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科目 英语
年级 高三
文件 high3 unit4.doc
标题 Feed the World
章节 第四单元
关键词 高三英语第四单元
内容
一、教法建议
【抛砖引玉】
本单元提出的是一个全世界都关注的问题：《全世界人的吃饭问题》。14-15两课是说明文。作者揭示了这样一个事实：世界人口不断增加，而耕地面积日益减少，世界每年要有十分之一的人中因饥饿而死亡。作者还指出了造成耕地面积减少的原因，并提出了改变这一现象的建议。
建议教师可选择有关录像片帮助学生深刻认识：保护耕地和控制人口过快增长的重要性；用问答和讨论的方法完成本单元的知识和能力目标。
【指点迷津】
本单元重点知识：
A)单词和词组：
*regret:
v. be sorry for the loss of; wish to have again; feel sorry for懊悔；抱歉；遗憾。后接不定式与-ing意思不同。接不定式意为“遗憾要去做……”
；接-ing已为“已做……而后悔”。
We deeply regretted his death.
I regret to say that I can’t help you. (比I am sorry to say that…较为正式的表达)
He regrets that he was rude to her.
他后悔对她不礼貌。
She regretted not having told you about it earlier.
她后悔没有早点告诉你这件事。
n. feeling of sadness at the loss of sth. or disappointment because sth. has or has not been done.懊悔；抱歉；遗憾。
I feel regret at her absence.
她没来，我感到很可惜。
We heard with regret that you were not successful in your plan.
听到你的计划没有成功，我们感到遗憾。
I waste no time in useless regret.
*provide: v.to supply; to prepare for提供；供给、装备；
搭配为：provide sb. sth.; provide sth. for sb. provide sb. with sth.
We can provide ourselves.
我们现在可以自给自足了。
The mother provided them some thick clothes.
母亲为他们准备了一些厚衣服。
We must provide food for the trip.
我们必须准备旅途中的食品。
The Red Cross provides food and clothes for the sufferers.
红十字会向难民提供食品和衣服。
*increase: v.[in’kris] to become greater in size, number, value etc.增加；繁殖。
The population of this town has increased to 2000,000.
城镇的人中去年增加了二十万。
The population of this town increased by 10 percent last year.
这个城镇的人口去年增加到二十万。
There has been a big increase in road accidents.
近来交通事故有所增加。
注意：increase的n.名词读音与动词不同[‘ inkris]，它的反义词为decrease v.减少；缩减。
*now and again; occasionally; at times; now and then时而
On my way home from school, I called on Granny Li now and again.
在放学回家的路上，我时而去看望李奶奶。
*help oneself to… serve oneself with food(drink) etc. 衣随便吃（喝）
Please help yourself to some fish. It is fresh.
鱼很新鲜，请随便尝尝。
*day by day; as time goes by 逐日；一天一天地
Day by day she learnt more about her work.
她日益了解了自己的工作。
*look forward to(doing) sth. 欣然期待（去做）谋事。
The little girl was looking forward to seeing her uncle from America.
那个小姑娘正盼望着见到从美国来的叔叔。
*be suitable for; be right for a purpose适宜的；适当的；恰当的。
Do you think this present is suitable for a little boy?
你认为这个礼物对于孩子合适吗？
*be in debt: owe a lot of money 欠债
The old man was in heavily debt in order to buy seeds.
那位老人为了买种子身负重债。
*make sense: have an understandable meaning有意义；有道理；讲得通；
be sensible是明智的；是合情合理的。
What you say makes no sense.
你说的话没有道理。
It doesn’t make sense to buy that expensive coat when these cheaper ones are just as good.
这件便宜的大衣也很好，何必也买那件贵的。
*earn one’s living: get money by working谋生； 挣钱生活
I start to earn my own living this very afternoon.
从今天下午开始，我自己挣钱养活自己了。
*for one thing: (used to introduce a reason for sth.用以引出谋事的理由 )一来
I’m afraid that I won’t be able to spend the weekend with you in Dalian. For one thing, I have no money and another I’m too busy.
恐怕我不能和你一起去大连度周末了，一来我没有钱，二来我太忙。
以上单词和词组可通过听对话录音，教师介绍过程中呈现，然后用问答讨论课文内容等方式再现以上单词和词组加深理解词义，掌握用法，紧后用句型转换或补全名子等方法巩固，开发运用。
B)本单元应掌握的重点文法知识：名词性从句
名词从句包括主语、表语、宾语和同位语从句。从总体上要注意两点：
连接主句与从句的连词有副词why, how, where, when, whether, if,它们在从句中充当状语成份，个有不同的词意，因此不能省略。代词who, whom, whose, what, which, 它们在从句中充当主语、定语、宾语，个有不同的词意，因此也不能省略。在联系中取舍哪一个词，本着缺什么成份，把它补齐，使句子在结构上与含意上完整就可以了。不同的连词，名子的意思也不同。例如：
Why/How/Where/When/Whether/Of what material the new house will be built hasn’t been decided yet.
为什么/怎样/在什么地方/什么时候/是否/用什么材料建这座房子还没有定下来。
【学法指要】
本单元语法难点：
1.掌握that在名词性从句中的用法。that在宾语从句中，不充当成份，也无词意，因此它可以省去；在主语、表语和同位语从句中，that虽然不充当成份，也无词意，但不能省略。
Today’s newspaper reports(that) sales of beef in China will increase.（宾语从句）
今天的报纸报道说，中国的牛肉销售量将会增加。
That land ownership in some countries is unfair is obvious.（主语从句）
在一些国家里，土地所有制的不公平是显而易见的。
The reason is that is has been raining for five days.（表语从句）
原因是已经下了五天的雨。
The reason that it has been raining for five days is why the crops has been flooded.
连续下了五天的雨，所以庄稼都泡在水里了。（同位语从句）
2.注意宾语从句中主句与从句谓语动词时态的呼应。
宾语从句中主句与从句谓语动词时态的呼应有三种情况：
A)主语谓语动词用现在和将来时态时，从句谓语动词可用任何所需要的时态。
Tom says that his sister is(was, will be) a doctor.
B)主句谓语动词用过去时态时，从句谓语动词则根据语境用过去时间的各种时态。这规律意也适用于主语、表语和同位语从句。
He thought the boy was honest.
I told him his brother was coming(would come).
We didn’t know whether they had finished their work.
注意：当从句说的内容是一般真理或客观事实时，从句谓语动词仍用一般现在时。
The mother told her little daughter that the earth goes round the sum.
He told me that the train for Beijing leaves at 10:30.
Somebody told me that you are a teacher.
3.否定转移
当主句的动词是think, believe, suppose, expect时，从句的否定要前移。
I don’t think she is right.
【妙文赏析】
Many centuries ago, all people had gathered seeds and plants to eat. They did not know how to farm or raise animals for food. Because they used stone tools and weapons, we call them the Stone Age people. There are people who still live much like these Stone Age people lived. They live in places that are hard to reach. Because they have met few outsiders, they do not know about modern inventions. They have not traded ways of doing things with others. For 25,000 years, groups of people have lived alone in the middle of Australia. One of the groups is the Aruba tatribe. They do not know how to farm, nor do they raise animals. The Artuntas spend most of their time searching for food and water. The men hunt animals with stone---tipped spears. The women and children look for roots, seeds and nuts. Several Artunta families live together. They have no houses. At night, they sleep around fires.
【思维体操】
阅读下列广告，回答1-5问题。
WUHAN PLUMBING(水管) & HEATING
Since 1992
Plumbing and Heating Installation(安装)
LARGE OR SMALL
Free
ESTIMATE(估计)
24 Hours 7 Days Service
Payment Open
8267896
261 Dong Fang Road
Wuchang
1.What is written above is _______.
A. a notice B. an address
C. an advertisement D. a poster
2.What service is offered free by Wuhan P.& H.?
A. Installation B. Quality of houses
C. Estimates of costs D. Large or small repairs
3.For which of the following problems would one call Wuhan P.& H.?
A. A leak(漏) in the roof.
B. Gas leak in the refrigerator.
C. Something wrong with wall plugs.
D. A broken bathroom pipe leaking water all over the floor.
4.The person who calls Wuhan P.& H. may discuss _____.
A. A duties B. experience C. cost D. salary
5.Wuhan is in _____ Province.
A. Hubei B. Hebei C. Hunan D. Henan
答案：CCDCA
【心中有数】
本单元的语法重点是名词性从句，而名词性从句的考查在高考试卷单项选择一题中一般情况下占20%，即在20个小题中有一个小题。如：
1.─I drove to Zhuhai for the air show last week.
─Is that _____ you had a few days off ?
A. why B. when C. what D. where (NMET99)
2.─It was _____ he said _____ disappointed me.
A. what; that B. that; that
C. what; what D. that; what (上海99)
答案：1.A；2.A
分析：
句1：从题干和所给的4个选择中不难看出本题考查的是表语从句。“I drove to Zhuhai for the air show.”提出一个事实，而第二句表明“I”不在的原因。故答案为A.why。
句2：该句考查的是强调句和主语从句。该句强调的是句中的主语，而该句的主语又是一个从句。从这个结构中可以看出第二个空和“It was”构成强调句，故第二个空应该是that；第一个空和“he said”构成主语从句；在这个从句中“said”一词后缺少宾语，故答案为A.what;that。
【动脑动手】
同步训练
I.单词拼写：
1.A country is not likely to develop without industry and a____.
2.Zhou Enlai will always be remembered as a great p_____.
3.The dish is not salty. Do you mind pouring some s____ on it?
4.Greatly to my r_____ , I am unable to accept your kind invitation.
5.His death means a great l____ to science.
6.It is not _____(合适) to grow cash crops here.
7.We don’t care what _____(材料) they really want.
8.The problem was how they could ______(偿还) so much.
9.They had to _____(承认) what they had done was wrong.
10.Who has won the first place will not be _____(公布) until the game is over.
II.单项选择
A)同步训练
11.I can not help _____ of my childhood _____ I see the wound in my leg.
A. think, when B. thinking, whenever
C. to think, when D. thought, no matter when
12.At the party we _____ to some ice cream.
A. helped B. to help C. helping D. were helped
13.______ the orders or you will be punished.
A. Have B. Receive C. Obey D. Place
14.─Is this machine _____ order or _____ good order?
─It works very well
A. in; in B. out of; in
C. in; out of D. out of; out of
15.We are all looking _____ the day when our country will be highly developed.
A. at B. for C. up D. forward to
16.The city was almost destroyed completely by an earth quake many years ago.
A. damaged slightly B. torn C. ruined D. broken
17.The expedition _____ no loss of life and returned to their base on time.
A. made B. got C. gained D. suffered
18.If you want a plant to ____, you had better _____ it in the garden.
A. plant; plant B. grow; plant
C. plant; grow D. be grown; grow
19.Last year farmers could not have their wheat crops _____ because of the bad weather.
A. increasing B. decreased
C. increased D. decreasing
20.It didn’t take her long to work ____ that she would soon have no money left.
A. at B. on C. for D. out
B)语法训练
21.It is _____ that the experiment should be made under low temperature.
A. said B. reported C. told D. suggested
22.______ man first made use of electricity is not exactly known.
A. When B. Whether C. That D. What
23.______ this material will be used in the product has not been decided yet.
A. If B. That C. What D. Whether
24.______ we are saying is more than ______ we will do.
A. That; that B. What; what
C. As; as D. Whatever; that
25.Our doubt is _____ he can do the experiment alone.
A. that B. if C. whether D.what
26.The reason ______ he didn’t come to our party was _____ he took a missing boy back home on his way here.
A. why; because B. why; that
C. that; why D. that; that
27.Do you have no idea ______?
A. how fast light travels B. how fast does light travel
C. how soon light travels D. how rapid light travels
28.Do you have no doubt _____ he will succeed in finding a new job?
