高中数学教学中的数学情境与提出问题_正弦定理_一_教学案例

114Vol.11,No.4200211JOURNALOFMATHEMATICSEDUCATIONNov.,20022002–08–28[2001]31963563200G632.4A1004–9894200204–0094–0411.13200195521.21.32224952AC+CB=AB32j22.112d=1kmAB1kmC|v1|=5km/h|v2|=3km/h2.2451BC2ABC3ABC4ABC5BC1223434452451AB2|v|v1v2435||||||222221=-=-=vvv°==⇒==376.0arcsin53||||sin21qqvv2AC3|AD|=|v1|=5|DE|=|AF|=|v2|=3AED=EAF=45°v2232?22?3244245342322?2.3?4RtABC24CcBbAasinsinsin==CcBbAasinsinsin==RtABCBC1BCADvEv1v2FvDEv1v2FBCABCAbca4A9611RtABCABC67335ADBECFABC3AD=bsinBCABE=csinCABCF=asinABCSABC=absinBCA=bcsinCAB=casinABCBCAcABCbCABa∠=∠=∠sinsinsin5ADBECFABC3AD=bsinBCA=csinABCBE=asinBCA=csinCABBCAcABCbCABa∠=∠=∠sinsinsin6CD=2rABCDAC=90°ABC=ADCrCDADCbABCb2sinsin==∠=∠rBCAcCABa2sinsin=∠=∠BCAcABCbCABa∠=∠=∠sinsinsinAC+CB=AB89103211203AC2?jABCBABC27jACAB=AC+CBjAB=j(AC+CB)=jAC+jCBjAC=0jCB=|j||CB|cos(C∠-°90)=asinCjAB=|j||AB|cosA∠-°90=csinAasinC=csinACcAasinsin=BbAasinsin=CcBbAasinsinsin==2.422225AEFDCBBCAcabD6BCA7j4974223BCABCABCABCBC3TeachingCaseaboutTheoremofSinesGUANLi-he(TongziNo.1MiddleSchool,GuizhouTongzi563200,China)Abstract:Withusingthemodethatsettingupmathematicalsituationorganization,enlightenmentandsoonwecreatedaconditionthatthestudentsundertookmathematicalactivitiesaboutposingandsolvingproblemindependently.Teachingprocesswasmadeaprocessinwhichstudentsgainedknowledgeontheirowninitiative,developedcapabilityandexperiencedmathematic.Keywords:theoremofsine;extracttriangle;mathematicalsituation[]