【目標(biāo)導(dǎo)航】1.培養(yǎng)留心觀察、勤于考證的意識(shí),能初步認(rèn)識(shí)到“行萬(wàn)里路”是增長(zhǎng)人生見(jiàn)識(shí)和鍛煉獨(dú)立生活能力的必要途徑。2.抓住特點(diǎn)描寫景物,重點(diǎn)突出,詳略得當(dāng)。3.在寫作活動(dòng)中了解祖國(guó)大好河山,增強(qiáng)熱愛(ài)家鄉(xiāng)和祖國(guó)的情感,學(xué)寫文情并茂的游記?!菊n時(shí)安排】2課時(shí)?!菊n時(shí)分配】建議第一課時(shí)進(jìn)行作文指導(dǎo)與寫作,第二課時(shí)進(jìn)行批改、評(píng)講、修改。了解作文文題,熟悉作文要求,搜集相關(guān)素材,為習(xí)作做準(zhǔn)備。1.游記常常要對(duì)某處景物做定點(diǎn)觀察,以寫出景物的特點(diǎn)。選擇你游覽過(guò)的一個(gè)景點(diǎn),圍繞其中的一處風(fēng)景,寫一個(gè)片段。200字左右。2.我們應(yīng)該都有過(guò)出游的經(jīng)歷。旅途中,我們不僅觀賞自然風(fēng)光,了解民風(fēng)民俗,同時(shí)也會(huì)有許多新奇的感受,產(chǎn)生很多思考和遐想。自擬題目,寫一篇游記。不少于600字。3.你一定看過(guò)一些展覽,參觀過(guò)一些紀(jì)念館或博物館,請(qǐng)選擇一次這樣的經(jīng)歷,以《參觀 》為題,寫一篇參觀記。不少于600字。
【設(shè)計(jì)意圖】以課文為本,積累知識(shí),領(lǐng)會(huì)其寫法,提高閱讀鑒賞能力是必須的,但文中的知識(shí)點(diǎn)很多,時(shí)間有限,教師不可能面面俱到。故本板塊設(shè)計(jì)側(cè)重反語(yǔ)的表達(dá)效果,教師啟發(fā)引路為輔,學(xué)生合作探究為主。三、總結(jié)交流,拓展延伸學(xué)完本文,我們思緒萬(wàn)千,有對(duì)雨果的欽佩,有對(duì)英法聯(lián)軍的痛恨,有對(duì)清政府的憤懣,有對(duì)戰(zhàn)爭(zhēng)的厭惡……請(qǐng)以《,我想對(duì)你說(shuō)》為題,說(shuō)一段話,談?wù)勀愕母邢?。【設(shè)計(jì)意圖】學(xué)以致用,才是教學(xué)的最好歸宿。引導(dǎo)學(xué)生與文本中的人、事對(duì)話,既可加深學(xué)生對(duì)所學(xué)知識(shí)的理解,又可鍛煉學(xué)生運(yùn)用知識(shí)、獨(dú)立思考的能力,還能激發(fā)為振興中華而發(fā)憤圖強(qiáng)的愛(ài)國(guó)激情。結(jié)束語(yǔ):一代名園圓明園毀滅了,它毀于英法侵略者之手,也毀于清政府的腐敗無(wú)能。它的毀滅,既是西方侵略者野蠻摧殘人類文化的見(jiàn)證,又是文明古國(guó)落后也要挨打的證明,我們中華民族不想欺侮其他民族,但也決不能允許別人欺侮我們。少年強(qiáng),則中國(guó)強(qiáng)!同學(xué)們,為了中華民族的偉大復(fù)興,為了圓明園類似的悲劇不再發(fā)生,我們要勤奮學(xué)習(xí),努力奮斗!
