2022年倒数的认识—教学设计 .pdf

《2022年倒数的认识—教学设计 .pdf》由会员分享，可在线阅读，更多相关《2022年倒数的认识—教学设计 .pdf（5页珍藏版）》请在淘文阁 - 分享文档赚钱的网站上搜索。

1、倒数的认识教学设计武威市古浪县曙光完全小学王顺琴教学内容：人教版六年级数学上册第页例教学背景：倒数的认识”是在学生掌握了整数乘法、分数加法和减法计算、分数乘法的意义和计算法则、分数乘法解决问题等知识的基础上进行教学的。“倒数的认识”是分数的基本知识，学好倒数不仅可以解决有关实际问题，而且还是后面学习分数除法、分数四则混合运算和应用题的重要基础。教学方法：让学生在大量的活动情境中去学习，去感受，鼓励学生自主探索，合作交流，从而将实际问题抽象成数学模型；让学生进行深入观察、分析、概括、互动交流的体验式学习，主动获得新知，从而理解倒数的意义，掌握求一个数倒数的方法。教学目标：.知识与技能通过创设情境

2、，使学生经历、探索、理解倒数的意义,并熟练掌握求一个数倒数的方法。.数学思考问题解决通过研讨、交流，培养学生观察、比较、分析、抽象、概括的能力。.情感与态度初步渗透“事物间是相互依存，对立统一”的辩证唯物主义的观点。教学重点：1.正确理解倒数的意义。2.掌握求倒数的方法。教学难点：正确理解倒数的意义。教学用具：多媒体课件教学设计：一、创设情境，引入概念师：同学们，让我们一起看一幅画。（课件出示）桂林山水美不美啊？生：美！师：美在哪里？生：山清水秀。生：水中还荡漾着山的倒影。师：是的，大自然中有美丽的倒影，生活中有些话也可以倒过来说，它仍然是一句完整通顺的话。谁能说说看？生：我爱妈妈，妈妈爱我。

3、生：亮晶晶，晶晶亮。生：生活美好，美好生活！师：同学们，说得真多啊！其实，在数学中也有这样的现象。师：谁能一下子就在括号里填上不为的合适的数？（课件出示）（）=()=()=1=()=()师：他们为什么能填得那么快呢？学了今天这节课的内容你就能知道其中的奥秘。51201520141571009983文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY

4、8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z

5、2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY

6、8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z

7、2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY

8、8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z

9、2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4板书课题：倒数的认识设计意图：引起学生兴趣的方式拉开一堂课的序

10、幕，充分调动学生学习的积极性；通过疑问让学生初步感知倒数的特征，同时为倒数意义的揭示打下伏笔。二、探究讨论，深入理解.观察思考，明确倒数的特征。他们为什么算得那么快呢，那让我们一起来观察观察，看看你有什么发现。重点强调：两个数的乘积是。两个因数的分子和分母交换了位置。2看来这些数确实有某种特点，你能再举出一些具有这些特点的算式么？谁知道在数学上存在这样关系的两个数叫什么呢？提问：你能说说在你心点中“互为倒数”的两个数有什么特点吗?提问：“互为”是什么意思？强调：倒数是指两个数之间的关系，这两个数相互依存，一个数不能叫倒数。判断正误并说说原因。（课件出示）因为=1，所以是倒数，也是倒数。（）=1

11、，所以、互为倒数。（）与的乘积为 1，所以和互为倒数。（）互为倒数的两个数可以这样表示：=（）三、运用概念，探讨方法1.出示例（课件出示）2143343443342321342371212771212771227127537261文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T

12、1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:

13、CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T

14、1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:

15、CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T

16、1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:

17、CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4 6 1 0 提出要求：找一找哪两个数互为倒数？.学生独立完成。.汇报找得结果。并说说是怎样找的？预设：看两个分数的乘积是不是。看

18、两个分数的分子与分母是否分别颠倒了位置。讨论一下这两种方法哪一种方法比较快？（第二种方法比较快，可以直接观察得到）4.通过具体实例总结归纳找倒数的方法。找分数的倒数：分子、分母交换位置。例和分子、分母交换位置，故的倒数是。找整数的倒数：先把整数看成分母是1 的分数，再交换分子和分母的位置。例：6 可以写成分数，故 6 的倒数是。四、出示特例，深入理解看一看，例 1 中的哪些数据没有找到倒数？（1、0）提问：1 和 0 有没有倒数？如果有，是多少？小组讨论、汇报。.关于 1 的倒数因为 111，根据“乘积是 1 的两个数互为倒数”，所以 1 的倒数是 1。也可以这样推导：1 可以写成，分子、分母

19、交换位置，还是1。故 1 的倒数是 1。.关于 0 的倒数。3553353553166111文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7

20、H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8

21、U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7

22、H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8

23、U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7

24、H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8

25、U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4因为 0 与任何数相乘都不等于1，所以 0 没有倒数。五、强化知识，巩固练习.求带分数、小数的倒数。（课件出示）2.完成教材第 28 页“做一做”。学生独立完成，集体交流订正。3.完成第 29 页第 1 题和第 2 题。六、回顾小结通过这节课的学习，你有什么收获呢？设

26、计意图：通过引导学生反思学习方法，让学生清楚地意识到自学讨论的作用。一方面是培养学生经常自己学习的习惯，另一方面可以提高学生的语言表达能力。文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 Z

27、Y8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3

28、Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 Z

29、Y8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3

30、Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 Z

31、Y8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4文档编码:CK4R3Z2T7H5 HN8L9Z5T1H9 ZY8T8U9J4G4