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人教A版高中数学必修二圆柱、圆锥、圆台和球的表面积与体积教学设计
1.圆柱、圆锥、圆台的表面积与多面体的表面积一样，圆柱、圆锥、圆台的表面积也是围成它的各个面的面积和。利用圆柱、圆锥、圆台的展开图如图，可以得到它们的表面积公式：2.思考1：圆柱、圆锥、圆台的表面积之间有什么关系？你能用圆柱、圆锥、圆台的结构特征来解释这种关系吗？3.练习一圆柱的一个底面积是S，侧面展开图是一个正方体，那么这个圆柱的侧面积是（ ）A 4πS B 2πS C πS D 4.练习二：如图所示，在边长为4的正三角形ABC中，E，F分别是AB，AC的中点，D为BC的中点，H，G分别是BD，CD的中点，若将正三角形ABC绕AD旋转180°，求阴影部分形成的几何体的表面积．5. 圆柱、圆锥、圆台的体积对于柱体、锥体、台体的体积公式的认识(1)等底、等高的两个柱体的体积相同．(2)等底、等高的圆锥和圆柱的体积之间的关系可以通过实验得出，等底、等高的圆柱的体积是圆锥的体积的3倍．
人教A版高中数学必修二总体集中趋势的估计教学设计
（2）平均数受数据中的极端值（2个95）影响较大，使平均数在估计总体时可靠性降低，10天的用水量有8天都在平均值以下。故用中位数来估计每天的用水量更合适。1、样本的数字特征：众数、中位数和平均数；2、用样本频率分布直方图估计样本的众数、中位数、平均数。（1）众数规定为频率分布直方图中最高矩形下端的中点；（2）中位数两边的直方图的面积相等；（3）频率分布直方图中每个小矩形的面积与小矩形底边中点的横坐标之积相加，就是样本数据的估值平均数。学生回顾本节课知识点，教师补充。 让学生掌握本节课知识点，并能够灵活运用。
人教A版高中数学必修二向量的减法运算教学设计
新知探究：向量的减法运算定义问题四：你能根据实数的减法运算定义向量的减法运算吗？由两个向量和的定义已知 即任意向量与其相反向量的和是零向量。求两个向量差的运算叫做向量的减法。我们看到，向量的减法可以转化为向量的加法来进行：减去一个向量相当于加上这个向量的相反向量。即新知探究（二）：向量减法的作图方法知识探究（三）：向量减法的几何意义问题六：根据问题五，思考一下向量减法的几何意义是什么？问题七：非零共线向量怎样做减法运算？ 问题八：非零共线向量怎样做减法运算？1.共线同向2.共线反向小试牛刀判一判(正确的打“√”，错误的打“×”)(1)两个向量的差仍是一个向量。 (√ )(2)向量的减法实质上是向量的加法的逆运算. ( √ )(3)向量a与向量b的差与向量b与向量a的差互为相反向量。 ( √ )(4)相反向量是共线向量。 ( √ )
人教A版高中数学必修二直线与平面垂直教学设计
1.观察（1）如图，在阳光下观察直立于地面的旗杆AB及它在地面影子BC,旗杆所在直线与影子所在直线的位置关系是什么？（2）随着时间的变化，影子BC的位置在不断的变化，旗杆所在直线AB与其影子B’C’所在直线是否保持垂直？经观察我们知道AB与BC永远垂直，也就是AB垂直于地面上所有过点B的直线。而不过点B的直线在地面内总是能找到过点B的直线与之平行。因此AB与地面上所有直线均垂直。一般地，如果一条直线与一个平面α内所有直线均垂直，我们就说l垂直α，记作l⊥α。2.定义：①文字叙述：如果直线l与平面α内的所有 直线都垂直，就说直线l与平面α互相垂直，记作l⊥α.直线l叫做平面α的垂线，平面α叫做直线l的垂面．直线与平面垂直时，它们唯一的公共点P叫做交点．②图形语言：如图．画直线l与平面α垂直时，通常把直线画成与表示平面的平行四边形的一边垂直．③符号语言：任意a?α，都有l⊥a?l⊥α.
