三角形中位线定理doc.docx

三角形中位线定理doc.docx

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三角形中位线定理doc

三角形中位线定理

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Theoremofmedianlineintriangle

FenghuamiddleschoolWuShifen

Teachingtarget

Knowledgetarget:

understsndtheconceptofmiddlelineintriangle;masterthetheoremofmedianlineintriangle;learntosolvesomesimpleproblemswithtrianglemiddlelinetheorem

Objective:

Toinvestigateandanalysisability,exploringabilityofsummarizing,reasoning,theabilitytotrainstudentstousethemethodtosolvetheproblemofdivergentthinkingofstudentslearningandinnovationabilityofstudentsinexperimentaltraining・

Theemotiongoal:

tocultivatestudents'scientificattitudeandpositiveanalysisofthespiritofexploringtheinfiltrationtothestudentsmovementandthetheorycomesfromthepracticeoftheworldoutlookofdialecticalmaterialism

thoughttostimulatetheenthusiasmofstudents

Improvestudents'interestinmaths

Teachingemphasis:

trianglemiddlelinetheoremanditsapplication：

trainingofconversionability

Teachingdifficulties:

theproofandapplicationofthetheoremofmedianlineintriangle

Teachingmethod:

thedesignofthisclassisbasedonthenewcurriculumstandardsandteachingmaterials

Inthecourseofteaching

Payattentiontothecultivationofstudents，inquiryability

Classisalsogiventostudents

Letstudentsexperieneetheprocessofknowledge

Developstudents'creativethinking

meanwhile

Payattentiontoinspiringandguidingstudents

Encouragestudentstodaretoguess

Carefulproofoftheideaofscientificresearch

Guidedbyteachers

Studentasthemainbody

Usingtheexperimentalobservation,inquiry,induction,theoreticalproof,andstrengthenthedeepeningofthefourstepteachingmethod

Inordertoachievetheteachingpurpose

Studymethod:

letthestudentsgrasptheexperimentandobservation,analysisandcomparison,discussionandinterpretation,summaryandinduction,consolidationandimprovementofscientificlearningmethods:

learnbyanalogy

Flexibleconversionlearningmethods

Learntoapplythethoughtofchangetosolveproblems

Teachingprocess:

First,createscenarios

Interestlearning

9

■

Twotrytoexplore

Acquirenewknowledge

1.putforwardtheconceptofthemedianlineoftriangle:

thelineofthemiddleofbothsidesofthetriangleiscalledthemiddlelineoftriangle

2.studentmapping:

pleasedrawthemiddleandmiddlelineofthetriangle

Andtellthemthedifference

3.studentslookatthemiddlelineofthetriangledrawninfront

Andanswerthequestion:

howmanymiddlelinesdoesatrianglehave?

Whatistherelationbetweenthemiddlelineofatriangleandthesidesofatriangle?

Inspirestudentstoguess

4.verifystudentobservationandconjecture:

movingpointA

Theshapeofthetrianglehaschanged

What，sthesame?

WhatistherelationbetweenthemedianlineDEofthetriangleandthethirdsideBC?

Whatkindofquantitativerelationshipdotheyhave?

5.askthestudentstocutthetrianglealongthemiddlelineDE

CouldyougetthedeltaADEandquadrilateralBDECsplicedintoaparallelogram?

6.aftertheaboveinquiryanddiscussion,thestudentswillconeludethatthemiddlelineofthetriangleisparalleltothethirdside

Andequaltohalfofthethirdside

Isthisconclusionuniversal?

Wehavetoproveitintheory

7.therearemanywaystoprovethistheorem

Thekeyishowtoaddanauxiliarylinethatcanguidestudentsindifferentwaystodemonstratethethinkingofactivestudents

Broadenstudents'thinking

Toimprovetheabilitytoanalyzeandsolveproblems,butalsotopointout

Whenapropositionhasmanywaysofprovingit

Tochoosearelativelysimplewaytoprove

8.isdiscussedbythestudents

Nameseveralmethodsofproof

Thentheteacher'ssummaryisshownbelow（L）extendDEtoF

send

LinkCF

AvailablebyADFC.

（2）extendDEtoF

send

Thequadrilateralthatusesdiagonalstodivideeachotherisaparallelogram

AvailableADFC.

