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初中道德与法治七年级上册师长情谊4作业设计

  • 新人教版高中英语必修3Unit 5 The Value of Money-Listening &Speaking&Talking教学设计

    新人教版高中英语必修3Unit 5 The Value of Money-Listening &Speaking&Talking教学设计

    4. A:We’d like to have someone to say a word at the beginning to welcome the group.B:↙Who?A:We thought that you or Dr.Johnson might do it.B用降调说Who,其意思是问,对方想让谁在开场时致欢迎词。Step 6 Pronunciation---Practice1. Listen to the short conversation and mark the intonation with ↗, ↙ or ↙, ↗. Then discuss with a partner what they intend to convey by using different intonation.Owner: You know what ?↗ It’s a million-pound bank note↙.Waiter 1: Really ?↗(question)Waiter 2: Really !↙(unbelievable and surprised)Waiter 3: Really ?!↙↗(first question then surprised)2. Listen to the conversations. Underline the parts that are stressed and mark the intonation. Then talk about the implied meanings of the responses with different intonations. Listen again and repeat.1) Henry: It’s a nice suit.Owner: Oh, it’s perfect!↙(The intonation means it is very suitable for Henry.)2) Henry: Well, that’s very kind of you.Owner: Kind, sir ?↗(what you said is not right) No, it’s kind of you. You must come whenever you want and have whatever you like. Just having you sit here is a great honour !!↙(welcome you to come again)3)Henry:Well, to be honest, I have none. Oliver:(happily) What luck!(excited) Brother↗, what luck!↙(It means “Didn’t you hear it?”)Henry: Well, it may seem lucky to you but not to me!↗(angry) If this is your idea of some kind of joke, I don’t think it’s very funny. Now if you’ll excuse me, I ought to be on my way.↙(If so, I would leave.)Roderick: Please don’t go↙...(hope Henry can wait for a moment)Part B Viewing and Talking---Describe people’s changing attitudes in a film clipStep 1 Before-listening---Tell the filmYou are going to watch part of the film The Million Pound Bank Note. Look at these photos and guess what happens in the film.

  • 新人教版高中英语必修3Unit 5 The value of money-Reading and Thinking教学设计二

    新人教版高中英语必修3Unit 5 The value of money-Reading and Thinking教学设计二

    ? Could you offer me some kind of work here?? I don’t want your charity, I just want an honest job.? Careless: I landed in Britain by accident.Step 7:Consolidation.? Find Henry? Roderick and Oliver were I .making a bet when they saw Henry, a poor young man. ? Know Henry? About a month ago, Henry was sailing and later he found himself carried out to sea by a strong wind. Fortunately, he 2.was spotted by a ship. And it was the ship that brought him to 3.England? Offer money to Henry ? Oliver and Roderick gave Henry a letter and told him that there was money in it. They 4.persuaded him to accept it, and made him 5.promise that it wouldn't be opened until 2 o'clock.Step 8:Language pointsa large amount of: a large quantity of; a great deal ofe.g. They bought a large amount of furniture before they moved their new house.make a bet: make an arrangement to risk money, etc. on an event of which the result is doubtful.e.g. We made a bet on the result of the match.permit sb to do something: allow somebody to do somethinge.g. My mother doesn’t permit me to ride in the street after it rained.by accident: as a result of chancee.g. I only found it by accident.stare at: look at somebody or something with the eyes wide open in a fixed gaze( in astonishment, wonder, fear, etc)to be honest: to tell you the truth; to be franke.g. To be honest, I don’t think we have a chance of winning.Step7 Homework:What do you think will happen to Henry? Will the bank-note help him or get him into trouble?

  • 新人教版高中英语必修3Unit 5 The Value of Money-Reading and Thinking教学设计一

    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

    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-Reading and thinking教学设计

    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 3 Food and Culture-Discovering useful structures教学设计