人教A版高中数学必修二直线与平面垂直教学设计
1.观察（1）如图，在阳光下观察直立于地面的旗杆AB及它在地面影子BC,旗杆所在直线与影子所在直线的位置关系是什么？（2）随着时间的变化，影子BC的位置在不断的变化，旗杆所在直线AB与其影子B’C’所在直线是否保持垂直？经观察我们知道AB与BC永远垂直，也就是AB垂直于地面上所有过点B的直线。而不过点B的直线在地面内总是能找到过点B的直线与之平行。因此AB与地面上所有直线均垂直。一般地，如果一条直线与一个平面α内所有直线均垂直，我们就说l垂直α，记作l⊥α。2.定义：①文字叙述：如果直线l与平面α内的所有 直线都垂直，就说直线l与平面α互相垂直，记作l⊥α.直线l叫做平面α的垂线，平面α叫做直线l的垂面．直线与平面垂直时，它们唯一的公共点P叫做交点．②图形语言：如图．画直线l与平面α垂直时，通常把直线画成与表示平面的平行四边形的一边垂直．
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。
人教版高中数学选修3离散型随机变量及其分布列(1)教学设计
4.写出下列随机变量可能取的值，并说明随机变量所取的值表示的随机试验的结果．(1)一个袋中装有8个红球，3个白球，从中任取5个球，其中所含白球的个数为X.(2)一个袋中有5个同样大小的黑球，编号为1,2,3,4,5，从中任取3个球，取出的球的最大号码记为X.(3). 在本例(1)条件下，规定取出一个红球赢2元，而每取出一个白球输1元，以ξ表示赢得的钱数，结果如何？[解] (1)X可取0,1,2,3.X＝0表示取5个球全是红球；X＝1表示取1个白球，4个红球；X＝2表示取2个白球，3个红球；X＝3表示取3个白球，2个红球．(2)X可取3,4,5.X＝3表示取出的球编号为1,2,3；X＝4表示取出的球编号为1,2,4；1,3,4或2,3,4.X＝5表示取出的球编号为1,2,5；1,3,5；1,4,5；2,3,5；2,4,5或3,4,5.(3) ξ＝10表示取5个球全是红球；ξ＝7表示取1个白球，4个红球；ξ＝4表示取2个白球，3个红球；ξ＝1表示取3个白球，2个红球．
人教版高中数学选修3离散型随机变量的方差教学设计
3.下结论.依据均值和方差做出结论.跟踪训练2. A、B两个投资项目的利润率分别为随机变量X1和X2，根据市场分析， X1和X2的分布列分别为X1 2% 8% 12% X2 5% 10%P 0.2 0.5 0.3 P 0.8 0.2求：(1)在A、B两个项目上各投资100万元， Y1和Y2分别表示投资项目A和B所获得的利润，求方差D(Y1)和D(Y2)；(2)根据得到的结论，对于投资者有什么建议？ 解：(1)题目可知，投资项目A和B所获得的利润Y1和Y2的分布列为：Y1 2 8 12 Y2 5 10P 0.2 0.5 0.3 P 0.8 0.2所以 ;; 解：(2) 由(1)可知 ，说明投资A项目比投资B项目期望收益要高；同时 ，说明投资A项目比投资B项目的实际收益相对于期望收益的平均波动要更大.因此，对于追求稳定的投资者，投资B项目更合适;而对于更看重利润并且愿意为了高利润承担风险的投资者，投资A项目更合适.
