Graphical Inequalities原创力要下载.docx

GraphicalInequalities

教学目标

Studentscandrawtheregionofinequalities.

教学过程

Askstudentstosketchthegraphof2x+3y=6.Askwhichsideofthelinewouldsatisfy2x+3y≤6.

Thenaturalinstinct,asthesignis‘lessthanorequalto’,istogofortheregionundertheline.Thisiscorrect.Butaskstudentshowtheycanbesure.Theansweristotestapoint.Suggesttostudentsthatthereisan‘obvious’choiceofapointtotest.

Iftheydonotcomeupwiththeanswer,tellthemthattheoriginisthebestpointtotestifitisn’tontheline,so2×0+3×0≤6.Thismeansthattheoriginisonthesiderequired.

Makesurestudentsrealisethattheanswerto2x+3y≤6isaregionandthatitisinfinitelybig.

Repeatwiththeinequalityx2.Askwhythisisdifferent.Studentsshouldrealisethatthereisonlyonevariableandtheinequalityisa‘strict’inequality.

Sketchtheregionandpointoutthatitisstillaregion,andthatthewaywedealwiththestrictinequalityistodrawtheboundarylineasadashedline.

Makesurestudentsareawareofthestepsinvolvedindrawingagraphicalinequality,asfollows.

Step1:Drawtheboundaryline(dashedorsolidasappropriate).

Step2:Testapointnotonthelinetoestablishwhichsideofthelineisrequired.

Acauseofconfusioniswhichsidetoshade.Examinationquestionsoftensay:MarktheregionclearlywithanR.Thereisnoestablishedconvention.

Groupworktomakesurestudentshasunderstoodtheprinciples.

StudentscanthendoHomework.Tellthemtonotethehintprovided.