyheightisfour.I’llgoaheadanddrawthisonthepaper,makinga“L”shape.NowI’mgoingtoconnectthebaseandheight(makingahypotenuse).Isiteasytofindtheperimeterusingtheboxesasaunit?NoitsnotsoI’mgoingtohavetomeasurethetriangleswitharuler.ThenI’llwritedowntheperimeter.NowI’llhavetodeterminetheareaofthetriangle.HowcanIfigurethatout?Icouldusetheformulawhichis½basexheight=aWefiguredthatoutyesterdaydidn’twe?Okaysousingthatweknowthattheareais4units!

• Thenthestudentswillbebrokenoffintogroupsandtheywillbeallowedtobeginplayingthegame.

• Thestudentswillbegivenmanipulativestouseiftheychooseasawaytosolveforareaandperimeter

DURING:Initially:Thestudentswillbreakoffintopairortriadstoworkontheirgame.Thestudentswillbeplayingthegameandtheinstructorwillmonitorforavarietyofthings:

• Mathematicalthinkingo Iwanttoseewhatkindofstrategiesthestudentschooseyouusewhen

determiningthearea.Dotheysticktotheformula?Dotheycount?Arethereotherstrategiesthattheyuse?IfIseeanystrategiesofinterest,Iwillrecordthem,andaskthestudentiftheywouldbecomfortablesharingthatstrategywiththeclasslater.

• CommunityofLearnerso Iwillbemonitoringthebehaviorofthestudentsintheclassroomandhelping

toavoidanyissuesinregardstoargumentsinpartnershipsandgroups

Questioning/WorthwhileExtensions:

• Iwillbegoingaroundtheroomandaskingexpandingquestionssuchas:o Howdidyousolvetheareaforthisone?o Canyoushowmehowyoudidthat?o Whatif_____wasdifferent,howwouldyousolveitthen?o Doyouthinkthereisaneasierwaytosolveforperimeterandarea?Explain

whyo Howdidyouthinkaboutthisproblem?o Canwerelatetothisinanotherway?o Wouldthesameideaworkfor…?o Canyoutalktomeaboutwhatyoudid?

AFTER:Bringtheclasstogether:Inthisportionofthelesson,wewilldiscussareaandperimeterasawhole,takinginaspectsofpastlessonstofuelthediscussion.

• Wewillbeginbytalkingaboutthegame.ThestudentswhosestrategiesthatIidentifiedearlierandwhowerewillingtosharewilldosowiththeclass.

• Iwouldwantthemtomakeconnectionsbetweenthedayoneanddaytwocontent.Suchasusingthestrategyofmakingtrianglesintoparallelogramstofindtheareaofthetriangle.

Wewillwrapuptheselessonsbyaskingabouthowwecanfindwaystouseareaandperimeterintherealworldaswellasinschool.

H. DIFFERENTIATION

DescribehowyouplantomeettheneedsofallstudentsinyourclassroomwithvariedinterestsandreadinesslevelsbycompletingONEofthesixboxesbelowforeachday.Youmaychoosethesameboxforeachday.Usethelearningprogressionstosupportyourdecisions.Includeaspecificdifferentiationplanforeachday.ThisconnectstoyourDuringPhaseActions:providingsupportandextensions.

Content Process Product

Interest

Students will be presented with the information in multiple forms, through manipulatives, drawing

and labeling, and physical movement.

Readiness

I will give students who need support extra

instruction. I will have student who I believe need

more support in the

process paired with a peer who doesn’t nee the extra support in this area. This will be determined based

on the pre-assessment. The students needs will be met through a combination of both peer and instructor support throughout the

tasks they have to perform. I. WHATCOULDGOWRONGWITHTHESELESSONSANDWHATWILLYOUDOABOUTIT?

ThinkaboutthisspecificallyforTHESElessonplans.ThisCANNOTincludefiredrills,interruptionsduetoannouncements,weather,orotheremergencies.

