三角形边的关系――任意两边之和大于第三边 教案

三角形边的关系――任意两边之和大于第三边 福州市乌山儒江名城港湾分校 张颐 教学内容: 四下册第五单元例3(82页)三角形边的关系——任意两边之和大于第三边 教学目标: 1.知识目标:知道“三角形任意两边的和大于第三边”;能判断给定长度的三条线段是否能围成三角形。 2.技能目标:通过猜想验证、合作探究，算一算、比一比，经历发现“三角形任意两边的和大于第三边”的活动过程，发展空间观念，培养逻辑思维能力;能运用三角形任意两边之和大于第三边解决生活中的简单问题，感受生活中处处有数学。 3.情感目标:体验“做数学”的成功感，激发学习数学的兴趣。 教学重点: 三角形三边关系的探究。 教学难点: 在活动中探索三角形三边的关系，发现“三角形任意两边的和大于第三边”的性质。 教具、学具准备: 实物投影仪、三角板、每人一套小棒。 教学过程: 一、动手操作，发现问题 师:三角形有几条边,用三根小棒能围成一个三角形吗, 生:能或不能 师:4根小棒你最多能摆几个三角形, 列举所有可能性。 请同学们拿出你准备好的(4?、3?、6?和10?;3cm、3cm、6cm、5cm;2cm、4cm、8cm、5cm;15cm、10cm、5cm、8cm的小棒，任意取3根围三角形，记录好每次所用小棒的长度，以及能否围成三角形，填好表格 第一根小棒长 第二根小棒长 第三根小棒长 能否围成三角形 2、学生汇报: (活动要求:1、用自己面前的小棒来围。2、小棒需首尾相连。3、围好后观察自己和别人围的情况。学生动手操作) 生汇报自己摆的情况。 二、探究原因 比较交流 (一)探究三根小棒有时围不成三角形的原因。 每个小组用刚才没摆成三角形的小棒合作进行研究 师:有的没摆成三角形，猜一猜可能跟三角形的什么有关,(生:跟边有关。师:这个摆不成的三角形，它的边怎么了,生:太短了。你指的是一条边吗,换另一条较短工边进去学生又发现可以变成一个三角形。 (二)汇报交流 引导生小结出:(比较小棒的长度)因为有两根小棒的长度的和小于第三根小棒的长度，and due diligence evaluations article 22nd head office, branch (jurisdiction), risk management, marketing management branch within the Department's credit business person assumed responsibility for the supervision and inspection and due diligence evaluations. Article 23rd, Head Office, branches (jurisdiction), risk management, Marketing Management Department through on-site and off-site inspection, investigation report, interviews with investigators for pre-loan investigation work by way of conducting supervision and inspection, quality evaluation pre-loan investigation work, and based on the evaluation results, the implementation of diversity management. 24th the control and inspection (a) the implementation of the credit system: there is no breach of credit policy relating to the granting of credit and the head office; (B) dual credit rating: timeliness of ratings, whether the provisions of the rating, rating results are accurate; (C) the survey contents: data collection is complete, report writing is comprehensive, indicators analysis is objective, real, conclusions and the facts are consistent and reasonable; (D) double implementation of investigations system: practical implementation of double system; (E) other supervision and inspection of the contents. 25th due diligence evaluation offices and branches (jurisdiction), risk management, Marketing Management Department agreed to carry out pre-loan investigation supervision and inspection work, evaluate whether investigators due diligence to determine whether the exemption should be. Investigators should be compatible with. Due diligence assessment should be based on the fact that, following the principles of objectivity, impartiality and fairness. Article 26th head 所以用它们围不成一个三角形。 师出示:两根小棒长度之和小于第三根小棒长度时，围不成三角形是这样的吗,这是咱们研究得出的第一个规律。还有不同的发现吗, 生:我们的三根小棒也围不成一个三角形，它们长度之间的关系是:两根小棒长度之和等于第三根小棒的长度。 (在实物投影仪上演示) 师:看来，当两根小棒的长度之和等于第三根小棒的长度时，也围不成三角形。 师:每根小棒相当于三角形的什么, 生:边。 师:这两个规律又可以怎么说呢,(引导生将小棒说成“边”) 生:我们通过探究发现了两个规律:1、两边之和小于第三边时，围不成三角形。2、两边之和等于第三边时，也围不成三角形。 三、引发猜想，实践验证 师:哦，这两种情况的小棒都不成围成三角形，那么谁能猜猜，怎样的三根小棒才能围成三角形呢, 当两边之和大于第三边时能围成三角形。 师:要想知道“三角形的两边之和是不是大于第三边”这一猜想是否正确，应该怎么办, (动手验证、观察表格中能围成的三角形的是否都是两边之和大于第三边。 师:想把验证的结果与大家分享吗, 师:现在你们想说些什么呢, 引导生小结出:事实证明，所有的三角形都是两边之和大于第三边，我们猜想是正确的。 在此过程中，师注意反例的运用。引导学生总结出光有两边之和大于第三边还不够，要是每两边之和都要大于第三边也就是任意两边。 四、构建模型，联系实际 、师:(出示练习)下面几组线段能围成三角形吗,为什么, 1 (1)3厘米、4厘米、5厘米(同时优化出快速判断的方法) (2)2厘米、4厘米、6厘米 (3)3厘米、6厘米、4厘米 (4)2厘米、4厘米、8厘米 2、师:同学们会用所学知识解决一些数学问题，很不错，继续看题: 出示课本上的引入题(解决聪聪的问题)同学们你们能用今天所学的知识来解释吗, 小明去学校，有几条路可走,最近的是哪一条,为什么, 3、能接受更难的挑战吗,用多长的小棒就能和2厘米、5厘米的小棒围成三角形? 