本文篇幅較長(zhǎng),并且有一字句不易理解,因而對(duì)高一學(xué)生來(lái)說(shuō)完全讀懂內(nèi)容有一些困難。這樣的話,老師就要做好引導(dǎo)工作,把一些難點(diǎn),或是出現(xiàn)詞類(lèi)活用比較多,局勢(shì)比較特殊的句子,老師可以先給學(xué)生畫(huà)出來(lái),存疑,或是與同學(xué)們一起討論解決。對(duì)那些不易懂的字詞就引導(dǎo)學(xué)生聯(lián)系上下文提供的語(yǔ)境、前后涉及的情節(jié)加以推測(cè)、判斷,以培養(yǎng)學(xué)生依據(jù)文脈推斷詞義的好方法。要求學(xué)生點(diǎn)出重點(diǎn)實(shí)詞、框出通假字,主要是為幫助學(xué)生積累和掌握一些文言文中常見(jiàn)的一詞多義、異讀現(xiàn)象、古今異義和通假現(xiàn)象的詞語(yǔ),并進(jìn)一步得出規(guī)律,指導(dǎo)今后的文言文學(xué)習(xí)。詞類(lèi)活用和特殊句式在文言文翻譯中難度較大,也是本文教學(xué)的兩大難點(diǎn)。要求學(xué)生標(biāo)出有活用現(xiàn)象的字和劃出句式特殊的句子,是基于兩點(diǎn)考慮:1、積累一定數(shù)量的第一手例句;2、引導(dǎo)學(xué)生加以分類(lèi),找出每類(lèi)的相同特征,并抽取出來(lái)形成規(guī)律性的東西,從而上升到理性認(rèn)識(shí),使學(xué)生能由學(xué)會(huì)一個(gè)到會(huì)學(xué)多個(gè)。翻譯過(guò)程中注重指導(dǎo)學(xué)生養(yǎng)成用符號(hào)法表示重點(diǎn)字句的好習(xí)慣,如點(diǎn)、框、圈、劃線等符號(hào)應(yīng)約定一致,便于突出翻譯中的重點(diǎn)、難點(diǎn)及復(fù)習(xí)。我的提示著重歸納了實(shí)詞“制”“亡”“遺”“利”等,名詞活用、形容詞活用、使動(dòng)用法,被動(dòng)句、狀語(yǔ)后置句。
Textbook: Senior English for China (Book 4), by Liu Daoyi Time Allotment: 1 period (40 minutes)Date: March 20, 2014Teaching aids: blackboard, Multi-media, Power Point, chalk I. Text Analysis (教材分析)This unit is about body language, and the text selected in the reading part demonstrates the difference and similarity of body language in many parts of the world. Through learning this passage, students are required to raise their awareness of using body language in different parts of the world. As body language is closely related to our daily life, it is easy to arouse students’ interest in learning this text. Reading skills and speaking training are designed around the text.II. Teaching Objectives (教學(xué)目標(biāo))By the end of the lesson, students will be able to:1. Language Skill Objective(語(yǔ)言技能目標(biāo)): develop reading ability (skimming and scanning)as well as speaking ability.2. Cultural Knowledge Objective(文化知識(shí)目標(biāo)): know about the cultural differences of using body language.3. Affective Objective(情感目標(biāo)): increase students’ awareness of using body language correctly in different cultures. III.Teaching Focuses and Difficulties(教學(xué)重點(diǎn)和難點(diǎn))1. Teaching Focuses(教學(xué)重點(diǎn)): the difference and similarity of body language in many parts of the world.2. Teaching Difficulties(教學(xué)難點(diǎn)): develop students’ reading abilities of skimming and scanning and ask the students to show their opinions with fluent English.
