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新人教版高中英语必修3Unit 5 The Value of Money-Listening &Speaking教学设计
Step 4: Listen again and decide if the following statements are true (T) or false (F).1 It was the first time Chen Liyan's story was reported. T口 F口2 Chen found 10,000 yuan in a small plastic bag in Taiyuan railway station口 F口3 Wang Zheng apologized to Chen because he couldn't offer her more money. T口 F口4 Chen took out a large loan to cure her daughter, T口 F口5 Wang set up a fundraising website for Chen's daughter after Chen told him about her situation. T口 F口Step 5：After listening, discuss the questions.1 What kind of person do you think Chen Liyan is?Chen Liyan is generous and honest because she returned a large sum of money to the owner.2 Did Chen return the money because she didn't need it?No. She returned the money because it was the right thing to do. Evidence for this is that she refused to accept the reward money because she felt that it had not been earned. 3 Is it common for people to do what Chen did?It depends on the culture. In some countries it is quite common to return money that has been found. In other countries, people believe "Finders are keepers!" 4 How did Wang Zheng feel about the return of his money?He must have been very happy and relieved to have gotten his money back. We know this because he thanked Chen repeatedly and even offered her a reward.5 Why did Ma Dongbao tell Wang about Chen's family?He must have had great sympathy for Chen and her daughter and wanted to help them.'We know this because he arranged help for them. 6 How did the news reporter feel about Chen's actions?The news reporter felt that it showed that money wasn't the most important thing in life. We know this because the reporter told us that this is what Chen believes. and then said, “that's a great attitude to take."
新人教版高中英语必修3Unit 5 The Value of Money-Reading and Thinking教学设计一
Everybody wants to get wealth.In today’s material world,making money or becoming wealthy symbolizes a person’s success and capability. Many people just make every effort, pay any price to attain greater wealth. With money,they can buy nice, large apartments in nice neighborhood. With money they can own luxurious cars. Wealth seems to bring all happiness in life.But is wealth the only road to happiness? Not really. There are many things in the world, which are beyond the means of money, such as friendship, love, health and knowledge. People are so preoccupied with struggling for money that they have no time or would not take the time to form or maintain friendship. What happiness can they feel living as lonely miserable creatures without love or friends in the world even if they accumulate tremendous wealth?In my opinion, people can’t do anything without money, but money is not everything. What money will bring you depends on your personal belief and goal in life. If you are kind enough to help others, especially the poor, money is a good thing to you. With it, you can do much more for the benefit of people and your country, and it will add to your own happiness. If you want money just for your own needs, you’ll never be satisfied or happy. In a word,you should have money spent for more people. Only then can money be the source of your happiness.Step 8 Homework4 students in a group, one acts Roderick, one Oliver, one servant and the fourth one acts Henry Adams, then listen to the tape, pay more attention to the difference between American English and British English in pronunciation, stress, tone.
新人教版高中英语必修3Unit 5 the value of money-Reading For Writing教学设计一
【参考范文】Narrator：(Henry is smiling as he leaves the restaurant. As he is walking down the street, he sees a sign for a place that cuts hair. He decides to get it cut. )H＝Henry；B＝Barber；R＝rude manH：Good afternoon, I'd like to get a cut, if I may. (The barber looks at Henry's hair and continues cutting another man's hair. )Er, I'd really like a haircut. As you can see it's much too long. B：(in a rude manner) Yes, I can see that. Indeed, I can. H：Fine, well I'll have a seat then. (He sits in one of the barber's chairs. The barber turns to look at Henry. )B：It's quite expensive here, you know！Are you sure you can afford it?H：Yes. I think so. (In comes the rude man. )R：Hey you there. I need a haircut quickly. Can you do me straightaway?B：All right, then, get in the chair and I'll see what I can do. R：Thank you. (sits down in one of the barber's chairs)H：Excuse me, but I was here first. Aren't you going to do my hair first?B：This man's in a hurry. H：Well so am I！I insist that you cut my hair first. B：OK, but I'll have to be quick. This gentleman is waiting. H：Thank you. (They both become quiet. After his hair is cut, the barber tells Henry how much he must pay. Henry shows the barber the bank note. )B：Why, Mr . . . (looks shocked)H：Adams. Henry Adams. I'm sorry, I don't have any change. R：You're that Mr Adams! Well，I'm glad I waited or I might never have known it was you. B：Why, Mr Adams, please don't worry！(wearing a big smile) Nothing to worry about！Nothing at all!Please come back any time, even if you only need too little hairs cut！It will be my honour to serve you!
