-
新人教版高中英语必修2Unit 1 Cultural Heritage-Listening＆Speaking＆Talking教案
Listening and Speaking introduces the topic of “Take part in a youth project”. The listening text is an interview about an international youth cultural heritage protection project. More than 20 high school students from seven countries participated in the project. The reporter interviewed two participants Stephanie and Liu Bin. By listening to the text, students can understand the significance of cultural heritage protection, and teenagers can use their knowledge, combine their own interests and advantages, etc. to participate in the action of cultural heritage protection. Listening and Talking introduces the theme of "Talk about history and culture". The listening text is a dialogue between two tourists and tour guides when they visit the Kremlin, red square and surrounding buildings. The dialogue focuses on the functional items of "starting a conversation", which is used to politely and appropriately attract the attention of the others, so as to smoothly start a conversation or start a new topic. The purpose of this section is to guide students to understand the history and current situation of Chinese and foreign cultural heritage in their own tourism experiences or from other people's tourism experiences, explore the historical and cultural values, and be able to express accurately and appropriately in oral communication.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 participate in cultural heritage protection activities.3. Instruct students to use functional sentences of the dialogue such as “I beg your pardon, but…” “Forgive me for asking, but…" and so on to start the conversation more politely and appropriately.
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 For Writing教案
This report is short, concise and has typical news content and language features. The title uses the verb phrases, embodying the characteristics of being concise and general. The introduction is the first two sentences in the first paragraph, describing the general situation of the cultural heritage protection project, including time, place, characters, events and other news elements, so that readers can see the main points of the news report at a glance. The main body is the second and third paragraphs, which report the important historical and cultural value of Mogao Grottoes and the production of Mogao Grottoes Material digital photos, which are of great significance to the inheritance of historical culture and the promotion of international cultural understanding, exchange and cooperation. Direct citation is used in the report, as well as background introduction and other news writing techniques.1. Get students to have a good understanding of some features about a news report by reading the text.2. Instruct students to write a summary about a news report properly using some newly acquired writing skills in this period.3. Develop students’ writing and cooperating abilities.4. Strengthen students’ great interest in writing discourses.1. Stimulate students to have a good understanding of how to a summary about a news report 2. Cultivate students to write a news report properly and concisely.Step 1: Lead in Do you think it is necessary for us to circulate our cultural heritage to the world? Why or why not?Do we need to learn more about other countries’ cultural heritage? Why or why not?Step 2: Read to discover details concerning the main body of the news report.
新人教版高中英语必修2Unit 2 Wildlife Protection-Discovering Useful Structure教案一
The activity topic of this section is "report an ongoing event", and the structure is the passive voice of present continuous tense. Rare wild animals are suffering from large-scale poaching, and species are on the brink of danger. Rescue operations are underway. "Being" and "suffering" are the meanings of the present progressive passive voice.The usage of present progressive passive voice is of great importance in writing a good discourse and appreciating some difficult language items, so it is vital to master it and use it flexibly in a context.1. Motivate Ss to deepen the understanding of the usage of present progressive passive voice in a fixed context.2. Enable Ss to master the usage of present progressive passive voice and use it flexibly in a context.3. Lead Ss to construct sentences or appreciate sentences used master it and use it flexibly in a context.1. Help students to appreciate the function of the usage of present progressive passive voice in a sentence2. Instruct students to write essays using the proper usage of present progressive passive voice.Look at the picture and tell me what are workers doing? What is the house being done?