A. if B. whether C. that D. whether or not
29.I kept looking at the man, wondering _______.
A. whether had I had seen him before
B. where I had seen him before
C. that I had seen him before
D. when I had seen before
30.The teacher told the children that man _____ any life on the moon.
A. didn’t find B. could not find
C. doesn’t find D. hasn’t been able to find
III.完型填空
In the 17th century corn was grown a lot in Tibet and Sichuan. At that time the land along the Changjiang River was becoming very 31 ;there was not enough 32 for the population. Farmers had to move 33 the hills, but they 34 rice there. They needed plant which didn’t need 35 water as rice. 36 they were able to grow the new corn.
Today, corn is found all over the world. It is a very useful plant that can be 37 in many different ways. People in the West often boil in 38 over an open fire. In many parts of the world corn 39 powder. The powder is then 40 water and other things, and made inot different kinds of food.
31.A. crowd
B. crowded
C. crowds
D. a crowd
32.A. rooms
B. places
C. room
D. place
33.A. into
B. in
C. to
D. on
34.A. hadn’t grown
B. didn’t grow
C. can’t raise
D. couldn’t grow
35.A. as many
B. as much
C. as much as
D. much as
36.A. Luckily
B. Unluckily
C. Fortunate
D. Unfortunately
37.A. cooking
B. to cook
C. prepared
D. done
38.A. all
B. whole
C. completely
D. each
39.A. makes into
B. be made to
C. be made from
D. is made into
40.A. mixed with
B. mixed to
C. mixing
D. to mix
IV.短文改错
Plants are very important living thing. Life could not
go on when there were no plants. This is why plants can
make food with air and, water, or sunlight. Animals and men
can’t make food with air, water or sunlight. Animals can get
its food by eating plants and other animals. Man gets his food by eating plants and animals, either. Therefore, animals, and
man need plants in order to live. This is that we find we find
such many plants around us. If you look carefully at the plants around you, you’ll find that there are many types plants. Some
plants are big, while others are small. Most of plants are green.
41.______
42.______
43.______
44.______
45.______
46.______
47.______
48.______
49.______
50.______
【创新园地】
语言功能 从下列各题的A、B、C、D四个选项中，选出一个最佳答案。
1.─My daughter has passed the exam.
─Congratulations! She’s really intelligent.
─_______
A. No, no, she is intelligent.
B. Oh, thank you!
C. Sometimes she is intelligent.
D. You are right.
2.─You forgot to feed the cat again!
─________
A. I can’t remember.
B. I don’t mind feeding her again.
C. I’ll do it now.
D. Yes, I did. What about you!
3.─Mum, I’ve cut my finger. It’s bleeding!
─________
A. Let me see.
B. Don’t worry.
C. Be careful
D. Let me have a look
4.─What’s happened to my library book?
─________
A. I’ve no idea.
B. You borrowed them from the library.
C. You bought them yesterday.
D. They’re about long life.
5.─Where is Tom this morning?
─He’s got a cold.
─________
A. Just tell him to take it easy.
B. What’s the matter with him?
C. He’s absent.
D. What? Where is he?
答案：
1.agriculture; 2.politician; 3.sauce; 4.regret; 5.loss
6.suitable; 7.materials; 8.repay; 9.admit; 10.announced
11-15BDCBD 16-20CDCCD 21-25BADBC 26-30BACBD
31-35BCADB 36-40ACBDA
Plants are very important living thing. Life could not
go on when there were no plants. This is why plants can
make food with
air and, water, or sunlight. Animals and men
can’t make food with air, water or sunlight. Animals can get
its food by eating plants and other animals. Man gets his food by eating plants and animals, either. Therefore, animals, and
man need plants in order to live. This is that we find we find
such many plants around us. If you look carefully at the plants around you, you’ll find that there are many types plants. Some
plants are big, when others are small. Most of plants are green.
41.things
42.if
43.and
44.Ö
45.their
46.too
47.why
48.so
49.of
50.while
【创新园地答案】
1.B; 2.C; 3.D; 4.A; 5.A
高二英语Lesson 88教案
Lesson 88
Lesson objectives:
1．Go over the three-skilled and four-skilled words: servant/ Let in/ mad/ brave/ cruel/ have a test/ deed/ in public and so on.
2．Go over the grammar: the - ing form as attributes and adverbials.
3．Practise writing a letter.
Teaching aids: a computer, a recorder, etc.
Teaching procedure:
A．Words and expressions
1．Galary: Play the game with the partner, only the words in Unit 22.
For example: S1: There're five letters.
S2: Is it a noun?
S1: No, S2……
If the man is hanged, S1 will win.
2．Complete the phrases or sentences, using the words in the following form. (Ex. Ⅰ in AB)
1)Many young people want to become a civil ________(公务员).
2) Don’t be so ________ to animals.
3) Everyone is ________ to succeed.
4) He was a ________ of war for many years.
5)I didn't believe what the ________ teller (算命者) said.
6)He put his oars (桨) in the water to ________ the smooth surface of the lake.
7) She is nervous waiting for the ________ of news.
8) Dr Manette suffered from ________ illness.
9) Chairman Mao is a ________ leader.
Possible answers: 1) servant 2) cruel 3) eager 4) prisoner 5) fortune
6) disturb 7) arrival 8) mental 9) noble
3．Using the following phrases to fill in the passage (Ex. Ⅱ in AB).
Let in; in public; sentence to death; do a good deed; in peace; fall in love with; suffer from
Romeo fell in love with Juliet at the first glance, but their families were enemies. Juliet's parents didn't let Romeo in their house, and forced her daughter to leave Romeo. So they couldn't stay together in public. A friar (修道士) did a good deed to marry Romeo and Juliet secretly.
By accident, Romeo killed Tybalt, a member of Juliet's family. The court sentenced Romeo to death. Romeo managed to escape. When Romeo returned, he found his wife, dead in peace, but in fact, Juliet didn't die. It was just a plan of the friar. Romeo suffered much from the death of Juliet. He killed himself and lay down by her side. When Juliet woke up from her death like sleep, seeing Romeo lying by her, dead, she knew what he had done and killed herself.
B．Sentences and patterns
1．Find partner
Card One: the news which surprises us Card Two: the boy who is sleeping
Card Three: the year that follows Card Four: the country which is
developing
Card Five: the boat that is floating Card Six: the surprising news
Card Seven: the sleeping boy Card Eight: the following year
Card Nine: the developing country Card Ten: the floating boat
Possible answers: One-Six / Two-Seven / Three-Eight / Four-Nine / Five-Ten
2．Chain drill: Two students say two sentences written in the cards and let another student join the two sentences together by using the v-ing form.
A: The man is our maths teacher.
B．He is sitting by the window.
C．The man sitting by the window is our maths teacher.
A: The students stood up.
B: When they saw the teacher entering the room.
C: Seeing the teacher entering the room, the students stood up.
A: He decides to have a bath.
B: He was wetted all over by the rain.
C: Being wetted all over by the rain, he decided to have a bath.
A: The children went away.
B: They were laughing.
C: The children went away laughing.
C．Paragraphs and passage
1．Read the passage and do the following exercises: (Ex. Ⅲ in AB)
Prison of the Abbaye,
Paris
21 June, 1792
Monsieur the Marquis
My house and yours were burnt to the ground. The villagers brought me to Paris and I was thrown into this prison. My crime, they tell me, is ‘Treason against the people’, and without your generous help, I will lose my head for it. I have tried to tell them that I have worked on your instructions for the people, and not against them. I have told them that it was you who instructed me to collect no rent or taxes from the villagers during these last years. But they tell me my crime is to have worked for an emigrant aristocrat. Monseigneur, please hear my cry for help! Please, save me from this house of horror!
Your faithful servant,
Gabelle
After reading the letter, what should Darnay think and what would he decide to do?
__________________________________________________________
__________________________________________________________
__________________________________________________________
Possible answer:
Having read the letter, Darney said to himself “Gabelle, the poor man. I really felt sorry for him. I must go back to Paris to save him, but my wife and my daughter, it is impossible for me to see them again. But I should answer for the trouble. Tomorrow I'll set off for Paris.”
2．Write on the cards according to the situations. (Ex Ⅳ in AB)
A．Christmas Day is coming. Xiaojun wants to send a Christmas card to Charlie.
B．Bill wants to send a birthday card to his brother and also tell him that everyone in the family misses him.
Homework
Write a letter to your pen friend, who has written to you for some advice about visiting Beijing. Give him/her some advice. You can use the following sentences.
A: The climate in Beijing is dry; spring is shorter with lots of wind.
B．Autumn is the best season in Beijing.
C．I suggest you come to Beijing in autumn.
D．Winter is longer and cold.
E: It snows occasionally.
F: You'd better not come to Beijing in spring or winter.
Possible Answer:
Dear John,
I'm very pleased to learn from your letter that you are getting on well with your studies and that you will come to Beijing. Now I'll answer the question in your letter and give you some advice about your visiting Beijing.
The climate in Beijing is very dry. Spring is shorter with Lots of wind. You'd better not come to Beijing in spring. In summer it's terribly hot. It often rains in July and August. Autumn is the best season in Beijing. The weather begins to get cool at the beginning of September. People like to go for outings in September, October and November. I suggest you come to Beijing in Autumn. Winter is longer and cold with strong wind. It snows occasionally. I hope my advice will be helpful to you.
I'm looking forward to seeing you in Beijing.
Yours ever
Li Xiaoj
科目 英语
年级 高一
文件 hihg1 unit8.doc
标题 Mainly revision
章节 第八单元
关键词 高一英语第八单元
内容
一、目的与要求
复习第一至第七单元出现过的语法项目
二、语言运用
运用所学的食物名称及有关“就餐”的日常交际用语，完成教科书和练习册中规定的听、说、写的任务；阅读课文“Food around the world”，深刻理解，完成有关课文内容的练习，并进一步练习定语从句，被动语态及各种动词时态的用法。
三、日常交际用语
本单元复习第一至第七单元的交际用语，小结如下：
1．介绍问好
①Hello/Hi. Nice to meet you.
②I’ll introduce you.
③Give one’s regards/best wishes/love to sb.
④I must go/be leaving now.
2．建议要求
①Here are some do’s and don’ts.
②Follow…instructions.
③What about…?
④Make sure that…
⑤Do what he/she tells you to do.
3．请求帮助
①Would you please say that again more slowly?
②Pardon? I’m sorry I know only a little English.
③I don’t quite fllow you.
④How do you pronounce/spell…?
⑤I have some difficulty in doing…
⑥What does…mean?
4．祝愿
①Have a good time.
②Good luck. Have a good tip.
③The same to you.
5．餐桌用语
①Would you like another piece of beancurd?
②How about some more…?
③Just a little, please…
④No, thanks. I’ve had enough.
⑤Help yourself to…
⑥Let me give you…
四、重点与难点分析
1．――Would you like another piece of beancurd? ――要不要再吃一块豆腐？
――Yes, please. ――好的，谢谢。
在口语中Yes常与please连用，“Yes, please”意为“好吧”，与此相反的是“No, thinks”，如：
①――Would you like another glass of juice? ――还要一杯果汗吗？
――No, thanks. ――不用了，谢谢。
②――Have some more cake, please. ――请再吃点蛋糕。
――No, thanks. I’m full/I’ve had enough. ――不用了，我已经饱了。
2．What a delicious supper! 多么美味的晚餐啊！
一般情况下三餐前不用冠词，have breakfast, have lunch, have supper吃早、中、晚饭。但当三餐前有定语修饰时，要带冠词，如：
①After a quick breakfast, Mary hurried to school. 匆匆吃过早饭后，Mary赶去上学。
②What a nice dinner we had at your house! 你家的晚饭太可口了！
3．Take turns to offer each other the foods in Part 2 in pairs.
