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Grade5MathematicsLessonPlan
ShapeandSpace
PreparedforEDUC5433
ElementarySchoolMathematicsMethods
October29,2008
PeterKennedyJacobLingleySheenMcDonaldLeighMuething
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TableofContentsIntroduction iSCOD2CalculatingAreasofIrregularShapes 1
ActivitySheetWhereHasMyPolyGon? 4
SCOD3DeterminingtheMeasureofRight,AcuteandObtuseAngles 5
ActivitySheetWhatsYourAngle? 8SCOD4DemonstratinganunderstandingoftherelationshipamongparticularSIunits. 9SCOD5DevelopingandUsingFormulasforAreasandPerimetersofSquaresandRectangles9SCOD6SolvingSimpleProblemsInvolvingVolumeandCapacity 9SCOD8DeterminingwhichUnitofMeasureisAppropriateinaGivenSituationandSolving9 ProblemsInvolvingLengthandArea
Lesson1RelationshipbetweenSIUnits 10ActivitySheetMeasurementScavengerHunt 12ActivitySheetMeasurementsofMe 13ActivitySheetMeasurementsinMyLife 15ActivitySheetMeasurementsatMySchool 16Lesson2PerimeterandArea 18ActivitySheetArea 20ActivitySheetPerimeter(easier) 21ActivitySheetPerimeter(harder) 23ActivitySheetAreaofaRectangle(remediationworksheet) 25ActivitySheetAreaandPerimeter(remediationworksheet) 27Lesson3VolumeandCapacity 29ActivitySheetReadingFromaScale 31ActivitySheetVolumeofaCylinder 33
SCOD7Estimatinganglesizeindegrees 35
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IntroductionTheselessonplansaredesignedtoaddressSpecificCurriculumOutcomes(SCOs)intheNewBrunswickMathCurriculumforGrade5.SpecificallytheyaddressSCOsD2toD8.TheseSCOsaredesignedtodevelopstudentsunderstandingandabilitytodefineshapesandspace.ThemainfocusoftheseSCOsismeasurement.Thisincludestopicssuchasunderstandingmetricunits;measuring,estimatingandidentifyingdifferentkindsofangles;calculatingareaandperimeter;andcalculatingvolumeandcapacity.OuraiminwritingthisbookletistoteachtheseSCOsthroughconstructivismandcollaboration.Constructivismmeansteachingstudentsthroughencouragingacreativeatmosphere,oftenusinggamesandmanipulatives,wherestudentscanlearnmaththroughattemptingtosolveproblemstheirownwayanddiscussingadiversityofsolutionswiththeirclassmates.Thisisopposedtothemethodofbeingshownonlyonewayofreachinganoutcomeandthentryingtoreplicatetheprocesswhilealwaysrelyingontheteacherfortherightanswer.Thisencouragesstudentsnaturalcuriosityandhelpsdeveloptheirselfconfidenceindoingmathematics.Collaborationmeansanatmospherewherestudentsareencouragedtoworktogethertosolveproblemsandtodothemajorityofschoolwork.Thisapproachfocusesonworkinginteamstohelpdevelopgoodproblemsolvingskillsthroughlearningfromotherstudentsaswellassocialinteractiveskillsthroughgroupdiscussion.ThelessonsthatarepresentedwithinthisUnitPlanarearrangeddependentoncurriculumoutcomesasdevelopedbytheAtlanticCanadaMathematicsCurriculumDocument.Thisarrangementisthoughttofacilitateconstructivistbasedlearning,andthusmaynotbeconducivetoeveryclassroom.Manyteachersmayadaptthearrangementsofindividuallessonswithinthisdocumenttotheirindividualspecifications.
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Grade5MathematicsLessonPlanMeasurement
Teacher:Mr.PeterKennedy Duration:50min Unit:ShapeandSpace
Outcome:Studentswilldemonstrateanunderstandingofanapplyconceptsandskillsassociatedwithmeasurement.
SCO(D2):Bytheendofgrade5,studentswillbeexpectedtocalculateareasofirregularshapes.
Objective:Studentsshouldbeabletousegeoboardstodisplaytheperimeterofanobjectorfigureandtohelpthemcalculatetheareasofavarietyofshapes.
Resources/Materials:
Geoboards
Elastics(atleast45pertable)
transparentgeoboardforinstructor(useonoverhead)
onlinegeoboard(http://nlvm.usu.edu/en/nav/frames_asid_172_g_2_t_3.html?open=activities),
WarmUpActivity(5minutes):
Theteachershouldholdupflashcardswithdifferentpolygons.Havestudentsworkingroupstocreatethepolygonsbyusingtheirbodiesandholdinghands.Havestudentscounteachpersonasoneunittodeterminetheperimeteroftheshapetheyhavemade.(Thereisnorightanswer.Studentsmayhavedifferentunitlengths.)