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 2 Wildlife Protection-Reading For Writing教案一
1. 标题首先根据海报的特点、格式写明标题。海报中往往把内容作为大标题。例如: Save the earth, Save the birds。2. 正文部分不同的海报其正文部分的侧重点不同。对于介绍性的海报, 首先要引出话题, 其次列出原因, 最后是总结。对于宣传类的海报, 要写明具体内容, 如: 活动内容, 地点以及参加活动的注意事项, 主持或举办单位等。1. 图片: 要选择引人注目的图片, 与主题要相关, 色彩明亮。话题句式 1. It is a treasure of our country. 它是我国的国宝。2. Believe it or not, at present only several thousand pandas exist in the world. 信不信由你, 目前世界上仅现存几千只熊猫。 3.It’s because of human activities that tigers are endangered. 正是因为人类的活动, 老虎处于濒危的状态。4. Many wild animals are in danger of dying out. 很多野生动物面临着灭绝的危险。 5. The government has taken effective measures to protect them. 政府已采取有效的措施来保护它们。6. People should raise the awareness of the protection of wild animals. 人们应该提高保护野生动物的意识。 7. It’s amazing that there are merely less than 1, 000 finless porpoises living in China. 非常令人吃惊, 目前中国仅有不足1 000只江豚。
新人教版高中英语必修2Unit 3 The Internet-Listening &Speaking＆Talking教案一
Listening and Speaking introduces the topic of “ask about online habits”. Many middle school students have been surfing the Internet for many years, but what they do with the Internet and how much time they spend every day may not be very clear to themselves, nor to other students. This section allows students to investigate their peers' Internet use, which is conducive to their mutual understanding and understanding of the Internet. It can also help them reflect on their own online behavior, learn from other people's good online habits, and get rid of their bad online behavior.The listening text of this section is an investigation interview. The investigators interview specific groups with the same questions to obtain information, so as to understand their views, practices or attitudes on this issue. There are two specific questions: “how much time do you spend online every day? What do you usually do online?”. The answers of the three respondents provide rich and different information, and achieve the purpose of the investigators. The oral discourse structure of survey interviews generally includes greeting and explaining the purpose of the interview, presenting the interview questions and the respondents' answers. Listening and Talking introduces the theme of “choosing the right application ". Listening text is a conversation between Laura and Xiao Bo. In this part of listening, “oink”； “piggy bank” may cause the students' hearing comprehension limitation. Oink refers to sound word and pig's sound. So, add some oink to my piggy bank is often used to describe "making a little money".1. Guide students to understand the content of listening texts in terms of listening for definitions.2. Cultivate students' ability to define words and understand an investigation interview.
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 3 The Internet-Reading for Writing教案二
8. However, the more polite you are, the less likely it is you will be attacked. 然而, 你越有礼貌, 你被攻击的可能性就越小。 Step 8 Writing---the articleHow to stay safe in the online chat roomToday I thought I’d blog about a question that has been asked many times--- how do you stay safe online and avoid bad experiences in the online chat room ? I’m not an expert, but many years as a blogger have taught me a thing or two.First of all, there’s the golden rule of the Internet: keep out of what makes you uneasy. Don’t post comments or click on anything. Second, protect your privacy. Don’t give out too much private information like your address, phone numbers, the ID numbers, etc. Third, be polite. If you are polite to others on the Internet, you won’t be attacked in normal situation. Finally, don’t believe in others easily and never meet someone you met online alone. It is very dangerous.Have you had any bad experiences online, or do you have some good advice for staying safe? Post your comments below!Step 9 Pair workExchange drafts with a partner. Use this checklist to help your partner revise his/her draft.1. Does the writer tell the reader what he/she know about the topic ?2. Are the tips and suggestions well organised ?3. Has the writer defined the new words ?4. Does the author include examples, comparison, or explanations ?5. Does the writer end by asking readers to leave comments and/or suggestions ?6. Can you find any grammar or spelling mistakes.Step 6 HomeworkPut up your revised draft in the classroom or read it to your class.
新人教版高中英语必修2Unit 3 The Internet-Reading For Writing教案一
⑦identity theft 身份盗窃⑧chat room 聊天室⑨draft your blog post 起草博客帖子⑩post embarrassing photos 张贴尴尬照片 【话题句式】 1. How do you stay safe online and avoid bad experiences on the Internet? 你如何在网上保持安全, 避免在网上的不良经历? 2. I’m not an expert, but many years as a blogger have taught me a thing or two. 我不是专家, 但作为一个博主, 我已经学了好几年了。 3. If you see or read something that makes you feel uncomfortable, leave the site immediately. 如果你看到或读到一些让你觉得不舒服的东西, 立即离开这个网站。4. Don’t give out your address or phone number. 别告诉别人你的地址或电话号码。 5. Identity theft is a common and serious problem. 身份盗窃是一个常见而严重的问题。6. Being online is no excuse for being rude, and you don’t want to become a target for a troll or cyberbully. 上网并不是无礼的借口, 你也不想成为发挑衅帖子的人或网络恶霸的目标。 7. Trolls often use several false names so that they can stay on a site. 发挑衅帖子的人经常使用几个假名, 这样他们就可以留在一个网站上。8. However, the more polite you are, the less likely it is you will be attacked. 然而, 你越有礼貌, 你被攻击的可能性就越小。
新人教版高中英语必修2Unit 4 History and Traditions-Reading and Thinking教案一