人教版高中数学选修3离散型随机变量的均值教学设计
对于离散型随机变量，可以由它的概率分布列确定与该随机变量相关事件的概率。但在实际问题中，有时我们更感兴趣的是随机变量的某些数字特征。例如，要了解某班同学在一次数学测验中的总体水平，很重要的是看平均分；要了解某班同学数学成绩是否“两极分化”则需要考察这个班数学成绩的方差。我们还常常希望直接通过数字来反映随机变量的某个方面的特征，最常用的有期望与方差.二、 探究新知探究1.甲乙两名射箭运动员射中目标靶的环数的分布列如下表所示：如何比较他们射箭水平的高低呢？环数X 7 8 9 10甲射中的概率 0.1 0.2 0.3 0.4乙射中的概率 0.15 0.25 0.4 0.2类似两组数据的比较,首先比较击中的平均环数,如果平均环数相等，再看稳定性.假设甲射箭n次，射中7环、8环、9环和10环的频率分别为：甲n次射箭射中的平均环数当n足够大时，频率稳定于概率，所以x稳定于7×0.1+8×0.2+9×0.3+10×0.4=9.即甲射中平均环数的稳定值(理论平均值)为9,这个平均值的大小可以反映甲运动员的射箭水平.同理，乙射中环数的平均值为7×0.15+8×0.25+9×0.4+10×0.2=8.65.
人教版高中数学选修3分类变量与列联表教学设计
一、 问题导学前面两节所讨论的变量,如人的身高、树的胸径、树的高度、短跑100m世界纪录和创纪录的时间等,都是数值变量,数值变量的取值为实数.其大小和运算都有实际含义.在现实生活中,人们经常需要回答一定范围内的两种现象或性质之间是否存在关联性或相互影响的问题.例如,就读不同学校是否对学生的成绩有影响,不同班级学生用于体育锻炼的时间是否有差别,吸烟是否会增加患肺癌的风险,等等,本节将要学习的独立性检验方法为我们提供了解决这类问题的方案。在讨论上述问题时,为了表述方便,我们经常会使用一种特殊的随机变量,以区别不同的现象或性质,这类随机变量称为分类变量.分类变量的取值可以用实数表示,例如,学生所在的班级可以用1,2,3等表示,男性、女性可以用1,0表示,等等.在很多时候,这些数值只作为编号使用,并没有通常的大小和运算意义,本节我们主要讨论取值于{0,1}的分类变量的关联性问题.
人教版高中数学选修3一元线性回归模型及其应用教学设计
1.确定研究对象，明确哪个是解释变量，哪个是响应变量；2.由经验确定非线性经验回归方程的模型；3.通过变换，将非线性经验回归模型转化为线性经验回归模型；4.按照公式计算经验回归方程中的参数，得到经验回归方程；5.消去新元，得到非线性经验回归方程；6.得出结果后分析残差图是否有异常 ．跟踪训练1.一只药用昆虫的产卵数y与一定范围内的温度x有关，现收集了6组观测数据列于表中： 经计算得： 线性回归残差的平方和: ∑_(i=1)^6?〖(y_i-(y_i ) ?)〗^2=236,64,e^8.0605≈3167.其中 分别为观测数据中的温度和产卵数，i=1,2,3,4,5,6.(1)若用线性回归模型拟合，求y关于x的回归方程 (精确到0.1）；(2)若用非线性回归模型拟合，求得y关于x回归方程为 且相关指数R2＝0.9522． ①试与(1)中的线性回归模型相比较，用R2说明哪种模型的拟合效果更好 ?②用拟合效果好的模型预测温度为35℃时该种药用昆虫的产卵数.(结果取整数).