    新人教版高中英语选修2Unit 3 Food and Culture-Discovering useful structures教学设计

    The newspaper reported more than 100 people had been killed in the thunderstorm.报纸报道说有一百多人在暴风雨中丧生。(2)before、when、by the time、until、after、once等引导的时间状语从句的谓语是一般过去时,以及by、before后面接过去的时间时,主句动作发生在从句的动作或过去的时间之前且表示被动时,要用过去完成时的被动语态。By the time my brother was 10, he had been sent to Italy.我弟弟10岁前就已经被送到意大利了。Tons of rice had been produced by the end of last month. 到上月底已生产了好几吨大米。(3) It was the first/second/last ... time that ...句中that引导的定语从句中,主语与谓语构成被动关系时,要用过去完成时的被动语态。It was the first time that I had seen the night fact to face in one and a half years. 这是我一年半以来第一次亲眼目睹夜晚的景色。(4)在虚拟语气中,条件句表示与过去事实相反,且主语与谓语构成被动关系时,要用过去完成时的被动语态。If I had been instructed by him earlier, I would have finished the task.如果我早一点得到他的指示,我早就完成这项任务了。If I had hurried, I wouldn't have missed the train.如果我快点的话,我就不会误了火车。If you had been at the party, you would have met him. 如果你去了晚会,你就会见到他的。

  • 新人教版高中英语选修2Unit 5 First Aid-Discovering useful structures教学设计

    新人教版高中英语选修2Unit 5 First Aid-Discovering useful structures教学设计

    You have no excuse for not going.你没有理由不去。He was punished for not having finished his homework.他因未完成作业而受到惩罚。2.动词­ing形式复合结构由物主代词或人称代词宾格、名词所有格或普通格加动词­ing,即“sb./sb.'s+doing”构成。动词­ing形式的复合结构实际上是给动词­ing形式加了一个逻辑主语。动词­ing形式的复合结构有四种形式:①形容词性物主代词+动词­ing②名词所有格+动词­ing③代词宾格+动词­ing④名词+动词­ingHer coming to help encouraged all of us.她来帮忙鼓舞了我们所有人。The baby was made awake by the door suddenly shutting.这个婴儿被突然的关门声吵醒了。Can you imagine him/Jack cooking at home?你能想象他/杰克在家做饭的样子吗?无生命名词无论是作主语还是作宾语都不能用第②种形式。Tom's winning first prize last year impressed me a lot.汤姆去年得了一等奖使我印象深刻。Do you mind my/me/Jack's/Jack leaving now?你介意我/杰克现在离开吗?Excuse me for my not coming on time.很抱歉我没能按时来。His father's being ill made him worried.他父亲病了,他很担心。We are looking forward to the singer's/the singer to give us a concert.我们盼望着这位歌手来给我们举办一场演唱会。

  • 人教A版高中数学必修一函数模型的应用教学设计(2)

    人教A版高中数学必修一函数模型的应用教学设计(2)

    本节通过一些函数模型的实例,让学生感受建立函数模型的过程和方法,体会函数在数学和其他学科中的广泛应用,进一步认识到函数是描述客观世界变化规律的基本数学模型,能初步运用函数思想解决一些生活中的简单问题。课程目标1.能利用已知函数模型求解实际问题.2.能自建确定性函数模型解决实际问题.数学学科素养1.数学抽象:建立函数模型,把实际应用问题转化为数学问题;2.逻辑推理:通过数据分析,确定合适的函数模型;3.数学运算:解答数学问题,求得结果;4.数据分析:把数学结果转译成具体问题的结论,做出解答;5.数学建模:借助函数模型,利用函数的思想解决现实生活中的实际问题.重点:利用函数模型解决实际问题;难点:数模型的构造与对数据的处理.

  • 人教A版高中数学必修一对数函数的图像和性质教学设计(1)

    人教A版高中数学必修一对数函数的图像和性质教学设计(1)

    本节课是新版教材人教A版普通高中课程标准实验教科书数学必修1第四章第4.4.2节《对数函数的图像和性质》 是高中数学在指数函数之后的重要初等函数之一。对数函数与指数函数联系密切,无论是研究的思想方法方法还是图像及性质,都有其共通之处。相较于指数函数,对数函数的图象亦有其独特的美感。在类比推理的过程中,感受图像的变化,认识变化的规律,这是提高学生直观想象能力的一个重要的过程。为之后学习数学提供了更多角度的分析方法。培养和发展学生逻辑推理、数学直观、数学抽象、和数学建模的核心素养。1、掌握对数函数的图像和性质;能利用对数函数的图像与性质来解决简单问题;2、经过探究对数函数的图像和性质,对数函数与指数函数图像之间的联系,对数函数内部的的联系。培养学生观察问题、分析问题和归纳问题的思维能力以及数学交流能力;渗透类比等基本数学思想方法。

  • 人教A版高中数学必修一函数y=Asin(ωχ+φ)教学设计(1)

    人教A版高中数学必修一函数y=Asin(ωχ+φ)教学设计(1)