• Thereareavarietyofthingsthatcouldpotentiallygowrongduringthislesson:o Therecouldbetechnologicalissues,suchasacopierbeingbrokendownor

computersfailingtowork.IwillhaveattemptedtoprintandensurethatIhavemymaterialspreparedfarpriortothedayofthelesson,butifIamunabletoensurethatthishappens,Iwillputtheimagesontheboardandhavethestudentscopythemdown

o Ifthereistoomuchtimeafterthelesson,Iwillallowthestudentstochooseamathrelatedactivityoutofthe“I’mdone!”boxortoworkonmissingworkorreading.

o IfIamrunningoutoftime,Iwillpushthedayoneactivitiesintodaytwo.Iwillcutthegameshortondaytwotoensuretimefordiscussionandclosing,

o Thestudentscouldnothavethepriorknowledgenecessarytoperformthedayonetask.IfthisoccursIwillincorporateareviewsession.

o Ifthestudentsareunabletocomeupwiththelanguagenecessarytoexplainwhytheformulafortheareaofthetriangleis½bxh=athenIwillpromptthemwithquestioningandscaffoldwherenecessary.

o Ifthestudentsgettoocompetitiveduring“BattleBoxes”Iwillaskthattheyrememberthatitisjustagameandthegoalislearningnotwinning.

AssessmentChecklist:Objective Students who

have met this objective

Students who aren’t there yet.

Comments

U1:theconceptsofperimeter,area,andvolume

K1:themeaningofperimeter;isthedistancearoundatwo-

dimensionalregion. K2:themeaningofarea;isthetwo-dimensionalspaceinsidearegion

K3:themeaningofvolume;isthecapacityofthecontainer.

D1:Determinetheperimeterofapolygon,withoutwithoutdiagrams,when

• Thelengthsofallsidesofapolygonthatisnotarectangleorsquarearegiven

• Thelengthandwidthofarectanglearegiven

• Thelengthofasideofasquareisgiven.

D2:Estimateanddeterminetheperimeterofapolygon,andareaofasquare,rectangle,andrighttriangle,usingonlywholenumbermeasurementsgiveninmetricorU.S.Customaryunits,andrecordthesolutionwiththeappropriateunitofmeasure

D3:Estimateand

determinetheareaofasquare,rectangle,andrighttrianglewithourwithoutdiagrams




D4:differentiateamongconceptsofarea,perimeter,andvolume

D5:developaprocedureoffindingvolumeusingmanipulatives

D6:determinethevolumeinstandardunitsD7:describepracticalsituationswherearea,perimeter,andvolumeareappropriatemeasurestouse,andjustifytheirchoicesorallyorinwriting.

D8:identifywhethertheapplicationoftheconceptsofperimeter,area,orvolumeisappropriateforagivensituation

LessonImplementationReflection&AssessmentAnalysis(Part5oftheLessonPlanningProject)

Assoonaspossibleafterteachingyourlessons,thinkabouttheexperience.Usethequestions/promptsbelowtoguideyourthinking.Bethoroughinyourreflectionandusespecificexamplestosupportyourinsights.1. Whatactuallyhappenedinyourlessons?Citeexamplesofdialogueorstudentwork.Howdid

youractualteachingofthelessonsdifferfromyourplans?Describethechangesandexplainwhyyoumadethem.

Iwasabletoteachmylessontotwoofmyroommates,bothofwhomarenon-educationmajors.Neitherofthemhaddealtwiththeconceptsofperimetersincehighschoolinanykindofeducationalsetting.IchoosetodothedaytwoprocedurewiththembecauseoftimeconstraintsandbecauseIbelievetheywouldneedalotofinstructionandpromptingtogetthroughtheproofsportionbecauseofalackofpriorknowledge.Mystudentswouldhavebeenassessedandinstructedbeforetoensuretheirreadinessforthetask,butIwasunabletodothisformyroommates.Theyplayedthegameagainsteachother,andtheywereabletoplayaroundwithrectanglesandwithtriangles.IwasabletoquestionthemastheydidthisandIspecificallyaskedabouttheirstrategies.Whenasked“howdidyousolvetheareaforthisone”bothrespondedwiththestandardformulathattheylearnedinmathclasses.Itriedtogetthemtoexplaintheiranswerstome,buttheyhadalotofdifficultyansweringtheopenendedquestions,andIfoundthattheywouldsimplyreplythattheydid“thewayyou’resupposedto?”TheytendedtogetconcernedwhenIaskedthequestions,worriedthattheyweredoingtheproblemsincorrectly.Forthisportion,Ifollowedmyguidelines,thoughIdidmakechangestotheafterportion.Icouldn’tfollowmydiscussionplanasmuchforthisbecausethereweresofewstudents.SoImodifiedandaskedthemtothinkaboutwhattheywouldhavedoneiftheydidn’tknowtheformula.Theyreliedsoheavilyontheformulathatthisquestionreallystumpedthemforawhile.Eventuallytheycametotheconclusionthattheycouldhavecountedthesquaresonthegraphpaper,buttheywouldhavehadtoestimatehowmanysquaresonthetrianglesbecauseofthediagonallines.Whenaskingabouttherealworldconnectionstheyfocusedalotonhomerenovation,likelybecauseourkitcheniscurrentlybeingrenovatedsotheyareabletoseethatinpractice.2. Analyzeyourassessmentdata.