Features of languages1．Finally, in the 20th century, the southern part of Ireland broke away from the UK, which resulted in the full name we have today: the United Kingdom of Great Britain and Northern Ireland．该句是一个复合句。该句主句为：the southern part of Ireland broke away from the UK；which resulted in the full name we have today为which引导的定语从句代指前面整句话的内容，we have today为定语从句修饰先行词name。译文：最后，在20世纪，爱尔兰南部脱离英国，这导致了我们今天有的英国的全名：大不列颠及北爱尔兰联合王国。2．Almost everywhere you go in the UK, you will be surrounded by evidence of four different groups of people who took over at different times throughout history．该句是一个复合句。该句主句为：you will be surrounded by evidence of four different groups of people；其中Almost everywhere you go in the UK为让步状语从句； who took over at different times throughout history为定语从句修饰先行词people。译文：几乎无论你走到英国的任何地方，你都会发现历史上有四种不同的人在不同的时期统治过英国。3．The capital city London is a great place to start, as it is an ancient port city that has a history dating all the way back to Roman times．该句是一个复合句。该句主句为：The capital city London is a great place to start; as it is an ancient port city that has a history dating all the way back to Roman times．为原因状语从句；dating all the way back to Roman times为现在分词短语作定语修饰history。
新人教版高中英语必修2Unit 4 History and Traditions-Reading for Writing教案
Step 1 Lead inThere are many interest of places in the UK. What do you know ?The Big Ben the London Tower the Thames RiverStep 2 Before reading---analyze the titleBeautiful Ireland and its traditionWe know that the article mainly tells about the beauty and traditions of Ireland. Step 3 While reading---Task 1Read the text and answer the following questions.Q1: What makes the Irish countryside exciting and inspiring?Its beauty and how it offers something for all the scenes.Q2: What are the best ways to experience some Irish traditions and cultures?By stopping by a village pub and relaxing with a drink and traditional meal while listening to music and watching dancingQ3: What is the meaning of “breathe in the sweet scent of fresh flowers while birds greet the new day with their morning song ?”It means to not just smell but also breathe in the smell of fresh flowers early in the morning as the birds sing their first song of the new day.Q4: What are the best ways to experience Chinese traditions and customs ?By travelling to different places and using all your senses to experience everything and by interacting with local people.Step 4 While reading---Task 2Analyze the descriptive paragraph1. Identify and underline the paragraph’s introductory sentence and the ending sentence.Introductory sentence: Ireland’s beautiful countryside has always had a great influence on its people and traditions.Ending sentence: And if you introduce yourself to a friendly face, you are more than likely to experience local culture and customs first-hand.2. The paragraph talks about different senses in different places. Write the senses and places in the order that they appear.
新人教版高中英语必修2Unit 5 Music-Discovering Useful Structures教案一
Step1:自主探究。1．(教材P52)Born(bear) in the USA on 2 January 1970, Whitacre began studying music at the University of Nevada in 1988．2．(教材P52) Moved(move) by this music, he said, “It was like seeing color for the first time．”3．(教材P56)I was very afraid and I felt so alone and discouraged(discourage)．4．(教材P58)Encouraged(encourage) by this first performance and the positive reaction of the audience, I have continued to play the piano and enjoy it more every day．Step2:语法要点精析。用法1：过去分词作表语1）．过去分词可放在连系动词be, get, feel, remain, seem, look, become等之后作表语，表示主语所处的状态Tom was astonished to see a snake moving across the floor．汤姆很惊讶地看到一条蛇正爬过地板。Finally the baby felt tired of playing with those toys．终于婴儿厌倦了玩那些玩具。注意：1）.过去分词作表语时与被动语态的区别过去分词作表语时，强调主语所处的状态；而动词的被动语态表示主语是动作的承受者，强调动作。The library is now closed．(状态)图书馆现在关闭了。The cup was broken by my little sister yesterday．(动作)昨天我妹妹把杯子打碎了。2）感觉类及物动词的现在分词与过去分词作表语的区别过去分词作表语多表示人自身的感受或事物自身的状态，常译作“感到……的”；现在分词多表示事物具有的特性，常译作“令人……的”。
新人教版高中英语必修2Unit 5 Music-Listening and Speaking教案
This lesson is about music. Students can classify the types of music through the instruments and its sound and can talk about their preferences about music, even join some activities and play a role in them according to their musical talents. On the basis, they are guided to use the languages to express their preferences and some plosive sounds and their rules.1. Classify the music types through the instruments and its sound.2. Listen and understand what the speakers’ preferences are and the reasons; talk about their own preferences and give their own reasons, using these sentences: “What kind of music do you like? And why? “ “Because it makes/gives me energy/peaceful.../touches my heart...”.3. Learn some plosives and the rules.4. Join some activities and play a role in them according to the talents. 1. Listen and understand what the speakers’ preferences are and the reasons;2. talk about their own preferences and give their own reasons, using these sentences: “What kind of music do you like? And why? “ “Because it makes/gives me energy/peaceful.../touches my heart...”.3. Learn some plosives and incomplete plosives and its rules.Step 1 Lead inPoint at the pictures on P50 and ask Q1: What are the people doing in the pictures below?Q2: What kind of music they are?Then play the MP3s one by oneStep 2 ListeningTask 1: A reporter from the school newspaper is interviewing students about music. Listen to the interviews. Draw lines between the words to make complete sentences. Some words will not be used.