人教A版高中数学必修一集合间的基本关系教学设计（1）
本节内容来自人教版高中数学必修一第一章第一节集合第二课时的内容。集合论是现代数学的一个重要基础，是一个具有独特地位的数学分支。高中数学课程是将集合作为一种语言来学习，在这里它是作为刻画函数概念的基础知识和必备工具。本小节内容是在学习了集合的含义、集合的表示方法以及元素与集合的属于关系的基础上，进一步学习集合与集合之间的关系，同时也是下一节学习集合间的基本运算的基础，因此本小节起着承上启下的关键作用.通过本节内容的学习，可以进一步帮助学生利用集合语言进行交流的能力，帮助学生养成自主学习、合作交流、归纳总结的学习习惯，培养学生从具体到抽象、从一般到特殊的数学思维能力，通过Venn图理解抽象概念，培养学生数形结合思想。
人教A版高中数学必修二直线与直线垂直教学设计
6.例二：如图在正方体ABCD-A’B’C’D’中，O’为底面A’B’C’D’的中心，求证：AO’⊥BD 证明：如图，连接B’D’,∵ABCD-A’B’C’D’是正方体∴BB’//DD’,BB’=DD’∴四边形BB’DD’是平行四边形∴B’D’//BD∴直线AO’与B’D’所成角即为直线AO’与BD所成角连接AB’,AD’易证AB’=AD’又O’为底面A’B’C’D’的中心∴O’为B’D’的中点∴AO’⊥B’D’,AO’⊥BD7.例三如图所示，四面体A－BCD中，E，F分别是AB，CD的中点.若BD，AC所成的角为60°，且BD＝AC＝2.求EF的长度.解：取BC中点O,连接OE,OF，如图。∵E,F分别是AB,CD的中点，∴OE//AC且OE=1/2AC,OF//AC且OF=1/2BD,∴OE与OF所成的锐角就是AC与BD所成的角∵BD,AC所成角为60°，∴∠EOF=60°或120°∵BD=AC=2,∴OE=OF=1当∠EOF=60°时，EF=OE=OF=1,当∠EOF=120°时，取EF的中点M,连接OM,则OM⊥EF,且∠EOM=60°∴EM= ,∴EF=2EM=
新人教版高中英语必修3Unit 2 Morals and Virtues-Discovering Useful Structure教学设计
1. 表示时间。Hearing these stories, I’m skeptical about the place. = When I heard these stories. . . 2. 表示原因。Not knowing his address, I can’t send this book to him. = Because/Since/As I don’t know his address. . . 3. 表示结果。His father died, leaving him a lot of money. =. . . and left him a lot of money4. 表示条件。Going straight down the road, you will find the department store. = If you go straight down the road. . . 5. 表示让步。Being tired, they went on working. =Although they were tired. . . 6. 表示行为方式、伴随情况或补充说明。He lay on the grass, staring at the sky for a long time. =. . . and stared at the sky for a long time注意：非谓语动词作状语时, 如所提供的动词不能和句子中的主语保持一致, 动词-ing形式必须有自己的逻辑主语, 通常由名词或代词来担任, 这就是独立主格结构。The last bus having gone, we had to walk home. (having gone的逻辑主语是the last bus, 而不是we)Weather permitting, the football match will be played on Friday. (permitting的逻辑主语是time, 而不是the football match)Step 7 Practice1. ________(study) hard, you are sure to get first prize. 2. People use plastic in their daily life, _______(leave) large amounts of waste. 3. ________(work) hard at your lessons, you are to succeed. 4. The old man, ____________(work) abroad for twenty years, is on the way back to his motherland. 5. ______________(finish) his homework, he was playing on the playground. Answers: 1. Studying 2. leaving 3. Working 4.having worked 5. Having finishedStep 8 HomeworkFinish the homework on Page 22.
新人教版高中英语必修3Unit 2 Morals and Virtues-Listening &Speaking＆Talking教学设计
Example:One day, a poor boy who was trying to pay his way through school by sending newspapers door to door found that he only had one dime(一角）left. He was so hungry that he decided to beg for a meal at the next house.However, he lost his nerve when a lovely young woman opened the door. Instead of a meal he asked for a drink of water. She thought he looked hungry so she brought him a large glass of milk. He drank it slowly, and then asked, “How much do I owe you?” “You don’t owe me anything,” she replied, “Mother has taught me never to accept pay for a kindness.” “Then I thank you from the bottom of my heart.” With these words, Howard Kelly left that house.Years later the woman became badly ill and was finally sent to the hospital in a big city. Dr. Howard Kelly, now famous, was called in. When he heard the name of the town she came from, a strange light filled his eyes. Dressed in his doctor’s clothes, Dr. Kelly went into her room and recognized her at once. From that day on, he gave special attention to her, and decided to do his best to save her life.At last the woman was saved. Dr. Kelly asked the business office to pass the final bill to him. He looked at it and then wrote something on the side. The bill was sent to the woman’s room. She was afraid to open it because she was sure that it would take the rest of her life to pay for it off. Finally she looked, and the note on the side of the bill caught her attention. She read these words: “Paid in full with a glass of milk, Dr. Howard Kelly.” Tear of joy flooded her eyes.