a. Sortyourassessmentdatabasedonwherestudentslieinthecontinuumtomasteryof

thelearningobjectives.Whichstudentshavemasteredthelearningobjectives?Whichstudentsareapproachingmastery?Whichstudentshavesimilarmisconceptions?Lookforpatternsamongstudentresponsesthatdemonstrateparticularareasofneed.Usethecontentand/orprocesslearningprogressionsthatfityourlearningobjectivestohelpyou.

i. InmylessonthatIactuallytaughtIfoundthembothtobeintheapproachingmasterycategory.IfIwereteachingthisisarealclassroomIwouldexpecttohaveaspreadofstudents,andwouldprobablygroupthembasedonthestrategiesthattheyused,togroupstudentswithsimilarthinkingtogetherinsomeinstances,andtogroupthemwithstudentswithdifferentthinkinginotherssotheyareabletolearnfromeachother.ThisisanintroductorylessononareaandperimetersoIwouldnotexpectanystudentstohavereachedmastery,andIwouldonlyexpectsometobeapproachingmastery.Therecouldbeavarietyofmisconceptionspresentincludingtheideathatareaistheinsideandperimeteristheoutside.Thismisconceptionmakesthembelievethatthe

twoconceptsareunrelatedandtheyareunabletoseetherelationshipbetweenthetwo.Therecouldalsobemisunderstandingsoftheformulas,whichwouldleadtocomputationerrorsandthusincorrectanswers.

b. Describeoverallwhattheanalysisofassessmentdatarevealstoyouaboutstudents’

understanding,knowledge,andskillsrelativetothelearningobjectives.i. Myanalysisisobviouslyquiteincomplete,butifIweretohavealotmore

studentsIwouldusemyassessmenttooltoevaluateeachstudentanddeterminewhichobjectivestheymetandwhichobjectivesstillneedwork.Iwouldthenplanmyfuturelessonsaroundthisdata,withafocusonachievingtheobjectivesandmasteryofthecontentforeachstudent.

c. Describeinstructionalgroupsthatemergefromyouranalysis.Foreachgroup,include

thefollowinginformation:• PatternGroups–Avoidgeneralnamessuchas,“advanced,”“on-target”,“few

holes”,“struggling;”striveforcontent-specificnamessuchas“ReadytoMakeGeneralizeableArguments”,“DirectModeling”,or“____CalculationError”

• Distinguishingcharacteristicsofeachgroup(bemorespecificthatyouwereinsection2b)

• Sampleresponsesfromeachgroup• Numberofstudentsineachgroup

Group1wouldbetheCalculationErrorgroup.Thesestudentsseemtounderstandthegeneralconceptsandareabletoexplaintheirthinking,buttendtogetthewronganswersduetoincorrectusageoftheformulasandmiscalculations.Therearefivestudentsinthisgroup.Sampleresponses.A=bxh,baseis7,heightis4a=7x4soa=26.GroupTwowouldbethegroupthatisreadytobegingeneralization.Thesestudentshaveachievedmasteryofthiscontent,havemetalltheobjectivesandarenowabletoapplythiscontenttoothercontentareasinmathematicsandothersubjects.Therearesevenstudentsinthisgroup.Sampleresponse:Iknowthattheareaofthistriangleis14becauseImadethetriangleintoarectangle,foundthattheareaoftherectanglewas28anddivideditbytwo.IknowIcandothisbecauseeverytrianglecanbecomearectangle.GroupThreewouldbetheclosetomasterygroup.Thisgroupisapproachingmasterybuthasn’treacheditjustyet.Theyunderstandthecontent,butareunabletogeneralizeandconnectwithotherareasofmathematics.Thereare3studentsinthisgroup.SampleResponse:Iknowtheareais14becausetheareaofatriangleis½bhandb=7andh=4.Thefinalgroupwouldbethe“needsmoreinteractionwithcontent”group.Thisgroupisnotyetfluentwiththeconceptsandneedalotmoreinteractionbeforetheywillbeabletoapproachmastery.Theyareunabletofindtheareaandperimeterwithoutscaffolding.Therearesixstudentsinthisgroup.SampleResponse:Ithinkthattheareais24.Becausetheareaofarectangleissomethingwithbase,right?

