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人教版新目標(biāo)初中英語八年級(jí)下冊(cè)It’s a nice day, isn’t it教案2篇
"Hello! Welcome to English class! Introduce yourself. Meet your new classmates." That's what the teacher says. What do you say? "Oh no!" It can be difficult talking to new people. But it can be fun, and you can make friends. How do you do it? Make small talk. Small talk is polite conversation. "Wang Nan is a great pingpang player, isn't she?" "I'd love to meet her, wouldn't you?" "It's been raining a lot, hasn't it?" Tag questions are a form of polite speech. To make small talk successfully, you should know how to make them. You should also know what topics to talk about. Try to learn this unit carefully. The next time you're in English class, you'll find out. Making small talk's easy, isn't it? (“你好！歡迎你！請(qǐng)做一下自我介紹。認(rèn)識(shí)一下你的新同學(xué)?！蓖ǔＴ谡n上老師會(huì)這樣說。你會(huì)說什么呢？“噢，不！”與陌生人談話太困難了。但是這也很有意思，并且你還能交到朋友。你該怎么做呢？閑聊。閑聊指得是禮貌的對(duì)話?！巴蹰且粋€(gè)很棒的乒乓球運(yùn)動(dòng)員，不是嗎？”“我希望自己能認(rèn)識(shí)她，你呢？“今年的雨水很多，不是嗎？”反意疑問句是一種禮貌用語。為了使得談話成功，你應(yīng)該知道怎樣去進(jìn)行閑聊。你還應(yīng)該知道與不同的人該談?wù)撌裁礃拥脑掝}。認(rèn)真的學(xué)習(xí)這個(gè)單元吧，下次在英語課上，你會(huì)發(fā)現(xiàn)與大家展開談話是一件很容易的事情，不信我們來試試。)
人教版新目標(biāo)初中英語八年級(jí)下冊(cè)He said I was hard-working教案2篇
This activity introduces some new vocabulary and provide oral practice using the target language.Task 1 . Ask four students to stand in front of the class, and the teacher asks them the following questions as a reporter.1.What are you going to do when you grow up?2.What are you going to do next week?3.What are going to do after school?The students will give different answers, then ask a good student to report what they said.I am going to e a doctor.What did she say?----------She said she was going to be a doctor.I am going to have a party on Friday night.What did he say?-------He said he was going to have a party on Friday night.I am going to do my homework.What did she say ?------ She said she was going to do her homework.I am going home after school.What did she say?-----She said she was going home after school.Say In this unit we are going to learn to use words like to report what someone said.Task 2. Read the instructions. Then ask a student to read the four questions. And write the words on the Bb. Explain what soap opera is.Task 3. Ask the students to Look at the pictures, point out the TV screens in the picture. Ask one girl to read what Marcia said.What did Marcia say? She said She said she was having a surprise party for Lana on Friday night. Repeat the other pictures in the same way.Activity3. Listen and number the pictures in activity 1a.
人教版新目標(biāo)初中英語八年級(jí)下冊(cè)How long have you been collecting shells教案2篇
Step Ⅱ Show the new words on the screen and teach the new words. Read the new words to students and ask them to repeat.Step Ⅲ 3aThis activity introduces new vocabulary and provides reading practice using the target language.In this activity first look at the four pictures.T: What can you see in the pictures?Ss: Four snow globes.T: Right. There are four snow globes in the pictures. And what are they?Ss: They are a monster, two polar bears, two penguins and a birthday cake.Write these words on the blackboard: snow globe; monster; polar bear; penguin and birthday cake. Read them to the class and ask students to repeat each one. Make sure students understand each word.Use a computer to show the E-mail message on the screen and read the message to students.Get students to read the e-mail on their own, and then draw lines connecting each snow globe and its description.Correct the answers.AnswersA line should connect each snow globe picture with the words that describe it in the letter.Step Ⅳ 3bThis activity provides writing practice using the target language.First review Activity 2a on Page 47.Then ask students to complete the message according to Activity 2a.Some partial sentences are given to students. Write about one person's collection.When students work, walk around the room checking the progress and offering help as needed.When they finish, ask some students to read their messages to the class.