新人教版高中英语选修2Unit 1 Science and Scientists-Discovering useful structures教学设计
The grammatical structure of this unit is predicative clause. Like object clause and subject clause, predicative clause is one of Nominal Clauses. The leading words of predicative clauses are that, what, how, what, where, as if, because, etc.The design of teaching activities aims to guide students to perceive the structural features of predicative clauses and think about their ideographic functions. Beyond that, students should be guided to use this grammar in the context apporpriately and flexibly.1. Enable the Ss to master the usage of the predicative clauses in this unit.2. Enable the Ss to use the predicative patterns flexibly.3. Train the Ss to apply some skills by doing the relevant exercises.1.Guide students to perceive the structural features of predicative clauses and think about their ideographic functions.2.Strengthen students' ability of using predicative clauses in context, but also cultivate their ability of text analysis and logical reasoning competence.Step1: Underline all the examples in the reading passage, where noun clauses are used as the predicative. Then state their meaning and functions.1) One theory was that bad air caused the disease.2) Another theory was that cholera was caused by an infection from germs in food or water.3) The truth was that the water from the Broad Street had been infected by waste.Sum up the rules of grammar:1. 以上黑体部分在句中作表语。2. 句1、2、3中的that在从句中不作成分，只起连接作用。 Step2: Review the basic components of predicative clauses1.Definition
新人教版高中英语选修2Unit 1 Science and Scientists-Learning about Language教学设计
Step 7: complete the discourse according to the grammar rules.Cholera used to be one of the most 1.__________ (fear) diseases in the world. In the early 19th century, _2_________ an outbreak of cholera hit Europe, millions of people died. But neither its cause, 3__________ its cure was understood. A British doctor, John Snow, wanted to solve the problem and he knew that cholera would not be controlled _4_________ its cause was found. In general, there were two contradictory theories 5 __________ explained how cholera spread. The first suggested that bad air caused the disease. The second was that cholera was caused by an _6_________(infect) from germs in food or water. John Snow thought that the second theory was correct but he needed proof. So when another outbreak of cholera hit London in 1854, he began to investigate. Later, with all the evidence he _7_________ (gather), John Snow was able to announce that the pump water carried cholera germs. Therefore, he had the handle of the pump _8_________ (remove) so that it couldn't be used. Through his intervention，the disease was stopped in its tracks. What is more, John Snow found that some companies sold water from the River Thames that __9__________________ (pollute) by raw waste. The people who drank this water were much more likely _10_________ (get) cholera than those who drank pure or boiled water. Through John Snow's efforts, the _11_________ (threaten) of cholera around the world saw a substantial increase. Keys： 1.feared 2.when 3. nor 4.unless 5.that/which 6.infection 7.had gathered 8.removed 9.was polluted 10.to get 11. threat
新人教版高中英语选修2Unit 1 Science and Scientists-Reading and thinking教学设计
Step 5： After learning the text, discuss with your peers about the following questions:1.John Snow believed Idea 2 was right. How did he finally prove it?2. Do you think John Snow would have solved this problem without the map?3. Cholera is a 19th century disease. What disease do you think is similar to cholera today?SARS and Covid-19 because they are both deadly and fatally infectious, have an unknown cause and need serious public health care to solve them urgently.keys:1. John Snow finally proved his idea because he found an outbreak that was clearly related to cholera, collected information and was able to tie cases outside the area to the polluted water.2. No. The map helped John Snow organize his ideas. He was