数形结合中小学教学课件

单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,专 题,4,数形结合思想,一、数形结合的概念及本质：,数形结合亦即：代数问题可以几何化（借形辅数），几何问题可以代数化（以数促形）。,数形结合的本质：数量关系决定了几何图形的性质，几何图形的性质反映了数量关系。,二、数形结合的应用：,（,1,）借助于数的精确性来阐明形的某些属性；,（,2,）借助于形的几何直观来阐明数之间的某种关系。,必要非充分条件,注：,探究集合命题间的充要性常利用数轴把数的问题看成点的问题,C,（,4,）一游泳池长,90m,，甲、乙两人分别在游泳池相对两边同时朝另一边游泳，甲的速度是,3m/,秒，乙的速度是,2m/,秒，若不计转向时间，则从开始到,3,分钟止，他们相遇的次数为（ ）,A.2 B.3 C.4 D.5,D,2,注：,本题利用方程的曲线解题，借用方程曲线图象，使抽象问题转化为形象问题来思考，这是突破解题困境的方法之一,。,注：,本题用数助形，解题的关键在理解题意，“椭圆上的点在圆外或圆上”，而不等式恒成立，可转化为,T0,。,X,O,Y,注：,数和形是变量关系的两种形式，故在解决一个数学问题时，往往存在着数,形之间的多次转换，巧妙地运用这种变形可使问题得到简捷地解答。,注：,在解不等式,f(x)g(x),时，若,f(x),与,g(x),的图象较易作出，则可考虑借助图形以求获得简解。,注：,在代数推理中，“形”可助你思考，但不能代替“数”上的演绎证明，即形上发现的信息必须严格证明才可运用。此外，在对抽象函数（如未给出解析式）进行的推理中，寻找满足条件的特例也是发现隐含信息的重要途径。如在对满足条件,f(xy)=f(x)+f(y)(x0,y0),的函数,f(x),进行有关推理时，常利用对数函数的性质，去联想猜测,f(x),的有益于破题的隐含信息，为推理提供方向。,Unit 9,Saving the earth,By Ivyriver 2006.9.27,What problems is the earth facing?,problems the earth is facing:,air pollution,water pollution,noise pollution,soil erosion,white pollution,overpopulation,poverty,war &violence,(rubbish),aids,What can we do to help the earth solve the problems its facing?,In order to help the earth, the United Nations held a meeting to discuss the problems.,Question:,Whats the name of the meeting?,The Earth Summit.,Welcome to,the Earth Summit,earth summit,Introduction,Body,Conclusion,Sample outline,Introduce the Earth Summit to the readers,.,What we can do,Para . 1,Para.1,Para.2 Para.3 Para.4 Para.5 Para.6,Para.7,impor-tance,Give more detailed information about the problems,Para,Main idea,Key words,1,A,1,to 1972 & 2002 Earth Summits,Take better care of the earth, problems facing our planet, progress made ,one of the theme,2,2,The big three and the results caused by them,Three biggest killers, contaminated drinking water,3, air,pollution,3,The,4,Of the richer countries,Poverty , war , violence ,do whatever to help ,Prosper ,sustainable development,4,How to save the earth,Understand ,existing serious problem ,5, changing how we live,6, Understanding of the Environment and their,6,to act are important,Students ,learning more , earth issues, better,Understanding of environment, willingness to act, what to do to help,7,One of the solutions to the problems -,7,Key to future , build a better society ,8,nature , put an end to , death &suffering , caused by the big three ,Brief introduction,sustainable development,poor sanitation,responsibilities,take action,willingness,education,in harmony with,1.When and where was the first Earth Summit held?,2. Whats the purpose of the first Earth Summit?,3. Where was the 2002 Earth Summit held?,4. Whats the main theme of this Earth Summit?,Read Para.1:,1.When and where was the first Earth Summit held?,2. Whats the purpose of the first Earth Summit?,In 1972 in Stockholm, Sweden,.,To,share,the ideas about ways to,take better care of,the earth.,3. Where was the 2002 Earth Summit held?,4. Whats the main theme of this Earth Summit?,In Johannesburg in South Africa.,One of the main themes of the summit was,“,sustainable development,”,or,the question how we can continue developing the world,without damaging,the environment.,Read Para.2:,1.Whats the “big three”?,2. How many people die from the “big three” every year?,3. How many people die from air pollution every year?,1.Whats the “big three”?,contaminated,drinking water,poor,sanitation,air pollution,the three biggest killers in the world,2. How many people die from the “big three” every year?,3. How many people die from air pollution every year?,More than seven million.,Almost three million.,Read Para.3:,1. What other problems were talked about in the meeting?,2. Global development is necessary. At the same time, global development,has bad effect(,影响,) on,us. In the text, whats the bad effect?,3. What did Chinas,then,Premier Zhu Rongji,stress,? And what should the developed countries do?,1. What other problems were talked about in the meeting?,Poverty, war and violence.,2. Global development is