3. Analyzeyourteachingstrategies.

a. Basedonyourassessmentdata,howeffectivewereyourteachingstrategiesforhelpingstudentsmeetthelearningobjectives?Justifyyouranalysisusingtheassessmentdata.

i. IbelievethatIwassuccessfuloverall.Thiswasmeanttobeanintroductorylevellessonthatsimplyintroducesthecontent,soitisexpectedthatsomestudentswillnotmeetmastery.Themajorityofthestudents(inthehypotheticalgroupsabove)wouldbeatwhatIconsideranacceptablelevelofunderstandingtomoveonwiththeunit.Icandifferentiatetheinstructionforthestudentsatthehighestandlowestlevelsgoingforward.

b. Describeatleastonewayyoucouldincorporatedevelopmentallyappropriatepractice

inabetterormorethoroughwayifyouweretoteachthislessonagain.i. Developmentallythestudentswillbeintheconcreteoperationalstage,

whichmeansthattheythinklogically,whichapplieswelltomathconceptsingeneral(McLeod,2009).BecauseofthisIwouldprobablyincorporatesomeaccesstomanipulativesinthefuture,andallowthestudentstofindtheareainthatway,givingthemaveryconcretepictureofarea.

c. Usethesereflectionsandyourteachingexperiencetoreviseyourlessonplans.Highlight

therevisionsandincludetherevisedlessonplansinyourPart5.4. Basedonyouranalysisofassessmentdataandteachingstrategies,writealessonplanfor“the

nextday”usingtheELED533lessonplanformat.Youmayhavethesame,similar,ordifferentlearningobjectives.BesurethatyourDuringPhaseincludesasmall-groupactivityforeachgroupdescribedinsection2c.Thiswillalsobeyourdifferentiationplanbasedonreadiness.Thesesmallgroupactivitiesshouldbestructuredtohelpdiversegroupsofstudents…

• …achievethesameUKDswithappropriatedegreesofsupportandchallenge,• …correctthemisconceptionsrevealedbytheassessment,and• …feelinvolvedinequallyrespectfultasks.

Mydaytwotaskwouldbeagamecalled“battleboxes”wherethestudentswouldplayinpartnerstogetthemostareaonthepagebyrollingdice.TheactivitywouldbeintroducesthroughaquickreviewoftheDay1activityandanexplanationoftheinstructionsofthegameandtheexpectationsoftheinstructor.Thenthestudentswouldbeabletoplaythegameusingdicetodeterminetheperimeteroftherectangles,andlatertriangles.Whiletheyplaythegametheinstructorwouldgoaroundtheroomaskingexpandingquestionsandobservingstrategies.Afterthegameisfinishedtheclasswouldengageinadiscussionaboutthestrategiestheyusedtoplayandtherealworldapplicationsfortheskillstheyhavelearned.

5. Asaresultofplanning,teaching,andanalyzingthislesson,whathaveyoulearnedorhad

reinforcedaboutyoungchildrenaslearnersofmathematics?a. Youngchildrenthinkconcretely,andwehavetoprovideforthisinourlessons.There

arealsoavarietyofpossiblemisconceptionsforthestudentstoencounterthroughoutschoolingthatcanmaketheconceptsofareaandperimeterdifficultforthemtounderstand.


reinforcedaboutteaching?a. Teachingmathematicsisnotassimpleasjustteachingtheconcepts.Childrencomeinto

classroomswithalargeamountofmisconceptions,andthesemisconceptionscancauseforalotofconfusioniftheyarenotdealtwith.Attimes,eventeacherscanbethecauseofthesemisconceptionsandweshouldbeawareofthemasweteachstudentstoensurewearenotgoingtobehinderingtheireducationdowntheroad.


reinforcedaboutyourself?a. I’malwaysverynervousaboutteachingmathematicsbutI’vefoundthroughthisclass

andthislessonplanningexperiencethatIammorequalifiedthanItendtobelieveIam.ThemoreIlearnaboutmathematicsthroughtheseclasses,themmoreIunderstandtheconceptsandfeelasifIwillbesuccessfulwhenteachingthemtomyownstudents.