（3）overC

WithDEextensionlinetoF

ADFC.canbeobtainedbycertificate

9.teachersummary:

（1）theuseofthetheorem・Themathematicallanguageexpressionofthetheorem

Threelearntosail

Examples:

verify:

inordertolinkanyquadrilateral,themidpointofthequadrilateralisparallelogram（studentsdrawandobserve

Askthestudentstoguess・）

Known:

inquadrilateralABCD

E,F,G,andHarethemidpointofAB,BC,CD,andDArespectively

Confirmation:

quadrilateralEFGHisaparallelogram

Canyouprovethatitisaparallelogram?

Whenstudentsdonotaddauxiliarylines

Theteacherinspiredagain

Somanymidpoint,whatdowethinkof?

Cantheproblemofquadrilateralbetransformedintoanygraphicproblem?

Enablestudentstoconnectdiagonallines

Forquadrilateralofdifferentshapes

Whereisthequadrilateralofwhichquadrilateralisit?

Let'stakealookatit:

Thequadrilateralformedbyanarbitraryquadrilateralisaparallelogram,andthemidpointofthequadrilateralisobserved・Theshapeofthequadrilateralisrelatedtotheelementsoftheoriginalquadrilatera1.Howdotheseelementsdetenuinetheshapeofthemidpointquadrilateral?

1）whichareconnectedbythemidpointofeachsideofthequadrilateralis

2）areconnectedwiththerectangularmidpointofeachsideare

3）whichareconnectedineachsideofthediamondpointis

4）inordertoconnectthequadrilateral,themidpointofthequadrilateralissquare

Thenthequadrilateralis

5）inordertoconnectthequadrilateral,eachsideofthemidpointdiamond

Thenthequadrilateralis

6）whichareconnectedwitheachother・Thediagonalquadrilateralisthemidpointofeachsideofthe

7）whichareconnectedindiagonalperpendiculartothe

midpointofeachsideofthequadrangleis

8）fourconnecteddiagonalequaltothemidpointofeachside

oftheshapeis

Fourassignment:

（omitted）

Teachingreflection

Weoftenhearstudentscomplainthatmathisdifficult

Thebiggestreasonisthatourmathematicsteachingisdivorcedfromthestudents'actuallife

Thenewcurriculumstandardattachesgreatimportancetotheconnectionbetweenmathematicsandreallife

Notonlythematerialrequirementsmustbecloselylinkedwiththeactuallifeofstudents,butalsorequiresmathematicsteachingmuststartfromthefamiliarlifesituationandinterestingthings・"

Providethemwithopportunitiesforobservationandoperation"

Whenthecontentofthestudyisclosetotheactuallifethatstudentsarefamiliarwith

Thehigherthestudents'willingnesstoacceptknowledge

Accordingtothischaracteristic

Beforeteachingthecontentofthenewcourse

Icreatedaproblemsituation

Toarousethecuriosityandthinkingofstudents

Stimulatestudents'interestinlearningandthirstforknowledge

Whileorganizingstudentstoexplorenewknowledge

Throughthemapping,observation,conjecture,hands-onexperiments,suchasaseriesof〃domathematics"process

Enablestudentstogivefullplaytotheirinitiative

Students'learningbecomesarecreationundertheguidanceofteachers^

Intheprocess

Studentsarealwaysveryactiveintheirthinking

getsb.'stailup

CutthetrianglealongthemiddlelineDE

TheADEandBDECquadrilateralsplicedintoaparallelogram・

Resolvethedifficulties

Forstudentsthatauxiliarylinebitlinetheoreminthetrianglesetclearobstacles

Theproofofthetheorembecameasimplematter

Thecreativepotentialofthestudentshasbeenfullyexcavated

Enjoyedthejoyofsuccess

Thewholeclassfeelsapitythatthedevelopmentofexamplesisnotenough

Notenoughtimeforstudentstothink

Ifyouusemediapresentations

Maybemoreintuitive

Theeffectisbetter

Throughthiscourseofstudyandresearch

Thestudentnotonlydiscoveredmanypropertiesofthemedianlineofthetriangle

Whatismoreimportantisthat・・・

Theprocessofdiscoveryoftheseproperties

Thestudents'practicalabilityhasbeentempered

Innovationconsciousnesshasbeencultivated

AndImyselfhaverealizedthecharmofthenewcurriculumidea

Teachersaretheorganizers,guidesandcollaboratorsofstudents'MathematicsLearning