able to identify those households that had had many deaths and check their water-drinking habits. He identified those houses that had had no deaths and surveyed their drinking habits. The evidence clearly pointed to the polluted water being the cause.3. SARS and Covid-19 because they are both deadly and fatally infectious, have an unknown cause and need serious public health care to solve them urgently.Step 6: Consolidate what you have learned by filling in the blanks:John Snow was a well-known _1___ in London in the _2__ century. He wanted to find the _3_____ of cholera in order to help people ___4_____ it. In 1854 when a cholera __5__ London, he began to gather information. He ___6__ on a map ___7___ all the dead people had lived and he found that many people who had ___8____ (drink) the dirty water from the __9____ died. So he decided that the polluted water ___10____ cholera. He suggested that the ___11__ of all water supplies should be _12______ and new methods of dealing with ____13___ water be found. Finally, “King Cholera” was __14_____.Keys: 1. doctor 2. 19th 3.cause 4.infected with 5.hit 6.marked 7.where 8.drunk 9.pump 10.carried 11.source 12.examined 13.polluted 14.defeatedHomework: Retell the text after class and preview its language points
新人教版高中英语选修2Unit 2 Bridging Cultures-Discovering useful structures教学设计
The grammar of this unit is designed to review noun clauses. Sentences that use nouns in a sentence are called noun clauses. Nominal clauses can act as subject, object, predicate, appositive and other components in compound sentences. According to the above-mentioned different grammatical functions, nominal clauses are divided into subject clause, object clause, predicate clause and appositive clause. In this unit, we will review the three kinds of nominal clauses. Appositive clauses are not required to be mastered in the optional compulsory stage, so they are not involved.1. Guide the students to judge the compound sentences and determine the composition of the clauses in the sentence.2. Instruct students to try to learn grammar by generalizing grammar rules, controlling written practice, and semi-open oral output.3. Inspire the students to systematize the function and usage of noun clause1.Instruct students to try to learn grammar by generalizing grammar rules, controlling written practice, and semi-open oral output.2.Inspire the students to systematize the function and usage of noun clauseStep1: The teacher ask studetns to find out more nominal clauses from the reading passage and udnerline the nominal clauses.
新人教版高中英语选修2Unit 3 Food and Culture-Reading and thinking教学设计
The discourse explores the link between food and culture from a foreign’s perspective and it records some authentic Chinese food and illustrates the cultural meaning, gerography features and historic tradition that the food reflects. It is aimed to lead students to understand and think about the connection between food and culture. While teaching, the teacher should instruct students to find out the writing order and the writer’s experieces and feelings towards Chinese food and culture.1.Guide the students to read the text, sort out the information and dig out the topic.2.Understand the cultural connotation, regional characteristics and historical tradition of Chinese cuisine3.Understand and explore the relationship between food and people's personality4.Guide the students to use the cohesive words in the text5.Lead students to accurately grasp the real meaning of the information and improve the overall understanding ability by understanding the implied meaning behind the text.1. Enable the Ss to understand the structure and the writing style of the passage well.2. Lead the Ss to understand and think further about the connection between food and geography and local character traits.Step1: Prediction before reading. Before you read, look at the title, and the picture. What do you think this article is about?keys:It is about various culture and cuisine about a place or some countries.
