eled 533 lesson plan format -...
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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
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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;
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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
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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,
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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!
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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
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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
• Square:whenthelengthofthesidesaregiven
• Rectangle:whenthelengthandwidtharegiven
• RightTriangle:whenthebaseandheightaregiven.
Iwillbeusingstudentworkasmydocumentation.ThroughstudentworkIamobservingifstudentsareusingavarietyofstrategiesdependingonthesituationtodeterminetheareaofasquare,rectangle,andrighttriangle.
Studentneedstobeusingorattemptingdifferentstrategiestoindicatetomethattheyareachievingorworkingtowardsmyobjective.Iftheyhaveachievedthisgoaltheywillbeabletousedifferentstrategiescorrectlyandflexiblywhileworking.Strategiescanbeexpressedverbally,throughindividualwork,orwithpartners.
D4:differentiateamongconceptsofarea,perimeter,andvolume
Iwillbeusingdiscussionasmydocumentation.WhileobservingandcommunicatingwithstudentsIamlookingforstudenttobeusinglanguagethatrepresentstheirunderstandingofthedifferencesamongtheconceptsofarea,perimeter,andvolumeastheyexplaintheirreasoningorstrategytosolvetheproblem.
Iwillknowstudentshaveachievedmyobjectiveswhentheyareabletoexpressthatareaandperimeteraregeometricmeasurementsusedtomeasureplanefiguresandvolumeisameasureofcapacityincubicunits.Studentswillalsobeabletoexpresswhatmakeseachmeasurement.
D5:developaprocedureoffindingvolumeusingmanipulatives
Iwillbeusingstudentworkasmydocumentation.ThroughstudentworkIamobservingifstudentsareusingavarietyofstrategies
Iwillknowstudentshaveachievedmygoalthroughtheirrepresentationofmodelscreatedtoexpressvolume
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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
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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
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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:
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• 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
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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
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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.
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• 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:
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• 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
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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-
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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
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determinetheareaofasquare,rectangle,andrighttrianglewithourwithoutdiagrams
• Square:whenthelengthofthesidesaregiven
• Rectangle:whenthelengthandwidtharegiven
• RightTriangle:whenthebaseandheightaregiven.
D4:differentiateamongconceptsofarea,perimeter,andvolume
D5:developaprocedureoffindingvolumeusingmanipulatives
D6:determinethevolumeinstandardunitsD7:describepracticalsituationswherearea,perimeter,andvolumeareappropriatemeasurestouse,andjustifytheirchoicesorallyorinwriting.
D8:identifywhethertheapplicationoftheconceptsofperimeter,area,orvolumeisappropriateforagivensituation
LessonImplementationReflection&AssessmentAnalysis(Part5oftheLessonPlanningProject)
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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
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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?
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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.
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6. Asaresultofplanning,teaching,andanalyzingthislesson,whathaveyoulearnedorhad
reinforcedaboutteaching?a. Teachingmathematicsisnotassimpleasjustteachingtheconcepts.Childrencomeinto
classroomswithalargeamountofmisconceptions,andthesemisconceptionscancauseforalotofconfusioniftheyarenotdealtwith.Attimes,eventeacherscanbethecauseofthesemisconceptionsandweshouldbeawareofthemasweteachstudentstoensurewearenotgoingtobehinderingtheireducationdowntheroad.
7. Asaresultofplanning,teaching,andanalyzingthislesson,whathaveyoulearnedorhad
reinforcedaboutyourself?a. I’malwaysverynervousaboutteachingmathematicsbutI’vefoundthroughthisclass
andthislessonplanningexperiencethatIammorequalifiedthanItendtobelieveIam.ThemoreIlearnaboutmathematicsthroughtheseclasses,themmoreIunderstandtheconceptsandfeelasifIwillbesuccessfulwhenteachingthemtomyownstudents.