两人一组，轮流请对方吃，第二部分中出现的食物。
△Take turns to do表示轮流做某事。It’s one’s turn to do…表示轮到某人做某事，如：
①They took turns to keep watch. 他们轮流站岗。
②It’s your turn to recite the passage. 轮到你背这篇短文了。
△offer 提供 r.n.提供之物
①He offered 10,000 dollars to help the poor. 他拿出1万美元帮助穷人。
②Could you offer me a cup of coffee, please? 请给我一杯咖啡好吗？
③My sister was offered a good chance to go abroad for further study of English.
我姐姐得到了一个出国深造英语的好机会。
④Would you like to accept the offer? 你愿意接受这个帮助吗？
⑤Thank you for your kind offer of help. 感谢你所提供的帮助。
4．When Christopher Columbus and his friend…, they discovered the plant “corn” there.Discover vt. 发现，看出，指揭示久已存在但从未被人知晓的客观事实，如：
①Many years ago, electricity was discovered. The discovery made people’s life changed a lot. 许多年前人们发现了电，电的发现使人们的生活发生了巨大的变化。
②We have discovered that he is a quite careful in his word. 我们发现他工作很仔细。
另一个动词invent指创造客观世界上从未有过的新事物，词义为“发明”，如：
①The computer was invented after electricity was discovered. It is one of the most
important inventions in the world.
发现了电之后才发明了电脑，电脑的发明是世界上最重要的发明之一。
②Electricity was not discovered by Edison, but he invented the electric light.
电不是爱迪生发现的，但他发明了电灯。
5．…there was not enough room for the population.
那儿已经没有足够大的地方装下这么多人了。
room在这里是一个不可数名词，意为空间，与space相近。
①There is no room left for the newcomer. 新到的人已经没地儿了。
②He took up too much room in our room. 他在我们的房间占了很大的地儿。
6．They needed a plant which didn’t need as much water as rice.
这是一个定语从句，意为：他们需要一种不象稻谷那样需要水的作物。
7．It is a very useful plant that can be prepared in many different ways.
这是一种非常有用的作物，可用许多不同的方法制做成食物。
1) prepare调制
How do you prepare the fish? 你怎么做这鱼？
2) prepare sth. Prepare to do sth. 准备……
①He is preparing his speech for tomorrow’s meeting. 他正在准备明天大会的演讲稿。
②I was about to prepare supper when the bell rang. 我正要做晚饭时门铃响了。
③What are you preparing to offer me? 你准备为我提供点什么？
④He is preparing to go abroad. 他正准备出国。
3) prepare sb. for sth. 使某人对某事有思想准备。
①The teacher is preparing the students for the coming examination.
老师让考生对即将到来的考试做准备。
②We must be prepared for failure again. 我们必须做好再次失败的心理准备。
4) be prepared to do sth. 乐于做某事。
①He’s not prepared to listen to your excuse. 他不乐意听你的解释。
②I’m prepared to help others. 我乐于助人。
8．Sometimes they cook it whole over an open fire.
有时候他们把整只玉米放在露天的火上烧烤。
whole表示“全部”一般不用来修饰复数名词，强调个体的完整。
①They cooked a duck whole over the fire and soon a delicious smell came out.
他们烤了一整只鸭子，很快香味就飘出来了。
②The man ate an egg whole at a time. 那人一次吞下一整个鸡蛋。
注意whole一般放在限定词后面，名词前，而all则放在限定词前面，如：
the whole class（整个班） my whole life（我整个生命）
three whole days（三整天） all my books（我所有的书）
all the students（所有的考生） all three days（三整天）
9．In many parts of the world corn is made into powder.
世界上还有许多地方把玉米磨成粉。
1) be made into意为“原料被加工成了……”
①We can make glass into different kinds of things. 我们可以把玻璃制成各种东西。
2) be made of指“成品是由什么原料制成的”能看出原材料。be made from则看不出原材料。
①Gas is made from coal. 煤气是由煤产生的。
②This kind of wine is made from grape. 这种酒是葡萄制成的。
③The desks are made of wood. 桌子是木头做的。
④The cloth is made of cotton. 这种布是用棉花制成的。
3) be made up of“由…组成”
①The novel is made up of ten parts. 这部小说有十部分组成。
②The sports team is made up of eleven members. 这支队由11人组成。
10．A number of other plants were found in America. 在美洲还发现了许多其他的作物。
A number of表示“很多”，与a lot of用法相同，后面接复数名词，如：
①A number of birds come to KunMing for the winter eveay year.
每年冬天有大量的鸟飞到昆明。
②A number of students are playing on the playground. But I don’t know what the number is.
很多学生在操场上玩，但我不知道有多少人。
the number of表示“…的数目”，谓语动词用单数，如：
③The number of the students in our school has risen this year.
今年我们学校学生的数目上升了。
五、定语从句
1．从定语从句和它修饰的先行词关系来看，有限制性和非限制性定语从句两种。
说 明
例 句
限制性定语从句
限定了先行词的范围和意思，这类从句不能省去。
I’ve found a man who can help you.
我找到了一个能帮助你的人。
Autumn in Beijing is the season which is neither hot not cold.
北京的秋天是不热也不冷的季节。
The factory where he worked was built in 1940.
他工作的那工厂建于1940年。
Is this school the one you visited yesterday?
这是你昨天参观的那所学校吗？
非限制性定语从句
只是对附加词进行补充说明，在意思上相当于一个并列的分句，如果省略，剩下的主句意思仍然清楚。书写时，从句和主句之间要用逗号分开，不能用that引导。
I knocked at the door of the chemist’s, which immediately opened.
我敲了一下药店的门，门很快就开了。
She has a sister, who is a musician.
她有一个是音乐家的姐姐。
They set up a school, where there were lots of students studying.
他们建了一所学校，有许多学生在那儿学习。
2．关系代词的用法
关系代词
用 法
例 句
that
做从句的主语或宾语，先行词可以是人也可以是物。
The table that stands over there is made of wood.
那边的桌子是用木头做的。
The book I gave you is well worth reading.
我给你的那本书很值得读。
The man that is talking to my father is my English teacher.
和我父亲谈话的那个人是我的英语老师。
which
做从句的主语或宾语，先行词是表示物的名词或代词。
The school (which) we visited is a famous one in Beijing.
我们参观的那所学校是北京的一所名校。
She hasn’t got enough money with which to buy the ring. 他没带够买戒指的钱。
who
whom
做从句的主语、宾语，其先行语为表示人的名词或代词。
Do you know the man who often makes speeches here?
你认识那个经常在这儿做演讲的人吗？
Who’s the woman (whom) you just referred to?
刚才你指的是哪个人？
whose
做从句的定语，先行词可以是人也可以是物。
LiMin is the boy whose father is an engineer.
李明这个男孩的爸爸是工程师。
I live in the house whose windows face north.
我住的房子窗子朝北。
3．在介词后的关系代词只能用whom（先行词为人），which（先行词既可是人也可是物）
4．关系副词的用法
关系副词
基本用法
例 句
when
在从句中做时间状语，其先行词为表示时间的名词或代词。
I still remember the day when I joined the Youth League. 我仍然记着入团的那一天。
I’ll never forget the time when we worked on the farm.
我永远不会忘记在农场工作的那段时光。
when
在从句中做地点状语，先行词为表示地点的名词和代词。
This is the bridge where you took photos.
这座桥是你照像的地方。
why
在从句中做原因状语常与reason连用。
I know the reason why she was angry.
我知道她为什么生气了。
5．定语中只能用that，不能用which的情况
▲被修饰的先行词为不定代词，all, much, something, everything, nothing, anything, none, the one等时，如：
We should do all that is useful to the people. 我们应该做一切有益于人民的事。
Do you mean the one that I bought yesterday? 你指的是我昨天买的吗？
▲先行词被only, any, few, little, no, one of, just, very等修饰时，如：
The only thing that we could do was to wait. 我们唯一能做的是等待。
The is the right person that I’m waiting for. 他就是我等的人。
△先行词被序数词修饰或本身是序数词时，如：
When we talk about WuXi, the first that comes to mind is Tai lake.
当我们谈起无锡时，首先想到的是太湖。
This is the third film that has been shown in our school this term. 这是我校本学期放映的第三部片子。
△先行词是最高级或被最高级修饰时，如：
The must important thing that should be done is how to stop him from going on.
最重要的是如何阻止他继续下去。
This book is the best one that I’ve read. 这本书是我看过的最好一本。
△如有两个从句，其中一个关系代词已用which，另一个关系代词用that，以避免重复。
Edison built up a factory which produced things that had never been seen before.
爱迪生办了一家工厂，生产过去从未见到过的东西。
6．定语从句中只能用which，不能用that的情况
△关系代词前有介词时
A zoo is a park in which many kinds of animals are kept for exhibition.
动物园是展览各种动物的乐园。
Is this the room in which Mr White lives?
这就是white先生住的房间吗？
▲which在从句中代替的是前面整个句子的意思时，不能用that
The street hasn’t been cleaned for weeks, which makes it very dirty.
街道好多星期没打扫了，因此整条街很脏。
He takes exercises everyday, which has done a lot of good to his health.
他每天运动，这对他的身体很有好处。
六、典型例题
1．――Who do you know the electricity?
――I don’t know who did it. But I know that Thomas Edison the electric lamp.
A. invented; invented B. discovered; invented C. found; found D. discovered; found
2．―― beancurd you’ve cooked!
――It’s very kind of you to say so.
A. How a nice B. What a nice C. How nice D. What nice
3．Wood can be made a great number of things. Look, this kind of paper is madewood.
A. into; of B. into; from C. from; into D. of; from
4．――Would you like another piece of cake?
―― .
A. Yes, please B. Yes, thanks C. No, please D. Yes, if you like
5．―― .
――Thank you.
A. Make yourself at home, Eat some fish B. You can eat some more fish by yourself
C. You’re free to eat some fish D. Help yourself to some fish
6．The farmers do their best to the market with enough vegetables.
A. supply B. feed C. prepare D. offer
7． students is more than two thousand in this school.
A. The number of B. A good many C. A number of D. plenty of
8．The car was too 6 people.
A. crowded with B. full of C. filled with D. small to
9．After the new technique introduced, the factory produced tractors in 1988 as the year before.
A. as twice many B. as many twice C. twice as many D. twice many as
10．――Do you think I could borrow your dictionary?
―― .
A. Yes, you may borrow B. Yes, you could C. Yes, go on D. Yes, help youself
答案：1――5．B、D、B、A、D 6――10．A、A、A、C、D
8．这辆车坐6个人太挤了，be crowded with意为“拥挤”
9．工厂引进新的技术之后，1988年生产的拖拉机是去年的2倍
10．“help yourself ” 除了有“自用食物”的意思外还有“自己动手做”的意思
七、语法练习
1．Finally came the day he had to begin his study for the next term.
A. till B. when C. since D. which
2．The train she was travelling was late.
A. by which B. on that C. on which D. /
3．Is some German friends visited last week.
A. this school where B. this school one C. this the school D. this school
4．Is there anyone in your class home is in the country?
A. who’s B. his C. whose D. that
5．He talked about the people and things interested him greatly during his stay here.
A. which B. that C. who D. they
6．This is the only verb can be used in this sentence.
A. that B. which C. it D. /
7．This is just the place I’m longing to visit these days.
A. where B. to which C. / D. to where
8．The house he visited yesterday was the one the great writer lived many years ago.
A. where; where B. which; which C. where; which D. which; where
9．The taxi a truck had knocked last night was destroyed.
A. which B. where C. at which D. into which
10．All is needed is a supply of oil.