Step 2 Pre-listeningAfter students finish their discussion, I will show a picture of Newton and ask them: Who is him? What is he famous for? Could you find out some words to describe him? Maybe students will answer that he is genius for his finding of theGravitation, making a great contribution to the progress of human being. At that time I will show another two pictures of Einstein and Hawking, letting students guess who they are and write down their idea about the Gravitation. For I have arranged them to search more information about the gravity before this class, Students have beenfamiliar with the topic and will not be afraid about this abstract conception, which is helpful for their listening.Step 3 While-listeningIn this step, students will be required to listen the material for three times. The first and listening is extensive listening and the second and third listening is intensive listening. In the first time, They are required to listen a material including Part 1 and Part 2 and choose the best summary of the listening text. After they choose the right answer, They also need work in group to explain what is wrong with the others. Then I will make a conclusion that we should pay attention to the first paragraph and last paragraph and some keys to get the main idea. By doing this, their capacity of generalization will have a great improvement.Before the second listening, I will ask students to scan the blank on the power point quickly and ask them to note down some key words .Then ask them to listen to the Part 1again and fill the first column of the chart. Maybe some students just show the ideas of these three scientists an still can’t catch their development of gravity. Therefore, I will ask them to listen to Part 2 again and fill in the rest. After finish the listening, I will give them ten minutes to discuss with their partner. I will also guidethem to improve their answers when they discuss with others.
Then I would ask them to think of a funny English or Chinese and tell it to partners. While telling stories, they can use expressions and some acting to help make the story funny. 5 minutes would be given to do this.Those stories they told there will be the material for their writing. Soletting them tell it at first is helpful. And they can make a difference between telling a funny story and writing it down. Generally speaking, it is difficult forstudents to write well because they don’t know what to write and how to write. Asking them to tell their own stories at first can help them come up with what to write.After their telling, I would invite someone to share his/her story with all of us and I would write it down on the blackboard.This example story would be used as a sample to illustrate the format of funny story. Different from a story from teacher or textbook, a story from students can obviously become a interesting material to draw students’ attention.Then I would ask the whole class to put this story into several parts. It might be a little bit difficult for them. So I would ask them to find out whether all the sentences are necessary. After delete some sentences, there are 6 sentences left behind. Then they can easily put them into three parts. After interaction with students, I would teach them the right terms for each part and conclude the format of funny story.This step is the key and difficult point in my lesson. So I mainly usetask-based teaching method in this part and the task for students was divided into several stages. With the separated difficult level, students can find there are usually three parts in writing. They can also learn to write without the unnecessary parts in the process of analyzing. And then I wouldn’t rush to tell them the right terms to them directly. Instead, I would ask them to name them by their own. A confused mind is better for acquiring knowledge.While-writing:Then I would give students 7 minutes to write down this story, without other requirements.With all the preparations in pre-writing, students’ difficulties were cleared. So it would be much easier for them to write down the story within 7 minutes. There are no other requirements because students’ first writing is actually a drafting. It would be revise and edit several times later. Writing, as a skill
Good morning, distinguished judges:It’s my honor to talk about my teaching ideas with you. Today my topic is Women of Achievement. My presentation consists of six parts: the analysis of teaching material and student, teaching aims, key and difficult points, teaching and studying method, teaching procedures and blackboard design.First, let’s focus on the analysis of teaching material. This lesson is from New Senior English for China Student’s Book 4 Unit 1, the reading part. The main topic of the passage is the introduction of a student of Africanwildlife. After this lesson, the students will learn more information about her studying chimps in Africa, and their reading and speaking abilities can be developed as well.The next part is the analysis of students. My students are in senior high students. They have learnt English for many years, they’ve known many words and sentences, but their speaking and reading abilities are still not very good. So I will practice their speaking and reading abilities through different exercises.According to the New Standard Curriculum and the present situation, I set the teaching aims as follows: firstly, knowledge aims. Students can grasp some new words, such as worthwhile, move off. Moreover, students can understand the content of the passage and get familiar with the topic of studying chimps in wildlife. Secondly, ability aims. Students can use reading strategies such as skimming and scanning in reading process. Thirdly, emotional aims. Students can have the awareness of protecting animals and care about animals.Based on the above analysis, the key point of this lesson is to get the main idea and the detailed information from the passage; the difficult point is to talk about the wildlife protection and use reading strategies.