necessary. At the same time, global development,has bad effect(,影响,) on,us.,In the text, whats the bad effect?,All too often, global development means rich people get,richer,while the poor get,poorer,.,the need for equality and fairness in the world,Chinas,then,Premier Zhu Rongji,stressed,Rich countries,have a responsibility towards,poor countries and must,do whatever they can to,help others.,3.,What did Chinas,then,Premier Zhu Rongji,stress,?,And what should the developed countries do?,Read Para.4:,1. How can we save the earth?,Only by,changing the way we live,can we,save the earth.,Read Para. 5,What did the visitor say in our text?,“,Had,I,known,that air conditioners,cause so much pollution, I,would,never,have,bought,one.,Not until,we know more,will we,be able to improve the,situation. If all of us make small changes, we could,make a big difference,.”,Read Para.4-6:,Do you think the Earth Summit is meaningful and helpful? Why?,the meaning of the Earth Summit:,To help people understand that,there exists,serious problems and that there is still time to,take action,.,(A better understanding of the environment is,necessary,as,is the willingness to act.),To tell us what we can do to help.,Read Para.7:,1. In order to solve the problem, whats the most important thing in the future?,2. Why is education so important?,In order to solve the problem, whats the most important thing in the future?,2. Why is education so important?,Education is,the key to,the future.,With better education, people will be able to build a better society,in harmony with,nature and perhaps,put an end to,the death and suffering caused by the big three.,b. Much of the poverty can,be wiped out,.,c.,There is a good chance that,we will see less violence and fewer wars.,Which is TRUE about the Earth Summit?,Its held every 3 years in Stockholm.,So far it has been held twice: in 1972 and in 2002.,C. Sustainable development is the only theme of the summit.,D. At the summit people discuss how to take good care of the earth.,2. Which of the following is the main cause of,millions of deaths in rural areas ?,A. Lack of drinking water,B. Poor sanitation,C. Air pollution,D. Freezing cold,3. According to the text, air pollution alone causes about _ of all the deaths in the world every year.,A. 6.5% B. 15% C. 20% D. 35%,4. At the summit, Chinas then Premier Zhu Rongji probably mentioned the following EXCEPT _.,International cooperation,Sustainable development,Ways of preventing some diseases from spreading,Equality and fairness in the world.,5. The fourth paragraph suggests that_.,Its not too late for us to do something to save the earth.,We neednt be so worried about the environment of the earth.,There are problems facing the earth, but not serious enough.,We will change our way of life sooner or later,.,6. One visitors words are quoted in the text in order to show _.,that the Earth Summit is very popular among ordinary people,that we can help save the earth by changing our way of life,how we can develop the world without damaging the environment,how people can stop the death and suffering caused by the “big three”,7. “ A better understanding of the environment is necessary,as,is the willingness to act.” The underlined word can be replaced by _.,A. which B. so C. and D. but,8. The key to solving the major problems facing the earth is _.,A. to educate the people of the world,B. to improve the living conditions of the people,C. to treat people equally and fairly,D. to hold conferences like the Earth Summit frequently,9.Which of the following best expresses the,main idea of the passage ?,A. Different countries have different opinions,about development,B. Equality and fairness are badly needed in,the todays world,C. The Earth Summit is a way to save the,earth,D. Sustainable development , the future for,the world,10.How many people,on earth,do not,have access to,clean,water?,20%,A. get close to,B. have chances to use,C. be free to use,D. get means to approach,Task 1: debate:,As we know the Earth Summit is a place to find solutions for the future. Some people say that money can solve all problems, but some say education. Which one do you agree? Money or Education?,Task 2: if you have the chance to attend the Earth Summit, what will you do?,Water is the source of life, but it is not inexhaustible. If we did not take action now, the last drop of water in the world would be mans tear!,水是生命之源，但它却不是取之不尽，用之不竭的。