人教版新目標(biāo)初中英語八年級(jí)下冊(cè)What were you doing when the UFO arrived教案2篇
(一).知識(shí)方面: 1.培養(yǎng)學(xué)生能運(yùn)用過去進(jìn)行時(shí)來描述、談?wù)撨^去某個(gè)時(shí)間正在發(fā)生的事情或動(dòng)作的意識(shí)和能力，能就過去某個(gè)時(shí)間正在發(fā)生的動(dòng)作做出正確的描述。 2.培養(yǎng)學(xué)生的想象力和角色扮演的合作能力。 3.培養(yǎng)學(xué)生講述過去發(fā)生的事情經(jīng)過的能力。能正確運(yùn)用一般過去時(shí)來講述故事。 (二).技能方面: 1.本單元的語言目標(biāo)是Talk about past events and tell a story（談?wù)撨^去的時(shí)間和講述一個(gè)故事），圍繞這一目標(biāo)，要涉及句型： What were you doing when the UFO arrived? ----I was sitting in the barber’s chair. The barber was cutting my hair. 因此必須學(xué)習(xí)standing、studying、cleaning、sleeping、cooking、making、eating、cutting、等表示地點(diǎn)的詞，以便為上述句型提供語言材料。2.學(xué)習(xí)過去進(jìn)行時(shí)的有關(guān)知識(shí)。Was/were+現(xiàn)在分詞，是該時(shí)態(tài)的表達(dá)式。 3.在學(xué)習(xí)過程中，要區(qū)分The boy was walking down the street when the UFO landed.和While the boy was walking down the street, the UFO landed.這兩種由when和while引導(dǎo)的狀語從句的句型結(jié)構(gòu)。注意它們的不同。
人教版新目標(biāo)初中英語八年級(jí)下冊(cè)Why don’t you get her a scarf教案
教師帶領(lǐng)學(xué)生復(fù)習(xí)有關(guān)描述寵物的詞匯，采用教師提問學(xué)生回答的方進(jìn)行。如：T：What animals do you think would be good pets？What animals do you think would be bad pets？What do you think are good animals for a six-year-old child？然后學(xué)生進(jìn)行 pairwork 練習(xí)。Task two: 師生互動(dòng)，學(xué)習(xí)探究 1、播放3a部分的錄音，引導(dǎo)學(xué)生一邊聽錄音，一邊跟讀。2、通過聽錄音學(xué)生回答以下問題：Why do you think pot-bellied pigs are popular？What are the advantages and disadvantages of keeping such a pet？教師對(duì)學(xué)生的回答進(jìn)行及時(shí)點(diǎn)評(píng)。3．學(xué)習(xí)范文，學(xué)習(xí)重點(diǎn)短語，為下步的模仿寫作提供語言素材。T :1. )Have you ever kept a pig as a pet?Do you like pigs? St.:No.…Why don’t you like to keep a pig? St: No.They’re too dirty and lazy(Do you know in some foreign countries like Hollyland, Australia,pigs are the most popular pet.there’s a kind of pig.(圖)it has an interesting name? it ‘s called a pot-bellied pig.) Now,let’s learn an article about this kind of interesting pet.2.)play the tapeSt.:Listen and repeat3.)show some Qs on computer(本子St.: read silently,then answerthe Qs(本子)4.)Ask ss. Close book and retell this passage.(what is a pot-bellied pig? Is it a good or bad pet? ) St.: retell it to each other“A pot –bellied pig is a popular pet now…”5.read the article together.St.:.practice reading
人教版新目標(biāo)初中英語八年級(jí)下冊(cè)Would you mind turning down the music教案
Step 4. Group work (4)1. Ask a pair of students to read the dialogue. Say, This activity provides speaking, listening and writing practice using the target language.2. Ask students to complete the work in groups.3. Check the answers with the whole class. 4. Explain some of the language points. Step 5. Word review (Self check 1)1. Ask students to read the words and the phrases given. 2. Fill in the blanks with proper forms of these words to complete the sentences. 3. Check the answers with the whole class. Homework:Do activity 2 on page 57 after class. Period 6Teaching aims: 1. Teach vocabulary words and the useful expressions. 2. Enable the students to learn etiquette in different culture. 3. Help the students learn how to behave politely in public places and in daily life. Teaching procedures:Step 1. RevisionHelp students to review the function of making requests through a free talk. Then lead them to the topic of etiquette. Explain the meaning of etiquette. Or, ask students to look it up in the dictionary. Step 2. Pre-reading (Section 1)1. Ask students to read the picture and make a list with their partner about how many rules of etiquette can be seen being broken.
