2022年圆内接正多边形教学设计2 .pdf

圆内接正多边形教学目标为：知识目标：（1）掌握正多边形和圆的关系；（2）理解正多边形的中心、半径、中心角、边心距等概念；（3）能运用正多边形的知识解决圆的有关计算问题；（4）会运用多边形知和圆的有关知识画多边形.能力目标：学生在探讨正多边形和圆的关系学习中，体会到要善于发现问题、解决问题，培养学生的概括能力和实践能力.情感目标：通过学习，体验数学与生活的紧密相连；通过合作交流，探索实践培养学生的主体意识.教学重点：掌握正多边形的概念与正多边形和圆的关系，并能进行有关计算.教学难点：正多边形的半径、边心距及边长的计算问题转化为解直角三角形的问题.教学设计第一环节课前准备活动内容：社会调查（提前一周布置）以 4 人合作小组为单位，开展调查活动：（1）各尽所能收集生活中各行各业、各学科中应用的各种正多边形形状的物体或照片.（2）对收集的其中最感兴趣的一件正多边形形状的物体进行研究.第二环节情境引入活动内容：各小组派代表展示自己课前所调查得到的正多边形形状的物体（可以是照片、资料、也可以是亲自仿制），并解说从中获取的知识（选34个小组代表讲解）第三环节圆内接正多边形的概念活动内容：学习圆内接正多边形及有关概念顶点都在同一个圆上的正多边形叫做圆内接正多边形.这个圆叫做该正多边形的外接圆.把一个圆n等分（3n），依次连接各分点，我们就可以作出一个圆内接正多边形.如图 335，五边形 ABCDE 是圆 O的内接正五边形，圆心O叫做这个正五边形的中心；OA是这个正五边形的半径；AOB是这个正五边形的中心角；BCOM，垂足为 M，OM 是这个正五边形的的边心距.在其他的正多边形中也有同样的定义.第四环节例题学习例：如图 336，在圆内接正六边形 ABCDEF 中，半径4OC，BCOG，垂足为 G，求这个正六边形的中心角、边长和边心距.解：连接 OD六边形 ABCDEF 为正六边形606360CODCOD 为等边三角形.4OCCD在COGRt中，4OC，2CG32OG正六边形 ABCDEF 中心角为 60，边长为 4，边心距为32.第五环节尺规作图活动内容：1、用尺规作一个已知圆的内接正六边形.2、用尺规作一个已知圆的内接正四边形.3、思考：作正多边形有哪些方法？第六环节练习与提高活动内容：1、分别求出半径为6cm的圆内接正三角形的边长和边心距.文档编码:CC10H4V10Y6B6 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HM9B3U5V10X5 ZQ6R8M3Z3E8文档编码:CC10H4V10Y6B6 HM9B3U5V10X5 ZQ6R8M3Z3E8活动目的：对本节知识进行巩固练习.第七环节课堂小结师生互相交流总结正多边形和圆的关系、正多边形的对称性和边数相同的正多边形相似的性质、正多边形的中心、半径、中心角、边心距等概念、如何计算正多边形的半径、边心距及边长，社会调查时学到的课外知识及切身感受等.第八环节布置作业课本习题 3.10 文档编码:CC10H4V10Y6B6 HM9B3U5V10X5 ZQ6R8M3Z3E8文档编码:CC10H4V10Y6B6 HM9B3U5V10X5 ZQ6R8M3Z3E8文档编码:CC10H4V10Y6B6 HM9B3U5V10X5 ZQ6R8M3Z3E8文档编码:CC10H4V10Y6B6 HM9B3U5V10X5 ZQ6R8M3Z3E8文档编码:CC10H4V10Y6B6 HM9B3U5V10X5 ZQ6R8M3Z3E8文档编码:CC10H4V10Y6B6 HM9B3U5V10X5 ZQ6R8M3Z3E8文档编码:CC10H4V10Y6B6 HM9B3U5V10X5 ZQ6R8M3Z3E8文档编码:CC10H4V10Y6B6 HM9B3U5V10X5 ZQ6R8M3Z3E8文档编码:CC10H4V10Y6B6 HM9B3U5V10X5 ZQ6R8M3Z3E8文档编码:CC10H4V10Y6B6 HM9B3U5V10X5 ZQ6R8M3Z3E8文档编码:CC10H4V10Y6B6 HM9B3U5V10X5 ZQ6R8M3Z3E8文档编码:CC10H4V10Y6B6 HM9B3U5V10X5 ZQ6R8M3Z3E8文档编码:CC10H4V10Y6B6 HM9B3U5V10X5 ZQ6R8M3Z3E8文档编码:CC10H4V10Y6B6 HM9B3U5V10X5 ZQ6R8M3Z3E8文档编码:CC10H4V10Y6B6 HM9B3U5V10X5 ZQ6R8M3Z3E8文档编码:CC10H4V10Y6B6 HM9B3U5V10X5 ZQ6R8M3Z3E8文档编码:CC10H4V10Y6B6 HM9B3U5V10X5 ZQ6R8M3Z3E8文档编码:CC10H4V10Y6B6 HM9B3U5V10X5 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ZQ6R8M3Z3E8文档编码:CC10H4V10Y6B6 HM9B3U5V10X5 ZQ6R8M3Z3E8文档编码:CC10H4V10Y6B6 HM9B3U5V10X5 ZQ6R8M3Z3E8文档编码:CC10H4V10Y6B6 HM9B3U5V10X5 ZQ6R8M3Z3E8文档编码:CC10H4V10Y6B6 HM9B3U5V10X5 ZQ6R8M3Z3E8文档编码:CC10H4V10Y6B6 HM9B3U5V10X5 ZQ6R8M3Z3E8文档编码:CC10H4V10Y6B6 HM9B3U5V10X5 ZQ6R8M3Z3E8文档编码:CC10H4V10Y6B6 HM9B3U5V10X5 ZQ6R8M3Z3E8四、教学设计反思1要创造性的使用教材教材只是为教师提供最基本的教学素材，教师完全可以根据学生的实际情况进行适当调整.2相信学生并为学生提供充分展示自己的机会通过课前小组合作社会调查、课堂展示正多边形的过程，为学生提供展示自己聪明才智的机会，并且在此过程中更利于教师发现学生分析问题解决问题的独到见解，以及思维的误区，以便指导今后的教学.课堂上要把激发学生学习热情和获得学习能力放在教学首位，通过运用各种启发、激励的语言，以及组织小组合作学习，帮助学生形成积极主动的求知态度.3在教学中注意的方面本节新概念较多，对概念的教学要注意从“形”的角度去认识和辨析，但对概念的严格定义不能要求过高.在概念教学中，要重视运用启发式教学，让学生从“形”的特征获得对几何概念的直观认识，鼓励学生用自己的语言表述有关概念，再进一步准确理解有关概念的文字表述，促进学生主动学习.通过形象生动的直观图形，给学生营造一个问题情景，通过问题的探索来调动学生的内在动力，提高学习积极性，提高探索知识的能力.4注意改进的方面在小组讨论之前，应该留给学生充分的独立思考的时间，不要让一些思维活跃的学生的回答代替了其他学生的思考，掩盖了其他学生的疑问.教师应对小组讨论给予适当的指导，包括知识的启发引导、学生交流合作中注意的问题及对困难学生的帮助等，使小组合作学习更具实效性.文档编码:CC10H4V10Y6B6 HM9B3U5V10X5 ZQ6R8M3Z3E8文档编码:CC10H4V10Y6B6 HM9B3U5V10X5 ZQ6R8M3Z3E8文档编码:CC10H4V10Y6B6 HM9B3U5V10X5 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