你能确定最长是多少厘米，最短是多少厘米, 4、把一根14厘米的小棒围成一个三角形(边取整厘米数)，可以怎么围, and due diligence evaluations article 22nd head office, branch (jurisdiction), risk management, marketing management branch within the Department's credit business person assumed responsibility for the supervision and inspection and due diligence evaluations. Article 23rd, Head Office, branches (jurisdiction), risk management, Marketing Management Department through on-site and off-site inspection, investigation report, interviews with investigators for pre-loan investigation work by way of conducting supervision and inspection, quality evaluation pre-loan investigation work, and based on the evaluation results, the implementation of diversity management. 24th the control and inspection (a) the implementation of the credit system: there is no breach of credit policy relating to the granting of credit and the head office; (B) dual credit rating: timeliness of ratings, whether the provisions of the rating, rating results are accurate; (C) the survey contents: data collection is complete, report writing is comprehensive, indicators analysis is objective, real, conclusions and the facts are consistent and reasonable; (D) double implementation of investigations system: practical implementation of double system; (E) other supervision and inspection of the contents. 25th due diligence evaluation offices and branches (jurisdiction), risk management, Marketing Management Department agreed to carry out pre-loan investigation supervision and inspection work, evaluate whether investigators due diligence to determine whether the exemption should be. Investigators should be compatible with. Due diligence assessment should be based on the fact that, following the principles of objectivity, impartiality and fairness. Article 26th head 三角形边的关系――任意两边之和大于第三边 教案 福州市乌山小学儒江名城港湾分校 张颐 教学内容: 四年级下册第五单元例3三角形边的关系——任意两边之和大于第三边 教学目标: 1.知识目标:知道“三角形任意两边的和大于第三边”;能判断给定长度的三条线段是否能围成三角形。 2.技能目标:通过猜想验证、合作探究，算一算、比一比，经历发现“三角形任意两边的和大于第三边”的活动过程，发展空间观念，培养逻辑思维能力;能运用三角形任意两边之和大于第三边解决生活中的简单问题，感受生活中处处有数学。 3.情感目标:体验“做数学”的成功感，激发学习数学的兴趣。 教学重点:三角形三边关系的探究。 教学难点:在活动中探索三角形三边的关系，发现“三角形任意两边的和大于第三边”的性质。 教具、学具准备: 实物投影仪、吸管、铁丝、剪刀、课件 教学过程: 一(激趣引入,引发想象 一根吸管剪成三段，头尾相连，会得到什么图形, 二(动手操作,发现问题 1.学生操作,提出要求. 2.反馈:三种不同的情况。 (1)其中两边长度相加小于第三边; (2)两边长度相加等于第三边; (3)每两边长度相加大于第三边 2(思考:为什么其它2种围不成三角形, 3. 第一次小结:三角形两条边的和大于第三边。 4(反例:前两种情况也是两边和大于第三边，你能表述严密些吗, 5(第二次小结:任意两边的和大于第三边. 三、构建模型，联系实际 1、师:(出示练习)下面几组线段能围成三角形吗,为什么, (1)3厘米、4厘米、5厘米(同时优化出快速判断的方法) (2)2厘米、4厘米、6厘米 (3)3厘米、6厘米、4厘米 (4)2厘米、4厘米、8厘米 2、师:同学们会用所学知识解决一些数学问题，很不错，继续看题: and due diligence evaluations article 22nd head office, branch (jurisdiction), risk management, marketing management branch within the Department's credit business person assumed responsibility for the supervision and inspection and due diligence evaluations. Article 23rd, Head Office, branches (jurisdiction), risk management, Marketing Management Department through on-site and off-site inspection, investigation report, interviews with investigators for pre-loan investigation work by way of conducting supervision and inspection, quality evaluation pre-loan investigation work, and based on the evaluation results, the implementation of diversity management. 24th the control and inspection (a) the implementation of the credit system: there is no breach of credit policy relating to the granting of credit and the head office; (B) dual credit rating: timeliness of ratings, whether the provisions of the rating, rating results are accurate; (C) the survey contents: data collection is complete, report writing is comprehensive, indicators analysis is objective, real, conclusions and the facts are consistent and reasonable; (D) double implementation of investigations system: practical implementation of double system; (E) other supervision and inspection of the contents. 