A. the thing B. that C. what D. which
答案： 1――5．B、A、C、C、B 6――10．A、C、D、C、B
2．She was travelling by brain. 所以此题应选A。
3．此题考查对先行词的判断能力。“This is the school,” “school ”是先行词。如果没有“the”, “this school ”后面要加“the one ”代替先行词“school”, This school is the one that…
5．当先行词既有人又有物时关系代词用“that”。
7．关系代词在从句中做宾语可以省略。
8．“The house ”在从句中做“visited ”的宾语，“the one ”在从句中做地点状语。
这句话的意思是：他昨天参观的那所房子几年前是一个伟大的作家居住的地方。
9．介词后用which. “knock at ”表示碰撞，昨天晚上一辆出租车被卡车撞坏了。
10．先行词是“All ”，关系代词只能用that。
科目 英语
年级 高一
文件 hihg1 unit8.doc
标题 Mainly revision
章节 第八单元
关键词 高一英语第八单元
内容
一、目的与要求
复习第一至第七单元出现过的语法项目
二、语言运用
运用所学的食物名称及有关“就餐”的日常交际用语，完成教科书和练习册中规定的听、说、写的任务；阅读课文“Food around the world”，深刻理解，完成有关课文内容的练习，并进一步练习定语从句，被动语态及各种动词时态的用法。
三、日常交际用语
本单元复习第一至第七单元的交际用语，小结如下：
1．介绍问好
①Hello/Hi. Nice to meet you.
②I’ll introduce you.
③Give one’s regards/best wishes/love to sb.
④I must go/be leaving now.
2．建议要求
①Here are some do’s and don’ts.
②Follow…instructions.
③What about…?
④Make sure that…
⑤Do what he/she tells you to do.
3．请求帮助
①Would you please say that again more slowly?
②Pardon? I’m sorry I know only a little English.
③I don’t quite fllow you.
④How do you pronounce/spell…?
⑤I have some difficulty in doing…
⑥What does…mean?
4．祝愿
①Have a good time.
②Good luck. Have a good tip.
③The same to you.
5．餐桌用语
①Would you like another piece of beancurd?
②How about some more…?
③Just a little, please…
④No, thanks. I’ve had enough.
⑤Help yourself to…
⑥Let me give you…
四、重点与难点分析
1．――Would you like another piece of beancurd? ――要不要再吃一块豆腐？
――Yes, please. ――好的，谢谢。
在口语中Yes常与please连用，“Yes, please”意为“好吧”，与此相反的是“No, thinks”，如：
①――Would you like another glass of juice? ――还要一杯果汗吗？
――No, thanks. ――不用了，谢谢。
②――Have some more cake, please. ――请再吃点蛋糕。
――No, thanks. I’m full/I’ve had enough. ――不用了，我已经饱了。
2．What a delicious supper! 多么美味的晚餐啊！
一般情况下三餐前不用冠词，have breakfast, have lunch, have supper吃早、中、晚饭。但当三餐前有定语修饰时，要带冠词，如：
①After a quick breakfast, Mary hurried to school. 匆匆吃过早饭后，Mary赶去上学。
②What a nice dinner we had at your house! 你家的晚饭太可口了！
3．Take turns to offer each other the foods in Part 2 in pairs.
两人一组，轮流请对方吃，第二部分中出现的食物。
△Take turns to do表示轮流做某事。It’s one’s turn to do…表示轮到某人做某事，如：
①They took turns to keep watch. 他们轮流站岗。
②It’s your turn to recite the passage. 轮到你背这篇短文了。
△offer 提供 r.n.提供之物
①He offered 10,000 dollars to help the poor. 他拿出1万美元帮助穷人。
②Could you offer me a cup of coffee, please? 请给我一杯咖啡好吗？
③My sister was offered a good chance to go abroad for further study of English.
我姐姐得到了一个出国深造英语的好机会。
④Would you like to accept the offer? 你愿意接受这个帮助吗？
⑤Thank you for your kind offer of help. 感谢你所提供的帮助。
4．When Christopher Columbus and his friend…, they discovered the plant “corn” there.Discover vt. 发现，看出，指揭示久已存在但从未被人知晓的客观事实，如：
①Many years ago, electricity was discovered. The discovery made people’s life changed a lot. 许多年前人们发现了电，电的发现使人们的生活发生了巨大的变化。
②We have discovered that he is a quite careful in his word. 我们发现他工作很仔细。
另一个动词invent指创造客观世界上从未有过的新事物，词义为“发明”，如：
①The computer was invented after electricity was discovered. It is one of the most
important inventions in the world.
发现了电之后才发明了电脑，电脑的发明是世界上最重要的发明之一。
②Electricity was not discovered by Edison, but he invented the electric light.
电不是爱迪生发现的，但他发明了电灯。
5．…there was not enough room for the population.
那儿已经没有足够大的地方装下这么多人了。
room在这里是一个不可数名词，意为空间，与space相近。
①There is no room left for the newcomer. 新到的人已经没地儿了。
②He took up too much room in our room. 他在我们的房间占了很大的地儿。
6．They needed a plant which didn’t need as much water as rice.
这是一个定语从句，意为：他们需要一种不象稻谷那样需要水的作物。
7．It is a very useful plant that can be prepared in many different ways.
这是一种非常有用的作物，可用许多不同的方法制做成食物。
1) prepare调制
How do you prepare the fish? 你怎么做这鱼？
2) prepare sth. Prepare to do sth. 准备……
①He is preparing his speech for tomorrow’s meeting. 他正在准备明天大会的演讲稿。
②I was about to prepare supper when the bell rang. 我正要做晚饭时门铃响了。
③What are you preparing to offer me? 你准备为我提供点什么？
④He is preparing to go abroad. 他正准备出国。
3) prepare sb. for sth. 使某人对某事有思想准备。
①The teacher is preparing the students for the coming examination.
老师让考生对即将到来的考试做准备。
②We must be prepared for failure again. 我们必须做好再次失败的心理准备。
4) be prepared to do sth. 乐于做某事。
①He’s not prepared to listen to your excuse. 他不乐意听你的解释。
②I’m prepared to help others. 我乐于助人。
8．Sometimes they cook it whole over an open fire.
有时候他们把整只玉米放在露天的火上烧烤。
whole表示“全部”一般不用来修饰复数名词，强调个体的完整。
①They cooked a duck whole over the fire and soon a delicious smell came out.
他们烤了一整只鸭子，很快香味就飘出来了。
②The man ate an egg whole at a time. 那人一次吞下一整个鸡蛋。
注意whole一般放在限定词后面，名词前，而all则放在限定词前面，如：
the whole class（整个班） my whole life（我整个生命）
three whole days（三整天） all my books（我所有的书）
all the students（所有的考生） all three days（三整天）
9．In many parts of the world corn is made into powder.
世界上还有许多地方把玉米磨成粉。
1) be made into意为“原料被加工成了……”
①We can make glass into different kinds of things. 我们可以把玻璃制成各种东西。
2) be made of指“成品是由什么原料制成的”能看出原材料。be made from则看不出原材料。
①Gas is made from coal. 煤气是由煤产生的。
②This kind of wine is made from grape. 这种酒是葡萄制成的。
③The desks are made of wood. 桌子是木头做的。
④The cloth is made of cotton. 这种布是用棉花制成的。
3) be made up of“由…组成”
①The novel is made up of ten parts. 这部小说有十部分组成。
②The sports team is made up of eleven members. 这支队由11人组成。
10．A number of other plants were found in America. 在美洲还发现了许多其他的作物。
A number of表示“很多”，与a lot of用法相同，后面接复数名词，如：
①A number of birds come to KunMing for the winter eveay year.
每年冬天有大量的鸟飞到昆明。
②A number of students are playing on the playground. But I don’t know what the number is.
很多学生在操场上玩，但我不知道有多少人。
the number of表示“…的数目”，谓语动词用单数，如：
③The number of the students in our school has risen this year.
今年我们学校学生的数目上升了。
五、定语从句
1．从定语从句和它修饰的先行词关系来看，有限制性和非限制性定语从句两种。
说 明
例 句
限制性定语从句
限定了先行词的范围和意思，这类从句不能省去。
I’ve found a man who can help you.
我找到了一个能帮助你的人。
Autumn in Beijing is the season which is neither hot not cold.
北京的秋天是不热也不冷的季节。
The factory where he worked was built in 1940.
他工作的那工厂建于1940年。
Is this school the one you visited yesterday?
这是你昨天参观的那所学校吗？
非限制性定语从句
只是对附加词进行补充说明，在意思上相当于一个并列的分句，如果省略，剩下的主句意思仍然清楚。书写时，从句和主句之间要用逗号分开，不能用that引导。
I knocked at the door of the chemist’s, which immediately opened.
我敲了一下药店的门，门很快就开了。
She has a sister, who is a musician.
她有一个是音乐家的姐姐。
They set up a school, where there were lots of students studying.
他们建了一所学校，有许多学生在那儿学习。
2．关系代词的用法
关系代词
用 法
例 句
that
做从句的主语或宾语，先行词可以是人也可以是物。
The table that stands over there is made of wood.
那边的桌子是用木头做的。
The book I gave you is well worth reading.
我给你的那本书很值得读。
The man that is talking to my father is my English teacher.
和我父亲谈话的那个人是我的英语老师。
which
做从句的主语或宾语，先行词是表示物的名词或代词。
The school (which) we visited is a famous one in Beijing.
我们参观的那所学校是北京的一所名校。
She hasn’t got enough money with which to buy the ring. 他没带够买戒指的钱。
who
whom
做从句的主语、宾语，其先行语为表示人的名词或代词。
Do you know the man who often makes speeches here?
你认识那个经常在这儿做演讲的人吗？
Who’s the woman (whom) you just referred to?
刚才你指的是哪个人？
whose
做从句的定语，先行词可以是人也可以是物。
LiMin is the boy whose father is an engineer.
李明这个男孩的爸爸是工程师。
I live in the house whose windows face north.
我住的房子窗子朝北。
3．在介词后的关系代词只能用whom（先行词为人），which（先行词既可是人也可是物）
4．关系副词的用法
关系副词
基本用法
例 句
when
在从句中做时间状语，其先行词为表示时间的名词或代词。
I still remember the day when I joined the Youth League. 我仍然记着入团的那一天。
I’ll never forget the time when we worked on the farm.
我永远不会忘记在农场工作的那段时光。
when
在从句中做地点状语，先行词为表示地点的名词和代词。
This is the bridge where you took photos.
这座桥是你照像的地方。
why
在从句中做原因状语常与reason连用。
I know the reason why she was angry.
我知道她为什么生气了。
5．定语中只能用that，不能用which的情况
▲被修饰的先行词为不定代词，all, much, something, everything, nothing, anything, none, the one等时，如：
We should do all that is useful to the people. 我们应该做一切有益于人民的事。
Do you mean the one that I bought yesterday? 你指的是我昨天买的吗？
▲先行词被only, any, few, little, no, one of, just, very等修饰时，如：
The only thing that we could do was to wait. 我们唯一能做的是等待。
The is the right person that I’m waiting for. 他就是我等的人。
△先行词被序数词修饰或本身是序数词时，如：
When we talk about WuXi, the first that comes to mind is Tai lake.
当我们谈起无锡时，首先想到的是太湖。
This is the third film that has been shown in our school this term. 这是我校本学期放映的第三部片子。
△先行词是最高级或被最高级修饰时，如：
The must important thing that should be done is how to stop him from going on.
最重要的是如何阻止他继续下去。
This book is the best one that I’ve read. 这本书是我看过的最好一本。
△如有两个从句，其中一个关系代词已用which，另一个关系代词用that，以避免重复。
Edison built up a factory which produced things that had never been seen before.
爱迪生办了一家工厂，生产过去从未见到过的东西。
6．定语从句中只能用which，不能用that的情况
△关系代词前有介词时
A zoo is a park in which many kinds of animals are kept for exhibition.