(1)一個(gè)快落山的太陽(yáng),跟大家講的,更多的是自己一生奮斗過(guò)來(lái)的體會(huì)。指61歲的老人。(2)加入人家說(shuō)我是權(quán)威,也許還馬馬虎虎。作者自謙的說(shuō)法,指成績(jī)還過(guò)得去。(3)明明是一個(gè)過(guò)去時(shí)態(tài),大家誤認(rèn)為是現(xiàn)在時(shí)態(tài)。指作者認(rèn)為自己不適合再做權(quán)威了。(4)扶植年輕人我覺(jué)得是一種歷史的潮流,當(dāng)然我們要?jiǎng)?chuàng)造條件,就是把他們推到需要刺激的風(fēng)口浪尖上。比喻重要的崗位或市場(chǎng)的前沿?!靖形蚓示渥印?.所以我知道自己是一個(gè)下午四五點(diǎn)鐘的太陽(yáng)。各位呢,上午八九點(diǎn)鐘的太陽(yáng),這是本科生;碩士生呢,九十點(diǎn)鐘的太陽(yáng);博士生呢,十點(diǎn)十一點(diǎn)鐘的太陽(yáng)。比喻,拉近了與聽(tīng)眾的距離,倍感親切、期望和鼓舞。2.所以1992年前電視臺(tái)采訪我,我基本上都拒絕了。透過(guò)細(xì)節(jié),體現(xiàn)了堅(jiān)持不懈的科研精神。
二、說(shuō)學(xué)情學(xué)生是課堂的主體,教師應(yīng)本著“因材施教”的理念結(jié)合學(xué)生的基本情況進(jìn)行備課。九年級(jí)的學(xué)生已經(jīng)有了較好的積累,基本詞匯、常見(jiàn)修辭等等都有了較為自如的把握。對(duì)于詩(shī)歌這種文體,他們已接觸過(guò)很多年。但由于對(duì)詩(shī)歌這種文體的情感把握還不夠精準(zhǔn)到位。此外,這一階段的學(xué)生已經(jīng)有了一定的寫作和口語(yǔ)表達(dá)能力,我將在本文的教學(xué)過(guò)程中設(shè)置口語(yǔ)表達(dá)及寫作的環(huán)節(jié),學(xué)生可通過(guò)實(shí)踐進(jìn)一步強(qiáng)化這方面的能力。三、說(shuō)教學(xué)目標(biāo)因此,基于教材和學(xué)情,我從課程標(biāo)準(zhǔn)中“全面提高學(xué)生語(yǔ)文素養(yǎng)”的基本理念出發(fā),設(shè)計(jì)了以下三個(gè)維度的教學(xué)目標(biāo):1.知識(shí)與能力:結(jié)合注釋解釋全文大意,并能初步體會(huì)是中蘊(yùn)含的情感。2.過(guò)程與方法:通過(guò)有感情地朗讀、獨(dú)立思考、討論、對(duì)文章中關(guān)鍵內(nèi)容的探究等過(guò)程,體會(huì)文章語(yǔ)言的優(yōu)美和表達(dá)的精妙。3.情感態(tài)度與價(jià)值觀:懂得詩(shī)人重新投入生活的意愿及堅(jiān)韌不拔的意志。
Ⅰ. Teaching Aims and Demands1. Knowledge Objects(1) Key Vocabularyoversleep(2) Target LanguageWhat happened?I overslept. And by the time I got up, my brother had already gotten in the shower.2. Ability Objects(1) Teach the students to use the new words.(2) Train the students to narrate past events with the Past Perfect Tense.(3) Train the students' listening and speaking skills with the target language.3. Moral ObjectIt’s a good habit to go to bed early in the evening and get up early in the morning. So you’ll never be in a hurry in the morning.Ⅱ. Teaching Key Points1. Key Vocabularyoversleep2. Target LanguageNarrate past events with the Past Perfect TenseⅢ. Teaching Difficult Points1. Train the students to narrate past events with the Past Perfect Tense.2. Train the students to understand the target language in spoken conversation.Ⅳ. Teaching Methods1. Thinking of examples from the students' real lives.2. Making sentences by looking at the pictures.Ⅴ. Teaching AidA tape recorderⅥ. Teaching ProceduresStep I Revision1. Revise the language points in Unit 8.Ask some questions like this: What volunteer work would you like to do?Help the students to answer, I’d like to…/I love to…/I hope to2. Practice the dialogue in Activity 3c on page 62 again. Get students to role play the similar dialogues with the following.
1. 教材分析本單元以how do things affect you?為話題, 從顏色、天氣、音樂(lè)、廣告、產(chǎn)品等方面談?wù)摿送饨缡挛锶绾斡绊懭说男那?。要求學(xué)生掌握表達(dá)某物或某事給人帶來(lái)的感覺(jué)、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(kāi)思維(1a)、聽(tīng)力(1b)、口語(yǔ)(1c)訓(xùn)練;第二模塊圍繞How does music affect you? 進(jìn)行聽(tīng)力(2a-2b)、口語(yǔ)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(kāi)訓(xùn)練,訓(xùn)練形式為閱讀和問(wèn)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(kāi)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(kāi)訓(xùn)練;第二模塊繼續(xù)圍繞How do things affect you? 進(jìn)行聽(tīng)力(2a-2b)、口語(yǔ)對(duì)話訓(xùn)練(2c);第三模塊圍繞“Advertising”這一話題展開(kāi)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(yǔ)訓(xùn)練形式展開(kāi)小組活動(dòng)。
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.