    本节课选自《普通高中课程标准实验教科书数学必修1》5.6.2节 函数y=Asin(ωx+φ)的图象通过图象变换,揭示参数φ、ω、A变化时对函数图象的形状和位置的影响。通过引导学生对函数y=sinx到y=Asin(ωx+φ)的图象变换规律的探索,让学生体会到由简单到复杂、由特殊到一般的化归思想;并通过对周期变换、相位变换先后顺序调整后,将影响图象变换这一难点的突破,让学生学会抓住问题的主要矛盾来解决问题的基本思想方法;通过对参数φ、ω、A的分类讨论,让学生深刻认识图象变换与函数解析式变换的内在联系。通过图象变换和“五点”作图法,正确找出函数y=sinx到y=Asin(ωx+φ)的图象变换规律,这也是本节课的重点所在。提高学生的推理能力。让学生感受数形结合及转化的思想方法。发展学生数学直观、数学抽象、逻辑推理、数学建模的核心素养。

  • 人教A版高中数学必修一函数模型的应用教学设计(1)

    人教A版高中数学必修一函数模型的应用教学设计(1)

    本节课选自《普通高中课程标准实验教科书数学必修1本(A版)》的第五章的4.5.3函数模型的应用。函数模型及其应用是中学重要内容之一,又是数学与生活实践相互衔接的枢纽,特别在应用意识日益加深的今天,函数模型的应用实质是揭示了客观世界中量的相互依存有互有制约的关系,因而函数模型的应用举例有着不可替代的重要位置,又有重要的现实意义。本节课要求学生利用给定的函数模型或建立函数模型解决实际问题,并对给定的函数模型进行简单的分析评价,发展学生数学建模、数学直观、数学抽象、逻辑推理的核心素养。1. 能建立函数模型解决实际问题.2.了解拟合函数模型并解决实际问题.3.通过本节内容的学习,使学生认识函数模型的作用,提高学生数学建模,数据分析的能力. a.数学抽象:由实际问题建立函数模型;b.逻辑推理:选择合适的函数模型;c.数学运算:运用函数模型解决实际问题;

  • 人教A版高中数学必修一集合的基本运算教学设计(2)

    人教A版高中数学必修一集合的基本运算教学设计(2)

    集合的基本运算是人教版普通高中课程标准实验教科书,数学必修1第一章第三节的内容. 在此之前,学生已学习了集合的含义以及集合与集合之间的基本关系,这为学习本节内容打下了基础. 本节内容是函数、方程、不等式的基础,在教材中起着承上启下的作用. 本节内容是高中数学的主要内容,也是高考的对象,在实践中应用广泛,是高中学生必须掌握的重点.课程目标1. 理解两个集合的并集与交集的含义,能求两个集合的并集与交集;2. 理解全集和补集的含义,能求给定集合的补集; 3. 能使用Venn图表达集合的基本关系与基本运算.数学学科素养1.数学抽象:并集、交集、全集、补集含义的理解;2.逻辑推理:并集、交集及补集的性质的推导;3.数学运算:求 两个集合的并集、交集及补集,已知并集、交集及补集的性质求参数(参数的范围);4.数据分析:通过并集、交集及补集的性质列不等式组,此过程中重点关注端点是否含“=”及?问题;

  • 人教A版高中数学必修一简单的三角恒等变换教学设计(1)

    人教A版高中数学必修一简单的三角恒等变换教学设计(1)

    四、小结1.知识:如何采用两角和或差的正余弦公式进行合角,借助三角函数的相关性质求值.其中三角函数最值问题是对三角函数的概念、图像和性质,以及诱导公式、同角三角函数基本关系、和(差)角公式的综合应用,也是函数思想的具体体现. 如何科学的把实际问题转化成数学问题,如何选择自变量建立数学关系式;求解三角函数在某一区间的最值问题.2.思想:本节课通过由特殊到一般方式把关系式 化成 的形式,可以很好地培养学生探究、归纳、类比的能力. 通过探究如何选择自变量建立数学关系式,可以很好地培养学生分析问题、解决问题的能力和应用意识,进一步培养学生的建模意识.五、作业1. 课时练 2. 预习下节课内容学生根据课堂学习,自主总结知识要点,及运用的思想方法。注意总结自己在学习中的易错点;

  • 人教A版高中数学必修一简单的三角恒等变换教学设计(2)

    人教A版高中数学必修一简单的三角恒等变换教学设计(2)