25th due diligence evaluation offices and branches (jurisdiction), risk management, Marketing Management Department agreed to carry out pre-loan investigation supervision and inspection work, evaluate whether investigators due diligence to determine whether the exemption should be. Investigators should be compatible with. Due diligence assessment should be based on the fact that, following the principles of objectivity, impartiality and fairness. Article 26th head 出示课本上的引入题(解决聪聪的问题)同学们你们能用今天所学的知识来解释吗, 小明去学校，有几条路可走,最近的是哪一条,为什么, 3、学校的木工师傅有两根木条的长分别是5米和4米，他要选择第三根木条(整米)，将它们钉成一个三角形木架。可以取几米的木条，你能帮助他确定第三根木条最长是多少米,最短是多少米吗, 能接受更难的挑战吗, 4、根据三角形的三边关系剪三段围成三角形中的奥秘解析: 把一根20厘米的小棒围成一个三角形(边取整厘米数)，可以怎么围, 板书: 三角形的三边关系 a+b>c b+c>a a+cc b+c>a a+c=b a+b>c b+c>a a+c>b 结论:三角形的任意两边之和大于第三边 and due diligence evaluations article 22nd head office, branch (jurisdiction), risk management, marketing management branch within the Department's credit business person assumed responsibility for the supervision and inspection and due diligence evaluations. Article 23rd, Head Office, branches (jurisdiction), risk management, Marketing Management Department through on-site and off-site inspection, investigation report, interviews with investigators for pre-loan investigation work by way of conducting supervision and inspection, quality evaluation pre-loan investigation work, and based on the evaluation results, the implementation of diversity management. 24th the control and inspection (a) the implementation of the credit system: there is no breach of credit policy relating to the granting of credit and the head office; (B) dual credit rating: timeliness of ratings, whether the provisions of the rating, rating results are accurate; (C) the survey contents: data collection is complete, report writing is comprehensive, indicators analysis is objective, real, conclusions and the facts are consistent and reasonable; (D) double implementation of investigations system: practical implementation of double system; (E) other supervision and inspection of the contents. 25th due diligence evaluation offices and branches (jurisdiction), risk management, Marketing Management Department agreed to carry out pre-loan investigation supervision and inspection work, evaluate whether investigators due diligence to determine whether the exemption should be. Investigators should be compatible with. Due diligence assessment should be based on the fact that, following the principles of objectivity, impartiality and fairness. Article 26th head 本节课主要是从以下几个板块展开课堂教学: 一、引入阶段:通过玩小棒，发出问题。教材上是从小明上学走中间这条路最近的主题图，用聪聪抛出的问题“这是什么原因”进入新课学习，我并没有直接采用，因为我觉得两点之间线段最短，这个道理谁都知道，但要让学生说出原因，就很困难了，有加大学生学习难度之可能。而是创设从玩小棒发现问题，作为情景导入，玩游戏是学生都喜欢的活动，在游戏中发现问题更能激发他们的学习兴趣、探究的欲望。 二、探究阶段:通过猜测、验证、总结发现规律。教材是把围得成与围不成两种情况下的材料，一并提供给学生进行探究发现，我预设到这样安排难度较大，不利于重点探究(为什么围不成)，也很难突破“任意”这一难点。因此，我分这样两个层次让学生猜测、验证、总结。第一层次，引导学生提出“为什么三根小棒有时不能围成三角形”这一探究重点，让学生利用手中的小棒进行探究，发现规律。在此基础上引发学生猜测“什么样的三根小棒能围成三角形”，并利用小棒实践验证，同时举出反例，突破本节课“任意”这一难点，然后总结得出三角形边的关系——任意两边之和大于第三边。 三、应用阶段:适当联系实际，解决问题。设计了三个层次的练习，第一是判断每组的三根小棒能否围成三角形，在学生判断时，根据学生的回答优化出快速判断三根小棒能否围成三角形的方法。第二是回归课本解决课本上主题图的问题，利用本节课所学知识，解释“为什么走中间一条路最近”的问题。第三让学生思考“用多长的小棒就能和2厘米、5厘米的小棒围成三角形”有一定的开放性，又能渗透区间思想 学校的木工师傅有两根木条的长分别是70厘米和100厘米，他要选择第三根木条(整厘米)，将它们钉成一个三角形木架。你能帮助他确定第三根木条最长是多少厘米,最短是多少厘米吗,教学内容:义务教育课程

