-
北师大初中九年级数学下册图形面积的最大值1教案
如图所示，要用长20m的铁栏杆，围成一个一面靠墙的长方形花圃，怎么围才能使围成的花圃的面积最大？如果花圃垂直于墙的一边长为xm，花圃的面积为ym2，那么y＝x(20－2x)．试问：x为何值时，才能使y的值最大？二、合作探究探究点一：二次函数y＝ax2＋bx＋c的最值已知二次函数y＝ax2＋4x＋a－1的最小值为2，则a的值为()A．3 B．－1 C．4 D．4或－1解析：∵二次函数y＝ax2＋4x＋a－1有最小值2，∴a＞0，y最小值＝4ac－b24a＝4a（a－1）－424a＝2，整理，得a2－3a－4＝0，解得a＝－1或4.∵a＞0，∴a＝4.故选C.方法总结：求二次函数的最大(小)值有三种方法，第一种是由图象直接得出，第二种是配方法，第三种是公式法．变式训练：见《学练优》本课时练习“课堂达标训练” 第1题探究点二：利用二次函数求图形面积的最大值【类型一】 利用二次函数求矩形面积的最大值
北师大初中九年级数学下册圆内接正多边形教案
解析：正多边形的边心距、半径、边长的一半正好构成直角三角形，根据勾股定理就可以求解．解：(1)设正三角形ABC的中心为O，BC切⊙O于点D，连接OB、OD，则OD⊥BC，BD＝DC＝a.则S圆环＝π·OB2－π·OD2＝πOB2－OD2＝π·BD2＝πa2；(2)只需测出弦BC(或AC，AB)的长；(3)结果一样，即S圆环＝πa2；(4)S圆环＝πa2.方法总结：正多边形的计算，一般是过中心作边的垂线，连接半径，把内切圆半径、外接圆半径、边心距，中心角之间的计算转化为解直角三角形．变式训练：见《学练优》本课时练习“课后巩固提升”第4题【类型四】 圆内接正多边形的实际运用如图①，有一个宝塔，它的地基边缘是周长为26m的正五边形ABCDE(如图②)，点O为中心(下列各题结果精确到0.1m)．(1)求地基的中心到边缘的距离；(2)已知塔的墙体宽为1m，现要在塔的底层中心建一圆形底座的塑像，并且留出最窄处为1.6m的观光通道，问塑像底座的半径最大是多少？
北师大初中九年级数学下册圆周角和圆心角的关系教案
解析：点E是BC︵的中点，根据圆周角定理的推论可得∠BAE＝∠CBE，可证得△BDE∽△ABE，然后由相似三角形的对应边成比例得结论．证明：∵点E是BC︵的中点，即BE︵＝CE︵，∴∠BAE＝∠CBE.∵∠E＝∠E(公共角)，∴△BDE∽△ABE，∴BE∶AE＝DE∶BE，∴BE2＝AE·DE.方法总结：圆周角定理的推论是和角有关系的定理，所以在圆中，解决相似三角形的问题常常考虑此定理．三、板书设计圆周角和圆心角的关系1．圆周角的概念2．圆周角定理3．圆周角定理的推论本节课的重点是圆周角与圆心角的关系，难点是应用所学知识灵活解题．在本节课的教学中，学生对圆周角的概念和“同弧所对的圆周角相等”这一性质较容易掌握，理解起来问题也不大，而对圆周角与圆心角的关系理解起来则相对困难，因此在教学过程中要着重引导学生对这一知识的探索与理解．还有些学生在应用知识解决问题的过程中往往会忽略同弧的问题，在教学过程中要对此予以足够的强调，借助多媒体加以突出.