Review:
Studentsshouldreviewthedefinitionofapolygonandgivesomeexamples.Studentsshouldthenreviewasaclasstheformulasforcalculatingtheareaofbasicshapes(square,rectangle,andtriangle).Theteachershouldwritetheformulasonawhiteboardorchartpaper.
LessonOverview:
1. Makesurethateachstudenthasageoboardand5or6elasticbands.2. Letthechildrenplaywiththeboardsfor3minutes.3. Modelashapeusingtheoverheadtransparencyandhavethestudentscreatetheshapeontheir
geoboard.4. Askthemhowmanysquaresarearoundtheoutsideoftheshape?5. Askthemwhatthisrepresents?Makesuretheyunderstandthatthisistheperimeterofthe
shape.6. Explainthateachsquarerepresentsaunit.7. Modelanewshapeforthestudentsandtellthemitrepresentsagarden.Explaintothemthat
youwanttodeterminehowlargeyourgardenissoyoucanbuytherightamountofsoil.
VocabularyWordBank
Perimeter
Area
Polygon
unit
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8. Askthemhowmanysquarestheyseeinsidetheshape?Dependingontheshapeyouchoose,studentsmayaskwhattodoiftherearehalfsquares.Askthestudentshowtheythinktheyshouldcountthem?Helpguidethemtothecorrectresponse.
9. Askthemwhattheythinkthenumberofsquaresrepresents?Facilitatethediscoverythatisrepresentsarea.
10. Havethestudentsmodel3moreshapesandhavethemcountthesquarestodeterminearea.11. Ifthestudentsappeartounderstandtheconcept,moveontothewordproblemworksheet.If
theydonot,keepworkingonmodelingshapesforthestudents.12. Whenyoumoveontotheworksheet,dothefirstproblemasaclass.Makesurestudents
understandhowtofindtherelevantinformationintheproblemandaremodelingitcorrectlyontheirgeoboards.
13. Havestudentsworkinsmallgroupstocompletetheworksheet.14. Ifstudentsfinishtheworksheetwithtimeremainingorappeartobestruggling,moveonto
enrichment/remediation.
Closure:
Modelafinalshapeontheboardandreviewhowtocalculatetheperimeterandtheareaoftheshape.Explaintothestudentsthatintheirnextlessontheywillbediscoveringhowtocalculateperimeterusingaformuladerivedfromthegeoboard.Explainthehomeworkforthelesson.
Assessment:
Inclassassessmentforthislessonwillbeinformal.Walkaroundtheclassasthestudentsareworkingandchecktoseethatstudentsaremodelingtheirshapescorrectlyusingthegeoboard.
Homework:
Eachstudentmustmakealistoffiveitemsintheirhouseholdthattheycouldcalculatetheareaofbyusingthemethodslearnedinclass.
Enrichment/Remediation:
1. Challengestudentstofindasmanyshapesaspossibleonageoboardwithagivenarea.Forexample,givenanareaof5squareunits.
2. Studentswhohaveshowncompetencywiththelessonsskillscanplayagamewithapartner.Onepartnerwillcreateapolygonontheirgeoboard.Theotherstudentwilltrytorecreatethesameshapeontheirgeoboardbyaskingquestionsabouttheshape.
3. Havestudentsusetheonlinegeoboardtoincorporatetechnologyintothelesson.4. Thiscanalsobeusedforstudentswhohaveanydifficultywithfinemotorskills.Theymay
strugglewiththeelastics.5. Studentswhoarestrugglingcanbegivenpremadeflashcardsthathaveanimageofashape
onageoboardincludingthenumericmeasurements.Studentsshouldattempttorecreatetheimagesontheirowngeoboard.
Evaluation:
Inasubsequentlesson,studentswillworkingroupstocreatewordproblemsabouttheareaofpolygons.Thesequestionswillbeusedtocreateaunittest.
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ImplicationsforFutureClasses:Thislessonwillhelpgivestudentsthefoundationfordeterminingtheareaofpolygonsandirregularshapes.Itisalsothefoundationforfuturediscoveryoftheformulaforcalculatingtheareaofapolygon.
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Where has my Poly-gon?
1 . Farmer John has a f ield of pigs, but they keep running away. He decides to put a fence up around his f ield so he wont lose his pigs. Farmer John makes his fence a rectangle that is 10 units long and 5 units wide. What is the total area the pigs wi l l have to play in? _________________________________
2. Stuntman Bob is doing his famous jump out of an airplane. When he parachutes down, he has to land on his target. His partner Steve mapped out the target with red paint on the grass. What was the total area of grass that Stuntman Bob could land in? _____________________
3. Toms dad wanted to build Tom a tree-house for his birthday. The trees in the back yard caused Toms dad to build the tree-house in an irregular space. What is the total area of Toms new tree-house? ______________
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Grade5MathematicsLessonPlanMeasurement
Teacher:Mr.JacobLingley Duration:50min Unit:ShapeandSpace
Outcome:Studentswilldemonstrateanunderstandingofanapplyconceptsandskillsassociatedwithmeasurement.