标准

excel标准偏差excel标准偏差函数exl标准差函数国标检验抽样标准表免费下载红头文件格式标准下载

实验教科书人教版数学四年级下册第82页例3。 教学目标: 1.知识目标:知道“三角形任意两边的和大于第三边”;能判断给定长度的三条线段是否能围成三角形。 2.技能目标:通过猜想验证、合作探究，算一算、比一比，经历发现“三角形任意两边的和大于第三边”的活动过程，发展空间观念，培养逻辑思维能力;能运用三角形任意两边之和大于第三边解决生活中的简单问题，感受生活中处处有数学。 3.情感目标:体验“做数学”的成功感，激发学习数学的兴趣。 教学重点:三角形三边关系的探究。 教学难点:在活动中探索三角形三边的关系，发现“三角形任意两边的和大于第三边”的性质。 教学准备:彩色纸条若干、课件、红、绿圆片。 教学过程: 一、情境激趣，发现问题 师(电脑出示例3图):看，小明正准备去上学呢～这是他上学的路线图，看一看，他上学的路线有几条, 生:有三条。 师:走哪条路距离最近, 生:走中间这条路距离最近。 师:你怎么知道的, (学生结合自己的生活经验各自表述。) 师:同学们很爱思考，能结合自己的生活经验来谈，说得都有道理。请同学们再看看图，小明上学的这几条路线围成两个什么图形, and due diligence evaluations article 22nd head office, branch (jurisdiction), risk management, marketing management branch within the Department's credit business person assumed responsibility for the supervision and inspection and due diligence evaluations. Article 23rd, Head Office, branches (jurisdiction), risk management, Marketing Management Department through on-site and off-site inspection, investigation report, interviews with investigators for pre-loan investigation work by way of conducting supervision and inspection, quality evaluation pre-loan investigation work, and based on the evaluation results, the implementation of diversity management. 24th the control and inspection (a) the implementation of the credit system: there is no breach of credit policy relating to the granting of credit and the head office; (B) dual credit rating: timeliness of ratings, whether the provisions of the rating, rating results are accurate; (C) the survey contents: data collection is complete, report writing is comprehensive, indicators analysis is objective, real, conclusions and the facts are consistent and reasonable; (D) double implementation of investigations system: practical implementation of double system; (E) other supervision and inspection of the contents. 25th due diligence evaluation offices and branches (jurisdiction), risk management, Marketing Management Department agreed to carry out pre-loan investigation supervision and inspection work, evaluate whether investigators due diligence to determine whether the exemption should be. Investigators should be compatible with. Due diligence assessment should be based on the fact that, following the principles of objectivity, impartiality and fairness. Article 26th head 生:围成了两个三角形。 师:小明上学的这几条路线围成了三角形，每一段路正好是三角形的一条边。那么，我们能不能用三角形三条边的关系来解释走哪条路最近的问题呢,今天，我们就一起来研究三角形三条边之间的关系。 (板书课题:三角形三边的关系) 二、合作探究，发现规律 1.初步感知，提出猜想。 师:老师准备了些纸条(a.10厘米，15厘米，20厘米;b.10厘米，10厘米，20厘米;c.10厘米，12厘米，26厘米)，谁愿意把这几组纸条分别当作三角形的三条边使它们首尾相接在黑板上摆出三角形, (学生踊跃上台摆三角形，用第一组纸条能顺利地摆出三角形，而用第二组和第三组纸条摆不出三角形。) 小组讨论，提出猜想。 生1:两条短的边太短了，围不起来。 生2:那条长的边太长了。 2.动手操作，发现结论。 师:请大家拿出信封里的纸条摆三角形，每摆一个，就把自己摆的结果和所用纸条的长度记录在表格中，最后算一算。然后在小组内讨论，把你的发现记下来。 (小组合作，动手操作，填写记录表。然后小组代表上台汇报并展示记录表。) 汇报要求:a.哪些情况下能摆成三角形,b.哪些情况下不能摆成三角形,c.你们有什么发现, 生1:两条线段的和大于第三条线段就能围成三角形。 生2:最长的那条线段小于另外两条线段的和才能围成三角形。 生3:任意两条线段的和一定要大于第三条线段，才能围成三角形。 生4:三角形较短的两条边的和大于最长的边。 生5:三角形两边的差小于第三边。 „„ 3.深入思考，完善结论。 师:三条线段中只要其中两条线段的和大于第三条线段就一定能围成三角形吗,说说黑板上的第二、三组线段为什么不能围成三角形。 生1:第二组线段中10厘米加10厘米等于20厘米，所以围不成三角形。 生2:第三组线段中10厘米加12厘米比26厘米小，所以围不成三角形。 师:请同学们读书上的结论，说说“任意两边”是什么意思。 