Language learning needs a context, which can help the learners to understand the language and then can product comprehensible output, so computer has the advantages to make the materials attractive.Part 3 Learning MethodsTask-based, self-dependent and cooperative learningPart 4 Teaching ProcedureStep One Lead-in“Interest is the best teacher.” Therefore, at the very beginning of the class, I should spark the students’ mind to focus on the centre topic “the band”. I’ll show some pictures of food to attract their attention and then bring some questions.Question:What kind of food they like?What should go into a good meal?The answers must relate to the diet. After this, the students will be eager to know something about a balance diet and this is the very time to naturally lead the class into Step 2Step 2 Reading for information: skimming and scanning In this step, I use Task-based Language Teaching method, which can give students a clear and specific purpose while skimming and scanning the context.Task 1 General ideaThe students will be asked to just glance at the title and the pictures of the passage, and then guess what they will read in the text. And they’ll be divided into groups of four to have a discussion.The purpose is to inspire the students to read actively, not passively. In addition, the task is to develop the students’ reading skill by making prediction and to encourage the students to express their thoughts in English and cooperate with each other.Task 2 Main idea of each paragraphCooperative learning can raise the students’ interest and create an atmosphere of achievement. Based on this theory, I divide the whole class into 4 groups to skim the whole text and get the main idea of each paragraph.
Knowledge objectives:(1) to make Ss grasp the usage of words, expressions and sentence structures: statistics, struggle, thanks to, rid of, some patterns for persuasion, the “ing” form as subject and object;(2)to use learnt knowledge to persuade sb.Ability objectives:(1) to develop Ss’ reading skills(skimming, scanning, word guessing);(2) to improve Ss’ speaking, communicating and cooperating skills.Emotional objectives:to make Ss know the contribution of Yuan,and learn his spirit and his simple life time.Teaching important and difficult points:(1) some words, expressions and sentence structures mentioned above;(2)the content of the text;(3)training their reading and speaking skills.Teaching methods: CLT, TBLT,QT.Learning strategies: CLS, QLS, TBLS.Teaching procedures:Step 1 lead-in: (1) teacher plays a piece of recent news from CCTV about the harvest of the super hybrid rice, and ask students whether they know Yuan or not, and talk about him and his contribution.(2)Brain storm: let Ss describe Yuan in their minds including his appearance, his living condition and so on.Step 2 fast reading tasks:(1)teacher introduces Yuan and super hybrid rice(2)make Ss read the text as fast as possible with questions. Such as: what’s the general ideaof this passage? What’s Yuan’ dream? (skimming and scanning skill)Step 3 intensive reading tasks(1)let Ss read the text silently, find topic sentence of each paragraph and draw the difficult sentences and the knowledge what they don’t understand.(words guessing)(2)teacher and Ss talk about the important words, expressions and sentences together, and ask Ss to retell the content of the text.(summarizing and paraphrasing)(3)teacher summarize this part.(4) read again following the courseware.