人教版新目標(biāo)初中英語九年級(jí)上冊(cè)Teenagers should be allowed to choose their own clothes教案2篇
Step 1 Greeting Greet the class and check the homeworkStep 2 A duty report The S on duty gives a report on the rules in his home and lead in 3a “Sun Fei’s and Wu Yu’s rules” Step 3 ReadingSs read the conversation and write the two girls’ rules in the chart. Check the answers.Get Ss to read after the tape and then read aloud by themselves. Then, T explains the language points.Step 4 Pairwork 3bRole play. Use the information in chart to practice with the conversation in 3a covered. They can look at the sample conversation in the right box.Step 5 Task 2 “Who’s the best reporter?”Make a survey by asking any 5 students the questions in the chart in activity 4. Then give out a report about it. See who is the best reporter? And the best reporter will get a nice ball-pen.Step 6 Summary and homework:Write out the report in your exercise-books.Period ThreeStep 1 Greeting and a duty reportThe S gives a duty report talking about his experience of being late for school. Lead in the question “Do you ever get to school late? How often do you get to school late? Always, usually, sometimes, or never?Step 2 1a Get Ss to finish writing.Step 3 Pairwork 1b Get Ss to talk about their answers with their partners using the sample conversation in the box on the right.Step 4 Listening practice2a Lead-in: What will happen if you get to school late? What about Peter? Let’s listen to a conversation between Peter and his father. Get Ss to finish 2a (As usual, for the first time, Ss only listen.) Check the answers.
人教版新目標(biāo)初中英語九年級(jí)上冊(cè)I used to be afraid of the dark教案
內(nèi)容提示1．本單元主要內(nèi)容是學(xué)會(huì)used to結(jié)構(gòu)。Used to +動(dòng)詞原形表示過去經(jīng)常、以前常常，只用于過去式中，用來表示現(xiàn)在已不存在的習(xí)慣或狀態(tài)。例如：They used to play football together．他們過去常在一起蹋足球。（現(xiàn)在不在一起踢了)2．used to的疑問形式和否定形式為Did you use to…?和I didn’t use to… 也可以用Used you to…?和I used not to…但現(xiàn)在多使用前者。例如：Did you used to swim in the river? 你過去常在河里游泳嗎?I didn’t use to play the piano． 我以前并不經(jīng)常彈鋼琴。教學(xué)目標(biāo)一、學(xué)習(xí)目標(biāo)（Language Goal） 1．學(xué)會(huì)陳述自己過去常做的事情。2．學(xué)會(huì)陳述自己過去的愛好等。3．能夠表達(dá)自己現(xiàn)在和過去在外表、性格、娛樂等方面的變化。4．能夠表達(dá)朋友、家人等現(xiàn)在和過去的變化。二、語言結(jié)構(gòu)（Language Structures） 1．I used to be short when I was young. 我年輕時(shí)個(gè)子很矮。 2． —Did you use to have straight hair? 你過去是直發(fā)嗎？—Yes, I did. 是的。 3． —Did you use to play the piano? 你過去彈鋼琴嗎？—No, I didn’t. 不，我不彈。 4．I used to be afraid of dark. 我過去害怕黑暗。 5．I’m terrified of the snakes. 我害怕蛇。