and due diligence evaluations article 22nd head office, branch (jurisdiction), risk management, marketing management branch within the Department's credit business person assumed responsibility for the supervision and inspection and due diligence evaluations. Article 23rd, Head Office, branches (jurisdiction), risk management, Marketing Management Department through on-site and off-site inspection, investigation report, interviews with investigators for pre-loan investigation work by way of conducting supervision and inspection, quality evaluation pre-loan investigation work, and based on the evaluation results, the implementation of diversity management. 24th the control and inspection (a) the implementation of the credit system: there is no breach of credit policy relating to the granting of credit and the head office; (B) dual credit rating: timeliness of ratings, whether the provisions of the rating, rating results are accurate; (C) the survey contents: data collection is complete, report writing is comprehensive, indicators analysis is objective, real, conclusions and the facts are consistent and reasonable; (D) double implementation of investigations system: practical implementation of double system; (E) other supervision and inspection of the contents. 25th due diligence evaluation offices and branches (jurisdiction), risk management, Marketing Management Department agreed to carry out pre-loan investigation supervision and inspection work, evaluate whether investigators due diligence to determine whether the exemption should be. Investigators should be compatible with. Due diligence assessment should be based on the fact that, following the principles of objectivity, impartiality and fairness. Article 26th head 第一根小棒长 第二根小棒长 第三根小棒长 能否围成三角形 第一根小棒长 第二根小棒长 第三根小棒长 能否围成三角形 第一根小棒长 第二根小棒长 第三根小棒长 能否围成三角形 第一根小棒长 第二根小棒长 第三根小棒长 能否围成三角形 第一根小棒长 第二根小棒长 第三根小棒长 能否围成三角形 and due diligence evaluations article 22nd head office, branch (jurisdiction), risk management, marketing management branch within the Department's credit business person assumed responsibility for the supervision and inspection and due diligence evaluations. Article 23rd, Head Office, branches (jurisdiction), risk management, Marketing Management Department through on-site and off-site inspection, investigation report, interviews with investigators for pre-loan investigation work by way of conducting supervision and inspection, quality evaluation pre-loan investigation work, and based on the evaluation results, the implementation of diversity management. 24th the control and inspection (a) the implementation of the credit system: there is no breach of credit policy relating to the granting of credit and the head office; (B) dual credit rating: timeliness of ratings, whether the provisions of the rating, rating results are accurate; (C) the survey contents: data collection is complete, report writing is comprehensive, indicators analysis is objective, real, conclusions and the facts are consistent and reasonable; (D) double implementation of investigations system: practical implementation of double system; (E) other supervision and inspection of the contents. 25th due diligence evaluation offices and branches (jurisdiction), risk management, Marketing Management Department agreed to carry out pre-loan investigation supervision and inspection work, evaluate whether investigators due diligence to determine whether the exemption should be. Investigators should be compatible with. Due diligence assessment should be based on the fact that, following the principles of objectivity, impartiality and fairness. Article 26th head 第一根小棒长 第二根小棒长 第三根小棒长 能否围成三角形 第一根小棒长 第二根小棒长 第三根小棒长 能否围成三角形 第一根小棒长 第二根小棒长 第三根小棒长 能否围成三角形 第一根小棒长 第二根小棒长 第三根小棒长 能否围成三角形 第一根小棒长 第二根小棒长 第三根小棒长 能否围成三角形 and due