北师大初中九年级数学下册直线和圆的位置关系及切线的性质教案
解析：(1)由切线的性质得AB⊥BF，因为CD⊥AB，所以CD∥BF，由平行线的性质得∠ADC＝∠F，由圆周角定理的推论得∠ABC＝∠ADC，于是证得∠ABC＝∠F；(2)连接BD.由直径所对的圆周角是直角得∠ADB＝90°，因为∠ABF＝90°，然后运用解直角三角形解答．(1)证明：∵BF为⊙O的切线，∴AB⊥BF.∵CD⊥AB，∴∠ABF＝∠AHD＝90°，∴CD∥BF.∴∠ADC＝∠F.又∵∠ABC＝∠ADC，∴∠ABC＝∠F；(2)解：连接BD，∵AB为⊙O的直径，∴∠ADB＝90°，∴∠A＋∠ABD＝90°.由(1)可知∠ABF＝90°，∴∠ABD＋∠DBF＝90°，∴∠A＝∠DBF.又∵∠A＝∠C，∴∠C＝∠DBF.在Rt△DBF中，sin∠DBF＝sinC＝35，DF＝6，∴BF＝10，∴BD＝8.在Rt△ABD中，sinA＝sinC＝35，BD＝8，∴AB＝403.∴⊙O的半径为203.方法总结：运用切线的性质来进行计算或论证，常通过作辅助线连接圆心和切点，利用垂直构造直角三角形解决有关问题．
中班语言课件教案：耳朵上的绿星星
活动准备：1、制作课件《耳朵上的绿星星》、故事录音带；2、教具：小草、玫瑰花、萤火虫、星星头饰；小松鼠指偶等；3、画有小松鼠图像的画纸（与幼儿人数相等）、幼儿画笔若干。活动过程：一、提出疑问，导入课题孩子们，你们你！小朋友们好！（小松鼠）哦，是小松鼠来了，咦，小松鼠你的耳朵上怎么还有星星呀？星星不是在天上吗？这是怎么回事？小松鼠：听了下面的故事，你们就知道了！请听故事《耳朵上的绿星星》！二、教师有感情的讲述第一遍故事。孩子们，你们说这个故事名字叫什么？（〈耳朵上的绿星星〉）师：小松鼠，我们的孩子说得对吗？小松鼠：对！师：那么，萤火虫为什么跑到你的耳朵上呢？小松鼠：要回答这个问题，先请你们看看我带来的图片吧！师：哟，小松鼠还给我们带了好看的图片，让我们快来看吧。三、播放课件，请小朋友欣赏，教师讲述第二遍故事。1、播放第一部分a、小松鼠上台表演节目，他想怎样来打扮自己b、小松鼠打扮了吗？（没有）为什么c、这件事情让谁看到了？（萤火虫）萤火虫怎么说的?它为什么说小松鼠真好？d、小松鼠没有戴用草编成的帽子、也没有戴用花编成的项链，那他是怎样去参加音乐会呢？2、播放第二部分a、晚上，小松鼠是怎样参加音乐会的？b、是呀！小松鼠一点也没打扮，可是幕布一拉开，台下的观众都惊呆了，他们看到了什么？
新人教版高中英语必修1Unit 1 Teenage Life-Reading and Thinking教案
【教材分析】The topic of this unit is about teenage life, which belongs to the theme context of “humans and oneself”.As teenagers who shoulder the responsibility of “Chinese great dream”, they must fully know themselves, including their strengths, weaknesses and challenges etc. They are supposed to improve themselves continuously and readily study their subjects, and thus foster their strategies and confidence in lifelong studies.This period is entitled the freshmen challenges, which mainly concerns some big challenges for new students in Senior high school. In this period, a teacher should lead students to find out what their challenges are and guide them to figure out how to crack the challenges and better themselves. More importantly, a teacher should instruct students to absorb new language points and appreciate the language. Besides, a teacher must instruct students to acquire some skills concerning reading efficiently and inspire them to talk more about their new school life, especially their new problems and solutions both at school and in life.【教学目标与核心素养】1. Enable students to acquire the basic usage of the new words and expressions concerning the freshmen challenges and learn to use them flexibly.2. Enable students to have a good understanding of the freshmen challenges in the new senior high school which is quite different from junior middle school.3. Develop students’ sense of cooperative learning and individual thinking capability. 4. Develop students’ different learning skills to solve different reading comprehensive problems.
新人教版高中英语必修1Unit 2 Travelling Around-Reading and Thinking教案
Good expressions that students can choose to use: help the travelers choose which tour to take1. In my opinion, you could/might choose…, because you prefer to…2. …could be a perfect choice for you, for…3. As far as I am concerned, you would enjoy…, for…4. …would probably suit you, because you enjoy/love/hate doing…Step 5 Passage ConsolidationLanguage appreciation:1. You can then spend three days exploring the rainforest with a local guide and enjoying the plants and animals unique to the rainforest. 在接下来的三天里，您可以在当地导游的陪同下，深入雨林进行探索，欣赏雨林特有的动植物。本句主体结构为spend some time doing sth. 2. Inca builders cut stones to exact sizes so that nothing was needed to hold walls together other than the perfect fit of the stones. 印加的建筑工人将石头切割成精确的尺寸，仅仅凭着石头间的完美契合，即可稳固墙体。本句为so that引导的结果状语从句。nothing与the perfect fit为并列成分; other than在句中意为“除了”。Step 6 HomeworkSuppose you will travel to Peru, write a short essay about your three-day tour plan.