在接下來(lái)的細(xì)讀環(huán)節(jié),我套用了高考對(duì)閱讀理解的考查方式設(shè)置了5個(gè)問(wèn)題,分別為三個(gè)推理判斷題,一個(gè)細(xì)節(jié)題和一個(gè)主旨大意題。學(xué)生需要對(duì)文章的內(nèi)容進(jìn)行分析、歸納、推理、猜測(cè)等高級(jí)思維活動(dòng)才能做出正確的回答。【設(shè)計(jì)意圖】這一過(guò)程是對(duì)學(xué)生進(jìn)行細(xì)讀的訓(xùn)練,培養(yǎng)學(xué)生獲取特定信息和挖掘文章深層次信息的能力。第三環(huán)節(jié):Intensive-reading (精讀) 15′第三個(gè)環(huán)節(jié)精讀,既是最重要的環(huán)節(jié),也是突破本課重難點(diǎn)的關(guān)鍵。首先,讓學(xué)生思考劇本中人物看到百萬(wàn)英鎊前后的態(tài)度發(fā)生了怎樣的變化。其次,讓學(xué)生仔細(xì)閱讀文章,找出可以表現(xiàn)人物態(tài)度變化的具體的語(yǔ)言和動(dòng)作。最后,讓學(xué)生總結(jié)人物的態(tài)度發(fā)生變化的根本原因是什么,從而引出Money Talks, 供學(xué)生思考。【設(shè)計(jì)意圖】通過(guò)一系列的活動(dòng)培養(yǎng)學(xué)生學(xué)習(xí)從人物的語(yǔ)言和動(dòng)作探究人物的心理,使學(xué)生進(jìn)一步體會(huì)戲劇語(yǔ)言的魅力,從而對(duì)文章背后所反映的社會(huì)問(wèn)題進(jìn)行思考,也為下一步的討論環(huán)節(jié)做好鋪墊。
通過(guò)寫(xiě)文章梗概,培養(yǎng)學(xué)生綜合運(yùn)用語(yǔ)言的能力,學(xué)習(xí)用恰當(dāng)?shù)挠⒄Z(yǔ)描述科學(xué)家的故事。這是本課的教學(xué)難點(diǎn)。教師可以使用完形填空的方式來(lái)幫助學(xué)生整理語(yǔ)篇,從而來(lái)降低難度。本課的教學(xué)重點(diǎn)的突破方法是:在閱讀前,讓學(xué)生初步了解得出科學(xué)觀點(diǎn)所需要的基本程序,從而輕松而自然地導(dǎo)入文章的閱讀;在閱讀過(guò)程中,由易到難設(shè)計(jì)快速閱讀和精讀的問(wèn)題,層層推進(jìn)各種閱讀活動(dòng),讓學(xué)生對(duì)閱讀內(nèi)容從整體感知到細(xì)節(jié)理解,最后深層讀懂整篇文章,同時(shí)加強(qiáng)閱讀策略的指導(dǎo),讓每個(gè)學(xué)生都主動(dòng)參與課堂教學(xué)活動(dòng),最終達(dá)到提高閱讀能力的目的。Step 4 Post-readingGroup Activities四人小組共同合作,在老師的適當(dāng)指導(dǎo)下,就以下2個(gè)問(wèn)題展開(kāi)討論,讓學(xué)生就所知、所學(xué)、所感和所想融入話題,然后抽若干同學(xué)代表作小組發(fā)言。1. What do you think about John Snow, and what should we learn from him?2. Cholera was 19th century disease, which two diseases are similar to cholera today? Why?
Good afternoon, everyone. It’s my great pleasure to be here sharing my lesson with you. The content of my lesson is Senior English for China Book5 Unit 3 Life in the Future. I’ll be ready to begin this lesson from six parts: Analysis of the teaching material, Analysis of the students, Teaching aims and important and difficult points, Teaching methods and aids, Teaching procedures, and Blackboard design. First, let me talk about the teaching material.Part 1 Analysis of the Teaching Material:This unit is about what human beings’ life will be like in about one thousand years. By studying of this unit, we’ll Enable the students to know the changes in humans’ life and some new inventions bringing about the change and develop the interest in science. This lesson plays an important part in the English teaching in this unit. This is an important lesson in Book Five. From this lesson, it starts asking the Ss to grasp contents of each passage. Therefore, this lesson is in the important position of the teaching material. If the Ss can learn it well, it will be helpful to make the Ss learn the rest of this unit.Part 2 Analysis of the SsAs Senior2 Ss, they are at different levels of English fluency, some of them have lost interest in English. So during the lesson, I arrange a variety of activities to let all of them join in to attract their interest and let them be confident and taste the joy of success.