diligence evaluations article 22nd head office, branch (jurisdiction), risk management, marketing management branch within the Department's credit business person assumed responsibility for the supervision and inspection and due diligence evaluations. Article 23rd, Head Office, branches (jurisdiction), risk management, Marketing Management Department through on-site and off-site inspection, investigation report, interviews with investigators for pre-loan investigation work by way of conducting supervision and inspection, quality evaluation pre-loan investigation work, and based on the evaluation results, the implementation of diversity management. 24th the control and inspection (a) the implementation of the credit system: there is no breach of credit policy relating to the granting of credit and the head office; (B) dual credit rating: timeliness of ratings, whether the provisions of the rating, rating results are accurate; (C) the survey contents: data collection is complete, report writing is comprehensive, indicators analysis is objective, real, conclusions and the facts are consistent and reasonable; (D) double implementation of investigations system: practical implementation of double system; (E) other supervision and inspection of the contents. 25th due diligence evaluation offices and branches (jurisdiction), risk management, Marketing Management Department agreed to carry out pre-loan investigation supervision and inspection work, evaluate whether investigators due diligence to determine whether the exemption should be. Investigators should be compatible with. Due diligence assessment should be based on the fact that, following the principles of objectivity, impartiality and fairness. Article 26th head and due diligence evaluations article 22nd head office, branch (jurisdiction), risk management, marketing management branch within the Department's credit business person assumed responsibility for the supervision and inspection and due diligence evaluations. Article 23rd, Head Office, branches (jurisdiction), risk management, Marketing Management Department through on-site and off-site inspection, investigation report, interviews with investigators for pre-loan investigation work by way of conducting supervision and inspection, quality evaluation pre-loan investigation work, and based on the evaluation results, the implementation of diversity management. 24th the control and inspection (a) the implementation of the credit system: there is no breach of credit policy relating to the granting of credit and the head office; (B) dual credit rating: timeliness of ratings, whether the provisions of the rating, rating results are accurate; (C) the survey contents: data collection is complete, report writing is comprehensive, indicators analysis is objective, real, conclusions and the facts are consistent and reasonable; (D) double implementation of investigations system: practical implementation of double system; (E) other supervision and inspection of the contents. 25th due diligence evaluation offices and branches (jurisdiction), risk management, Marketing Management Department agreed to carry out pre-loan investigation supervision and inspection work, evaluate whether investigators due diligence to determine whether the exemption should be. Investigators should be compatible with. Due diligence assessment should be based on the fact that, following the principles of objectivity, impartiality and fairness. Article 26th head