新人教版高中英语必修2Unit 5 Music-Reading For Writing教案一
(4)Now we have heard a number of outstanding speeches ... 我们已经聆听了许多精彩的发言……(5)Because we wanted the nations of the world, working together, to deal with ... 因为我们希望全世界各国团结起来去应对……(6)And if we do not act ... 如果我们不采取行动……(7)Now, I share the concerns that have been expressed ... 我也同意对于……表达的担心(8)Let us show the world that by working together we can ... 让我们告诉全世界，通过一起努力我们可以……(9)It is now time for us to ... 是时候我们……(10)And I have always wished that ... 我一直希望……(11)Thank you for letting me share this day with me.感谢你们和我共度这一天。实践演练：假如你是高中生李华，你校将举办一次以“音乐”为主题的演讲比赛，请你按照主题，写下你的演讲稿。注意：词数100左右。First of all, thank you for listening to my speech. My topic is: love music like love yourself.Music is like the air we need to maintain our normal lives around us. You can't imagine how terrible a world without music would be. Movies and TV shows have no music, only dry conversations and scenes; mobile phones only vibrations; streets only noisy crowds; cafes, western restaurants only depressed meals. What a terrible world it is!As a student, I hope we all can enjoy the fun brought by music in our spare time. Instead of just listening to music, we can even make our own music. Let's enjoy the fun of music!Thanks again for your attention!
新人教版高中英语选修1Unit 3 Fascinating Parks教案
2. Explore the significance of the establishment of Sarek National Park.Q1: Which event is the most important one in the park’s history?Ss: The establishment of Sarek national park in 1909 is the most important one.Q2: Is it worth making a place like Sarek a national park? Give your reasons.Ss: Yes. In this way, the place can be kept in its natural state and natural beauties and other rare and valuable resources can be preserved instead of being destroyed by endless exploitation driven by profits.Q3: How does the writer organize his introduction to the history of Sarek?Ss: The writer organizes his introduction in the sequence of time, using time indicators such as “used to”, “around 9,000 years ago”, “soon after”, “following the reindeer”, and “in 1909”.Q4: What is the feature of the language used to introduce the history of the park?Ss: The introduction to the park is to provide facts, using time indicators to organize the events. Sentences starts with “third person” and passive voice is used more often, feeling objective.【设计意图】学生寻找和梳理公园历史上的重要事件，体会人与自然的和谐关系，评鉴介绍性语言的特点。【核心素养提升点】发展自主提取、梳理文本信息能力，训练逻辑思维和高阶思维。Activity 3: Highlighting the secret of the text