动物园是展览各种动物的乐园。
Is this the room in which Mr White lives?
这就是white先生住的房间吗？
▲which在从句中代替的是前面整个句子的意思时，不能用that
The street hasn’t been cleaned for weeks, which makes it very dirty.
街道好多星期没打扫了，因此整条街很脏。
He takes exercises everyday, which has done a lot of good to his health.
他每天运动，这对他的身体很有好处。
六、典型例题
1．――Who do you know the electricity?
――I don’t know who did it. But I know that Thomas Edison the electric lamp.
A. invented; invented B. discovered; invented C. found; found D. discovered; found
2．―― beancurd you’ve cooked!
――It’s very kind of you to say so.
A. How a nice B. What a nice C. How nice D. What nice
3．Wood can be made a great number of things. Look, this kind of paper is madewood.
A. into; of B. into; from C. from; into D. of; from
4．――Would you like another piece of cake?
―― .
A. Yes, please B. Yes, thanks C. No, please D. Yes, if you like
5．―― .
――Thank you.
A. Make yourself at home, Eat some fish B. You can eat some more fish by yourself
C. You’re free to eat some fish D. Help yourself to some fish
6．The farmers do their best to the market with enough vegetables.
A. supply B. feed C. prepare D. offer
7． students is more than two thousand in this school.
A. The number of B. A good many C. A number of D. plenty of
8．The car was too 6 people.
A. crowded with B. full of C. filled with D. small to
9．After the new technique introduced, the factory produced tractors in 1988 as the year before.
A. as twice many B. as many twice C. twice as many D. twice many as
10．――Do you think I could borrow your dictionary?
―― .
A. Yes, you may borrow B. Yes, you could C. Yes, go on D. Yes, help youself
答案：1――5．B、D、B、A、D 6――10．A、A、A、C、D
8．这辆车坐6个人太挤了，be crowded with意为“拥挤”
9．工厂引进新的技术之后，1988年生产的拖拉机是去年的2倍
10．“help yourself ” 除了有“自用食物”的意思外还有“自己动手做”的意思
七、语法练习
1．Finally came the day he had to begin his study for the next term.
A. till B. when C. since D. which
2．The train she was travelling was late.
A. by which B. on that C. on which D. /
3．Is some German friends visited last week.
A. this school where B. this school one C. this the school D. this school
4．Is there anyone in your class home is in the country?
A. who’s B. his C. whose D. that
5．He talked about the people and things interested him greatly during his stay here.
A. which B. that C. who D. they
6．This is the only verb can be used in this sentence.
A. that B. which C. it D. /
7．This is just the place I’m longing to visit these days.
A. where B. to which C. / D. to where
8．The house he visited yesterday was the one the great writer lived many years ago.
A. where; where B. which; which C. where; which D. which; where
9．The taxi a truck had knocked last night was destroyed.
A. which B. where C. at which D. into which
10．All is needed is a supply of oil.
A. the thing B. that C. what D. which
答案： 1――5．B、A、C、C、B 6――10．A、C、D、C、B
2．She was travelling by brain. 所以此题应选A。
3．此题考查对先行词的判断能力。“This is the school,” “school ”是先行词。如果没有“the”, “this school ”后面要加“the one ”代替先行词“school”, This school is the one that…
5．当先行词既有人又有物时关系代词用“that”。
7．关系代词在从句中做宾语可以省略。
8．“The house ”在从句中做“visited ”的宾语，“the one ”在从句中做地点状语。
这句话的意思是：他昨天参观的那所房子几年前是一个伟大的作家居住的地方。
9．介词后用which. “knock at ”表示碰撞，昨天晚上一辆出租车被卡车撞坏了。
10．先行词是“All ”，关系代词只能用that。
Date Sep1 Class 1
Lesson 1 and Lesson3
Knowledge&ability: 1.The vocabulary in Lesson 1and Lesson 3
2.Learn the grammar: the Present Perfect Tense.
3.Grasp when to use the Present Perfect Tense.
Process & method :By the drill“have got” used fluently. Make the Ss get the information about the new grammar, try to grasp the grammar with “ever” “just”
Culture: The method of English learning
Moral, attitude & value: Be helpful and try to be a person who has the sense of responsibility.
Main & difficult points
1. Know when to use the Present Perfect tense.
2. Grasp the construction “have (has) + Vp.p. ” pay attention to the adv. just, ever.
3. Tell the difference between the past tense and the Present Perfect tense.
Teaching procedure
A multi-media computer
Teaching procedure
Content
Teacher’s activities
Students’ activities
Intention
Pre-task
The method of studying English in the new term.
1. Have you got a notebook for taking notes in class?
2. Have you got the newspaper about English Studying?
3. Have you found a magazine or a newspaper about it?
4. Have you ever read an English newspaper?
5. This term we’ll have another Class for reading English newspaper to improve the ability of reading.
Yes, I have.
No, I haven’t
No, we haven’t. We have got magazines.
Yes, I have ever read an English newspaper.
I have just bought an English newspaper.
While training the drill, exchange the method of studying English.
1. Take notes
2. Newspapers for reading class
Try to make sentences with “just” and “ever"
While-task
Practice the Present Perfect Tense.
1. Create the situation about the Present Perfect Tense.
Have you had breakfast?
Yes, I have just finished it.
Have you ever eaten the pizza?
No, I haven’t.
Not even once.
Do more exercises.
1. Have you ever--?
2. I have just done.
Use “ever” and “just” fluently.
On the blackboard
Lesson 1 ∽ Lesson 3
Have you got ---?
Have you ever/just read an English newspaper?
Some past participles of Verbs.
Reflection:
Dalian Gezhi Middle School English Teaching Plan Unit 1 Lesson 2
Date Sep 2 Class 2
Lesson 2
Teaching aims
Knowledge & ability: 1.The words related to the text.
2.Language points in the text.
3.Some information about the library.
4. Improve the speed of reading English text.
Process & method : Before the new class. The Ss should be given a chance to have the exam about the vocabulary in the text. Make the Ss have the good habit of pre-reading. Try to talk about the rules in the library then come back to the text.
Culture: Libraries in different countries.
Moral, attitude & value: Be ready to help others. obey the rules in the library.
Main & difficult points
1. Grasp the useful phases and make sentences with them.
2. Learn to make the useful phrases used into the composition. E.g. used to / put down/ pay for / come up with.
3. A few sentences with attribute classes.
Teaching tools
Teaching procedure
A multi-media computer
Teaching procedure
Content
Teacher’s activities
Students’ activities
Intention
Pre-task
Free talk about the present perfect tense.
1. Have you borrowed the books from the library?
2. Have you ever lost the book in the library?
3. Have you ever heard of the rules about borrowing books?
4. Have you paid for the lost book?
5. If you lose a library book. What happens?
Yes. I have just / ever borrowed a novel.
No, not even once.
Yes. We have ever head of
Have a discussion about the question.
Review the grammar then come to the new lesson.
While-task
Read the text with the questions given by the teacher
Questions to the Ss:
1. Why does Grandma often borrow the books from the library?
2. How does she get all her lost book at last?
3. Who helped Grandma think of the ways to get the lost book?.
4. Do you think it a good way to encourage people to return books?
First read it once with the questions Then listen to the tape once.
The Ss ask the questions each other without books, try to get the main idea, maybe some Ss can tell the story. try to follow them then open the books to make sure of it.
Improve the speed of reading English, and train the ability of expressing English.
Lesson 2
1. Some past participles of Verbs.
2. Some phases about the text.
3. Language points from the Students about the text.
Reflection:
Dalian Gezhi Middle School English Teaching Plan Unit 1 Lesson 4
Date Sep 3 Class 3
Lesson 4
Knowledge & ability: 1.Some words
2.Know the information in the library.
3.Tell the difference between the past tense and the present perfect tense while practicing the Perfect Tense.
4.Write a composition.
Process & method: 1.Create the situation to get the idea about the difference between the two tenses.
2.Give more chances to express themselves.
Culture: To know sth about libraries in different countries.
Moral, attitude & value: Love what you do. Enjoy the work and life.
Main & difficult points
1. Know all the words about Part 4 in Lesson 4
2. Know when or how to use the past tense and the Present Perfect tense.
3. Writing.
Teaching tools
A multi-media computer
Teaching procedure
Content
Teacher’s activities
Students’ activities
Intention
Pre-task
The words of this lesson
1. Create a story to make the students understand the new words.
2. Have you borrowed the book in the library: on the computer screen?
Try to follow the teacher than get the information about Part 4 in L4.
No, I haven’t.
Yes, but I have never tried it.
Make the awful words lively and grasped easily.
While-task
Writing
Listening
Reading
1. Have you got the library you can borrow the books on the computer screen?
2. Introduce one of the library you have ever been to Finish Part 2 and a story on P96 in wb.
Make the Ss Listen to the tape with a few questions
Give the Ss time to do the reading.
1. Have teamwork.
2. Interview one of the librarians by creating the situation to get the information about.
Try to get the idea by “who” “when” “how” “why” Read ‘Miss Forgetful as quickly as they can.
Grasp the vocabulary in Part.
Train the ability of writing.
On the blackboard
Lesson 4.
1. Some words about Part 4
2. Have you ever spoken to a foreigner?
Yes, I have.
When did you first speak to a foreigner?
Last year.
Reflection:
Teaching Plan
Topic
Unit One (BookⅠ)
Teaching aims
Knowledge and ability:
1. English letters from A to N.
2. Everyday English about greetings.
3. Train the students’ ability of speaking English.
Process and method:
Students greet to each other with the greetings and try to introduce themselves begin with “I’m …”
Moral, attitude and value:
Students learn to be polite to each other and to others and train themselves good manners.
Main and difficult points
1. Learn to pronounce and write the letters correctly.
2. Know how to greet to each other.
3. Learn to use the right greetings in the right situation.
Teaching tools
A computer, cards and tapes.
Teaching procedure
Teachers’ activities
Students’ activities
Step One
Letters from A to N
Prepare some cards and tapes to teach the students English letters
Listen, read and write letters
Step Two
1.The teacher greets to the students with the greeting words in English. Such as good morning? How are you? Nice to meet you.
2.My name is …?
What’s your name?
What’s this (that)?
It’s …
3.Join in the students to practise.
4.Correct the students’ mistakes and tell them to use the different greetings in different situation. Help them to use the greetings correctly.
1. Make response to the teachers’ greetings in English.
2. Practice in pairs greeting to each other.
3. Drills
What’s your name?
My name is… .
4. Make dialogues with the sentence patterns.
Step Three
Consolidati-ons
1. Write down the letters in the right way.
2. Make dialogues with the greetings they learnt.
3. Test paper.
Check the results.
Unit 1 Lesson 1
Teaching aims
Knowledge and Ability:
1.Letters from Aa-Gg.
2.Everyday English about greeting and Abbreviate.
3.Suggestions for Junior English study.
Process and method:
Students learn letters by using cards and everyday English by actions and gestures.
Moral attitude and value:
1. Encourage students to display more initiative in English study.
2. Be polite to others.
Main and difficult points
1. Pay special attention to the sound in the 7 letters.
2. Know something about falling tone.
3. Know the letters, vowels and consonants.
Teaching tools
A multi-media computer, cards
Teaching procedure
Content
Teacher’s activities
Students’ activities
Intention
Time
Pre-task
Introduction and everyday English about greetings
1. Good morning class!
2. I’m your new teacher. My name is…What’s your name?
3. Nice to meet you!
1. Good morning, Ms…
2. My name is …
3. Nice to meet you!
Can understand and learn useful expressions about greeting.
10’
While-task
Spelling, pronunciation and writing letters.
1.show and read letters on BL.
1.look and follow teachers to read.
2.Write as what the teacher tells them.
Grasp the correct ways of spelling and writing of letters.