新人教版高中英语必修1Unit 3 Sports and Fitness-Reading and Thinking教案
2. Sort out detailed information about Michael Jordan.（1） Understand the transitional sentence.Q: Which part is about Michael Jordan as a master? Which part is about the example he set?（2） Have the Ss Focus on why Michael Jordan is a master and what good examples Michael Jordan set when they’re reading. And think about these questions as below:Q1: How does the author describe his impressive skills?Q2: How do you understand “time seemed to stand still”?Q3: What does “graceful” mean?Q4. Which sentence do you think best describes his mental strength?Q5. Which words is important in the sentence in describing his mental strength? Why?Q6: How do you understand “unique”?Q7: What can we learn from Michael Jordan?Step 5 Discussing and recommendingRecommend their own living legends of sports.Work in groups to choose your own living legend of sports and give the reasons of your choice. Step 6 HomeworkReview the stories of Lang Ping and Michael Jordan, and try to retell them.
新人教版高中英语必修1Unit 4 Natural Disasters-Discovering Useful Structures教案
【教材分析】This teaching period mainly deals with the grammar: the restrictive relative clauses.This period carries considerable significance to the cultivation of students’ writing competence and lays a solid foundation for the basic appreciation of language beauty. The teacher is expected to enable students to master this period thoroughly and consolidate the knowledge by doing some exercise of good quality.【教学目标与核心素养】1. Get students to have a good understanding of the basic usages of the restrictive relative clauses.2. Enable students to use the restrictive relative clauses flexibly.3. Develop students’ speaking and cooperating abilities.4. Strengthen students’ great interest in grammar learning.【教学重难点】How to enable students to have a good understanding of the restrictive relative clauses, especially the uses of the relative words such as which, that, who, whom.【教学过程】Step1: 语法知识呈现定语从句（一）—关系代词的用法在复合句中, 修饰名词或代词的从句叫定语从句。定语从句通常由关系代词或关系副词引导，说明事物的具体信息，从句位于被修饰词之后。被定语从句修饰的词叫先行词，引导定语从句的词叫关系词，关系词指代先行词，并在定语从句中充当成分。关系词有两种：关系代词who, whom ,whose, that, which, as和关系副词when, where, why。
新人教版高中英语必修1Unit 4 Natural Disasters-Reading & Thinking教案
5. Read to get detailed information about Paragraph 5.Q1. What shows the revival of Tangshan?Q2. How can Tangshan revive itself and get up on its feet again?Q3. In times of disasters, how can we go through it?T: In times of disasters, we should unify, show the wisdom and stay positive.Step 4 Activity 4 Highlighting the theme and reflecting1. Make a summary of the text.2. Further understand the titleQ: After our learning, why do you think the earth didn’t sleep on that night?T: An earthquake happened. The people in the earthquake suffered a lot, and the people outside Tangshan were concerned about the people there a lot.3. Reflect through discussion on what can be learnt after reading.T: Disasters are powerful. Unpreparedness can be deadly. Life is weak, but if people work together to help each other, disasters can be defeated.There is no love from disaster, but we have love in the human heart.Step 5 Assignment How does the writer convey that the earthquake was deadly, and that people were helpless during the earthquake? Try to find some attractive and impressive expressions and note them down.