人教版新目標(biāo)初中英語九年級(jí)上冊(cè)How do you study for a test教案2篇
內(nèi)容提示本單元主要內(nèi)容是學(xué)會(huì)利用verb十by／with gerund表示方式方法來討論學(xué)習(xí)英語的策略，認(rèn)識(shí)自己在學(xué)習(xí)方面的長處和不足。初步了解現(xiàn)在完成時(shí)的結(jié)構(gòu)和用法?，F(xiàn)在完成時(shí)由助動(dòng)詞have／has+動(dòng)詞的過去分詞構(gòu)成，主要表示過去發(fā)生的某一動(dòng)作對(duì)現(xiàn)在仍有影響或造成的后果，常與already，yet，just，ever，never等副詞連用。教學(xué)目標(biāo)一、學(xué)習(xí)目標(biāo)（Language Goal） 1. Talk about how to study . 學(xué)會(huì)討論各種學(xué)習(xí)方法和策略。2. Find out your suitable learning methods. 找出適合自己的學(xué)習(xí)方法。 二、語言結(jié)構(gòu)（Language Structures） 1. Verb + by with gerund by＋動(dòng)名詞短語 表示“通過…途徑，方法” 2. How questions have引導(dǎo)的特殊疑問句 三、目標(biāo)語言（Target Language） 1. How do you study for tests ? 你是怎樣準(zhǔn)備考試的？Well , I study by working with my classmates. 哦，我和同學(xué)們一起學(xué)習(xí)。2. Have you ever studied with a group ? 你曾經(jīng)參加過學(xué)習(xí)小組嗎？Yes , I have . I’ve learned a lot that way . 是的，參加過。通過這種方式我學(xué)了許多。
人教版新目標(biāo)初中英語九年級(jí)上冊(cè)It must belong to Carla教案
一、Section A該部分有4個(gè)模塊。第一模塊圍繞Whose volleyball is this? 這一話題展開思維（ 1a）、聽力（1b）、口語（ 1c）訓(xùn)練；第二模塊圍繞上一模塊中的話題進(jìn)行聽力（ 2a-2b）、口語訓(xùn)練（ 2c）；第三模塊繼續(xù)圍繞前兩個(gè)模塊中的“making inferences”展開訓(xùn)練。訓(xùn)練形式為閱讀排序（ 3a）和兩人問答（3b）；第四模塊仍就上一話題展開討論。二、Section B該部分有4個(gè)模塊。第一模塊要求根據(jù)圖畫和所提供的單詞寫出合理的句子；第二模塊在聽力（ 2a-2b）和分角色口語訓(xùn)練（ 2c）的基礎(chǔ)上，繼續(xù)進(jìn)行“推測”訓(xùn)練; 第三模塊圍繞“Strange events in Bell Tower neighborhood”這一話題展開閱讀（ 3a）和寫作（3b -3c）訓(xùn)練；第四模塊以dream為話題展開小組活動(dòng)。三、Self Check該部分有3個(gè)模塊。第一模塊以填空形式對(duì)所學(xué)詞匯進(jìn)行訓(xùn)練；第二模塊就8個(gè)諺語展開閱讀和討論。
人教版新目標(biāo)初中英語九年級(jí)上冊(cè)Where would you like to visit教案2篇
The First PeriodⅠ．Teaching Aims and DemandsKnowledge Objects（1） Key Vocabularytiring, educational, fascinating, thrilling, peaceful, exotic, trek, jungle, take it easy, explore, historic, site（2） Target LanguageWhere would you like to go on vacation?I’d like to trek through the jungle, because I like exciting vacations．2． Ability Objects（1）Train students to talk about places they would like to visit with the target language．（2）Train students to describe vacations with different adjectives．（3）Train students' listening skill．3． Moral Object,It′s more interesting to go on vacating somewhere instead of staying at home．