统编版二年级语文上第1课小蝌蚪找妈妈教学设计教案
《小蝌蚪找妈妈》是统编版二年级上册第一单元的一篇富有童趣的课文。课文以浅显的文字生动地描写了小蝌蚪找妈妈的故事，同时向学生叙述了小蝌蚪是怎样变成青蛙的。从教材编排看，课文中人物角色较多，语言生动趣味性强，是进行朗读训练的典型教材：从教材结构看，课文二三四自然段段落相仿，也是进行学法指导的最佳范例。课文中的动词用得巧，增强了表达效果。课文3幅插图，分别画的是第二至五自然段的内容，不仅生动地展现出小蝌蚪找妈妈的过程，而且有序地呈现出蝌蚪的变化过程:长出后腿--长出前腿--尾巴不见了。插图画面色彩鲜艳，形象活泼生动，极具吸引力和感染力。 1.认识“塘、脑”等14个生字，读准多音字“教”，会写“两、哪”10个生字。2.正确、流利、有感情地分角色朗读课文。3.结合课文内容，借助课文图片，按顺序说清楚小蝌蚪成长的变化过程，感受小蝌蚪遇事主动探索的精神，增强阅读科学童话的兴趣。4.知道青蛙是捕捉害虫的能手，是庄稼的好朋友，树立保护青蛙的意识。 1.教学重点：能分角色朗读课文，借助图片、表示时间变化的句子、表示动作的词语，了解课文内容。2.教学难点：能按顺序说清楚小蝌蚪成长的变化过程，感受小蝌蚪遇事主动探索的精神，增强阅读科学童话的兴趣。 2课时
统编版二年级语文上识字2树之歌教学设计教案
《树之歌》是统编版二年级上册第二单元的一篇识字课文。介绍树木特征的归类识字歌，描写了杨树、榕树、梧桐树……等11种树木，表现了大自然树木种类的丰富。课文安排了一组“木”字旁归类识字。把树木的名称集中在一首诗歌中，让学生在感受美丽景色、感受美好生活的同时，认识事物，认识表示树木的汉字，感知不同树木的名称。教学的过程中可引导学生在诵读文本的同时，体现多样的识字形式，要将识字教学与阅读文本有机融合, 在反复的读书体会中，引导学生发现汉字规律，运用形声字形旁表义、声旁表音的特点归类识字，并鼓励学生运用已经掌握的方法自主识字。 1.认识“梧、桐”等15个生字，会写“杨、壮”等10个生字。学会运用形声字的特点自主识字。2.正确、流利地朗读儿歌，并背诵全文。3.通过看图和读儿歌，初步了解11种树木的基本特点。积累与树木有关的语句。4.引导学生学会观察身边的事物，树立爱护花草树木的意识。 1.教学重点：学会本课生字，利用形声字特点掌握木字旁的8个生字。朗读课文，背诵课文。了解不同树木的特点。2.教学难点：能按掌握形声字的构字特点，了解11种树木的基本特点。积累与树木有关的语句。能背诵课文。 2课时
统编版二年级语文上识字1场景歌教学设计教案
《场景歌》是统编版二年级上册第二单元的一篇识字课文。这是一组数量词归类识字。把数量词分类集中在四幅不同的图画之中，让学生在感受美丽景色、感受美好生活的同时，认识事物，认识表示事物的汉字，初步感知不同事物数量词的表达方式。全文共五节。第一节是一幅大海风景图。第二节是一幅山村田园风光图。第三节是一幅公园景色图。第四幅是少先队员活动的场面。教师要充分调动学生的积极性，采用各种各样的方法，让学生自己认字，朗读。在教学的过程中，通过结合图片和上下文，欣赏美丽景色，感受美好生活，同时认识事物，初步感知不同事物数量词的表达方式。 1.认识“帆、艘”等10个生字，会写“处、园”等10个生字。2.正确朗读课文。初步感受场景展示的美丽景色，了解不同事物数量词的不同的表达。3.选择照片或图画，仿照课文，学习用数量词表达生活中的事物。4.培养学生留心观察周围事物的习惯，培养学生的观察能力和想象能力。 1.教学重点：会认、会写课文相关生字。正确朗读课文。背诵课文。初步感受场景展示的美丽景色，了解不同事物量词的不同表达。2.教学难点：培养学生留心观察周围事物的习惯，培养学生的观察能力和想象能力。学习用数量词表达生活中的事物。 2课时
统编版三年级语文上第19课海滨小城教学设计教案