新人教版高中英语必修1Unit 5 Languages Around the World-Reading for Writing教案
Step 3: Read to sum upRead it again and sum up the problems of the three students, and then write down the advice that was given from others.Step 4: Work in pairs. List your learning problems in English and brainstorm some useful advice.Useful expressions ? I don't know how to…... Is a big difficulty for me. I cannot ...? You might try …. It's very important to…? I have no idea how/what .My biggest problem is .... ? I (also) have trouble with. My advice is …. This worked for me.? l cannot understand the teachers’ English in class.Step 5 Homework：为提高我校学生的英语口语水平，我们将举办英语演讲比赛(English- speaking contest)，请你根据下面的信息，以学生会(the Students‘ Union)的名义写一份海报，欢迎全校同学参加，届时特邀本校美籍教师史密斯先生颁奖。? 报名时间 9月30日以前(报名:signup)? 报名地点 学生会办公室? 比赛时间 10月9日晚7:00~9:00? 比赛地点 学校大会议室? 奖励 前8名
新人教版高中英语必修2Unit 1 Cultural Heritage-Discovering Useful Structure教案二
This theme of the part is “ Describe people or things in greater detail”. Students have learned the grammar(restrictive relative clauses) in Book 1, and further review and consolidate its structure “prep+relative pronouns(which/whom)” and the relative adverbs(when, where and why), besides students should understand its form, meaning and functions. In this section, students should be able to express the grammar correctly in daily communication and in the writing. 1. Review the basic usages of relative pronouns and adverbs of attributive clauses . 2. Learn to use some special cases about restrictive relative clauses.3. Learn to write sentences with restrictive relative clauses flexibly according to the context.1. Review the basic usages of relative pronouns and adverbs of attributive clauses .2. Learn to use some special cases about restrictive relative clauses.3. Learn tow rite sentences with restrictive relative clauses flexibly according to the context.Step 1. Observe the following sentences, and mark the relative pronouns and the adverbs. 1. After listening to the scientists who had studied the problems, and citizens who lived near the dam, the government turned to the United Nations for help.2. Temples and other cultural sites were taken down piece by piece, and then moved and put back together again in a place where they were safe from the water.Step 2 PracticePlease complete these sentences with relative pronouns and relative adverbs and answer the following questions.Questions: 1. What is the head noun ?2. What relative words should be used ?3. What elements do they act in these sentences ?
新人教版高中英语必修2Unit 2 Wildlife Protection-Reading for Writing教案二
This lesson aims at making a poster about protecting wildlife after reading some posters. During reading students are guided to understand the content and try to summarize the posters with one sentence. Then students are guided to try to make a poster about protecting wildlife.1. Read the two posters and try to understand the summary sentences.2. Look at the two posters and try to understand what emotions they express.3. Try to summarize the features of posters4. Try to make a poster about wildlife.1. Look at the two posters and try to understand what emotions they express.2. Try to summarize the features of posters3. Try to make a poster about wildlife.Step 1 Lead inLook at the the posters on the textbook and ask:Which emotions do the posters communicate ?Step 2 Read the poster and answer the questions.1. What do you think of the animals in the poster on the left ?I think it is frightening and ugly.2. Why do we should protect the ugly animals ?All species--the good, the bad, and the ugly-- should be treated equally.The world needs all kinds--without variety, our planet cannot survive.3. Why are billions of trees being cut down every year ?To make paper for humans.4. What result will be lead to after the trees are cut down ?A lost of animal homes are being destroyed./The habitat of wildlife is being destroyed.Step 3 Find the feature of posters1. What does each poster use to stir up emotions ?On the left, it makes us a little frightened and it looks a little ugly, but it can activate our curiosity--What is it? And What is wrong with it?On the right, it makes us feel a little sad and want to protect them.
新人教版高中英语必修2Unit 1 Cultural Heritage-Reading and Thinking教案一
The theme of the reading and thinking is about “Understanding how a problem was solved”.The Listening & Speaking & Talking is about international co-work to protect the Mount Tai, in which the students from seven countries came up with many solutions even create the Mount Tai App. This section aims at showing how to solve a difficult and even tough problem about protecting the cultural heritage by the international co-work. So in this section, cultivating students’ international awareness is very clear and important. Concretely, with the economic development, how to balance the protection of cultural relics and social development is a big challenge for human. In the 1950s, the Egyptian government wanted to build the Aswan Dam across the Nile to control floods, produce electricity and water farms. But the proposal led to protests because it would destroy a lot of cultural relics. The Egyptian had no choice but ask the UN for help. Therefore, a international cooperation about how to protect the cultural relics began, which involved the time length about 20 years and a large amount of fund. Then, the problems was solved. 1. Read quickly to get the main idea and the structure of the article; read careful to get detailed information.2. Learn to use the reading strategy---making a timeline3. Learn how to solve a tough problem by asking for help and cooperation4. Have the international awareness and understand the great strength of international cooperation.1. Read quickly to get the main idea and the structure of the article; read careful to get detailed information.2. Learn to use the reading strategy---making a timeline.3. Learn how to solve a tough problem by asking for help and cooperation.