今天我們來(lái)介紹一下必修五第四單元的授課方式。這個(gè)單元的題目是Making the news。應(yīng)該是學(xué)生比較感興趣的話題,學(xué)生往往對(duì)新聞工作充滿好奇,所以我們可以利用這個(gè)機(jī)會(huì)多設(shè)計(jì)一些師生互動(dòng)和學(xué)生互動(dòng),來(lái)激發(fā)起學(xué)習(xí)的積極性,提高學(xué)習(xí)效率。同時(shí)我們可以利用這個(gè)單元不僅幫助學(xué)生掌握語(yǔ)言知識(shí),培養(yǎng)語(yǔ)言能力,同時(shí)讓其了解新聞工作的重要性,培養(yǎng)起社會(huì)智能感。這個(gè)單元分為六個(gè)課時(shí),它的教學(xué)目標(biāo)是這樣的:語(yǔ)言目標(biāo)是掌握詞匯表中的常用單詞和短語(yǔ),掌握倒裝句的一些基本用法。 技能目標(biāo)是能初步掌握約會(huì)的基本句型并在真實(shí)的場(chǎng)景下正確運(yùn)用。新聞報(bào)道類(lèi)文章的寫(xiě)作技能。采訪的基本規(guī)范和溝通技能。情感目標(biāo)是對(duì)新聞報(bào)道的客觀性和真實(shí)性有更好的理解。對(duì)新聞?dòng)浾叩穆殬I(yè)有更深入的了解,并能體會(huì)其工作的重要性。下面我們來(lái)介紹一下第一課時(shí)的授課方式,第一課的教學(xué)目標(biāo)是這樣的第一課時(shí)的教學(xué)目標(biāo)語(yǔ)言目標(biāo):單詞:Occupation, journalist, editor, photographer, curious, personality, enthusiasm
《勸學(xué)》是普通高中課程標(biāo)準(zhǔn)試驗(yàn)教科書(shū)語(yǔ)文必修三第三單元的重點(diǎn)篇目,該文集中反映著名思想家荀子在學(xué)習(xí)問(wèn)題上的觀點(diǎn)和精彩斐然的論證藝術(shù)。該單元所選課文都是古代的議論性散文。通過(guò)本單元的學(xué)習(xí)在于讓學(xué)生感受我國(guó)傳統(tǒng)文化的精神,掌握基礎(chǔ)的文言語(yǔ)法知識(shí),學(xué)習(xí)如何清晰有力的表達(dá)自己的思想和見(jiàn)解。本文安排在單元的第一篇,如何指導(dǎo)學(xué)生學(xué)好這篇課文,是實(shí)現(xiàn)“授之以漁”,樹(shù)立學(xué)生學(xué)好文言文的信心,掌握文言學(xué)習(xí)方法的關(guān)鍵。根據(jù)新課標(biāo)倡導(dǎo)從“知識(shí)與能力”、“過(guò)程與方法”、“情感態(tài)度與價(jià)值觀”三方面出發(fā)設(shè)計(jì)課程目標(biāo)的要求和高一的學(xué)生對(duì)于文言文的知識(shí)還在積累的階段,應(yīng)該注重基礎(chǔ)知識(shí)的積累和一定量的誦讀的實(shí)際情況。我擬確定以下教學(xué)目標(biāo):1,了解荀子論述學(xué)習(xí)的思想,明確學(xué)習(xí)要靠積累、堅(jiān)持不懈、專(zhuān)心致志的道理。2,掌握積累文言實(shí)詞、虛詞,活用、古今異議等現(xiàn)象和固定句式。
Teaching plan for Unit 1 book3Good morning, teachers. It’s my great pleasure to be here because I can share my lesson with you and I can learn a lot from it. I’ll begin my lesson from the following four parts, the teaching material, the teaching methods, the studying methods and the teaching procedure.Firstly, let me talk about the teaching material. The content of my lesson is the reading passage festivals and celebrations of Unit 1 Festivals around the world. This passage is about festivals and celebrations. By studying this passage, we’ll enable the students to know that festivals exit everywhere, and many of festivals in different countries celebrate similar ideas. As we all know, the reading passage is the center of each unit. If the Ss can learn it well, it will be helpful to make the Ss learn the rest of this unit.After studying the teaching material, I think the teaching aims are as the followings:1. Knowledge aims:(1) The Ss can master the usage of the important words andexpressions.