中二数学教学笔记

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1、中二數學教學筆記Chapter06SquareRootsandPythagoras’Theorem(平方根及畢氏定理／勾股定理)數學新里程﹙第二版﹚SectionTopicTeachingNotesClassworkorHomework6.1SquaresandSquareRoots-Studentsshouldbeabletorecallthedefinitionofsquareandsquareroot.-Studentsshouldbeabletowritedownthevaluesofthefollowing:x,

2、-xwherexisaperfectsquare(平方數).Ex.6AQ.1,46.2TheValuesofSquareRoots-Studentsshouldbeabletoestimatethevaluesofsquareroots.Ex.6AQ.2-Studentsshouldbeabletoobtainthevaluesofsquarerootsusingcalculatorandroundingoffinthestatedconditions.Ex.6AQ.3,66.6IrrationalNumbers(無理數)

3、-Studentsshouldbeabletoidentifyrealnumbers(實數)underrationalnumbers(有理數)andirrationalnumbers(無理數).-Studentsshouldbeabletoexpressnumbersinsurdform(根式).-Studentsshouldbeabletocarryout4arithmeticoperationsofsurds.Ex.6EQ.1-5-Studentsshouldbeabletorationalizefractions.E

4、x.6FQ.1-7-Studentsareappreciatedtoexploretranscendentalnumber(超越數)ontheirown.6.3Pythagoras’Theorem(500–600B.C.)-Studentsshouldbeabletostatethenecessaryconditioninusing畢達哥拉斯定理Pythagoras’Theorem.畢氏定理-StudentsshouldbeabletoapplyPythagoras’Theoremtosolveproblems.Ex.6B

5、Q.1,9百牛定理HecatombProposition-Studentsshouldbeabletosolvethespecialproblems.木匠定理Carpenter'sTheoremEx.6BQ.12,14,16新娘之椅Bride'sChair驢橋定理﹙法國和比利時等國﹚商高定理﹙商高時代~1100B.C.﹚陳子定理﹙由陳子才提出﹚勾股定理/勾股弦定理﹙周脾算經﹚6.4ProofofPythagoras’Theoremandits-Studentsshouldbeabletogivesomeexamplesof

6、theproofofConversePythagoras’Theorem.-StudentsshouldbeabletousetheConverseofPyth.Th.(畢氏定理的逆Ex.6CQ.1-2定理)toidentifywhetheratriangleisaright-angledtriangle.6.5ApplicationsofPythagoras’Theorem-Studentsshouldbeabletodrawtheright-angledtriangleforthegivenEx.6DQ.2-7prob

7、lems.-StudentsshouldbeabletoapplyPythagoras’Theoremtosolvetheproblem.參考書籍：1.數學拾趣：梁易天、劉應泉編著：「無理由的數」2.十萬個為甚麼⎯⎯數學篇I，新世紀篇：「甚麼叫做『勾股數組』'﹖」3.十萬個為甚麼⎯⎯數學篇II，新世紀篇：「為甚麼中國把『畢達哥拉斯定理』稱為『勾股定理』﹖」註：香港考試局：准用計算機型號名稱思考題1.那個三角形的面積較大﹖1313131310242.【九章算術】中的一個問題：節錄自【十萬個為什麼？數學篇】『今有池方一丈，葭生

8、其中央，出水一尺，引葭赴岸，適與岸齊。問水深、葭長各幾何？』方池每邊長一丈，池底的中心生一根蘆葦，透出水面的部分長一尺，把蘆葦的頂端引到岸邊，葦頂恰和水面相齊。問池心水深和蘆葦長各多少？3.試計算題中的未知數值：(a)(b)(c)201213198512amnc4.求下圖三角形周界：A(-3,7)B(5