    它位于三角函数与数学变换的结合点上,能较好反应三角函数及变换之间的内在联系和相互转换,本节课内容的地位体现在它的基础性上。作用体现在它的工具性上。前面学生已经掌握了两角和与差的正弦、余弦、正切公式以及二倍角公式,并能通过这些公式进行求值、化简、证明,虽然学生已经具备了一定的推理、运算能力,但在数学的应用意识与应用能力方面尚需进一步培养.课程目标1.能用二倍角公式推导出半角公式,体会三角恒等变换的基本思想方法,以及进行简单的应用. 2.了解三角恒等变换的特点、变换技巧,掌握三角恒等变换的基本思想方法. 3.能利用三角恒等变换的技巧进行三角函数式的化简、求值以及证明,进而进行简单的应用. 数学学科素养1.逻辑推理: 三角恒等式的证明; 2.数据分析:三角函数式的化简; 3.数学运算:三角函数式的求值.

  • 人教A版高中数学必修一同角三角函数的基本关系教学设计(2)

    人教A版高中数学必修一同角三角函数的基本关系教学设计(2)

    本节内容是学生学习了任意角和弧度制,任意角的三角函数后,安排的一节继续深入学习内容,是求三角函数值、化简三角函数式、证明三角恒等式的基本工具,是整个三角函数知识的基础,在教材中起承上启下的作用。同时,它体现的数学思想与方法在整个中学数学学习中起重要作用。课程目标1.理解并掌握同角三角函数基本关系式的推导及应用.2.会利用同角三角函数的基本关系式进行化简、求值与恒等式证明.数学学科素养1.数学抽象:理解同角三角函数基本关系式;2.逻辑推理: “sin α±cos α”同“sin αcos α”间的关系;3.数学运算:利用同角三角函数的基本关系式进行化简、求值与恒等式证明重点:理解并掌握同角三角函数基本关系式的推导及应用; 难点:会利用同角三角函数的基本关系式进行化简、求值与恒等式证明.

  • 人教A版高中数学必修一正弦函数、余弦函数的图像教学设计(2)

    人教A版高中数学必修一正弦函数、余弦函数的图像教学设计(2)

    由于三角函数是刻画周期变化现象的数学模型,这也是三角函数不同于其他类型函数的最重要的地方,而且对于周期函数,我们只要认识清楚它在一个周期的区间上的性质,那么它的性质也就完全清楚了,因此本节课利用单位圆中的三角函数的定义、三角函数值之间的内在联系性等来作图,从画出的图形中观察得出五个关键点,得到“五点法”画正弦函数、余弦函数的简图.课程目标1.掌握“五点法”画正弦曲线和余弦曲线的步骤和方法,能用“五点法”作出简单的正弦、余弦曲线.2.理解正弦曲线与余弦曲线之间的联系. 数学学科素养1.数学抽象:正弦曲线与余弦曲线的概念; 2.逻辑推理:正弦曲线与余弦曲线的联系; 3.直观想象:正弦函数余弦函数的图像; 4.数学运算:五点作图; 5.数学建模:通过正弦、余弦图象图像,解决不等式问题及零点问题,这正是数形结合思想方法的应用.

  • 人教A版高中数学必修二立体图形直观图教学设计

    人教A版高中数学必修二立体图形直观图教学设计

    1.直观图:表示空间几何图形的平面图形,叫做空间图形的直观图直观图往往与立体图形的真实形状不完全相同,直观图通常是在平行投影下得到的平面图形2.给出直观图的画法斜二侧画法观察:矩形窗户在阳光照射下留在地面上的影子是什么形状?眺望远处成块的农田,矩形的农田在我们眼里又是什么形状呢?3. 给出斜二测具体步骤(1)在已知图形中取互相垂直的X轴Y轴,两轴相交于O,画直观图时,把他们画成对应的X'轴与Y'轴,两轴交于O'。且使∠X'O'Y'=45°(或135°)。他们确定的平面表示水平面。(2)已知图形中平行于X轴或y轴的线段,在直观图中分别画成平行于X'轴或y'轴的线段。(3)已知图形中平行于X轴的线段,在直观图中保持原长度不变,平行于Y轴的线段,在直观图中长度为原来一半。4.对斜二测方法进行举例:对于平面多边形,我们常用斜二测画法画出他们的直观图。如图 A'B'C'D'就是利用斜二测画出的水平放置的正方形ABCD的直观图。其中横向线段A'B'=AB,C'D'=CD;纵向线段A'D'=1/2AD,B'C'=1/2BC;∠D'A'B'=45°,这与我们的直观观察是一致的。5.例一:用斜二测画法画水平放置的六边形的直观图(1)在六边形ABCDEF中,取AD所在直线为X轴,对称轴MN所在直线为Y轴,两轴交于O',使∠X'oy'=45°(2)以o'为中心,在X'上取A'D'=AD,在y'轴上取M'N'=½MN。以点N为中心,画B'C'平行于X'轴,并且等于BC;再以M'为中心,画E'F'平行于X‘轴并且等于EF。 (3)连接A'B',C'D',E'F',F'A',并擦去辅助线x轴y轴,便获得正六边形ABCDEF水平放置的直观图A'B'C'D'E'F' 6. 平面图形的斜二测画法(1)建两个坐标系,注意斜坐标系夹角为45°或135°;(2)与坐标轴平行或重合的线段保持平行或重合;(3)水平线段等长,竖直线段减半;(4)整理.简言之:“横不变,竖减半,平行、重合不改变。”