(2)The Ss can use the __________________ (grammar) in the proper situation.Make students know about the festivals all over the world and the detail of the festivals, such as origin, content, and the date of the holiday festivals.2. Ability aims:(1) Students can talk about festivals and celebrations in English(2) To improve the student’s reading ability, especially their skimming and scanning ability.3. Emotion aims:Make the Ss know about the foreign festivals, and respect other countries’ custom.Next, let’s come to the important points and the difficult points.The important point is how to make the Ss understand the text better and the difficult point is how can they talk about it. secondly, Teaching Methods:1. task-based Language Teaching2. Computer assisted language teaching.3. question-and–answer methodThirdly, Studying Methods:
【點(diǎn)津】 1.不定式的復(fù)合結(jié)構(gòu)作目的狀語(yǔ) ,當(dāng)不定式或不定式短語(yǔ)有自己的執(zhí)行者時(shí),要用不定式的復(fù)合結(jié)構(gòu)?即在不定式或不定式短語(yǔ)之前加 for +名詞或賓格代詞?作狀語(yǔ)。He opened the door for the children to come in. 他開(kāi)門(mén)讓孩子們進(jìn)來(lái)。目的狀語(yǔ)從句與不定式的轉(zhuǎn)換 英語(yǔ)中的目的狀語(yǔ)從句,還可以變?yōu)椴欢ㄊ交虿欢ㄊ蕉陶Z(yǔ)作狀語(yǔ),從而使句子在結(jié)構(gòu)上得以簡(jiǎn)化??煞譃閮煞N情況: 1?當(dāng)目的狀語(yǔ)從句中的主語(yǔ)與主句中的主語(yǔ)相同時(shí),可以直接簡(jiǎn)化為不定式或不定式短語(yǔ)作狀語(yǔ)。We'll start early in order that/so that we may arrive in time. →We'll start early in order to/so as to arrive in time. 2?當(dāng)目的狀語(yǔ)從句中的主語(yǔ)與主句中的主語(yǔ)不相同時(shí),要用動(dòng)詞不定式的復(fù)合結(jié)構(gòu)作狀語(yǔ)。I came early in order that you might read my report before the meeting. →I came early in order for you to read my report before the meeting.
4.已知△ABC三個(gè)頂點(diǎn)坐標(biāo)A(-1,3),B(-3,0),C(1,2),求△ABC的面積S.【解析】由直線方程的兩點(diǎn)式得直線BC的方程為 = ,即x-2y+3=0,由兩點(diǎn)間距離公式得|BC|= ,點(diǎn)A到BC的距離為d,即為BC邊上的高,d= ,所以S= |BC|·d= ×2 × =4,即△ABC的面積為4.5.已知直線l經(jīng)過(guò)點(diǎn)P(0,2),且A(1,1),B(-3,1)兩點(diǎn)到直線l的距離相等,求直線l的方程.解:(方法一)∵點(diǎn)A(1,1)與B(-3,1)到y(tǒng)軸的距離不相等,∴直線l的斜率存在,設(shè)為k.又直線l在y軸上的截距為2,則直線l的方程為y=kx+2,即kx-y+2=0.由點(diǎn)A(1,1)與B(-3,1)到直線l的距離相等,∴直線l的方程是y=2或x-y+2=0.得("|" k"-" 1+2"|" )/√(k^2+1)=("|-" 3k"-" 1+2"|" )/√(k^2+1),解得k=0或k=1.(方法二)當(dāng)直線l過(guò)線段AB的中點(diǎn)時(shí),A,B兩點(diǎn)到直線l的距離相等.∵AB的中點(diǎn)是(-1,1),又直線l過(guò)點(diǎn)P(0,2),∴直線l的方程是x-y+2=0.當(dāng)直線l∥AB時(shí),A,B兩點(diǎn)到直線l的距離相等.∵直線AB的斜率為0,∴直線l的斜率為0,∴直線l的方程為y=2.綜上所述,滿足條件的直線l的方程是x-y+2=0或y=2.