Ⅱ． Teaching Key Points1． Key Vocabularytiring, educational, fascinating, thrilling, peaceful, exotic, trek, jungle, take it easy, explore, historic, site2． Target LanguageTalk about different places with the target language．Ⅲ． Teaching Difficult Points1． Describe vacations with different adjectives．2． Talk about different places with the target language．Ⅳ． Teaching Methods1． Teaching by illumination2． Teaching by doing chain drills3． Teaching by pairworkⅤ． Teaching Aids1． A tape recorder2． Some pictures of different places with famous views
人教版新目標(biāo)初中英語九年級(jí)下冊(cè)Rainy days make me sad教案
1. 教材分析本單元以how do things affect you？為話題, 從顏色、天氣、音樂、廣告、產(chǎn)品等方面談?wù)摿送饨缡挛锶绾斡绊懭说男那椤Ｒ髮W(xué)生掌握表達(dá)某物或某事給人帶來的感覺、看法或影響等。共設(shè)計(jì)了四個(gè)部分的內(nèi)容：Section A 該部分有4個(gè)模塊：第一模塊圍繞Which restaurant would you like to go to?這一話題展開思維（1a）、聽力（1b）、口語（1c）訓(xùn)練；第二模塊圍繞How does music affect you? 進(jìn)行聽力（2a-2b）、口語訓(xùn)練（2c）；第三模塊繼續(xù)圍繞how do colors in the restaurant affect you這一話題展開訓(xùn)練，訓(xùn)練形式為閱讀和問題體驗(yàn)（3a）和小組活動(dòng)（3b）；第四模塊仍就How do things affect you這一話題以調(diào)查的形式展開討論。Section B該部分有4個(gè)模塊：第一模塊圍繞產(chǎn)品廣告對(duì)人們的影響這一話題以“配對(duì)”（1a）與“列舉”（1b）兩種形式展開訓(xùn)練；第二模塊繼續(xù)圍繞How do things affect you? 進(jìn)行聽力（2a-2b）、口語對(duì)話訓(xùn)練（2c）；第三模塊圍繞“Advertising”這一話題展開閱讀（3a-3b）和寫作（3c）訓(xùn)練；第四模塊圍繞How posters affect you這一話題以口語訓(xùn)練形式展開小組活動(dòng)。
人教版新目標(biāo)初中英語九年級(jí)下冊(cè)Could you please tell me where the restrooms are教案
Step Ⅰ RevisionCheck homework． Ask a few students to read the article in 3a．Then ask a few students to read their guides．Step Ⅱ Part 1Look at the words in the box． Ask a student to read them． Make sure the students understand the meaning of the words． You are to fill in the blanks with the words． In some cases, students may need to use another form of the word, for example adjusting for tense or subject/ verb agreement．Ask students to fill in the blanks on their own．Check the answers． Step ⅢPart 2Go through the instructions with the class．Look at the example with the students．Ask students what the answer would be．Ask a student to read the question and answer it．Excuse me, could you tell me where the bank is, please?The bank is across the street from the shopping malt．Get students to complete the work in pairs．Check the answers． Ask a few students to read their questions．Step Ⅳ Just for Fun!Ask all the students to read the conversation． Ask: What is funny about this cartoon? Help students to explain． A Martian is a person from the planet Mars．