20’
Abbrevication
Explain some of the abbreviations
Remember the correct meanings of them.
Can know the meaning of abbreviations.
Post-task
1.-Good morning.
-_________
A. Thanks B. And you ? C. Hello! D. Go
od morning!
2.?Nice to meet you!
-__________
A. Hello B. Good morning! C. Nice to meet you ,too D. Thanks
1. ?Sit down , please.
-__________
A. Thank you. B. Yes C. Fine D. Hello
2. 身份证______
3. 中国民航______
4. 光盘______
Practice
1. ?How are you today?
-__________
A. Not good B. I’m fine, thanks
C. And you D. How are you?
2. ?What’s your name?
-__________
A. I’m Jim Green B. Mary King
C. My name is Wei Hua
D. My name Wang Lin
3. 工商管理硕士______ 4.香港______
4. 文学学士______ 5.中国篮球协会______
Check the results of learning
Blackboard design
Unit 1 Lesson 1
1. Good morning!
2. ?What’s your name?
-My name is…
3. -Nice to meet you.
-Nice to meet you, too.
Homework
1. Act part or make up dialogues of greetings.
2. EX.2 in wb
3. Finish off copybooks.
Reflection
2 虽然是第一堂英语课，单也尽量用英语组织教学，尽量给学生创造英语情景，通过手势、表情、动作等示意，帮助学生听懂课堂用语和日常交际用语。
Topic
Teaching aims
Knowledge and Ability:
1. Spelling , pronunciation and writing letters from H toN.
2. Everyday English.
3. Improve the ability of oral English.
Process and method:
Students learn letters by using cards and everyday English by actions and gestures.
Moral, attitude and value: 1.Be polite to others.
2.Learn to care for others.
Main and difficult points
1. To listen, say, read and write letters from H to V.
2. The pronunciation of the letter H.
3. The answer to the question How are you? is fine , not well .
Teaching tools
A multi-media computer, cards
Teaching procedure
Contents
Teacher’s activities
Students’ activities
Intention
Time
Pre-task
Everyday English
1. Perform the dialogue:
Good morning. My name is MS…What’s your name?
How are you?
I’m fine, too
2.Drill the action chain.
Practice:
1.Goodmorning My name is Ms…
Fine, thank you. And you?
2. Switch roles and repeat.
To improve to students’ oral English.
8’
While-task
Everyday English letters and abbreviations
1. Listen, check and encourge students to act out their own dialogue.
2. Spelling, pronuncation and writing letters.
3. Explain some of the Abbreviations.
1. Make up their own dialogues and act them out.
2. Read and write as what the teacher tells them.
3. Remember the meanings of them.
1. Tocommunicate with each other using everyday English today.
2. To grasp the correct way of spelling and writing letters.
3. Can know the meanings of them
18’
Post-task
1. 补全对话 2. A B 栏搭配
A: Hello! A
B: ______________ 1 .Good morning!
A: ______________ 2. what’s your name,
B: John Brown. Please.
A: Nice to meet you. 3 .How are you today?
B: ______________ 4 .Nice to meet you!
A: Sit down, please . 5. Hello!
B:______________ B
a. I’m fine, thanks.
b. Hello!
c. Mary King
d .Morning!
e. Nice to meet you, too.
Practice
7’
书面表达:魏华早上遇到了她班级的一名新同学Lucy,请把他们见面的对话写下来．
Wei Hua:______________________________
Lucy:________________________________ WeiHua:______________________________
Lucy:________________________________ WeiHua:______________________________
Lucy:________________________________
To improve their ability of write English
7’
Blackboard design
Lesson 2
Sit down, please!
How are you? H h I i J j K k L l M m N n
Fine ,thank you.
Homework
1. Listen to the tape and record their own tapes.
2. Ex.3 in wb
3. Finish off copybooks.
Reflection
第二堂英语课训练内容开始增多,如果没有足够的时间,也不必匆忙和担心,让学生感到自信和从容是最重要的.
Topic
Lesson 3
Teaching aims
Knowledge and ability:
1. The song Good morning to you! And the drill: what’s this? It’s…
2. Summarize the pronunciation of letters form A to N
3. Train the students ability of summary.
Process and method:
1. Students base on their situation around, organize the language and try to express clearly.
2. Learn the song by listening to the tape.
3. Summarize the letter’s pronunciation by themselves.
Moral, attitude and value: Be polite to others.
Main and different point
1. Learn to sing English song and the pattern What’s this? It’s…
2. Summarize the letters’ pronunciation.
Teaching tools
A multi-media computer
Teaching procedure
Content
Teacher’s activities
Students’ activities
Intention
Time
Pre-task
The song Good morning to you! And the summary of the letters’ pronunciation
1.Play the tape and sing the song with students
2.Help and encourage the students summarize the letters’ pronunciation.
1.Listen to the tape and try to learn the English song.
2.Summarize the letters’ pronunciation by themselves.
1..Learn to sing the English song and try to feel English in the song.
2.Improve the students’ ability of summary.
15’
While-task
The pattern what’s this? It’s …
1. Ask and answer with students.
2. Drill action chain.
3. Arrange the game.
1. Ask and answer in pairs
What’s this?
It’s …
Yes, It is.
No, it isn’t
2.Enjoy in the game.
To use the patterns to communicate with each other.
10’
Post-task
( )1.-______- Fine, thanks.
A. How do you do? B. How old are you?
C. How are you? D. Nice to meet you.
( )2 ?Nice to meet you.
-________________
A. Nice to meet you, too. B. Thank you.
C. How are you. D. And you?
( )3. ?What’s this? -_________ “B”.
A. This is B it C It’s D It’s a
)4. What, it, is, morning, to, good, you, thank, meet.
A: Good morning, Mr li.
B: ____ ____ ,Wei Hua.
A: How are you?
B: Fine, _____ ____ . Are you?
A: I’m fine, _____.Nice to _____ you.
B: Nice to meet you, ______
A: ______this?
B:______ a book.
A:______ ______ .Goodbye.
Practice
10’
1.______(坐下), please.
2. Good morning, ________.(同学们)
3. Nice to ______(见面) you.
4. ?How are you? -_______(很好), _______(谢谢)
5. ?What is _______(这个)? -It’s B.
Check the results of learning
5’
Blackboard design
A H J K What is this?
F L M N It is …
B C D E G What is = What’s
It is = It’s
Homework
1. Exx.3.4 in wb
2. Make up their own dialogues and act them out.
Reflection
缩写形式在英语中很重要.学生可能已经听到I’m(I am),而在本课将要教他们What’s(What is).缩略形式通常是比较容易说的,但是如果首先教会完全形式它就更容易被理解更容易被听懂.首先要确信使学生知道这两种形式,并且能够读出这两种形式。
Topic
Teaching aims
Knowledge and ability:
1. The patterns of greetings in this unit.
2. Train the students’ ability of listen, speaking, reading, writing and sunmmary.
Process and method:
Students base on the patterns of greeting to make up their own dialogue, and try to express themselves clearly and fluently.
Moral, attitude and value: Be polite to others and care for each other.
Main and different points
1. The patterns of greeting.
2. The letters’ spelling, pronunciation and writing.
Teaching tools
A multi-media computer.
Teaching procedure
Teachers’ activities
Students’ activities
Intention
time
Pre-
task
Patterns about greetings (according to the pictures)
1. Who is the girl?
2. Who is the teacher?
3. Check students to read aloud.
4. Encourage students to act out.
1.She is …
2.She is …
3.Read aloud
4.Act out the dialogues.
Improve the students’ abilities of listening, speaking, reading and writing.
8’
While-
task
1.The dialogue in the textbook
2.Checkpoint1
1.Play the tape
2.Guide students
3. to act out the dialogues they have made up.
4.Ask and answer with students going through checkpoint.
1.Listen to the tape.
2.Act out the dialogues they’re made up
3.Go through the patterns of greeting in checkpoint 1.
To use the patterns to communicate with each other.
10’
Post-
task
Ⅰ.补全对话
1.-Thanks a lot.
-________
2.-________my new house.
-Thank you.
3.-How are you today?
-Very well, _______?
4-What’s this?
-________a tree
5.-Please sit down.
-_________
Ⅱ.单词拼写
1. Good _______(上午), class
2. ________(高兴)to meet you.
3. ?How are you? -__________(很好),thanks
4. ________(下午),Mr. Brown
5. ________(欢迎)to China.
Ⅲ 选择
( )1. ?Thank you very much.
-__________. which is not right?
A. Don’t thank me B. You are welcome
C. That’s OK D. That’s all right
( )2. ?Welcome to our class
-_________
A. You are welcome B. That’s all right
C. Welcome to our class, too D. Thank you
Check the result of learning
22’
Blackboard
Lesson 4
-Welcome to our school. This is …
-Thank you.
Homework
1. Go though the contents in this unit.
2. Make up their our dialogues and act them out.
Reflection
这一课主要是复习课,和本单元其他课不一样.它有两页长,在本课后面的复习要点部分,列出了西药学习的主要语言点,教会学生如何有效利用这部分内容非常重要.
Unit Four Science in English
Lesson Three A knowledge Quiz
1. Fractions
2. Phrases
That’s right / correct.
3. Talking about the earth and space
4. Making comments
5. Expressing appreciation
Daily talk
1. How old are you?
2. How old is our country?
3. How old is our Party?
4. How old is our Earth?
5. How many of the students in your class are girls?
6. How many of the students in your class are boys?
7. How much of the Earth’s surface is land?
8. Is it about one-third or two-thirds?
9. Are deserts in the sea or on the land?
10. Is the sun a star or a planet?
11. What moves around the sun? (Planets)
12. Does the sun set in the east or west?
13. Where does the sun rise?
14. Is our Earth a star or a planet?
15. How many planets are there around the sun?
16. Are the Class Two students having a test?
17. Are the Class Two students having a quiz?
18. What are the Class Two students doing?
19. What are they having an English class or a geography class?
20. Have you had a class like that?
1. Are they having a knowledge quiz about the Earth and space?
2. What are the Class Two students doing?
3. Who’s asking questions?
4. Are the students’ answers correct?
That’s right / correct.
A: Do you live at
B: That’s right.
A: Is your telephone number…?
B: That’s right.
5. How much of the Earth’s surface is water?
6. How much of the world’s land surface is desert?
Well done.
A: We’ve decorated our classroom.
B: Well done.
7. You’ve all got a very good knowledge of the Earth and space, haven’t you?
8. You’re history teacher has got a very good knowledge of Chinese history, hasn’t he?
9. She has a very good knowledge of music, doesn’t she?
10. We can learn a lot of knowledge, can’t we?
1. Recite the text
2. Copy the words and text
3. Recite the text
Daily talk
1. How many numbers are there in a fraction? (Two)
2. What is the difference between the first and the second number?
(a cardinal number / an ordinal number)
3. When do you need to add “s” to the second number?
(When the first number is larger than one.)
4. How do you say 3/4 and 7/10 in English?
(three-fourths and seven-tenths)
Listening I II
Work in four groups
Writing
Daily talk
1. Explain
2. Finish the exercise
Homework
Exercises in WB
Daily talk
Language focus
Ex I / II / III on the blackboard
Skill focus
Daily talk
Listening comprehension
Read the passage and answer the questions below.