SCO(D3):Bytheendofgrade5,studentswillbeexpectedtodeterminethemeasureofright,acuteandobtuseangles.
Objective:Manystudentsinelementarymathclassesfindthemeasurementofanglesadifficultconceptsincetheindividualdegreeunitsareminisculeandcircularincomparisontoothermeasurementtechniquesthathavebeenpreviouslydemonstratedtothestudents.
Theprincipleobjectivefromthislessonplanistoreducetheproblemsencounteredduringanglemeasurementwithaprotractorasameasurementtool.Thiswillbeachievedbythegradualintroductionofanglemeasurementconceptsbymeansofsimplifiedprotractordesign.
Resources/Materials:
Transparencies(quarterofapageforeachstudent)
PermanentMarkers
CakeDiagramwith360sections
PhotocopiedRealProtractorsonTransparencies
WarmUpActivity(5minutes):
Inanefforttoinitiatemathematicthoughtsinrelationtoanglemeasurement,explaintothestudentsthatyouareapartofthelargestbirthdaypartyintheworldwith360guests.Itisyourjobasthecakecuttertoserve360piecesoutofonesinglecake.Youcanallowthestudentstomaketheinferencethatawholecakerepresents360pieces:sincethisistrue,askthem:howmanypiecesareinahalfofthecake?,aquarter?.Thestudentsshouldthenbeexplainedthatsincethiscakeisacircle,everypiecerepresentsadegreeofacircle.Thisillustrationwillhelpthemperceivefromthevisualofaquarterofacake,howmanydegreesmaybeinaquarterofacircle,andthuswillformthebasisofanglemeasurement.
Review:
Buildingonconceptslearnedingrade4,studentswillcontinuetolearnhowmeasureangles.Particularlytograde5students,theywillnowberequiredtounderstandanglesintermsofdegreesasopposedtoturnsinaccordancetowhattheylearnedingrade4.Studentshavepreviouslyclassifiedanglesaseitherright,acuteandobtusesimplybyjudgingtheiroverallappearance.Thegoalsofthisparticularoutcomewillensurethattheynowbegintounderstandtherelevanceofdegreeunitsinrelationtotheseanglecategories.
VocabularyWordBank:
protractor degreeunit measurement quarter half whole fractionalpieces
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LessonOverview:
1) Afterthewarmupactivity,quicklyreviewtheconceptsofangleclassificationwiththestudents.Usingtheattachedangles,askthemtoidentifyinunison,aseriesofobtuse,rightaswellasanacuteangles.
2) Asaclass,introducethemtowhatarealprotractorlookslikebyshowingthemanenlargedteacherversion(seeattachedhandout).Quicklyreviewtheconceptsnecessarytomeasureangles;i.e.:howtoalignthebottomoftheprotractorwiththevertexoftheangleandthatitisnecessaryforthearmoftheangletoextendtothemeasuredunitsoftheprotractor.
3) Separatetheclassintogroupsoffour,andexplaintothemthatitistheirturntoconstructaprotractorusingthesemicircularshapesprecutoutofTransparencies.Inanefforttoemphasizethecompositionofangles,havethemfoldthesemicircularpiecesofconstructionpaperinhalfandlabelthefoldlineas90.Thenhavethemfoldtheedgeofthecircletowardsthefoldline,creasingitwhentheygetthere.Labelthisfoldlineas45.Theycanfurtherfoldtheedgeintothe45lineandaskthemtolabelwhattheybelievethatlineis.Isitobtuseoracute?
4) Usingthenewlyconstructedprotractors,havestudentsestimatetheanglesonaworksheet(seeattached)simplybycomparing.
5) Studentscannowbeintroducedtorealprotractorsthathavebeenphotocopiedontotransparencies.Itwillgreatlyhelpthestudentsiftheseprotractorsonlyhavenumberinginonedirection.Makesurethattheprotractorsmeasuringvertexisontheedgeoftheprotractorsothatstudentsarenotconfusedbywastedspaceonthebottomoftheprotractor.
6) Usingtheirprotractors,havestudentscreateanacuteangle,whichislessthanhalfthesizeofarightangle.
7) Usingaseparatesheetofpaper,askeachstudenttodrawashapethatcontainsatleast4obtuseanglesand3acuteangles.Thenhavestudentstradetheseshapeswithanotherstudentandaskthemtoidentifytheobtuseandacuteangles,andmeasurethemusingtheirprotractors.
Closure:Brieflyreviewwiththeclasswhatwasaccomplishedtoday.Asawaytosolidifywhatitisthattheylearned,havethemlookaroundtheclassandestimatebylookingataprotractorwhatsomeoftheanglesareintheclassroom.Theycannowestimateintermsofdegreeunitsasopposedtosimplythedescriptors:acute,obtuse,andrightangles.