新人教版高中英语必修3Unit 2 Morals and Virtues-Reading and Thinking教学设计
The topic of this part is “Learn to make choices in life”.The Listening & Speaking & Talking part aims at the moral dilemmas, and this part is about making choices in life. The heroin is Lin Qiaozhi, a famous medical scientist, made a great contribution to our country’s medical care. Most importantly, her life experience can inspire our students whether in studying or the development of career. she had moral dilemmas and life choices, which are similar to the students who will step into society. Besides, Lin has quite good virtues like kindness, self-improvement, insistence, job-loving , generosity and responsibility, which is worth being learned.Concretely, this article is a biography about Lin Qiaozhi. The article tells her whole life according the timeline, among which the life choices is emphasized. For example, whether married or chased her dream, returned home or stayed abroad, family or public, her choices all reflected her faith, spirit, responsibility and devotion.1. Fast reading to get the detailed information about Lin Qiaozhi; careful reading to do the deductive information.2. Learn the reading skills--deductive judgement according the context.3. Study the structure features and language features. 4. Communicate about Lin’s life choices and reflect their own life choices.1. Learn the reading skills--deductive judgement according the context.2. Study the structure features and language features.3. Communicate about Lin’s life choices and reflect their own life choices.Step 1 Lead in---Small talkWhat are some important life choices?Importance choices: university study, jobs and marriage partners. Because they can determine our future.
新人教版高中英语必修3Unit 2 Morals and Virtues-Reading for Writing教学设计
1. 这个寓言是一个关于一位国王古寓言。 The fable is an old fable about a king.2.作者用这个故事让读者对于社区的问题负有个人责任的必要印象深刻。The author used the story to impress upon readers with the need to take personal responsibility for problems in the community.3. 这个故事十分成功的实现了它的目的。The story was quite successful in achieving its purpose.Step 7 WritingPlease write a review of the story according the outline above.The fable is an old fable about a king who thought his people are lazy, so he put a large stone in the middle of the road and hides and waited to see if anyone will try to move it.The author used this story to impress upon readers with the need to take personal responsibility for problems in the community. The story was quite successful in achieving its purpose, and I liked it because it had a clear moral.However, while the moral of the story is clear, the actions of the king seemed pointless to me, because none of the characters in the story learnt anything. For this reason, I think there are better stories that can be used to impress upon people with the need for personal responsibility.Step 8 Pair workExchange drafts with a partner. Use this checklist to help your partner revise his/her draft.1. Does the writer give a short description of the story ?2. Does the description include the most important details of the story ?3. Does the writer give his or her opinion about the character or their actions ?4. Is the review well-organised ? 5. Does the writer use the -ing form as the adverbial correctly in the writing ?6. Are there any grammar, spelling, or punctuation errors ?Step 9 HomeworkPut up your revised draft in the classroom or read it to your class.
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 4 Journey Across a Vast Land教学设计
当孩子们由父母陪同时，他们才被允许进入这个运动场。3．过去分词(短语)作状语时的几种特殊情况(1)过去分词(短语)在句中作时间、条件、原因、让步状语时，相当于对应的时间、条件、原因及让步状语从句。Seen from the top of the mountain (＝When it is seen from the top of the mountain), the whole town looks more beautiful.从山顶上看，整个城市看起来更美了。Given ten more minutes (＝If we are given ten more minutes), we will finish the work perfectly.如果多给十分钟，我们会完美地完成这项工作。Greatly touched by his words (＝Because she was greatly touched by his words), she was full of tears.由于被他的话深深地感动，她满眼泪花。Warned of the storm (＝Though they were warned of the storm), the farmers were still working on the farm.尽管被警告了风暴的到来，但农民们仍在农场干活。(2)过去分词(短语)在句中作伴随、方式等状语时，可改为句子的并列谓语或改为并列分句。The teacher came into the room, followed by two students (＝and was followed by two students)．后面跟着两个学生，老师走进了房间。He spent the whole afternoon, accompanied by his mom(＝and was accompanied by his mom)．他由母亲陪着度过了一整个下午。
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