Homework
Skill focus Ex. 4 5 6
Daily talk
Check focus Ex 4 5 6
Homework
Go over the three lessons in Unit Four
高考数学专题―数学思想方法
数形结合法
数与形的结合，使抽象思维与形象思维结合起来，实现概念与形象、表象与联系的转化，化难为易，是数学解题的重要思想方法之一。进行数形结合的信息转换主要有三个途径：一是通过坐标系的建立，引 入参变量，化静为动，以动求解；例如：解不等式：，
可设，则平面上轨迹双曲线上坐标的取值范围即为原不等式的解；二是转化，例如将转化为点与的距离；将转化为点与的直线斜率；三是构造，即可构造几何模型、构造函数或构造一个图形，例如求的值，可以构造一个顶角为的等腰三角形，利用相似形性质算出。
第一讲
[要求与考点] 理解和掌握数形结合法在函数、方程、最值中的应用。
例1、 函数的最大、最小值。
分析：可以看成是点与点两点
值由过点的圆的两条切线所决定。如图
解：设的斜率为，则为：
即。
故
解得：
即
说明：凡形如的代数式，一般都可看作点和点的连线的斜率，本题也可以用万能公式代换后，利用判别式求解，但运较繁。用判别式法须注变量范围的变化。
例2、求函数的值域。
分析：原函数在令后可以化为的范围可看着是当直线与四分之一圆有交点时，直线在纵轴上的截距的范围，如图。
，的范围可
看作是当直线与四分之一圆
有交点时，直线在纵轴上的截
解：令，原函数变为
∴
引入变量，得：
∵ 直线的斜率为，过四分之一圆上点时，
截距，直线与四分之一圆相切时，，
∴ 截距
∴
说明：仿照本例可解决形如或的函数的值域问题。
本例也可在写成后，把点看成是既在直线上，又在圆上，联立方程组即可求得的取值
范围。
例3、已知函数在上有最小值1，求实数的值；
[分析]函数是关于的二次函数，对称轴是，应就其对称轴是否在上加以讨论。
解：∵是以为对称轴，开口向上的抛物线；
当时，在上的最小值是，如图1，解得：
当时，的最小值是，如图2，解得
当时，应是如图3 , 在上的最小值是，但此方程无解，∴这种情况不存在。
图1 图2 图3
例4、方程有两个不相等的实数根，求的取值范围.
与函数的图象交点的横坐标.函数
的图象由
(半圆)和 (等轴双曲线
当或,时,此二函数的
图象有两个交点,即原方程有两个不相等的实数根.
例5、设是以为直径的单位圆上半圆周上的任意一点，于求的最大值；
建立坐标系，如图；则半圆方程为：
，设点坐标为，，
则
所以，
令 ，则 ，且，
∴
∴当时，有最大值
法2、如图，设，，
∵ 为直径，∴，且，
∴ ，，，
所以
（以下求解同法一）
练 习
1、已知实数满足，则
（1）的取值范围是 ；
（2）的取值范围是 ；
（3）的取值范围是 ；
2、函数的最大值是 ；
3、抛物线弦垂直于轴，若弦长为，则焦点到弦的距离为 ；
4、如果实数满足求的最大最小值；
5、求函数的值域；
6、为何实数时，方程有且仅有一个实根；
数形结合法 第二讲
[要求与考点] 理解和掌握数形结合法在解不等式，不等式的证明、集合，复数等问题中的应用。
例1、 解不等式，
[分析] 由于不等式中含参数和绝对值，对解的讨论将十分困难，若用数形结合法可较易地解决这一问题。
当时，两曲线
它们的横坐标分别为， 图1
故解集为
当时，两曲线交于三点，如图2，
故解集为
当时，，两曲线交于两点，如图3
故解集为
图2 图3
例2、已知，且，，求证：
间的距离间的平方，点在直线
上，点在直线上，如图，
显然，平行直线上任意两点的距离大于或等于
说明：凡形如的等式皆可视为点在直线上，若则可用基本不等式证明即；
例3、已知，求证：
[分析] 与余弦定理很相似，可视为，即三角形中夹角的第三边长，原不等式的左端可看作是图中周长，由正弦定理有：
中， C
同样可以得另外两式，三式相加即可。
说明：还可以看作，它表示两点，
间的距离，也可以看成复数的模；本题用复数法证明更为简捷。
例4、已知，，求证：
证明：设是上任意一点，
当且仅当时，到原点取最近距离，
∴在直线上，直线交圆于点，
间最近距离，故有，原式成立；
例5、已知，且，求当为何值时，有最大值；
[分析] 设复数所对应的点为，
几何意义是点到和
连线的夹角；的
几何意义是到两点、
问题转化为在上求一点，使它与
和连线的夹角最大，如图，
过、和相切的较小圆的切点即为所求；
略解：、两点的垂直平分线方程为，
设圆心为，则，解得：
，，其较小圆的圆心为，半径为 ；
设切点的坐标为，∵ 得：
故切点为，所求复数为。
说明：本题充分利用了图形的几何性质，避免了复杂的计算。
[本节评注] 数形结合法思想在解题中的应用关键是：一要多类比，多联想，将代数式通过转化、变形，赋予它鲜明的几何意义；二要挖掘已有图形的几何性质，利用其性质尽量简化运算或论证。
作 业
1、复数满足，则的辐角主值的取值范围是 ；
2、解不等式；
3、已知，求复数为何值时，
（1）取最大值？最小值？
（2）取最大值？最小值？
4、已知均大于零，且，
求证：
[文件] sxglija0030.doc
[科目] 数学
[年级] 高中
[章节]
[关键词] 锥体/体积
[标题] 锥体的体积
[内容]
锥体的体积
北京陈经纶中学 丁益祥
教学目标
1.使学生掌握锥体的体积公式及其初步应用；
2.通过三棱锥体积公式的探求，教学生学习观察、类比、归纳、猜想等合理推理方法，培养
学生分析、综合、抽象、概括等逻辑推理能力；
3.通过三棱锥体积公式的探求，培养学生独立思考、刻苦钻研、孜孜以求的毅力及勇于探索
创新的精神等良好的个性品质.
教学重点和难点
三棱锥体积公式及其探求.
教学设计过程
师:前几节课我们先后学习了祖■原理和柱体的体积公式，在开始讲本章知识下久，我们还
学习了锥体平行于底面的截面的性质.现在请同学们分别回忆一下上述三个知识内容，谁来
回答锥体平行于底面的截面的性质是什么?
生1:如果棱锥(或圆锥)被平行于底面的平面所截，那么截面和底面相似，并且它们面积的
比等于截得的棱锥(或圆锥)的高和原棱锥(或圆锥)高的平方比.
师:很好!下面谁来回答祖■原理是如何叙述的?
生2:夹在两个平行平面间的两个几何体，被平行于这两个平面的任意平面所截，如果截得
的两个截面的面积总相等，那么这两个几何体的体积相等.
师:回答正确.请同学们一起回答:柱体的体积公式是怎么表示的?
生:柱体的体积等于它的底面积乘以高，即V柱体=Sh.
师:当这个柱体是圆柱时，其体积还有别的表达形式吗?
生3:V圆柱=πr2h,其中r是底面半径，h是圆柱的高.
师:不错.谁能说说底面积是S，高是h的柱体体积公式的探求思路吗?
生4:我们构造一个与所给柱体等底面积等高的长方体，把它与所给柱体的下底面放在同一
个平面α上.由于它们上、下底面平行，且等高，故它们的上底面必在与α平行的同一个平
面β内，现在用平行于α的任意平面去截它们时，由于所得的截面都与它们的底面分别平行
，因此截面积都等于S.由祖■原理知，它们的体积相等，而V长方体=Sh，所以V柱体=Sh.
师:很好!生4利用祖■原理获得了等底面积等高的柱体与长方体(两个柱体)等体积，那么等
底面积等高的两个锥体的体积之间有什么关系呢?(师边问边板书“等底面积等高的两个锥体
的体积之间的关系”一语)
生:相等.
师:你们怎么知道它们的体积是相等的.
生:猜想的.(也有的说是估计的)
师:猜想也好，估计也罢，都是有风险的，尽管如此，但它常常是“发现”的先导.能证实
你们的猜想吗?
生5:用祖■原理.设有任意两个锥体，不妨选取一个三棱锥，一个圆锥，并设它们的底面
积都是S，高都是h(如图1).①把这两个锥体的底面放在同一个平面α上，由于它们的高相
等，故它们的顶点必在与α平行的同一个平面β上，即这两个锥体可夹在两个平行平面α，
β之间；②用平行于平面α的任意平面去截这两个锥体，设截面面积分别为S1，S2，截面和
顶点的距离是h1,体积分别为V1，V2，则由锥体平行于底面的截面性质知:
所以=， 故S1=S2.
由祖■原理知:V1=V2.
(生叙述师板书)
师:完全正确!我们再请一位同学用命题的形式完整地叙述一下上述问题的条件和结论.
生6:如果两个锥体的底面积相等，高也相等，那么它们的体积相等.
师:同学们对生6的概括有不同意见吗?
生:没有!
师:生6的概括是正确的，但我们可以叙述得更简练一些.
生6:对了，可以叙述为:等底面积等高的两个锥体的体积相等.
师:很好!这个命题是课本中第100页的定理.(师随即把前面板书的“等底面积等高的两个
锥体体积之间的关系”一语中的“之间的关系”五字擦掉，补上“相等”二字，同时在前面
添上“定理”二字)我们干脆请生6再重申一下:定理有哪几个条件?结论是什么?
生6:条件有两个:一个是两个锥体的底面积相等，另一个是这两个锥体的高相等.结论是体
积相等.
(由学生提出问题、分析问题并解决问题，这是对学生最高层次的要求.当学生达不到这个
层次时，可由老师提出问题，学生分析问题和解决问题.老师提出问题后要给学生观察、比
较、分析、归纳、猜想、发现的时间.著名数学教育家波利亚曾指出:只要数学的学习过程
稍能反映出数学发明的过程，那么就应当让猜想、合理推理占有适当的位置.猜想后还要严
格地证明，合情推理与逻辑推理并重，既教证明又教猜想，这才是解决问题的完整过程.)
师:上述定理只是回答了具有等底面积等高的两个锥体的体积之间的相等关系，但这个体积
如何求出，能否像柱体那样有一个体积公式仍然是一个谜.然而它却给我们求锥体体积一个
有益的启示:只须找到一个“简单”的锥体作为代表，如果这个代表的体积求出来了，那么
，由上述定理即可获得其它锥体的体积了.请同学们思考用怎样的“简单”锥体作代表来研
究呢?
生:三棱锥!(一小部分同学有些疑惑)
师:能说说你们的想法吗?
生7:因为我们较熟悉棱锥，而在棱锥中，三棱锥底面多边形的边数量少，似乎要更“简单
”些.
师:有道理!我们选出的“代表”当然应该首先是我们熟悉的，由于三角形是最简单的多边
形，类比地，我们有理由这样说，三棱锥是较“简单”的棱锥.那么，怎样研究三棱锥的体
积呢?(板书:三棱锥的体积，并作出一个底面积为S的，高为h的三棱锥A′-ABC，如图2)
生:……(思维受阻)
师:(启发一下)请同学们回忆一下求如下两个图形(图3)面积的方法:
生8:对(1)可将它分成一个半圆和一个正方形，分别计算出它们的面积，再相加即可；对(2
)，可将三角形先补成一个平行四边形，然后求出平行四边形的面积，再除以2即得三角形
面积.
(在生8叙述时，师图示如下)
师:先割后补与先补后割是处理几何问题时常用的方法，即我们常说的割补法.类比地，能
否将这一思维方式迁移到探求三棱锥的体积上来呢?
生:(几乎异口同声地)能!
师:那么是采用先割后补，还是先补后割呢?邻近的同学可以相互讨论一下.
(学生之间小声讨论，选择这两种方法的学生都有)
师:我们请一位同学说说自己选择的方法及其理由，谁来说?生9想好了吗?
生9:我认为先补后割比较好，至于先割后补，我觉得不行.
师:能说说否定先割后补的理由吗?
生9:……(似有难色)
师:谁能试着割一下?
生10:对一个三棱锥进行分割，实际上是用一个平面去截它.无论怎么截，得到的要么仍是
三棱锥，要么是比三棱锥更为复杂的几何体.所以对三棱锥再分割是不合适的.