本單元主要圍繞著有關(guān)瀕臨滅絕的動(dòng)物這一話題,學(xué)習(xí)了應(yīng)該怎樣保護(hù)我們的環(huán)境,以及就某一問(wèn)題展開(kāi)辯論。目標(biāo)提示語(yǔ)言目標(biāo)能夠運(yùn)用所學(xué)知識(shí),就某一問(wèn)題展開(kāi)辯論。認(rèn)知目標(biāo)1、復(fù)習(xí)一些語(yǔ)法:現(xiàn)在進(jìn)行時(shí)、一般現(xiàn)在時(shí)、用used to 表示一般過(guò)去時(shí)、現(xiàn)在完成時(shí)、一般過(guò)去時(shí)的被動(dòng)語(yǔ)態(tài)。2、學(xué)會(huì)表達(dá)同意和不同意。3、學(xué)會(huì)以下基本句型:We’re trying to save the manatees.Manatees eat about 100 pounds of food a day.There used to be a lot of manatees.In 1972,it was discovered that they were endangered.Some of the swamps have become polluted.情感目標(biāo)了解一些瀕臨滅絕的動(dòng)物的生活習(xí)性和瀕臨滅絕的原因,教育學(xué)生應(yīng)該如何保護(hù)環(huán)境。教學(xué)提示充分利用多媒體等教學(xué)設(shè)備,創(chuàng)設(shè)與本課話題相關(guān)的情境,如各種不同種類的動(dòng)物、動(dòng)物園以及有關(guān)環(huán)境的畫畫等等。圍繞著本單元的教學(xué)目標(biāo),設(shè)計(jì)一些貼近學(xué)生實(shí)際的教學(xué)任務(wù),如讓學(xué)生談?wù)撟约鹤钕矚g的動(dòng)物,如何拯救瀕危動(dòng)物,如何保護(hù)環(huán)境等等。讓學(xué)生根據(jù)所學(xué)知識(shí),就動(dòng)物園是否對(duì)動(dòng)物有利以及其他的話題進(jìn)行辯論。
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(kāi)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.
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
已知一水壩的橫斷面是梯形ABCD,下底BC長(zhǎng)14m,斜坡AB的坡度為3∶3,另一腰CD與下底的夾角為45°,且長(zhǎng)為46m,求它的上底的長(zhǎng)(精確到0.1m,參考數(shù)據(jù):2≈1.414,3≈1.732).解析:過(guò)點(diǎn)A作AE⊥BC于E,過(guò)點(diǎn)D作DF⊥BC于F,根據(jù)已知條件求出AE=DF的值,再根據(jù)坡度求出BE,最后根據(jù)EF=BC-BE-FC求出AD.解:過(guò)點(diǎn)A作AE⊥BC,過(guò)點(diǎn)D作DF⊥BC,垂足分別為E、F.∵CD與BC的夾角為45°,∴∠DCF=45°,∴∠CDF=45°.∵CD=46m,∴DF=CF=462=43(m),∴AE=DF=43m.∵斜坡AB的坡度為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,它的上底的長(zhǎng)約為3.1m.方法總結(jié):考查對(duì)坡度的理解及梯形的性質(zhì)的掌握情況.解決問(wèn)題的關(guān)鍵是添加輔助線構(gòu)造直角三角形.