四年级下册综合实践活动教学计划及教案
一、教材分析 1、教材内容及所处地位综合实践活动是在新一轮基础教育课程改革中应运而生的新型课程。所谓综合实践活动，主要指以学生的兴趣和直接经验为基础，以与学生学习生活和社会生活密切相关的各类现实性、综合性、实践性问题为内容，以研究性学习为主导学习方式，以培养学生的创新精神、实践能力及体现对知识的综合运用为主要目的一类新型课程。具有以下特点： 1、基于兴趣与直接经验。2、回归生活世界。3、立足实践。4、着眼创新。5、以研究性学习为主导学习方式：（1）以转变学生的学习方式为出发点。（2）强调知识的联系和综合运用。（3）注重过程。（4）强调开放。（5）重视师生互动。四年级下册综合实践活动课程要培养学生对生活、学习的积极态度，使他们具备一定的交往合作能力、观察分析能力、动手操作能力；要让他们初步掌握参与社会实践的方法，信息资料的搜集、分析和处理问题的方法以及研究探索的方法；使学生形成合作、分享、积极进取等良好的个性品质，成为创新生活的小主人。2、单元内容分析本教材包括?方法与指导?和?活动与探究?两部分内容， ?方法与探究? 主要是让学生掌握如何进行采访，通过一系列活动，掌握采访的准备、注意事项、具体实施，及最后的交流总结，培养学生交往能力。 ?活动与探究?包括六个主题，主题一我们身边的标志，通过让学生认识标志，体会含义。学会分类，最后学会制作标志，循序渐进，蕴含了创新、守规、审美等能力的培养；主题二早餐与健康通过谈论，调查、分析讨论培养学生交流总结能力，树立健康生活意识；主题三，有趣的丝网花，通过制作培养学生合作、审美、动手能力；主题四巧手做风筝继续对学生进行培养;主题五植物的扦插与嫁接，与现实生活联系密切，通过活动掌握方法，体验快乐，体验劳动的乐趣；主题六争做小小志愿者，通过了解体验志愿者的活动，丰富阅历，培养学生的服务意识，自身获得提升与发展。教材的重点、难点：重点：学会交流，提升能力；认识各种标志，学会制作；学会健康的生活；通过制作丝网花、风筝、植物的扦插于嫁接，学会制作，提高动手能力，通过体验小小志愿者，提高服务意识。难点：教学中让学生亲身参与、主动实践，在实践中综合运用所学知识解决各种实际问题，提高解决实际问题的能力。学习基础：四年级学生已具备了一定的实践能力，因此要逐步培养学生一些探究问题的方法，提高学生的动手意识，能够从生活和学习中挖掘自己感兴趣的活动主题，能够试着和同学展开小组合作学习，在有效的活动中不断提高学生的动手与创新的潜能。
《说文明话， 做文明人》主题班会教案
2、文明礼貌用语我知道。学生二：“三文明”教育活动已经轰轰烈烈的展开了。在学习三文明教材中，我们有一项特殊的作业——收集文明礼貌用语，现在我们就八仙过海，各显神通，看谁语言美。(开火车）学生发言。学生一：听同学们的发言，我已经感受到了我们的语言的确很美，希望在以后的生活中，我们能经常用优美的语言与人交流。3、读书笔记展览。学生二：“文明”教育活动已经渗透到每个同学的心里，我们班同学写了读书笔记。请按顺序依次参观。4、文明手抄报展览。5、为获奖同学颁发奖状。（自制奖状）学生一：我们学了那么多，最终目的就是让我们“说文明话，行文明举，做文明人”。请欣赏〈文明礼仪歌谣〉
北师大初中九年级数学下册正切与坡度1教案
已知一水坝的横断面是梯形ABCD，下底BC长14m，斜坡AB的坡度为3∶3，另一腰CD与下底的夹角为45°，且长为46m，求它的上底的长(精确到0.1m，参考数据：2≈1.414，3≈1.732)．解析：过点A作AE⊥BC于E，过点D作DF⊥BC于F，根据已知条件求出AE＝DF的值，再根据坡度求出BE，最后根据EF＝BC－BE－FC求出AD.解：过点A作AE⊥BC，过点D作DF⊥BC，垂足分别为E、F.∵CD与BC的夹角为45°，∴∠DCF＝45°，∴∠CDF＝45°.∵CD＝46m，∴DF＝CF＝462＝43(m)，∴AE＝DF＝43m.∵斜坡AB的坡度为3∶3，∴tan∠ABE＝AEBE＝33＝3，∴BE＝4m.∵BC＝14m，∴EF＝BC－BE－CF＝14－4－43＝10－43(m)．∵AD＝EF，∴AD＝10－43≈3.1(m)．所以，它的上底的长约为3.1m.方法总结：考查对坡度的理解及梯形的性质的掌握情况．解决问题的关键是添加辅助线构造直角三角形．
北师大初中九年级数学下册垂径定理教案
方法总结：垂径定理虽是圆的知识，但也不是孤立的，它常和三角形等知识综合来解决问题，我们一定要把知识融会贯通，在解决问题时才能得心应手．变式训练：见《学练优》本课时练习“课后巩固提升”第2题【类型三】 动点问题如图，⊙O的直径为10cm，弦AB＝8cm，P是弦AB上的一个动点，求OP的长度范围．解析：当点P处于弦AB的端点时，OP最长，此时OP为半径的长；当OP⊥AB时，OP最短，利用垂径定理及勾股定理可求得此时OP的长．解：作直径MN⊥弦AB，交AB于点D，由垂径定理，得AD＝DB＝12AB＝4cm.又∵⊙O的直径为10cm，连接OA，∴OA＝5cm.在Rt△AOD中，由勾股定理，得OD＝OA2－AD2＝3cm.∵垂线段最短，半径最长，∴OP的长度范围是3cm≤OP≤5cm.方法总结：解题的关键是明确OP最长、最短时的情况，灵活利用垂径定理求解．容易出错的地方是不能确定最值时的情况．