There is no such thing as Martian food on Earth, and the clerk looks silly because he is trying to think of where there is a Martian restaurant．Invite some pairs of students to present this conversation to the rest of the class．Step Ⅴ Summary and HomeworkIn this class, we’ve done much writing practice using the key vocabulary words and the target language presented in this unit． After class, please finish the questions in 2 in your exercise books． Then finish the exercises on pages 47～48 of the workbook as well．The Seventh Period Ⅰ Teaching Aims and Demands1． Knowledge Objects（1） Key Vocabularyimage, adventure, jealousy, hero, crime, journey, brave, no longer, show interest in, take it easy, become interested in, plain looks（2）Text:Grown-ups like cartoons, too．2． Ability Objects（1） Fast-reading to get a general idea of the text．（2） Careful-reading to get the detailed information in the text．
人教版新目標(biāo)初中英語九年級(jí)下冊(cè)I’ll help clean up the city parks教案
Talk about offering help (P60)I’ll help clean up the city parks.A: I’d like to work ...B: You could help ...Talk about ways to tell people about the Clean-Up Day (P61)We need to ...We can’t ...I’ll ...Talk about the work the volunteers do (P62)These three students all volunteer their time to help other people.Somebody loves to ... / helps ... / plans to ... / wants to ...A: What do you like doing?B: I like ... A: What kind of volunteer work do you think I could do?B: You could ...1. 重點(diǎn)詞匯advertisement, fix, repair, pleasure, blind, deaf, shut, carry, specially, fetch2. 認(rèn)讀詞匯hunger, homeless, cheer, clean-up, sign, establish, major, commitment, elementary, veterinarian, coach, similar, call-in, strategy, disabled, organization, unable, support, appreciate, donation, part of speech, pronoun, adverb, preposition, conjunction, donate, Jimmy, Sally3. 詞組clean up, cheer up, give out, put off, set up, think up, take after, fix up, give away, put up, hand out, work out, at once
人教版新目標(biāo)初中英語九年級(jí)下冊(cè)You’re supposed to shake hands教案
教學(xué)目標(biāo)：1. 掌握本單元一些重點(diǎn)詞匯的寫法和用法。2. 學(xué)會(huì)自如談?wù)摬妥蓝Y儀。Step 1 RevisionAsk some students to retell the customs at the table in France in the passage in 3a.Step 2 Self checkPart 1. Fill in each bland with the correct word given. Students do the exercises by themselves at first. Then check the answers. Ask the students to comprehend the sentences and help them point out uses of some words, like “arrive (at / in) sw., spend time / money on sth , spend time / money (in) doing sth.”Part 2. Read about Fan Ling’s experience in a western restaurant. Understand the passage. Point out some key points in the passage.1. be / get used to doing sth. 