一、本章知識(shí)要點(diǎn): 1、銳角三角函數(shù)的概念; 2、解直角三角形。二、本章教材分析: (一).使學(xué)生正確理解和掌握三角函數(shù)的定義,才能正確理解和掌握直角三角形中邊與角的相互關(guān)系,進(jìn)而才能利用直角三角形的邊與角的相互關(guān)系去解直角三角形,因此三角形函數(shù)定義既是本章的重點(diǎn)又是理解本章知識(shí)的關(guān)鍵,而且也是本章知識(shí)的難點(diǎn)。如何解決這一關(guān)鍵問(wèn)題,教材采取了以下的教學(xué)步驟:1. 從實(shí)際中提出問(wèn)題,如修建揚(yáng)水站的實(shí)例,這一實(shí)例可歸結(jié)為已知RtΔ的一個(gè)銳角和斜邊求已知角的對(duì)邊的問(wèn)題。顯然用勾股定理和直角三角形兩個(gè)銳角互余中的邊與邊或角與角的關(guān)系無(wú)法解出了,因此需要進(jìn)一步來(lái)研究直角三角形中邊與角的相互關(guān)系。2. 教材又采取了從特殊到一般的研究方法利用學(xué)生的舊知識(shí),以含30°、45°的直角三角形為例:揭示了直角三角形中一個(gè)銳角確定為30°時(shí),那么這角的對(duì)邊與斜邊之比就確定比值為1:2。
4.x的值是否可以任意取?如果不能任意取,請(qǐng)求出它的范圍,[x的值不能任意取,其范圍是0≤x≤2]5.若設(shè)該商品每天的利潤(rùn)為y元,求y與x的函數(shù)關(guān)系式。[y=(10-8-x) (100+100x)(0≤x≤2)]將函數(shù)關(guān)系式y(tǒng)=x(20-2x)(0 <x <10=化為:y=-2x2+20x (0<x<10)…(1)將函數(shù)關(guān)系式y(tǒng)=(10-8-x)(100+100x)(0≤x≤2)化為:y=-100x2+100x+20D (0≤x≤2)…(2)三、觀察;概括1.教師引導(dǎo)學(xué)生觀察函數(shù)關(guān)系式(1)和(2),提出問(wèn)題讓學(xué)生思考回答;(1)函數(shù)關(guān)系式(1)和(2)的自變量各有幾個(gè)? (各有1個(gè))(2)多項(xiàng)式-2x2+20和-100x2+100x+200分別是幾次多項(xiàng)式?(分別是二次多項(xiàng)式)(3)函數(shù)關(guān)系式(1)和(2)有什么共同特點(diǎn)? (都是用自變量的二次多項(xiàng)式來(lái)表示的)(4)本章導(dǎo)圖中的問(wèn)題以及P1頁(yè)的問(wèn)題2有什么共同特點(diǎn)?讓學(xué)生討論、歸結(jié)為:自變量x為何值時(shí),函數(shù)y取得最大值。2.二次函數(shù)定義:形如y=ax2+bx+c (a、b、、c是常數(shù),a≠0)的函數(shù)叫做x的二次函數(shù), a叫做二次函數(shù)的系數(shù),b叫做一次項(xiàng)的系數(shù),c叫作常數(shù)項(xiàng).
(3)若要滿足結(jié)論,則∠BFO=∠GFC,根據(jù)切線長(zhǎng)定理得∠BFO=∠EFO,從而得到這三個(gè)角應(yīng)是60°,然后結(jié)合已知的正方形的邊長(zhǎng),也是圓的直徑,利用30°的直角三角形的知識(shí)進(jìn)行計(jì)算.解:(1)FB=FE,PE=PA;(2)四邊形CDPF的周長(zhǎng)為FC+CD+DP+PE+EF=FC+CD+DP+PA+BF=BF+FC+CD+DP+PA=BC+CD+DA=23×3=63;(3)假設(shè)存在點(diǎn)P,使BF·FG=CF·OF.∴BFOF=CFFG.∵cos∠OFB=BFOF,cos∠GFC=CFFG,∴∠OFB=∠GFC.∵∠OFB=∠OFE,∴∠OFE=∠OFB=∠GFC=60°,∴在Rt△OFB中,BF=OBtan∠OFB=OBtan60°=1.在Rt△GFC中,∵CG=CF·tan∠GFC=CF·tan60°=(23-1)×3=6-3,∴DG=CG-CD=6-33,∴DP=DG·tan∠PGD=DG·tan30°=23-3,∴AP=AD-DP=23-(23-3)=3.方法總結(jié):由于存在性問(wèn)題的結(jié)論有兩種可能,所以具有開(kāi)放的特征,在假設(shè)存在性以后進(jìn)行的推理或計(jì)算.一般思路是:假設(shè)存在——推理論證——得出結(jié)論.若能導(dǎo)出合理的結(jié)果,就做出“存在”的判斷,若導(dǎo)出矛盾,就做出“不存在”的判斷.