Homework:
Havestudentsreturntotheirhousesandmakenoteofsurfacesintheirkitchenthatareeitheracuteorobtuseangles.Answerscaninclude:sinkfaucets,pothandles,stovehandles,tablelegs,etc.
Assessment:
Attheendoftheclasscollecttheworksheetandgradeforthelevelofcompletionandunderstanding.
Instructorshouldbeabletocirculatethroughouttheclassroomensuringthateachstudentcomprehendsthesubjectmatter,andmarkhisorherachievementwithaparticipationrubric.
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Enrichment:
Therearevariousactivitiesthatcanbeusedforenrichment.Havestudentsponderhowtheywouldusetheirnewprotractortomeasureanglesthataregreaterthan180.Also,askthemtoexplaintheadvantagesanddisadvantagesofchairbacksthatareobtuse/acute/oratrightanglestoyourback.Ifstudentsareparticularlyinterestedinthetopic,theycanmakeapostertopromotetheircontemporaryfurnituredesignsovertraditionalfurnituredesignsfoundintheclassroom.
Remediation:
Studentswhoarehavingdifficultywiththesubjectmatterofthelessoncouldworkonanattachedproblemsheettofurtherpromotetheirunderstandingofanglemeasurement.Theseanglescouldbesimplisticvariationsof90,45and135anglesthathavebeenrotatedaroundtheirvertex.Perhapsifthereisastrongstudentworkingonanenrichmentproject,thentheycanlendahandtothestudentswhoneedfurthersupport.
Evaluation:
Atthebeginningofnextclass,askstudentstoformulatewordproblemsthatcouldbeusedtotesttheirknowledgeofanglemeasurementforaunittest.Thisenablesthemtoalreadyknowsomeaspectsoftheevaluationprocedureandthereforewilllimittheunknownsattesttime.
PossibleImplicationsforFutureClasses:
Withtheinformationgleamedfromthislesson,studentswillnowhavethepreliminaryconceptsinplacetobegintheirunderstandingofvolume,perimeteraswellastrigonometry.
InformationabovecompiledwithreferencetotheAtlanticCanadaMathematicsCurriculumGuide.
LessonResourcePack:
SampleSimpleProtractor
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Grade5MathematicsLessonPlanMeasurement
Teacher:Mr.LeighMuething Duration:3x50min Unit:ShapeandSpace
Outcome:Studentswilldemonstrateanunderstandingofanapplyconceptsandskillsassociatedwithmeasurement.
SCO(D4):Bytheendofgrade5,studentswillbeexpectedtodemonstrateanunderstandingoftherelationshipamongparticularSIunits.
SCO(D5):Bytheendofgrade5,studentswillbeexpectedtodevelopanduseformulasforareasandperimetersofsquaresandrectangles.
SCO(D6):Bytheendofgrade5,studentswillbeexpectedtosolvesimpleproblemsinvolvingvolumeandcapacity.
SCO(D8):Bytheendofgrade5,studentswillbeexpectedtodeterminewhichunitofmeasureisappropriateinagivensituationandsolveproblemsinvolvinglengthandarea.
Objective:Thisunitwillteachthebasicsofmeasurementandestimation.StudentswilldevelopaconcreteunderstandingoftheSI(metric)systemandtherelationshipsamongthevariousunits.Theywilldeveloptheirunderstandingofwhichmeasuretouseinagivensituation.Theywilllearnhowtodeveloptheformulaeforperimeter,area,volumeandcapacityandhowtosolvesimpleproblemsassociatedwiththem.Theywillalsopracticeestimatingallofthesemeasures.
Resources/Materials:
Lesson1o Tapemeasures(1foreachstudent)o Rulers(1foreachstudent)o pencilo MeasurementScavengerHuntsheetso Timer(orsomethingthatmakesnoise)o Largeworldmapo Miscellaneousobjectstomeasure(anduseanythingalreadyintheclassroom)o Ropepieces(1metrelong)o Scissorso Yarn
Lesson2o 2cm2GridPapero Setsof36squaretiles(1foreachgroup)
Lesson3o Setsof7miscellaneouscontainerslabeled1to6with1labeledtarget(1foreachgroup)o Measuringcups(1foreachgroup)o Containersofriceorbeans(1foreachgroup)o Scoopsandfunnels(1ofeachforeachgroup)o Setsofcontainerslabeledwiththeirvolume(1foreachgroup)
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VocabularyWordBank:
Notethatscalesofeach(milli,centi,deci,kilo)andtheirrelationshipstoeachotherwillbediscussed.
Background(Lesson1):
Thislessonwillencompassthebasicunitsinthemetricsystemanddemonstratetherelationshipsbetweenthem.(ie.1km=100dm=1000m=10,000cm100,000mm)Studentswillpracticemeasuringobjectsanddevelopingformulaedeterminingperimetre,area,volumeandcapacity.Studentswillpracticesolvingproblemsassociatedwiththeseconceptsaswellasestimatingmeasurementsandconfirmingtheirestimates.