如果我们现在不采取行动，世界上的最后一滴水将是人类的眼泪！,Language Points,1.whats _ here is the whole future of the industry.,A.at question B.in question C .at issue D.at problem,at issue = in question,=being discussed /debated,Have you seen the latest of the magazine?,issue=,important topic for discussion;point in question,Eg.debate/ avoid / confuse / raise,an issue,issue=,one of a regular series of publications,（出版物的）期号,issue,stamps / shares/ the magazine,V.= publish,2. _,（概括的说），,the subject is so important.,In summary,summarize /summarise V.=sum up,He summarised /summed up his speech in a few words.,make /write /give a summary of,写摘要,3. The Greens _ to live a simple life.,A. are content B.is content,C.are contented D. is contented,content,n.predict its content,content adj.,be content to do sth,He,is content to remain,where he is now.,他安于现状,=be willing to do,be content with sth,=,be satisfied with,Dont be content with small success.,content sb./oneself with sth V.,一块冰淇淋足以让小孩子满足了,。,An icecream is enough to content the child.,4.A.be representative ( of sb./ sth.) adj,=be typical of sb/ sth,我是代表其他成员提出要求的,.,My demand is representative of,that,（,=the demand,）,of the other members,B.a representative of sb /sth n.,= typical example of a class or group,典型，有典型的人或事物,展览会是现代中国艺术的代表,The exhibition is,a representative of,the modern Chinese art .,a legal representative,法定代理人,5.Swittzerland has _ the sea _the River Rhine.,A.an access to ; by B. access to; via,C.an access to ; through D.access to ; across,gain /get/ have access to,A.access to sth= approach to sth,什么是成功之道,？,What is the,access to,success,?,B. access to sb / sth,= means of approaching or entering,(a place); way in,（接近或进入某地方的方法；通路,=opportunity or right to use sth or approach sb,Its difficult to gain,access to,him,.,接近他很难,6.on earth /on the earth,What,_ do you mean,？,你究竟是什么意思？,when ,what ,who,where ,how,whyon earth/ in the world,used for emphasis,look / be /feel like nothing on earth,= very bad;unwell;peculiar,他穿着奇装怪服难看级了,He,looks like nothing on earth,in those strange clothes.,on earth,7. I have never been to this _ island _before.,A.alone;lonely B. alone; alone,C.lonely; lonely D.lonely; alone,1.,alone:,A.with out any companions,I dont like going out,alone,after dark.,B.without the help of other people or things,I prefer to work on it,alone.,2.leave / let sb/sth alone,not try to influence or change sb/sth;,not touch sb/sth,不想左右或改变某人；不触摸,我早告诉过你,不要动我的东西,Ive told you before -,leave,my things,alone.,3.let alone,I havent decided on the menu yet,let alne,bought the food.,我还没决定吃什么菜呢，更不必说买好了,=without considering,不必考虑,8.He came here_to see you, _after he heard that you returned from abroad.,A.specially;mainly B.especially; specially,C.specially; especially D.especially; especially,9.If we _ to develop the world successfully,we must,make that everyone is able to take part in the new,world we create.,A.ought B.are going C.are D.ready,be to do sth,A.expressing duty ;necessity,You,are to report,to the police,.,B.expressing arrangement;purpose;intention,They,are to be,married.,C.expressing posibility,The book,was,not,to be,(could not be) found.,D.expressing destiny,He,was,never,to,see his wife again.,10.The end of the holiday came _ soon.,A.all too B.too much C.too only D.none too,all+ too/ adjs /advs,=more than desirable,过于,all too often/ soon /quickly,他过于兴奋,He was all too excited.,11.Among the speakers was Chinas,then,Premier,Zhu Rongji, who stressed the need for quality and,fairness in the world.,A.then attrib,.,The,then,Prime Minister took her husband with her on all her travels.,当时的首相每次外出都与夫偕行,B.stress,= put stress or emphasis on sth,在会议上，他强调了教育的重要性,。