《海滨小城》《海滨小城》是一篇写景的美文。作者按由远及近的顺序，分别描绘了海天远景图、海上日出图、渔船归来沙滩图、小城庭院图、小城公园图、小城街道图。作者正是用这一幅幅的画面，抓住其中景物的特点，展现了海滨小城的美丽景色。本课在语言表达上也很有特点。作者运用“棕色、白色、灰色金黄色”等一系列表示颜色的词语，写出了海滨之美；以总起句的方式概括了小城庭院、公园、街道的特点。在教学中，要通过多种形式的朗读，将学生带入文字勾勒的画面，从而了解课文写了海滨小城的哪些景象，以及这些景色的特点，体会总起句的作用，进而积累语言，仿照课文练习表达。选编这篇课文的主要意图是加强学生自主阅读实践活动，加强对写景状物这一类文章特点的感悟，进一步学习抓住事物特点、按空间变换顺序记叙的表达方法。 1.认识本课“滨、鸥”等11个生字，正确认读多音字“臂”，会写“灰、渔”等13个生字，会写“海滨、街道”等16个词语。2.结合插图学习课文，理解课文内容。了解课文描写的主要景物及其样子。3.能找出第4～6自然段的关键语句，借助关键语句理解段落的意思。4.体会作者热爱家乡的感情，增强环境保护意识。 1.教学重点：理解课文内容，了解海滨小城的美丽的场景及其特点，从中体会作者对家乡的热爱之情。2.教学难点：能通过学习课文，体会作者热爱家乡的感情，增强环境保护意识。 2课时
统编版三年级语文上第16课金色的草地教学设计教案
《金色的草地》是第五单元的第二篇课文，是一篇精读写作课文，本单元的语文元素是 “留心观察周围的事物”。本组单元只有两课，第二课明确了本课主要的学习内容，学会观察并运用作者的观察方法写出自己的观察。课文先讲兄弟两个在住处窗前一大片草地上自由自在、无拘无束、尽情玩耍的情景，使我们真切地感受到了大自然带给他们的快乐。课文接着写了“我”无意中发现草地的颜色在不同的时间是不一样的；再仔细观察，又发现了草地颜色变化的原因。最后作者总结全文，可爱的草地和有趣的蒲公英给他们生活带来了快乐，还给他们带来了探索发现的喜悦。 1.正确、流利地朗读课文，会认“蒲、英”6个生字，会写“盛、耍等13个生字。会写“窗前、蒲公英”等13个词语。2.理解课文内容，了解草地颜色的变化情况及原因。3.品读感悟，体会“我”观察的细致，引导学生体会文中“我”对蒲公英的感情变化。4.能自己观察某一种动物、植物或一处场景的变化情况并和同学们交流。 1.教学重点：理解课文内容，了解草地颜色的变化情况及原因。品读感悟，体会“我”观察的细致，引导学生体会文中“我”对蒲公英的感情变化。2.教学难点：能自己观察某一种动物、植物或一处场景的变化情况并和同学们交流。 2课时
统编版三年级语文上第18课富饶的西沙群岛教学设计教案
《富饶的西沙群岛》是部编版小学语文三年级上册第六单元的一篇精读课文。本课的结构清晰，语言生动，富有儿童情趣。文章结构分明，先总写西沙群岛风景优美、物产丰富，再分别介绍了海水、海底生物、海岛上的鸟三方面的内容，表达了作者对祖国海疆的热爱和赞美之情。本单元的语文要素是“借助关键语句理解一段话的意思”，本课在开篇的第一自然段就有了概括整篇文章的中心句“那里风景优美、物产丰富，是个可爱的地方”。课文的第五自然段也围绕“西沙群岛也是鸟的天下”这个关键句进行描述。课后习题的“选择你喜欢的部分，向别人介绍西沙群岛”“从下面的图片选择一幅图，写几句话”等学习要求。目的在于让学生借助关键句理解课文和一段话的意思，提升学生理解感悟和运用语言的能力。 1.会认“饶、优”9个生字，会写“优、浅”等13个生字，读准多音字“参”。能联系上下文理解“风景优美、物产丰富、五光十色”等词语的意思。2.有感情地朗读课文。了解课文是从海水、海底的生物、海岛上的鸟三个方面描写西沙群岛的美丽富饶的。3.能选择一幅图，用几句话描写图上的景观。 1.教学重点：能通过理解词句，了解西沙群岛的美丽富饶。理解文中部分难句子。2.教学难点：掌握文中的写作手法，尝试运用到习作中。 2课时