LessonOverview(Lesson1):
Section1RelationshipbetweenSIUnits45minutesReference(VandeWallep.410)Introduction(15minutes)MeasurementScavengerHunt
1. PassoutMeasurementScavengerHuntsheets2. Explainthatstudentsneedtofindobjects,people,containers,placesetctofillinanswers3. Explainthat10minwillbegivenandifthisisnotenoughtimethenitcanbefinishedfor
homework4. Allow10mintofillinsheet5. Give2minuteand1minutewarningsandsaywhentimeisfinished6. Discussanswersfor5min7. Explainthatstudentscanfinishlaterinclassiftheyfinishtheirworkearlyorforhomework
DiscusstheScavengerHunt Whataresomeobjectsthatstudentsfound?(writethemontheboardincm) Whataresomeplacesthatstudentschose?(writethemontheboardinkmWhydoweusecertainunitsforheight,distanceetc.?
Tomakemeasurementseasiertounderstand Tomakewritingmeasurementseasier
ThinkPairShareActivity(10minutes)Whatdoweusetheunitsfor?
1. Writemetresscales(milli,kiloetc.)onboardincolumns.2. Askstudentstobrainstormwhateachisusedfor.3. Give2minutestothinkindividually,2minutestobrainstorminpairs.4. Discussusesforeachunitasaclass,writingusesinthecolumnsbeloweachunit.
a. Ex.kmmcmb. Distancedistance,heightheight,lengthofsmallobjects
Metreso Length,Width,Distance,Perimeter,o Area,Volume
Literso Capacity
Gramso Mass
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Activity(10minutes)AboutOneUnit(VandeWalle410)
1. WriteprefixesforSIsystema. Ex.kilo,deci,centi,milli
2. Whatistherelationshipbetweenthedifferentunits?a. Ex.1km=100dm=1000m=10,000cm100,000mm
3. Havestudentsbrainstormobjectsthatareapproximately1metrelong,wide,around(circle)etc.4. Givestudents1metreropepiecesandgive5minutestofindasmany1metreobjectsastheycan5. Discussanswersasaclassandwriteontheboard
AssessmentActivity(10minutes)MeasurementsofMe1. Passoutsheets2. Groupstudentsintopairs.3. Havestudentsmeasureeachothersotheycanfillintheirbooklets.4. Havestudentscutoutandtietheirbookletstogetherwithyarn.5. Note:Theseworksheetswillbechangedtometricmeasurements
Homework: FinishMeasurementScavengerHuntandMeasurementsofMeRemediation:MeasurementsinmyLifeworksheetEnrichment: MeasurementsatmySchoolbookletAssessment:Takenoteoflevelofunderstandingthroughclassdiscussions,completionofactivitiesand
completionofhomework.
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MeasurementScavengerHunt
ObjectsandPeople Containers Places something that is about 1.5 meters long
something that holds more than 300 milliliters of liquid
A city that is more than 100 kilometers away from Fredericton
something that is more than 75 centimeters wide
Something that can hold liquid from at least 3 pop cans
A country that is more than 1000 km away from Canada.
someone who is more than 80 centimeters tall
Someone who drinks at least 2 liters of liquid each day
A continent that is bigger than North America
someone whose arms are more than 30 centimeters long.
The amount of liquid I have drank so far today
An island which is smaller than Prince Edward Island
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Name _______________________
Date ________________________
Write or draw items in your home where you
use the following measurements:
Gram Kilogram Milligram Liter
Millimeter Centimeter Meter Kilometer
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LessonOverview(Lesson2):
Section2PerimetreandArea45MinutesWarmup(10minutes)
1. ReviewMeasurementScavengerHuntandMeasurementsofMeactivitiesasaclass.2. Writetablesonboardtocompareanswers.
StudentsdiscussanswerstoScavengerHuntinasmallgroup StudentsdiscussanswerstoScavengerHuntasaclass Writeanswersontheboardundercolumnswithquestionsasheadings Askquestionsaboutthedifferentmeasurements Ex.Whydowehavedifferentunitsinthemetricsystem? (tomeasuredifferentthingssuchaslargeandsmallsizes,smallandverygreatdistancesand
solidsandliquids) Whydoweusedifferentunitsofthosemeasurements? (heightofpeoplevs.heightofbuildings,glassofwatervs.theocean)
Activity(10minutes)FixedPerimetres(VandeWalle401)
1. Passout2cm2gridpaper2. ExplaintaskDrawallpossiblerectangleswithaperimeterof24cmandshowanexample.3. Checktoensureunderstandingofconceptofperimetre(distancearoundanobject)4. Discusshowtofindperimetre.(length+width+length+width)5. Explainthattheyshouldrecordthedimensionsofalloftherectanglesinatable.6. Showthemhowtodrawatable.