,He,stressed,the importance of education,at the meeting.,lay/put place stress on sth,重视,/,强调,一些学生不重视英语学习。,Some Students,lay/put little,stress,on English study.,under great stress,在很大的压力下,He is,under great stress,because of his new work.,12.have / take /bear (a) responsibility for,承担。的责任,Its ones responsibility to do sth,Its my responsibility to lock the doors.,我负责锁门。,be resposible for,13. If you dont go to the party,_.,A.So do I B.nor do I C.so will I D.nor will I,as is the willingness to act,=so is the willingness to act,14. The key _the problem is to meet the,demand _ by the customers.,to solving; making B.to solving ,made,C.to solve;making D. to solve; made,the key to sth / doing sth,=thing that provides access,control or understanding,关键；要诀,the key to the questions,15.He soon found himself _ his new co-workers.,A. in harmony with B. along well with,C. get along well with D. at harmony with,in harmony,（,with sb/sth,）,=,agreeing / matching,协调一致，相配,大海与天空的和谐构成一幅美妙图画。,harmony,=,agreement / pleasing combination of,related things,一致，匀称，协调,The harmony of sea and sky makes a,beautiful picture,.,My cat and my dog live,in,perfect,harmony,.,我的猫和狗生活的非常和谐。,16. put an end to sth,=stop sth from happening abolish sth,终止，废止,我们结束争吵吧。,Lets,put an end to,this quarrel.,come to an end,The meeting came to an end early.,bringto an end,He brought his lecture to an end,around 10 oclock.,17.wipe out,A. clean the inside of,搽拭。内部,The vase wasnt wipedout properly before it was put away.,这个花瓶没檫干净就收起来了。,2.removeor cancel sth,除去或取消某事物,wipe out,还清债物,wipe out ones debts,C.destroy sth completely,Doctors are trying to,wipe out,such a disease.,医生正在尽力消除这种疾病,18. There is a chance that.,chance,=possibility / likelihood,chance of (doing) sth/ to do sth/ that,有可能得到今晚演出的票吗？,Is there any,chance,of getting tickets for tonight?,She has a goog chance/ no chance/ not much chance,/ only a slim chance of winning.,take measures/steps,take action,(on),be content to do sth,be content with sth,a contented smile,have/gain/get access to n/ving,with violence,lay/put/place stress on,under the stress of ,take/bear/have responsibility for,in harmony with,out of harmony with,put an end to sth; bring sth to end,采取措施,采取行动,乐于做某事,对,满意,一个满意的微笑,通往,有,权利,/,机会,猛烈地,用力地,强调,重视,在压力下,对,负责,有责任,与,和谐,与,不和谐,结束,wipe out,have no alternative but to,defend sb from,issue stamps,take part in,have willingness to do;,be willing to do ,air conditioner,in co-operation with,sustainable development,have equality with,draw a conclusion,live in poverty,make an outline,消灭,擦洗,只好,别无选择不得不,保护某人免遭,发行邮票,参加,愿意做某事,空调,与,合作,可持续发展,和,一样平等,得出结论,过得很贫穷,列提纲,对,更好的理解,常常,经常,取得很大进步,交换意见,地球上,究竟,对,有害,/,不好,少些,农村,劝某人做某事,a better understanding of ,all too often,make much progress,share ideas,on earth,be bad for,be harmful to,less of,rural area,advise sb to do sth,advise doing sth,advise sb against sth,=advise sb not to do sth,1.Tom is our r_at the meeting.,2.He is c_to live in the countryside.,3.The dead-end street was the only a_ to her home.,4.He s_,the point,that we should be,punctual.,5. I must try to w_ out the memory of the terrible event.,6. There are a_ answers to your question.,7. She was deeply a_by his words.,8. The man knocked on the door with great v_.,epresentative,ontent,ccess,tressed,ipe,lternative,ffected,iolence,1.,学生应有使用好图书馆的便利条件,.,(access),Students must have access to a good library.,2.,用完浴缸后你擦洗了吗,?,Have you wiped out the bath after using it?,3.,天气是我们耽搁的主要原因,.,(be responsible for),The weather,is responsible for,the delay.,4.,政府答应对空气污染采取行动,.,The government has promised to take action,on the air pollution.,5.,疾病开始侵袭他的视力,.,(affect),The disease is beginning to affect her eyesight.,(sb),bring to an end,(sth),come to an and,(sth),draw to an en,(sb),put an end to,使,.,结束,完成，结束,结束，制止,We should put an end to the war.,The meeting came to an end early.,He brought his lecture to an end about ten oclock.,接近尾声,