师:其他同学以为如何?
生:生10的解释是对的.
师:既然如此，我们可否定先割后补，而肯定先补后割，刚才生9就是这个意见，现在也是
大家的意见了，那么，补成怎样的几何体较合适呢?
生:补成三棱柱.
师:谁能具体说说?
生11:把三棱锥A′-ABC以底面ΔABC为底面，AA′为侧棱补成一个三棱柱ABC-A′B′C′
.
师:请你在黑板上具体补出来.
生11:(上黑板补画图形如图5)
师:生11完成了补形的任务，下面该进行什么工作了?
生:分割.
师:如何分割.
生:分割成三个三棱锥.
师:请生12上来具体分割一下.
(生12上黑板分割三棱柱ABC-A′B′C得三棱锥1，2，3.如图6)
师:很好!生12的图形画得很规范.现在请同学们预测一下分割而得的三个三棱锥之间有何
关系?
生:体积相等.
师:能简要地说明你们预测的依据吗?
生13:我没有证明，但我想它们的体积应该相等，这是因为刚才回忆求三角形面积时，将三
角形补成一个平行四边形(平面图形)后再分割成的两个三角形等面积.类比地，我们将三棱
锥补成一个三棱柱(空间图形)后再分割成三个三棱锥当然应该体积相等.
师:生13由平面图形的处理结果类比地预测空间图形的相应结果不无道理.同学们的预测实
际上也是我们的希望.而怎样使我们的希望、预测变为现实，还需要严格证明，那么怎样证
明这三个三棱锥1，2，3等体积呢?
(引导学生思考两个锥体等体积的依据――前面定理的条件:(1)等底面积，(2)等高)
生14:(生14叙述，师板书)在三棱锥1，2中，SΔABA′=SΔB′A′B，又由于它们有相同顶
点C，故高也相等，所以V1=V2.又在三棱锥2，3中，SΔBCB′=SΔB′C′C，它们有相同顶
点A′，故高也相等.所以V2=V3，所以V1=V2=V3.
生15:在证得V1=V2后，再证明V1=V3也很方便.
(生15叙述，师板书)
因为在三棱锥1，3中，SΔABC=SΔA′B′C′，高也相等(都等于三棱锥的高).所以V1=V3.
故V1=V2=V3=V三棱柱.而V三棱柱=Sh，
所以 V三棱锥=Sh.
师:非常好!到目前为止，我们已经解决了三棱锥的体积问题，也就是说，解决了一个“锥
体大家庭”中的“代表”的体积问题.那么一般锥体的体积又如何呢?(设一般锥体的底面积
为S，高为h)
生:V锥体=Sh.(师板书)
师:谁能对这一结果的来源作出解释?
生16:构造一个三棱锥，使其底面积为S，高为h，由于等底面积等高的锥体的体积相等，故
V锥体=V三棱锥=1 3Sh.
(教学生学会证明是重要的，让学生对某一问题作出解释也是必要的.它可以使学生从整体
上把握问题的来龙去脉，在某种情况下比只让学生机械的证明要好.它是培养学生语言表达
能力，数学交流能力，培养学生数学素养的一个重要途径.)
师:生16从整体上就一般锥体的体积公式的获得作了简明扼要的解释.我们知道，圆锥是一
类典型的特殊锥体，对于圆锥的体积，有何别的表达式?
生17:V圆锥=πr2h.(师板书)
师:这里r,h的意义分别是什么?
生17:r表示圆锥的底面半径，h表示圆锥的高.
师:至此，我们已获得了锥体的体积公式V锥体=Sh.对圆锥来说，还可以用底面半径r及
高h来表达体积，即V圆锥=πr2h.作为应用，请同学们看这样一个问题:
(用投影仪打出)
(由课本第103页练习题1改编)
如图7，在正方体ABCD-A′B′C′D′中，已知棱长为a，求:
(1)三棱锥B′-ABC的体积；
(2)这个三棱锥的体积是正方形体积的几分之几；
(3)B到平面AB′C的距离?
(若没时间，可留做课后思考，要求用两种方法求解)
(请生18解答(1)，(2)，生19解答(3)，其余同学在座位上完成，师巡视)
(生18板演(1)(2))
(1)因为 正方体棱长为a，所以 SΔABC=a，高h=a.
所以VB′-ABC=SΔABC・h=・a・a=a.
(2)因为 V正方体=a，
所以VB′-ABC∶V正方体=.
(生19板演(3))
解法1:如图8.
过B作BO⊥面AB′C于O，则O必为ΔAB′C的重心.连AO并延长交B′C于M，
因为 AB′=B′C=CA=a,
所以 AM=・a=a,OA=AM=a.
在RtΔAOB中，BO==，
即B到面AB′C的距离为a.
解法二:
设B到面AB′C距离为h,
因为 AB′=B′C=CA=a，
所以 SΔAB′C= (a)=a，
因此 ・a・h=VB-AB′C= VB′-ABC =・a・a=a，
故h=a 即B到面AB′C的距离为a.
(师生共同评判)
师:我们让生19说说解法二的思路.
生19:我注意到三棱锥B?AB′C与三棱锥B′?ABC是同一个三棱锥.
所以 ・SΔAB-C・h=VB-AB′C=VB-ABC，而VB′-ABC易求，SΔAB′C也易求，这样h
即可求出.
师:非常好.生19的方法一是常规方法，而方法二则巧用了三棱锥的体积，使问题的求解变
得十分简捷.这种方法称作顶点转换法，有时也称作等积转换法.事实上三棱锥(即四面体)的
每一个顶点都可作为棱锥的顶点，和它相对的面都可作为相应的底面，这是三棱锥(四面体)
特有的性质.在一定的条件下，它为我们求解顶点到底面的距离提供了捷径，应当引起我们
的注意.
今天这节课我们主要学习了锥体的体积公式，下面请同学们就知识和思维能力两个方面作一
下小结.(请学生自行小结，师生共同补充完善)
1.知识方面:通过本节课学习，我们利用割补法获得了三棱锥的体积公式，进而获得了一般
锥体的体积公式，并初步体会了其应用；
2.思维能力方面:又一次体会了联想、类比、猜测、证明等合情推理及逻辑推理的方法在探
索新知识方面的重要作用.
作业:略.
课堂教学设计说明
1.关于教学目标的制定
在课堂教学中实施和推进素质教育，正愈来愈被广大教师所重视.由于学生的素质是多方面
的，这就决定了课堂教学的目标应该是多元化的.
(1)锥体的体积是多面体和旋转体这一章的重点内容之一，在体积问题中有着重要的地位，
将锥体的体积公式及其初步应用作为本节课的教学目标之一是完全合适的.
(2)学生思维方法的好与差，推理能力的强与弱，在一定程度上反映了学生素质的高与低.
因此，如何通过课堂教学，教学生学习合情推理的方法，培养学生逻辑推理能力，是我们制
定教学目标时必须认真思考的.
(3)未来社会不仅要求人们具有丰富的文化科学知识，而且还需要人们具有顽强的毅力及创
新的意识.教学目标3正是据此而制定的.
2.关于教学重点和难点的确定
本节课的核心内容是锥体的体积，而锥体体积公式的探求需要教师逐步唤醒学生割补思想的
记忆，努力使学生自行发现知识，掌握知识，发展学生的创造性思维，这对教师和学生都是
较高的高求.因而锥体的体积公式及其探求既是教学的重点，又是教学的难点.
3.关于教学过程的设计
本节课按如下五个方面展开:
(1)复习三个问题――①锥体平行于底面的截面的性质；②祖■原理；③柱体的体积公式及
其探求思路；
(2)等底面积等高的两个锥体的体积之间的关系；
(3)三棱锥的体积公式的探求；
(4)一般锥体的体积公式，圆锥的体积公式；
(5)锥体体积公式的简单应用.
有目的地做好旧知识的复习，为顺利地进行新课的讲授奠定了基础.(1)中的三个复习题主
要是为推导“等底面积等高的两个锥体的体积相等”这一定理而准备的.提问时应注意必要
的顺利.
这里，祖■原理在问题③的回答中要应用，因而放在③前面提问.而由问题③的“探求思路
”的回答中，利用祖■原理获得了“等底面积等高的柱体和长方体等体积”的结论，很自然
地让人产生“等底面积等高的锥体体积之间有何关系”的联想.这样，旧课的复习很自然地
过渡到了新课的讲授.因此，把问题③放在最后复习比把问题①放在最后复习要好得多.
“等底面积等高的锥体的体积相等”这一结论是推导三棱锥体积公式的重要工具.由复习题
③中“探求思路”的回忆，引导学生先猜后证，让学生自己发现知识，自行“制造”推导三
棱锥体积公式的“工具”，这是发挥学生主体作用的重要体现.
三棱锥体积公式的探求是本节课的核心内容，如果像教材中那样，直接将三棱锥补成一个三
棱柱，然后将其分割成三个三棱锥，再求体积，那么，虽然教师备课可以少用许多时间，然
而，学生对“怎样想到利用割补法”，“为什么要先补后割”往往疑惑不解.这里，在(3)
中插入两个几何图形面积公式的探求思路的回忆，旨在唤醒学生割补思想的记忆，启发学生
的思维.通过联想类比，学生感悟探求三棱锥体积也用割补法已水到渠成.尔后，围绕“先
割后补”还是“先补后割”的问题，引导学生自己动手一试，相互讨论，比较优劣，从而肯
定“先补后割”，并对“如何补，怎样割”，鼓励学生自己操作.最后，让学生自己推导公
式，这是对学习主体的尊重，这样做旨在为学生扫清这一知识形成过程中的思维障碍，使整
个思维过程和知识形成过程构成一个完美的统一体.显然，这种教学氛围的营造，使学生在
旧知识的温故中，发现了打开新知识宝库大门的钥匙，在探索知识奥秘的征途上，创造性的
迈开了自己坚实的一步.学生表现出了极强的思维积极性和探索毅力，创新意识，创造能力
和创造精神得到了培养.
由三棱锥体积公式的探求到一般锥体体积公式的获得，再到圆锥体积公式的表达，这是特殊
―一般―特殊的思维过程.经常有意识的进行这样的训练，学生的思维方法、思维能力必将
得到极大的提高.
§4.3(1) 对数的概念
【教学目标】
⒈ 理解对数的概念，明确底数、真数、对数的取值范围；
⒉ 理解对数式与指数式中对应量的关系，掌握对数式与指数式的互化；
⒊ 理解常用对数与自然对数的概念；
⒋ 初步掌握几个基本的对数恒等式；
⒌ 通过对计算器的利用，逐步实现计算器与数学的整合．
【教学重、难点】
对数的概念．
【教学过程】
一、引入：(教科书P114页)
已知底数和幂的值，求指数，引出对数问题．
二、定义：
一般地，如果
(
)的
次幂等于
，就是
，那么数叫做以为底的对数，记作
．
其中，叫做对数的底数，叫做真数．
例如：
，读作：以3为底9的对数为2 ．
概念分析：研究对数式
中各字母的取值范围：
： ； ： 
； ：
．
三、常用对数：以10为底的对数叫做常用对数；
的常用对数
简记作 
．
自然对数：以无理数
为底的对数叫做自然对数．
的自然对数
简记作 
．
四、利用定义证明对数恒等式：
五、课堂练习：
1. 将下列指数式写成对数式：
2. 将下列对数式写成指数式：
3.
求下列各式中的
：
4. 利用计算器计算下列各数的值（精确到0.001）
☆ 猜想真数为何值时，对数为正数或负数．
・经计算发现：
当
时，
；
当
时，
．
☆ 试用指数函数的性质验证上述的猜想．
・对于函数
，当
时，
；
当
时，
， 其中
六、课堂小结：对数的概念．
七、布置作业：教科书P116：1~5．