習(xí)慣做某事2. begin with = start with 以….開頭3. crowd v. 擠滿，塞滿 the crowd 人群 crowded adj. 擁擠的Then students discuss about how she would solve her problem. Ask some to share their stories with others.Part 3. Complete the crossword by looking at the sentences on the left. Then check the answers.
部編版語文九年級(jí)上冊(cè)《中國人失掉自信力了嗎》教案
一、導(dǎo)入新課我們已經(jīng)學(xué)過魯迅先生的不少文章，學(xué)過他的小說，看他用無數(shù)生動(dòng)的形象表達(dá)他在時(shí)代里的“吶喊”與“彷徨”；學(xué)過他的散文，與他一同在失落中“朝花夕拾”，安靜地回憶過往。今天，我們將學(xué)習(xí)魯迅先生的一篇雜文，看他是如何作為民族斗士，將手中的筆，變成抨擊敵人的槍。二、教學(xué)新課目標(biāo)導(dǎo)學(xué)一：學(xué)習(xí)駁論，理清思路1．初讀課文，找出對(duì)方的錯(cuò)誤觀點(diǎn)，并說說作者是怎樣引出這一觀點(diǎn)的。明確：對(duì)方的錯(cuò)誤觀點(diǎn)是“中國人失掉自信力了”。開篇以似乎確鑿的事實(shí)為據(jù)，用一句話指出了三個(gè)階段中“中國人”表現(xiàn)出來的三種不同的態(tài)度：盲目驕傲，夜郎自大；盲目崇拜，借助外援；今不如昔，祈求鬼神。即由自夸到崇洋，到自欺欺人、虛無渺茫的態(tài)度變化。因此有人“慨嘆”：“中國人失掉自信力了?！边@是論敵的論點(diǎn)。
《小步舞曲教案》教案
教學(xué)過程：一、邊欣賞音樂邊介紹巴赫及其求學(xué)之路。通過背景音樂和文字說明，使同學(xué)們掌握一些有關(guān)西方音樂的文化。二、初步了解小步舞曲。通過文字?jǐn)⑹?，簡單了解小步舞曲。三、講述《小步舞曲》曲的音樂內(nèi)容。對(duì)節(jié)奏、速度、力度、節(jié)拍以及體裁進(jìn)行了解。四、結(jié)合譜例分段學(xué)習(xí)《小步舞曲》。1、學(xué)習(xí)樂曲A’段。說明：依據(jù)樂曲創(chuàng)作背景，合理創(chuàng)設(shè)“舞會(huì)”情景，從而有效激發(fā)學(xué)生學(xué)習(xí)興趣，用舞蹈表現(xiàn)手段演繹此樂段，發(fā)展了學(xué)生的舞蹈表演能力，享受到美的愉悅。2、學(xué)習(xí)樂曲B段。說明：利用形象、直觀的圖式輔助以及一系列貼近學(xué)生思維邏輯的問答討論，激發(fā)學(xué)生的思考，幫助學(xué)生準(zhǔn)確把握樂段情緒，并能用指揮、伴奏等方式表現(xiàn)該樂段。3、完整欣賞《小步舞曲》。說明：學(xué)生在完整欣賞樂曲時(shí)能夠鞏固樂曲主題的記憶，并且聽辨、感受樂曲兩個(gè)不同主題情緒，培養(yǎng)學(xué)生獨(dú)立的音樂感受和見解。五、視頻欣賞。說明：通過視屏欣賞，使同學(xué)們以一個(gè)更直觀的郊區(qū)去理解和學(xué)習(xí)作品，并使同學(xué)對(duì)作品有更深刻的記憶。引起學(xué)生共鳴，領(lǐng)悟音樂的美感，愉悅身心，獲取樂趣，從而激起學(xué)習(xí)的情趣。
空間向量及其運(yùn)算的坐標(biāo)表示教學(xué)設(shè)計(jì)人教A版高中數(shù)學(xué)選擇性必修第一冊(cè)
一、情境導(dǎo)學(xué)我國著名數(shù)學(xué)家吳文俊先生在《數(shù)學(xué)教育現(xiàn)代化問題》中指出:“數(shù)學(xué)研究數(shù)量關(guān)系與空間形式,簡單講就是形與數(shù),歐幾里得幾何體系的特點(diǎn)是排除了數(shù)量關(guān)系,對(duì)于研究空間形式,你要真正的‘騰飛’,不通過數(shù)量關(guān)系,我想不出有什么好的辦法…….”吳文俊先生明確地指出中學(xué)幾何的“騰飛”是“數(shù)量化”,也就是坐標(biāo)系的引入,使得幾何問題“代數(shù)化”,為了使得空間幾何“代數(shù)化”,我們引入了坐標(biāo)及其運(yùn)算.二、探究新知一、空間直角坐標(biāo)系與坐標(biāo)表示1.空間直角坐標(biāo)系在空間選定一點(diǎn)O和一個(gè)單位正交基底{i,j,k},以點(diǎn)O為原點(diǎn),分別以i,j,k的方向?yàn)檎较?、以它們的長為單位長度建立三條數(shù)軸:x軸、y軸、z軸,它們都叫做坐標(biāo)軸.這時(shí)我們就建立了一個(gè)空間直角坐標(biāo)系Oxyz,O叫做原點(diǎn),i,j,k都叫做坐標(biāo)向量,通過每兩個(gè)坐標(biāo)軸的平面叫做坐標(biāo)平面,分別稱為Oxy平面,Oyz平面,Ozx平面.