新人教版高中英语必修2Unit 2 Wildlife Protection-Reading and Thinking教案一
The listening and speaking part aims at how to protect and help endangered animals by listening, speaking and talking about the facts and reasons. This lesson analyzes the decreasing clause of Tibetan antelope population and the measures of protecting Tibetan antelopes. So students can be guided to learn to analyse the title and use different reading skills or strategies, like scanning, skimming and careful reading.1. Read quickly to get the main ideas and the purpose of going to Tibetan; read carefully to understand what the author see and think.2. Understand the sentences of the present continuous passive voice such as “Much is being done to protect wildlife.” and the inverted sentence “Only when we learn to exist in harmony with nature can we stop being a threat to wildlife and to our planet.”3. Enhance the awareness of protecting wildlife.4. Cultivate the reading methods according to different materials.1. Read quickly to get the main ideas and the purpose of going to Tibetan; read carefully to understand what the author see and think.2. Understand the sentences of the present continuous passive voice such as “Much is being done to protect wildlife.” and the inverted sentence “Only when we learn to exist in harmony with nature can we stop being a threat to wildlife and to our planet.”3. Cultivate the reading methods according to different materials.Step 1 Leading-inWatch a video about elephants and whales and then ask:Why are they endangered ? They are killed/hunted
新人教版高中英语必修2Unit 2 Wildlife Protection-Reading and Thinking教案二
The theme of this unit is human and nature, focusing on the theme of wildlife protection. Nature is a complex ecosystem, in which there are delicate balance between animals and plants. Because of the role of the food chain, the extinction of one species will produce influence, causing a series of chain reaction. Large scale extinction of species will have a serious and even irreversible impact on the ecosystem, resulting in immeasurable losses. Therefore, it is of great significance to protect wild species. To protect wild species is to protect human beings themselves. The motto of this unit is "when the buying stops, the killing can too,” which is a public service advertising slogan to protect wildlife. It tells people that every rhinoceros horn, every fur, every bowl of shark fin soup, every Ivory product, and every tiger bone product, etc. consumed by human beings, are innocent wild animals slaughtered behind them. The mission of wild aid is to ban illegal trade in endangered wildlife and mitigate climate change. It aims to educate the public to reduce the consumption demand for endangered wildlife products through public publicity and improve the awareness of environmental protection.1. Improve the awareness of wildlife protection by acquiring the knowledge of wildlife protection.2. Focus on environmental protection and protection of all lives.3. Analysis of the living environment of wild animals with appropriate thinking mode.4. Skillfully use the vocabulary and grammar knowledge of this unit to cultivate self-study ability according to the unit content5. Develop cooperative learning ability through discussion and other ways1. Enable the Ss to talk about the current situation of wild animals.2. Guide the Ss to summarize the main idea of each paragraph as well as the main idea of the text.
新人教版高中英语必修2Unit 3 The Internet-Discovering Useful Structure教案一
This unit is about the Internet, which has a great influence to our humans and our lives. During the Listening & Speaking & Talking and Reading and Thinking section, the influence in examples has been shown. Thus, use the Present Perfect Tense is appropriate. However, in order to show the justice or weaken the doer of the behavior/action, it’s better to use the Present Perfect Passive Voice than the Present Perfect Tense. Besides, having learned to use the Present Perfect Passive Voice, students can beautify their language in their writing. 1. Learn the structure of the Present Perfect Passive Voice and its functions. 2. Learn to change the sentences with the Present Perfect Passive Voice into the sentences with the Present Perfect Passive Voice. 3. Learn to write sentences with the Present Perfect Passive Voice flexibly according to the context. 1. Learn the structure of the Present Perfect Passive Voice and its functions. 2. Learn to change the sentences with the Present Perfect Passive Voice into the sentences with the Present Perfect Passive Voice. 3. Learn to write sentences with the Present Perfect Passive Voice flexibly according to the context. Step 1 Observe the following sentences, then change the sentences into passive voice.He has been selected to take part in the sports meeting．(肯定句)他已被挑选出来参加运动会。The ink has not been removed from his overcoat．(否定句)墨迹还没有从他外套上去掉。
新人教版高中英语必修2Unit 3 The Internet-Reading and Thinking教案二