教學(xué)目標(biāo):1、理解并掌握正切的含義,會(huì)在直角三角形中求出某個(gè)銳角的正切值。2、了解計(jì)算一個(gè)銳角的正切值的方法。教學(xué)重點(diǎn):理解并掌握正切的含義,會(huì)在直角三角形中求出某個(gè)銳角的正切值。教學(xué)難點(diǎn):計(jì)算一個(gè)銳角的正切值的方法。教學(xué)過(guò)程:一、觀察回答:如圖某體育館,為了方便不同需求的觀眾設(shè)計(jì)了多種形式的臺(tái)階。下列圖中的兩個(gè)臺(tái)階哪個(gè)更陡?你是怎么判斷的?圖(1) 圖(2)[點(diǎn)撥]可將這兩個(gè)臺(tái)階抽象地看成兩個(gè)三角形答:圖 的臺(tái)階更陡,理由 二、探索活動(dòng)1、思考與探索一:除了用臺(tái)階的傾斜角度大小外,還可以如何描述臺(tái)階的傾斜程度呢?① 可通過(guò)測(cè)量BC與AC的長(zhǎng)度,② 再算出它們的比,來(lái)說(shuō)明臺(tái)階的傾斜程度。(思考:BC與AC長(zhǎng)度的比與臺(tái)階的傾斜程度有何關(guān)系?)答:_________________.③ 討論:你還可以用其它什么方法?能說(shuō)出你的理由嗎?答:________________________.2、思考與探索二:
解析:根據(jù)銳角三角函數(shù)的概念,知sin70°<1,cos70°<1,tan70°>1.又cos70°=sin20°,銳角的正弦值隨著角的增大而增大,∴sin70°>sin20°=cos70°.故選D.方法總結(jié):當(dāng)角度在0°cosA>0.當(dāng)角度在45°<∠A<90°間變化時(shí),tanA>1.變式訓(xùn)練:見(jiàn)《學(xué)練優(yōu)》本課時(shí)練習(xí)“課堂達(dá)標(biāo)訓(xùn)練”第10題【類型四】 與三角函數(shù)有關(guān)的探究性問(wèn)題在Rt△ABC中,∠C=90°,D為BC邊(除端點(diǎn)外)上的一點(diǎn),設(shè)∠ADC=α,∠B=β.(1)猜想sinα與sinβ的大小關(guān)系;(2)試證明你的結(jié)論.解析:(1)因?yàn)樵凇鰽BD中,∠ADC為△ABD的外角,可知∠ADC>∠B,可猜想sinα>sinβ;(2)利用三角函數(shù)的定義可求出sinα,sinβ的關(guān)系式即可得出結(jié)論.解:(1)猜想:sinα>sinβ;(2)∵∠C=90°,∴sinα=ACAD ,sinβ=ACAB .∵AD<AB,∴ACAD>ACAB,即sinα>sinβ.方法總結(jié):利用三角函數(shù)的定義把兩角的正弦值表示成線段的比,然后進(jìn)行比較是解題的關(guān)鍵.
[教學(xué)目標(biāo)]1、 理解并掌握正弦、余弦的含義,會(huì)在直角三角形中求出某個(gè)銳角的正弦和余弦值。2、能用函數(shù)的觀點(diǎn)理解正弦、余弦和正切。[教學(xué)重點(diǎn)與難點(diǎn)] 在直角三角形中求出某個(gè)銳角的正弦和余弦值。[教學(xué)過(guò)程] 一、情景創(chuàng)設(shè)1、問(wèn)題1:如圖,小明沿著某斜坡向上行走了13m后,他的相對(duì)位置升高了5m,如果他沿著該斜坡行走了20m,那么他的相對(duì)位置升高了多少?行走了a m呢?2、問(wèn)題2:在上述問(wèn)題中,他在水平方向又分別前進(jìn)了多遠(yuǎn)?二、探索活動(dòng)1、思考:從上面的兩個(gè)問(wèn)題可以看出:當(dāng)直角三角形的一個(gè)銳角的大小已確定時(shí),它的對(duì)邊與斜邊的比值________;它的鄰邊與斜邊的比值________。(根據(jù)是__________________。)2、正弦的定義 如圖,在Rt△ABC中,∠C=90°,我們把銳角∠A的對(duì)邊a與斜邊c的比叫做∠A的______,記作________,即:sinA=________=________.3、余弦的定義 如圖,在Rt△ABC中,∠C=90°,我們把銳角∠A的鄰邊b與斜邊c的比叫做∠A的______,記作=_________,即:cosA=______=_____。(你能寫出∠B的正弦、余弦的表達(dá)式嗎?)試試看.___________.