FixedPerimetresActivityReview(5minutes)
ExampleQuestionsHowmanyrectanglesarepossible?Whatdimensionsarepossible?Whatisperimetre?
Activity(10minutes)FixedAreas(VandeWalle401402)
1. Give1setof36tilestoeachgroup2. ExplainTaskMakeasmanyrectanglesasyoucanwhichincludeallofthe36tiles3. Checktoensureunderstandingofconceptofarea(amountofspaceanobjectcovers)4. Explainthattheyshouldrecordthedimensionsofalloftherectanglesthattheymakeinatable5. Demonstratehowtodrawthetable
FixedAreasActivityReview(5minutes)
ExampleQuestionsHowmanyrectanglesarepossible?Whatdimensionsarepossible?Whatisarea?Howdoyoufindtheareaofanobject?(lengthxwidth)
ClassDiscussionAreaandPerimeter(5minutes)
ExampleQuestionsHowwouldyoudefineperimetreandarea?Whatarethedifferencesbetweenthem?Howdofindtheperimetreandareaofotherobjects?
Homework:PerimeterWorksheet1or2(dependingonunderstandinginclass)andAreaWorksheet
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Remediation:AreaRemediationWorksheet,AreaPerimeterRemediationWorksheetEnrichment:GraphPlotting(VandeWalle402)
Studentscandrawgraphstoillustratetherelationshipbetweenperimeterandareaintherectanglesthattheycreated.Theycanprepareashortpresentationtopresenttotheclass.
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LessonOverview(Lesson3):
Section3VolumeandCapacity45MinutesWarmUp10MinutesAreaandPerimetreStudentswhopreparedthegraphcanpresentittotheclass.Ifnostudentspreparedthisthentheteachercanpresentthegraphtotheclass.ThiswillleadtoaclassdiscussiononPerimetreandarea.ExampleQuestionsWhatisperimetre?Whatisarea?Howaretheyrelated?Whataresomeinterestingpointsoftherelationship?Thingstomention
Forafixedareatheshapewiththesmallestperimeterisasquare. Forafixedperimeter,therectanglewiththelargestareaisasquare. Theshapewiththesmallestperimeterandafixedareaisacircle. Foraconstantareathefatterashape,thesmalleritsperimetre,theskinnierashape,thelarger
itsperimetre.ActivityCapacitySort15minutes(VandeWalle403)
1. HandoutsetsoflabeledcontainerswithtargetcontainerandCapacitySortworksheet.2. Explainthatstudentswillestimateifcontainerscanholdmoreorlessthanthetargetcontainer3. AskthemtodiscussintheirgroupsandwritetheiranswersinthefirsttableonCapacitySort
4. Handoutmeasuringcups,riceorbeansandscoopsandfunnelstogroups.5. Explainthatstudentswillmeasurecontainerstoseeiftheycanholdmoreorlessthanthe
targetcontainer.6. AskthemtodiscussintheirgroupsandwritetheiranswersinthesecondtableonCapacity
Sort
7. Asaclassdiscusswhatstudentsfoundandwhattheconceptofcapacityis.(howmuchacontainercanhold,usuallymeasuredinliters,millilitersetc.)
ActivityVolumeLineup10minutes(VandeWalle403)
1. Handoutcontainerslabeledwithvolumes.2. Explainthatstudentsmustsortallofthecontainersfromleasttogreatestvolumes
3. Asaclassdiscusswhatstudentsfound,whethertheactivitywasdifficultornot(andwhyorwhy
not),andwhattheconceptofvolumeis(howmuchspaceacontainertakesup)ClassDiscussionCapacityandVolume10minutes
ExampleQuestionsWhatiscapacity?Whatisvolume?Howaretheymeasured?Howaret heyrelated?Howdoyoufindthem?Homework:ReadVolumeReadingExplanationandVolumeWorksheetRemediation:Teachercanpairstudentshavingdifficultywithstudentsprogressingquicklysothat
theycanexplainbothactivities.Theteachercanspendtimehelpingstudentshavingdifficultyaswellifnecessary.
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Enrichment:ReadVolumeReadingExplanationandusemeasuringcontainerstonotehowmuchwaterdifferentobjectsdisplace.Writedowntheamountofdisplacementfordifferentobjectsandexplainwhyyouthinkdifferentobjectsdisplacedifferentamountsofwater.
Assessment:Takenoteoflevelofunderstandingthroughclassdiscussions,completionofactivitiesand
completionofhomework.
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www.randommasters.com.au F9 Educational Pty Ltd, 2007
1000
25
200 250100 50
400 500200 100
600 750300 150
Q.1 Q.2 Q.3
500 250 1000 Q.4
400
Q.5100
75
Reading from a ScaleVolume from Metric Measuring Cylinders
By examining the scale markings, determine the volume represented by each small division/graduation.