Q5：What's Jan's next goal?Her next goal is to start a charity website to raise money for children in poor countries.Q6：What can we learn from her experiences?We learn that when we go through tough times, we can find help and support from other people online. We learn that we can feel less lonelyStep 5: While reading---rethinkingQ1: What is Jan’s attitude to the Internet ?Thankful/Grateful, because it has changed her and her life.Q2: What writing skills is used in the article ?Examples(Jan’s example, the 59-year-old man’s and the 61-year-old woman’s example)Q3: Can you get the main idea of the article ?The Internet has changed Jan’s life/Jan’s life has been changed by the Internet.Step 6 Post reading---Retell the storyMuch has been written about the wonders of the World Wide Web. There are countless articles (1)telling(tell) us how the Internet has made our lives more convenient. But the Internet has done a lot (2)more(much) for people than simply make life more convenient. People’s lives (3) have been changed(change) by online communities and social networks so far. Take Jan for example, who developed a serious illness that made her (4)stuck(stick) at home with only her computer to keep (5)her(she) company. She joined an online group (6)where she could share problems, support and advice with others. She considered the ability to remove the distance between people as one of the greatest (7)benefits(benefit). She was so inspired (8)that she started an IT club in which many people have been helped. She has started to learn more about how to use the Internet to make society better. Her next goal is to start a charity website to raise money (9)for children in poor countries. Jan’s life has been (10)greatly(great) improved by the Internet.
新人教版高中英语必修2Unit 4 History and Traditions-Listening＆Speaking＆Talking教案一
This unit is about history and traditions. From the opening page, we can know that this unit will introduce the history and traditions around the world. As Marcus Garvey says “A people without the knowledge of their past history, origin and culture is like a tree without roots”, it is important for students to realize the importance and value of knowing the history and traditions and their further meanings. And this part ( listening and speaking ) is divided into two parts: Part A---share views on historic sites, Part B ---talk about a visit to a historic tourist destination. By talking with a foreigner, the speakers introduce the historic attractions and their cultures. Part A is that William, a British student, who was going to visit the Confucius Temple and a Chinese student, Xiao Kong, who was going to the Confucius Temple to meet with the members of the research group, went together and exchanged their views on the Confucius Temple, Confucius, Confucius' descendants and Confucius' educational thoughts. Part B is a conversation between Xiao Yan, a youth hostel receptionist and Paul, a backpacker about the feelings and experience after visiting the Chinese famous tourist attraction Pingyao.1. Guide students to understand the content of listening texts in terms of the whole and key details; 2. Cultivate students' ability to guess the meaning of words in listening; discuss with their peers how to talk about historic spots and great person.3. Instruct students to use functional sentences of showing one’s excitement, surprise and disappointment.1. Guide students to understand the content of listening texts in terms of the whole and key details; 2. Cultivate students' ability to discuss with their peers the related topics.3. Enable students to use the functional items of showing one’s excitement, surprise and disappointment.
新人教版高中英语必修2Unit 4 History and Traditions-Discovering Useful Structure教案二
This teaching period mainly deals with grammar: The past participle is used as attributive and objective complement.1. Guide students to review the basic usages of the past participle used as attributive and objective complement.2. Lead students to learn to use some special cases concerning the past participle used as attributive and objective complement flexibly.3. Strengthen students’ great interest in grammar learning.1. Help students to appreciate the function of the past participle used as attributive and objective complement.2. Instruct students to write essays using the past participle used as attributive and objective complement.Step1:温故而知新。Analyze the underlined phrases and then sum up the common usages of the past participles.1．(教材P41)They had castles built(build) all around England, and made changes to the legal system．2．(教材P42)They use the same flag, known(know) as the Union Jack，．．．3．(教材P42)Judy and I had our car parked(park) in an underground car park near Trafalgar Square, where we could get our car battery charged(charge)．Common points: f the past participle used as attributive and objective complement.Step 2:过去分词作定语时的意义1．及物动词的过去分词作定语，在语态上表示被动；在时间上，常表示动作已经发生或完成，有时也不表示时间性。Our teacher watched us doing the experiment and gave us a satisfied smile at last．我们的老师看着我们做实验，最后给了我们一个满意的微笑。The plan put forward at the meeting will be carried out soon．会上提出的计划将很快被执行。2．不及物动词的过去分词作定语，它不表示被动意义，只强调动作完成。Many little kids like gathering fallen leaves in the yard．