algebra equations：代数方程

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1、AlgebraEquationsLevel1:SolvingSimpleLinearEquationsI.IntroductionA.Prerequsite:Thisworkcanbestartedassoonasthechildcandobasicintegerarithmeticwiththefourarithmeticoperations.Equationswithsubtractioninthemrequireanintroductiontonegativenumbers.Equationswithdivisio

2、ninthemcanbecreatedsoasnottoneedfractions,butmoretypically,willrequireanunderstandingofthefractionformofintegerdivision(asopposedtotheintegerform—i.e.,quotientandremainder—ofdivision.)Inaddition,theequationsthatinvolveparenthesistypicallyrequirearefresherontheuse

3、ofthedistributivelaw(suchasintroducedintheearliestworkwiththetrinomialcube.)Thisrefreshershouldshowmultiplicationasalargerectanglethatcontainstwosmallerrectanglessignifyingtwomultiplications.Hencea(b+c),theonerectangleequalsab+ac,thetworectangularpartsofthelarger

4、ectangle(thewholeisthesumoftheparts.)A.Description:B.Material:Somethingtorepresentunits.Gram-centimetercubesworkwell.AlsosomethingtorepresentX.Itispossibletousecupsthatrepresentanunknownnumberofunitcubes.Rodsalsoworkwell,especiallyiftheyresembleyourunitsincrossse

5、ction.Iuserepaintedcuisenairerodsthatwereoriginallymadeforusewiththedecanomialsquarepresentation.C.Youalsoneedtwoplatformstorepresentthetwosidesoftheequation.Inapinch,twopiecesofplainpaperwilldo.Placethesewithanequalsignbetweenthem.II.PlanoftheWork:A.1-StepEquati

6、ons1.Addition:e.g.X+6=202.Multiplication:e.g.5X=303.Subtraction:e.g.X-4=114.Division:e.g.X/3=2B.2-StepEquationswithmultiplicationandaddition:e.g.2X+5=17C.3-StepEquationsrequiringcombiningliketerms:e.g.3X+4+2X=19D.3-StepEquationswithunknownsonbothsides:e.g.4X+2=6+

7、2XE.3-StepEquationsinvolvingparenthesis:e.g.2(3X+5)=28III.Presentation:Book1Layouttwosheetsofpaperwithanequalssigninbetween(seeillustration.)·ConstructtheequationX+2=8.·Say,“Thesearethesamenumber.”·Pointtothesidewiththe8andsay,“Thisis8.”·PointtothesidewiththeX+2a

8、ndsay,“Thisisalso8.Theyareboth8.”·Nowsimultaneouslytaketwounitsawayfrombothsidesandsay,“Nowtheyareboth6.SoX(pointtotheX)is6(pointtothe6.)”·NowconstructX+3=7.·A