Use this to determine the volume of water in the cylinder (in millilitres).
200 800 1000
Q.6
Q.7
150 1500
50 500
50
100
200 2000
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www.randommasters.com.au F9 Educational Pty Ltd, 2007
The difference between each pair of marked volumes is 500ml, split into 4 divisions.
Therefore, each division represents 125ml. The total volume of water in the cylinder is
1750ml.
The difference between each pair of marked volumes is 25ml, split into 5 divisions.
Therefore, each division represents 5ml. The total volume of water in the cylinder is 90ml.
Reading from a Scale : Solutions
Q.1
Q.2
The difference between each pair of marked volumes is 100ml, split into 5 divisions.
Therefore, each division represents 20ml. The total volume of water in the cylinder is
360ml.
The difference between each pair of marked volumes is 50ml, split into 5 divisions.
Therefore, each division represents 10ml. The total volume of water in the cylinder is
110ml.
Volume from Metric Measuring Cylinders
Q.6
Q.7
To determine the volume represented by each small division/graduation, divide the difference between
two marked volumes by the number of divisions between them.
The difference between each pair of marked volumes is 250ml, split into 5 divisions.
Therefore, each division represents 50ml. The total volume of water in the cylinder is
700ml.
The difference between each pair of marked volumes is 50ml, split into 2 divisions.
Therefore, each division represents 25ml. The total volume of water in the cylinder is
50ml.
Q.3
Q.4
Q.5
The difference between each pair of marked volumes is 200ml, split into 5 divisions.
Therefore, each division represents 40ml. The total volume of water in the cylinder is
680ml.
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www.randommasters.com.au F9 Educational Pty Ltd, 2007
r = 15mm
Q.1
h = 16m
Q.2
h = 20mm
r = 7m
Q.3
r = 6cm Q.4 r = 17m
h = 7m
h = 11cm
Q.5
r = 2mm
h = 12mm
Volume of a Cylinder
Using this formula, calculate the volume of the cylinders pictured below.
Like prisms, the volume of a cylinder can be calculated using the general formula
Volume of Prism = Area of Base ! Height. So, the volume of a cylinder can be calculated using the
specific formula:
Volume of Cylinder =
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www.randommasters.com.au F9 Educational Pty Ltd, 2007
! ! " #
Q.1 Volume = "r# ! h
= "!15#!20
= 14137.17 mm$
Q.2 Volume = "r# ! h
= "!7#!16
= 2463.01 m$
Q.3 Volume = "r# ! h
= "!6#!11
= 1244.07 cm$
Q.4 Volume = "r# ! h
= "!17#!7
= 6355.44 m$
Q.5 Volume = "r# ! h
= "!2#!12
= 150.8 mm$
Volume of a Cylinder : Answers
Note : Answers in this exercise are calculated using ! to full calculator accuracy. If the approximation ! =
3.14 is used, answers will be slightly less than those shown.
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Grade5MathematicsLessonPlanMeasurement
Teacher:Ms.SheenaMcDonald Duration:50min Unit:ShapeandSpace
Outcome:Studentswilldemonstrateanunderstandingofanapplyconceptsandskillsassociatedwithmeasurement.
SCO(D7):Bytheendofgrade5,studentswillbeexpectedestimateanglesizeindegrees.
Objective:Thegoalistobeabletoestimatethemeasureofangleswithin510degreesoftheiractualsize.Aswellasbeingabletolookatanangleandgiveanestimateoftheclosestangleinname.Thestudentsshouldalsobeabletotakeanangleindegreesandbeabletoestimatewhatitmightlooklike.
Resources/Materials:
PipeCleanersorStraws
Protractors
Transparencies
HandoutsforHomeworkActivity
WarmUpActivity:
GetallthestudentstostandupandplaySimonsayswiththem.WhileplayingthegameSimonsaystoputtheirarmsacertainwayanddemonstratethedifferentanglesthattheymaybemakingwiththeirarmsafterinstructingthemtodoso(3minutes).
BackupActivity(Ifextratime):Distributepatternblocksandhavestudentsusetheirhandmadeprotractorstofinddifferentanglesfoundwithintheblocks.
Review:
Reviewthedifferentnamesoftheanglesthatareknownanddemonstratesomecommontricksthatwillhelpthemtorememberthedifferentangles(2minutes).
Arightanglewhichis90
AnAcuteanglewhichislessthan90butmorethan0
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Andobtuseangleismorethan90butlessthan180
Astraightangleis180
Andareflexangleismorethan180butlessthan360
Drawtheseanglesontheboardorontheprojectorandthendrawahappyfaceintheacuteangleandcallitacuteangle.Drawacookiemonsterlikefaceintheobtuseangleandthestudentscanmaketheconnectionthatheatetoomancookiessoheisabiggerangle(2minutes).