【答案】B [由直線方程知直線斜率為3,令x=0可得在y軸上的截距為y=-3.故選B.]3.已知直線l1過(guò)點(diǎn)P(2,1)且與直線l2:y=x+1垂直,則l1的點(diǎn)斜式方程為_(kāi)_______.【答案】y-1=-(x-2) [直線l2的斜率k2=1,故l1的斜率為-1,所以l1的點(diǎn)斜式方程為y-1=-(x-2).]4.已知兩條直線y=ax-2和y=(2-a)x+1互相平行,則a=________. 【答案】1 [由題意得a=2-a,解得a=1.]5.無(wú)論k取何值,直線y-2=k(x+1)所過(guò)的定點(diǎn)是 . 【答案】(-1,2)6.直線l經(jīng)過(guò)點(diǎn)P(3,4),它的傾斜角是直線y=3x+3的傾斜角的2倍,求直線l的點(diǎn)斜式方程.【答案】直線y=3x+3的斜率k=3,則其傾斜角α=60°,所以直線l的傾斜角為120°.以直線l的斜率為k′=tan 120°=-3.所以直線l的點(diǎn)斜式方程為y-4=-3(x-3).
解析:當(dāng)a0時(shí),直線ax-by=1在x軸上的截距1/a0,在y軸上的截距-1/a>0.只有B滿足.故選B.答案:B 3.過(guò)點(diǎn)(1,0)且與直線x-2y-2=0平行的直線方程是( ) A.x-2y-1=0 B.x-2y+1=0C.2x+y=2=0 D.x+2y-1=0答案A 解析:設(shè)所求直線方程為x-2y+c=0,把點(diǎn)(1,0)代入可求得c=-1.所以所求直線方程為x-2y-1=0.故選A.4.已知兩條直線y=ax-2和3x-(a+2)y+1=0互相平行,則a=________.答案:1或-3 解析:依題意得:a(a+2)=3×1,解得a=1或a=-3.5.若方程(m2-3m+2)x+(m-2)y-2m+5=0表示直線.(1)求實(shí)數(shù)m的范圍;(2)若該直線的斜率k=1,求實(shí)數(shù)m的值.解析: (1)由m2-3m+2=0,m-2=0,解得m=2,若方程表示直線,則m2-3m+2與m-2不能同時(shí)為0,故m≠2.(2)由-?m2-3m+2?m-2=1,解得m=0.