用空間向量研究直線、平面的位置關(guān)系（2）教學(xué)設(shè)計(jì)人教A版高中數(shù)學(xué)選擇性必修第一冊(cè)
跟蹤訓(xùn)練1在正方體ABCD-A1B1C1D1中,E為AC的中點(diǎn).求證:(1)BD1⊥AC;(2)BD1⊥EB1.(2)∵(BD_1 ) ?=(-1,-1,1),(EB_1 ) ?=(1/2 "," 1/2 "," 1),∴(BD_1 ) ?·(EB_1 ) ?=(-1)×1/2+(-1)×1/2+1×1=0,∴(BD_1 ) ?⊥(EB_1 ) ?,∴BD1⊥EB1.證明:以D為原點(diǎn),DA,DC,DD1所在直線分別為x軸、y軸、z軸,建立如圖所示的空間直角坐標(biāo)系.設(shè)正方體的棱長為1,則B(1,1,0),D1(0,0,1),A(1,0,0),C(0,1,0),E(1/2 "," 1/2 "," 0),B1(1,1,1).(1)∵(BD_1 ) ?=(-1,-1,1),(AC) ?=(-1,1,0),∴(BD_1 ) ?·(AC) ?=(-1)×(-1)+(-1)×1+1×0=0.∴(BD_1 ) ?⊥(AC) ?,∴BD1⊥AC.例2在棱長為1的正方體ABCD-A1B1C1D1中,E,F,M分別為棱AB,BC,B1B的中點(diǎn).求證:D1M⊥平面EFB1.思路分析一種思路是不建系,利用基向量法證明(D_1 M) ?與平面EFB1內(nèi)的兩個(gè)不共線向量都垂直,從而根據(jù)線面垂直的判定定理證得結(jié)論;另一種思路是建立空間直角坐標(biāo)系,通過坐標(biāo)運(yùn)算證明(D_1 M) ?與平面EFB1內(nèi)的兩個(gè)不共線向量都垂直;還可以在建系的前提下,求得平面EFB1的法向量,然后說明(D_1 M) ?與法向量共線,從而證得結(jié)論.證明:(方法1)因?yàn)镋,F,M分別為棱AB,BC,B1B的中點(diǎn),所以(D_1 M) ?=(D_1 B_1 ) ?+(B_1 M) ?=(DA) ?+(DC) ?+1/2 (B_1 B) ?,而(B_1 E) ?=(B_1 B) ?+(BE) ?=(B_1 B) ?-1/2 (DC) ?,于是(D_1 M) ?·(B_1 E) ?=((DA) ?+(DC) ?+1/2 (B_1 B) ?)·((B_1 B) ?-1/2 (DC) ?)=0-0+0-1/2+1/2-1/4×0=0,因此(D_1 M) ?⊥(B_1 E) ?.同理(D_1 M) ?⊥(B_1 F) ?,又因?yàn)?B_1 E) ?,(B_1 F) ?不共線,因此D1M⊥平面EFB1.
用空間向量研究直線、平面的位置關(guān)系（1）教學(xué)設(shè)計(jì)人教A版高中數(shù)學(xué)選擇性必修第一冊(cè)
二、探究新知一、空間中點(diǎn)、直線和平面的向量表示1.點(diǎn)的位置向量在空間中,我們?nèi)∫欢c(diǎn)O作為基點(diǎn),那么空間中任意一點(diǎn)P就可以用向量(OP) ?來表示.我們把向量(OP) ?稱為點(diǎn)P的位置向量.如圖.2.空間直線的向量表示式如圖①,a是直線l的方向向量,在直線l上取(AB) ?=a,設(shè)P是直線l上的任意一點(diǎn),則點(diǎn)P在直線l上的充要條件是存在實(shí)數(shù)t,使得(AP) ?=ta,即(AP) ?=t(AB) ?.如圖②,取定空間中的任意一點(diǎn)O,可以得到點(diǎn)P在直線l上的充要條件是存在實(shí)數(shù)t,使(OP) ?=(OA) ?+ta, ①或(OP) ?=(OA) ?+t(AB) ?. ②①式和②式都稱為空間直線的向量表示式.由此可知,空間任意直線由直線上一點(diǎn)及直線的方向向量唯一確定.1.下列說法中正確的是( )A.直線的方向向量是唯一的B.與一個(gè)平面的法向量共線的非零向量都是該平面的法向量C.直線的方向向量有兩個(gè)D.平面的法向量是唯一的答案:B 解析:由平面法向量的定義可知,B項(xiàng)正確.