  • 人教A版高中数学必修二事件的相互独立性教学设计

    人教A版高中数学必修二事件的相互独立性教学设计

    问题导入:问题一:试验1:分别抛掷两枚质地均匀的硬币,A=“第一枚硬币正面朝上”,B=“第二枚硬币正面朝上”。事件A的发生是否影响事件B的概率?因为两枚硬币分别抛掷,第一枚硬币的抛掷结果与第二枚硬币的抛掷结果互相不受影响,所以事件A发生与否不影响事件B发生的概率。问题二:计算试验1中的P(A),P(B),P(AB),你有什么发现?在该试验中,用1表示硬币“正面朝上”,用0表示“反面朝上”,则样本空间Ω={(1,1),(1,0),(0,1),(0,0)},包含4个等可能的样本点。而A={(1,1),(1,0)},B={(1,0),(0,0)}所以AB={(1,0)}由古典概率模型概率计算公式,得P(A)=P(B)=0.5,P(AB)=0.25, 于是 P(AB)=P(A)P(B)积事件AB的概率恰好等于事件A、B概率的乘积。问题三:试验2:一个袋子中装有标号分别是1,2,3,4的4个球,除标号外没有其他差异。

  • 人教版高中数学选择性必修二等差数列的前n项和公式(1)教学设计

    人教版高中数学选择性必修二等差数列的前n项和公式(1)教学设计

    高斯(Gauss,1777-1855),德国数学家,近代数学的奠基者之一. 他在天文学、大地测量学、磁学、光学等领域都做出过杰出贡献. 问题1:为什么1+100=2+99=…=50+51呢?这是巧合吗?试从数列角度给出解释.高斯的算法:(1+100)+(2+99)+…+(50+51)= 101×50=5050高斯的算法实际上解决了求等差数列:1,2,3,…,n,"… " 前100项的和问题.等差数列中,下标和相等的两项和相等.设 an=n,则 a1=1,a2=2,a3=3,…如果数列{an} 是等差数列,p,q,s,t∈N*,且 p+q=s+t,则 ap+aq=as+at 可得:a_1+a_100=a_2+a_99=?=a_50+a_51问题2: 你能用上述方法计算1+2+3+… +101吗?问题3: 你能计算1+2+3+… +n吗?需要对项数的奇偶进行分类讨论.当n为偶数时, S_n=(1+n)+[(2+(n-1)]+?+[(n/2+(n/2-1)]=(1+n)+(1+n)…+(1+n)=n/2 (1+n) =(n(1+n))/2当n为奇数数时, n-1为偶数

  • 人教版高中数学选择性必修二变化率问题教学设计

    人教版高中数学选择性必修二变化率问题教学设计

    导语在必修第一册中,我们研究了函数的单调性,并利用函数单调性等知识,定性的研究了一次函数、指数函数、对数函数增长速度的差异,知道“对数增长” 是越来越慢的,“指数爆炸” 比“直线上升” 快得多,进一步的能否精确定量的刻画变化速度的快慢呢,下面我们就来研究这个问题。新知探究问题1 高台跳水运动员的速度高台跳水运动中,运动员在运动过程中的重心相对于水面的高度h(单位:m)与起跳后的时间t(单位:s)存在函数关系h(t)=-4.9t2+4.8t+11.如何描述用运动员从起跳到入水的过程中运动的快慢程度呢?直觉告诉我们,运动员从起跳到入水的过程中,在上升阶段运动的越来越慢,在下降阶段运动的越来越快,我们可以把整个运动时间段分成许多小段,用运动员在每段时间内的平均速度v ?近似的描述它的运动状态。

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