Ifthestudentsarentmakingtheconnectionandarestillhavingahardtimerememberingthedifferentangles,thenshowthemaclockorfractionwheelandtrytoassociateclockfaceswithangles.At6oclockitisa180anglewhichisastraightangle.At3and9oclockitmakesrightanglesfromtheminutehandand2oclockisanacuteangle.4oclockthenmakesanobtuseangleandthenifyouadd2morehourstotheobtuseitmakes6oclockwhichisbacktothestraightangle.Thisactivitymaynotworkandmaybeharderforsomestudentstounderstandsincesomeofthemhaveahardtimetellingtimeandreadingaclock(3minutes).
Makesuretopointouttothemthatanglesaremeasuredindegreesandshowthemthesymbolforit,whichis(1minute).
LessonOverview:
Providestudentswithpipecleanersorstrawsthattheycanbendtoformanglesandworkwith.Askthemtomakedifferentanglesandthencomparetheirestimateswiththeirneighbours.Thenallowthemtocompareittoyoursontheprojector.Explaintothemandshowthemthatevenifthepipecleanersarelongeritdoesntchangetheangleontheinside.Continuetoaskthemtomakedifferentangles.(5minutes)
Nexthavepairsofstudentsworktogether.Onestudentmakesanangleandtheotherestimatesthesize.Theycancheckthemeasurementusingtheirprotractors.(4minutes)
Ontheoverheadgiveananglesuchas45andaskthestudentstodrawit.Thenallowthemtocompareittoyoursontheprojectorandrepeatwithdifferentangles.(5minutes)
Closure:
Wrapupthelessonbygoingoverthedifferentanglesandnamesthattheyreviewedtoday.Brieflyrecapthewaysthattheycaneasilyrememberthedifferentanglesusingtheclockmethodorfacesintheangles.RemindthemthatanglesareeverywhereandtheydemonstratedthisbyplayingSimonsaysandmakingangleswiththeirarmsandthattheycanbelookingforanglesalmostanywhereandwhenevertheywant.Remindthemthatanglesaremeasuredindegreeswiththesymbol.Remindthemthatitdoesntmatterhowlongsomethingissuchasthepipecleanersorstrawsitistheangleinthemiddlethattheyaretryingtoestimate.Whentheyareestimatinganglestheycanalwaysuseaprotractortochecktheirworkortheycanaskafriend.Remindthemthattheynotonlylearnthowtoestimatetheanglebylookingatthepicturebuttheycandrawapicturewhengivenanangleestimateaswell.Askthemiftheyhaveanyquestionsthatwerentansweredthroughouttheclassorifthereissomethingthattheydontunderstandandwouldlikesomeclarificationto.(4minutes)
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Homework:
Givethestudentsoneofthehandoutsthatyoumade.Askthemtoclassifyeachanglenameaswellasanestimateoftheanglesizeindegrees.Makesurestudentshaveatleast20minutestoworkonthisattheendofclassandtellstudentsthatifnotfinishedinclasstheymayfinishitinhomeworkforthenextclass.(20minutes).
Assessment:
Havestudentswritethenumbersfrom1to10inacolumnintheirnotebook.Showthem5anglesoneatatimeandaskthemtoestimateeachandrecordtheirestimates.Besuretoshowtheanglesinavarietyofpositions.Thenaskthemtotakethelast5columnsandmakeupanglesoftheirown,givingtheangleestimateandthedrawingofit.Afterwardsgoovertheirsolutionsandaskthestudentstosharethestrategiestheyused.Ifyoufeeltheneedyoumaypickuptheworktogetabetterassessmentofthestudentswork.Repeatthisactivityatthebeginningofthenextclassorafewdayslaterandnoteanyimprovementstudentshavemade.(5minutes)
Nextaskstudentswhichanglesizedoyoufindeasytoestimateandwhy?(3minutes)
Askstudentsiftheycannameanangleordifferentanglesthattheylearnedtodayandmentioneverythingtheyknowaboutit.(3minutes)
Enrichment:
Showthestudentanangleof135andtellthemthatsomeonesaiditwas45.Askthestudentstoexplainhowtheymightthinksuchanerrorcouldbemade
Remediation:
Haveanextrasheetofexamplesorproblemsreadyforchildrenwhomightbehavingproblemsordifficultiesunderstandingthefirsthandout.Thisextrahandoutwillnotbeextrahomeworkitwouldjustbeanotherworksheetthatwecoulddotogethertohelpthemgetalittlemorepracticeandunderstandingangleswithusingtheprotractorlongerinsteadoftryingtoestimatetheangle.Perhapsiftheyhadmorepracticeusingtheprotractoritmightbeeasierforthemtoseetheangleandthengraduallyoncetheyunderstoodittheycouldmovetotheotherhandoutandtrytodosomeestimates.
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Title - Intro - ToCElem_Math_Unit_Plan