【高教版】中职数学基础模块上册：2.3《一元二次不等式》教案设计
教师姓名 课程名称数学班 级 授课日期 授课顺序 章节名称§2.3 一元二次不等式教 学 目 标知识目标：1、理解一元二次不等式和一元二次方程以及二次函数之间的关系 2、理解一元二次不等式的解集的含义 3、一元二次不等式的解集与二次函数图像的对应 技能目标：1、会解一元二次方程 2、会画二次函数的图像 3、能结合图像写出一元二次不等式的解集 情感目标：体会知识之间的相互关联性，体会数形结合思想的重要性教学 重点 和 难点重点： 1、一元二次不等式的解集的含义 2、一元二次不等式与二次函数的关系 难点： 1、将一元二次不等式和一元二次方程以及二次函数联系起来 2、在函数图像上正确的找到解集对应的部分教 学 资 源《数学》（第一册） 多媒体课件评 估 反 馈课堂提问 课堂练习作 业习题2.3课后记本节课内容是比较重要的，是一元二次方程、一元二次函数、一元二次不等式的结合，相关知识点融会贯通，数形结合的思想方法在这有很好的运用。三种情况只要讲清楚一种，另外两种可由学生自行推出结论。
【高教版】中职数学基础模块上册：2.4《含绝对值的不等式》教案设计
教师姓名 课程名称数学班 级 授课日期 授课顺序 章节名称§2.4 含绝对值的不等式教 学 目 标知识目标：1、理解绝对值的几何意义 2、掌握简单的含绝对值不等式的解法 3、掌握含绝对值不等式的等价形式 技能目标：1、会解形如|ax+b|＞c或|ax+b|＜c的绝对值不等式 情感目标：通过学习，体会数形结合、整体代换及等价转换的数学思想方法教学 重点 和 难点重点： 1、绝对值的几何意义 2、基本绝对值不等式|x|＞a或|x|＜a的解 难点： 1、去绝对值符号后不等式与原不等式保持等价性教 学 资 源《数学》（第一册） 多媒体课件评 估 反 馈课堂提问 课堂练习作 业习题2.4课后记不等式的基本性质是初中就学习过的内容，分式不等式的解法是哦本节课的一个重点和难点，尤其是不等号另一边不为0的情况，需要移项，这一点在强调前学生考虑不到，因此解题错误多。区间是个新内容，学生往往将连续的正数写作一个区间，这是常见的错误，要进行提醒。另外，在均值不等式这里稍微补充了一些内容，引起学生的兴趣。
高教版中职数学基础模块下册：6.1《数列的概念》教案设计
【教学目标】1. 理解数列的通项公式的意义，能根据通项公式写出数列的任意一项，以及根据其前几项写出它的一个通项公式．2. 了解数列的递推公式，会根据数列的递推公式写出前几项．3.培养学生积极参与、大胆探索的精神，培养学生的观察、分析、归纳的能力．教学重点 数列的通项公式及其应用．教学难点 根据数列的前几项写出满足条件的数列的一个通项公式．教学方法 本节课主要采用例题解决法．通过列举实例，进一步研究数列的项与序号之间的关系．通过三类题目，使学生深刻理解数列通项公式的意义，为以后学习等差数列与等比数列打下基础．【教学过程】 环节教学内容师生互动设计意图导 入⒈数列的定义 按一定次序排列的一列数叫做数列． 注意：（1）数列中的数是按一定次序排列的； （2）同一个数在数列中可以重复出现． 2. 数列的一般形式 数列a1，a2，a3，…，an，…，可记作{ an }． 3. 数列的通项公式： 如果数列{ an }的第n项an与n之间的关系可以用一个公式来表示，那么这个公式就叫做这个数列的通项公式． 教师引导学生复习． 为学生进一步理解通项公式，应用通项公式解决实际问题做好准备．
高教版中职数学基础模块下册：6.3《等比数列》优秀教案设计