(2)由題意可得-10x2+180x+400=1120,整理得x2-18x+72=0,解得x1=6,x2=12(舍去).所以,該產(chǎn)品的質(zhì)量檔次為第6檔.方法總結(jié):解決此類問(wèn)題的關(guān)鍵是要吃透題意,確定變量,建立函數(shù)模型.變式訓(xùn)練:見(jiàn)《學(xué)練優(yōu)》本課時(shí)練習(xí)“課后鞏固提升”第8題三、板書(shū)設(shè)計(jì)二次函數(shù)1.二次函數(shù)的概念2.從實(shí)際問(wèn)題中抽象出二次函數(shù)解析式二次函數(shù)是一種常見(jiàn)的函數(shù),應(yīng)用非常廣泛,它是客觀地反映現(xiàn)實(shí)世界中變量之間的數(shù)量關(guān)系和變化規(guī)律的一種非常重要的數(shù)學(xué)模型.許多實(shí)際問(wèn)題往往可以歸結(jié)為二次函數(shù)加以研究.本節(jié)課是學(xué)習(xí)二次函數(shù)的第一節(jié)課,通過(guò)實(shí)例引入二次函數(shù)的概念,并學(xué)習(xí)求一些簡(jiǎn)單的實(shí)際問(wèn)題中二次函數(shù)的解析式.在教學(xué)中要重視二次函數(shù)概念的形成和建構(gòu),在概念的學(xué)習(xí)過(guò)程中,讓學(xué)生體驗(yàn)從問(wèn)題出發(fā)到列二次函數(shù)解析式的過(guò)程,體驗(yàn)用函數(shù)思想去描述、研究變量之間變化規(guī)律的意義.
解析:首先求得圓的半徑長(zhǎng),然后求得P、Q、R到Q′的距離,即可作出判斷.解:⊙O′的半徑是r= 12+12=2,PO′=2>2,則點(diǎn)P在⊙O′的外部;QO′=1<2,則點(diǎn)Q在⊙O′的內(nèi)部;RO′=(2-1)2+(2-1)2=2=圓的半徑,故點(diǎn)R在圓上.方法總結(jié):注意運(yùn)用平面內(nèi)兩點(diǎn)之間的距離公式,設(shè)平面內(nèi)任意兩點(diǎn)的坐標(biāo)分別為A(x1,y1),B(x2,y2),則AB=(x1-x2)2+(y1-y2)2.【類型四】 點(diǎn)與圓的位置關(guān)系的實(shí)際應(yīng)用如圖,城市A的正北方向50千米的B處,有一無(wú)線電信號(hào)發(fā)射塔.已知,該發(fā)射塔發(fā)射的無(wú)線電信號(hào)的有效半徑為100千米,AC是一條直達(dá)C城的公路,從A城發(fā)往C城的客車車速為60千米/時(shí).(1)當(dāng)客車從A城出發(fā)開(kāi)往C城時(shí),某人立即打開(kāi)無(wú)線電收音機(jī),客車行駛了0.5小時(shí)的時(shí)候,接收信號(hào)最強(qiáng).此時(shí),客車到發(fā)射塔的距離是多少千米(離發(fā)射塔越近,信號(hào)越強(qiáng))?(2)客車從A城到C城共行駛2小時(shí),請(qǐng)你判斷到C城后還能接收到信號(hào)嗎?請(qǐng)說(shuō)明理由.
我們知道圓是一個(gè)旋轉(zhuǎn)對(duì)稱圖形,無(wú)論繞圓心旋轉(zhuǎn)多少度,它都能與自身重合,對(duì)稱中心即為其圓心.將圖中的扇形AOB(陰影部分)繞點(diǎn)O逆時(shí)針旋轉(zhuǎn)某個(gè)角度,畫出旋轉(zhuǎn)之后的圖形,比較前后兩個(gè)圖形,你能發(fā)現(xiàn)什么?二、合作探究探究點(diǎn):圓心角、弧、弦之間的關(guān)系【類型一】 利用圓心角、弧、弦之間的關(guān)系證明線段相等如圖,M為⊙O上一點(diǎn),MA︵=MB︵,MD⊥OA于D,ME⊥OB于E,求證:MD=ME.解析:連接MO,根據(jù)等弧對(duì)等圓心角,則∠MOD=∠MOE,再由角平分線的性質(zhì),得出MD=ME.證明:連接MO,∵ MA︵=MB︵,∴∠MOD=∠MOE,又∵M(jìn)D⊥OA于D,ME⊥OB于E,∴MD=ME.方法總結(jié):圓心角、弧、弦之間相等關(guān)系的定理可以用來(lái)證明線段相等.本題考查了等弧對(duì)等圓心角,以及角平分線的性質(zhì).