解析:①過(guò)原點(diǎn)時(shí),直線方程為y=-34x.②直線不過(guò)原點(diǎn)時(shí),可設(shè)其方程為xa+ya=1,∴4a+-3a=1,∴a=1.∴直線方程為x+y-1=0.所以這樣的直線有2條,選B.答案:B4.若點(diǎn)P(3,m)在過(guò)點(diǎn)A(2,-1),B(-3,4)的直線上,則m= . 解析:由兩點(diǎn)式方程得,過(guò)A,B兩點(diǎn)的直線方程為(y"-(-" 1")" )/(4"-(-" 1")" )=(x"-" 2)/("-" 3"-" 2),即x+y-1=0.又點(diǎn)P(3,m)在直線AB上,所以3+m-1=0,得m=-2.答案:-2 5.直線ax+by=1(ab≠0)與兩坐標(biāo)軸圍成的三角形的面積是 . 解析:直線在兩坐標(biāo)軸上的截距分別為1/a 與 1/b,所以直線與坐標(biāo)軸圍成的三角形面積為1/(2"|" ab"|" ).答案:1/(2"|" ab"|" )6.已知三角形的三個(gè)頂點(diǎn)A(0,4),B(-2,6),C(-8,0).(1)求三角形三邊所在直線的方程;(2)求AC邊上的垂直平分線的方程.解析(1)直線AB的方程為y-46-4=x-0-2-0,整理得x+y-4=0;直線BC的方程為y-06-0=x+8-2+8,整理得x-y+8=0;由截距式可知,直線AC的方程為x-8+y4=1,整理得x-2y+8=0.(2)線段AC的中點(diǎn)為D(-4,2),直線AC的斜率為12,則AC邊上的垂直平分線的斜率為-2,所以AC邊的垂直平分線的方程為y-2=-2(x+4),整理得2x+y+6=0.
一、情境導(dǎo)學(xué)前面我們已經(jīng)得到了兩點(diǎn)間的距離公式,點(diǎn)到直線的距離公式,關(guān)于平面上的距離問(wèn)題,兩條直線間的距離也是值得研究的。思考1:立定跳遠(yuǎn)測(cè)量的什么距離?A.兩平行線的距離 B.點(diǎn)到直線的距離 C. 點(diǎn)到點(diǎn)的距離二、探究新知思考2:已知兩條平行直線l_1,l_2的方程,如何求l_1 〖與l〗_2間的距離?根據(jù)兩條平行直線間距離的含義,在直線l_1上取任一點(diǎn)P(x_0,y_0 ),,點(diǎn)P(x_0,y_0 )到直線l_2的距離就是直線l_1與直線l_2間的距離,這樣求兩條平行線間的距離就轉(zhuǎn)化為求點(diǎn)到直線的距離。兩條平行直線間的距離1. 定義:夾在兩平行線間的__________的長(zhǎng).公垂線段2. 圖示: 3. 求法:轉(zhuǎn)化為點(diǎn)到直線的距離.1.原點(diǎn)到直線x+2y-5=0的距離是( )A.2 B.3 C.2 D.5D [d=|-5|12+22=5.選D.]
【教學(xué)過(guò)程】一、從實(shí)際情景入手,引入新知,使學(xué)生學(xué)會(huì)在具體情景中用數(shù)對(duì)確定位置1.談話引入。今天有這么多老師和我們一起上課,同學(xué)們歡迎嗎?老師們都很想認(rèn)識(shí)你們。咱們先來(lái)給他們介紹一下我們班的班長(zhǎng),可以嗎?2.合作交流,在已有經(jīng)驗(yàn)的基礎(chǔ)上探究新知。(1)出示要求:以小組為單位,想一想,可以用什么方法表示出班長(zhǎng)的位置,把你的方法寫(xiě)或畫(huà)在紙上。匯報(bào):班長(zhǎng)的位置在第4組的第三個(gè),他在從右邊數(shù)第二組的第三排…哪個(gè)小組也用語(yǔ)言描述出了班長(zhǎng)的位置?請(qǐng)班長(zhǎng)起立,他們的描述準(zhǔn)確嗎?剛才同學(xué)們的描述有什么相同和不同?(都表示的是班長(zhǎng)的位置,有的同學(xué)說(shuō)第幾組,第幾行,第幾排……)看來(lái)在日常生活中,我們可以用組、排、行、等多種方式,還可以從不同的方位來(lái)描述物體的位置。為了我們?cè)诖_定位置的時(shí)候語(yǔ)言達(dá)成一致,一般規(guī)定:豎排叫列,橫排叫行。