授课 日期 班级16高造价 课题： §6.3等比数列 教学目的要求： 1.理解等比数列的概念，能根据定义判断或证明一个数列是等比数列；2.探索并掌握等比数列的通项公式； 3.掌握等比数列前 n 项和公式及推导过程，能用公式求相关参数； 教学重点、难点:运用等比数列的通项公式求相关参数 授课方法： 任务驱动法 小组合作学习法 教学参考及教具（含多媒体教学设备）： 《单招教学大纲》 授课执行情况及分析： 板书设计或授课提纲 §6.3等比数列 1．等比数列的概念 （学生板书区） 2. 等比数列的通项公式 3.等比数列的求和公式
高教版中职数学基础模块下册：8.3《两条直线的位置关系》教案设计
教 学 过 程教师 行为学生 行为教学 意图 *揭示课题 8．3 两条直线的位置关系（二） *创设情境 兴趣导入 【问题】 平面内两条既不重合又不平行的直线肯定相交．如何求交点的坐标呢？ 图8－12 介绍 质疑 引导 分析 了解 思考 启发 学生思考 *动脑思考 探索新知 如图8－12所示，两条相交直线的交点，既在上，又在上．所以的坐标是两条直线的方程的公共解．因此解两条直线的方程所组成的方程组，就可以得到两条直线交点的坐标． 观察图8－13，直线、相交于点P，如果不研究终边相同的角，共形成四个正角，分别为、、、，其中与，与为对顶角，而且． 图8－13 我们把两条直线相交所成的最小正角叫做这两条直线的夹角，记作． 规定，当两条直线平行或重合时，两条直线的夹角为零角，因此，两条直线夹角的取值范围为． 显然，在图8－13中，（或）是直线、的夹角，即． 当直线与直线的夹角为直角时称直线与直线垂直，记做．观察图8－14，显然，平行于轴的直线与平行于轴的直线垂直，即斜率为零的直线与斜率不存在的直线垂直． 图8－14 讲解 说明 讲解 说明 引领 分析 仔细 分析 讲解 关键 词语 思考 思考 理解 思考 理解 记忆 带领 学生 分析 带领 学生 分析 引导 式启 发学 生得 出结 果
【高教版】中职数学拓展模块：1.3《正弦定理与余弦定理》教案设计
教 学 过 程教师 行为学生 行为教学 意图 *揭示课题 1.3正弦定理与余弦定理． *创设情境 兴趣导入 在实际问题中，经常需要计算高度、长度、距离和角的大小，这类问题中有许多与三角形有关，可以归结为解三角形问题． 介绍 播放 课件 质疑 了解 观看 课件 思考 学生自然的走向知识点*巩固知识 典型例题 例6 一艘船以每小时36海里的速度向正北方向航行（如图1－9）.在A处观察到灯塔C在船的北偏东方向，小时后船行驶到B处，此时灯塔C在船的北偏东方向，求B处和灯塔C的距离（精确到0.1海里）. 图1－9 A 解因为∠NBC=，A=，所以.由题意知 (海里). 由正弦定理得 （海里）. 答：B处离灯塔约为海里. 例7 修筑道路需挖掘隧道，在山的两侧是隧道口A和(图1－10），在平地上选择适合测量的点C，如果，m，m，试计算隧道AB的长度（精确到m）． 图1－10 解 在ABC中，由余弦定理知 =． 所以 m. 答：隧道AB的长度约为409m. 例8 三个力作用于一点O（如图1－11）并且处于平衡状态，已知的大小分别为100N，120N，的夹角是60°，求F的大小（精确到1N）和方向． 图1－11 解 由向量加法的平行四边形法则知，向量表示F1，F2的合力F合，由力的平衡原理知，F应在的反向延长线上，且大小与F合相等. 在△OAC中，∠OAC=180°60°=120°，OA=100， AC=OB=120，由余弦定理得 OC= = ≈191（N）. 在△AOC中，由正弦定理，得 sin∠AOC=≈0.5441， 所以∠AOC≈33°，F与F1间的夹角是180°–33°=147°. 答：F约为191N，F与F合的方向相反，且与F1的夹角约为147°． 引领 讲解 说明 引领 观察 思考 主动 求解 观察 通过 例题 进一 步领 会 注意 观察 学生 是否 理解 知识 点