Grade 5 Mathematics Lesson Plan Shape and...

Grade5MathematicsLessonPlan

ShapeandSpace

PreparedforEDUC5433

ElementarySchoolMathematicsMethods

October29,2008

PeterKennedyJacobLingleySheenMcDonaldLeighMuething

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

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

2

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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Teacher:Mr.JacobLingley Duration:50min Unit:ShapeandSpace


SCO(D3):Bytheendofgrade5,studentswillbeexpectedtodeterminethemeasureofright,acuteandobtuseangles.

Objective:Manystudentsinelementarymathclassesfindthemeasurementofanglesadifficultconceptsincetheindividualdegreeunitsareminisculeandcircularincomparisontoothermeasurementtechniquesthathavebeenpreviouslydemonstratedtothestudents.

Theprincipleobjectivefromthislessonplanistoreducetheproblemsencounteredduringanglemeasurementwithaprotractorasameasurementtool.Thiswillbeachievedbythegradualintroductionofanglemeasurementconceptsbymeansofsimplifiedprotractordesign.


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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Teacher:Mr.LeighMuething Duration:3x50min Unit:ShapeandSpace


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.


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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Gram Kilogram Milligram Liter

Millimeter Centimeter Meter Kilometer

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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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29


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.

31

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

32


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.


Therefore, each division represents 5ml. The total volume of water in the cylinder is 90ml.

Reading from a Scale : Solutions

Q.1

Q.2



360ml.



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.



700ml.



50ml.

Q.3

Q.4

Q.5



680ml.

33


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 =

34


! ! " #

Q.1 Volume = "r# ! h

= "!15#!20

= 14137.17 mm$


= "!7#!16

= 2463.01 m$


= "!6#!11

= 1244.07 cm$


= "!17#!7

= 6355.44 m$


= "!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.

35


Teacher:Ms.SheenaMcDonald Duration:50min Unit:ShapeandSpace


SCO(D7):Bytheendofgrade5,studentswillbeexpectedestimateanglesizeindegrees.

Objective:Thegoalistobeabletoestimatethemeasureofangleswithin510degreesoftheiractualsize.Aswellasbeingabletolookatanangleandgiveanestimateoftheclosestangleinname.Thestudentsshouldalsobeabletotakeanangleindegreesandbeabletoestimatewhatitmightlooklike.


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)

37

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

Grade 5 Mathematics Lesson Plan Shape and...

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