預(yù)設(shè) 不知走了多久,就在身心俱疲之際,眼前忽然出現(xiàn)一片仙境。清澈的溪流蜿蜒流動(dòng),與溪石相撞,發(fā)出清脆的聲響。沿著溪流走上幾百步,兩岸仍是一片片茂密的桃花林,晴空下,桃枝交錯(cuò),紛紛擾擾;桃花繽紛迷離,似紅云,似粉霞。而桃林地面上則青草蔥蘢,就連路過(guò)的清風(fēng)也沾上桃香,惹下了一場(chǎng)桃花雨。只見(jiàn)那些花瓣調(diào)皮地在空中起舞,最后或落在岸上,與青草私語(yǔ),或落于溪中,隨流水旅行……設(shè)問(wèn)2:看到這樣一片美麗而又奇特的桃花林,漁人又有什么感受呢?預(yù)設(shè) “忽逢”一詞體現(xiàn)了漁人的驚喜之情。“漁人甚異之,復(fù)前行,欲窮其林”,體現(xiàn)了漁人十分好奇,急切地想探尋桃花林的心理。(2)在朗讀中感受美。(教師指導(dǎo)學(xué)生在朗讀中感受桃林之美和漁人之驚喜。)朗讀指導(dǎo):“忽逢”要讀出驚喜,速度稍快,“數(shù)百步”三字要強(qiáng)調(diào)重讀,以體現(xiàn)桃林的范圍之廣。“中無(wú)雜樹(shù),芳草鮮美,落英繽紛”要以“二二”的節(jié)奏斷開(kāi),但前后之間要語(yǔ)氣貫連,讀得似斷實(shí)連,語(yǔ)速要稍慢,將一幅幅畫(huà)面徐徐呈現(xiàn)出來(lái),就像放電影一般,以體現(xiàn)漁人此刻的癡迷沉醉之情。
4.組織材料師:一篇游記作品,既要有“靈魂”“血肉”,還得有“筋骨”——材料安排。請(qǐng)大家運(yùn)用我們上節(jié)課學(xué)習(xí)的方法來(lái)組織材料。方法:(1)按照自己的游蹤或獨(dú)特體驗(yàn),安排寫(xiě)作順序。(2)能突出參觀場(chǎng)所特征的要詳寫(xiě),其余的略寫(xiě)或不寫(xiě)。(3)豐富文章內(nèi)容:適當(dāng)加入敘事,引入一些典故、傳說(shuō)、史料、評(píng)價(jià)或詩(shī)文名句。示例:(1)寫(xiě)作順序:以作者的參觀路線為線索。(2)詳略安排:詳寫(xiě)魯迅先生北京故居的工作室兼臥室,以突出魯迅簡(jiǎn)樸、惜時(shí)的品質(zhì)和忘我工作的精神品質(zhì);詳寫(xiě)陳列大廳是為了贊揚(yáng)先生的民族精神。其余的略寫(xiě)。(3)引入內(nèi)容:引用古詩(shī)句“望崦嵫而勿迫,恐鵜之先鳴”,表現(xiàn)先生惜時(shí)的品質(zhì)。(生交流,師點(diǎn)評(píng))預(yù)設(shè) (1)寫(xiě)作順序:一樓的青銅器—二樓的陶器—三樓的古代畫(huà)作。
四、總結(jié)歸納,延伸拓展師:作者“觀古今于須臾,撫四海于一瞬”,把時(shí)間的概念,從人們?nèi)粘5母杏X(jué)延伸到自然界中,引出了關(guān)于時(shí)間的又一種境界。請(qǐng)同學(xué)們根據(jù)你所知道的課內(nèi)外知識(shí),完成下面的拓展任務(wù):拓展任務(wù)一巖石記錄時(shí)間的重要方式是它保存了許多的歷史痕跡。請(qǐng)閱讀課文第22—29段并分組討論,說(shuō)說(shuō)巖石保存了哪些歷史痕跡,它對(duì)人類有著怎樣的意義,你從中得到了哪些啟示。 (生分小組探討,批注,然后交流回答)預(yù)設(shè) 示例:①記錄了地殼的活動(dòng);②記錄了氣候的變化;③記錄了古代生物的狀況;④記錄了地球歷史的發(fā)展過(guò)程;⑤記錄了自然界某些轉(zhuǎn)瞬即逝的活動(dòng)。意義與啟示:對(duì)巖石的研究,不僅使我們?cè)鲩L(zhǎng)了知識(shí),對(duì)自然界與史前歷史有了更多的認(rèn)識(shí),還使我們擁有了開(kāi)發(fā)史前資源的可能性,能為人類謀取幸福。我們要秉承這種辯證主義思想觀念,發(fā)揚(yáng)科學(xué)探索的精神,在人類前行的歷史上,貢獻(xiàn)出一份力量。
預(yù)設(shè) (1)“大道”可以理解為治理社會(huì)的最高準(zhǔn)則?!按笸敝溉寮业睦硐肷鐣?huì)或人類社會(huì)的最高階段?!按蟮乐幸病笔侵笀?zhí)政者施行“大道”,老百姓便可以生活在安定和平的大同社會(huì)。(2)天下為公;選賢與能,講信修睦。(3)“大同”社會(huì)是以“五帝之世”的傳聞為依據(jù),經(jīng)過(guò)加工提煉而后構(gòu)想出來(lái)的一個(gè)理想社會(huì)的模式。意在建立一個(gè)合理的社會(huì),以消除現(xiàn)實(shí)社會(huì)中的黑暗現(xiàn)象和不合理的地方。3.拓展延伸師:你認(rèn)為這種理想社會(huì)在當(dāng)時(shí)實(shí)現(xiàn)了嗎?如何理解這種思想?(生交流討論,師引導(dǎo))預(yù)設(shè) “謀閉而不興,盜竊亂賊而不作”是一種和平安定的局面,是對(duì)“大同”社會(huì)的一個(gè)總結(jié),這個(gè)理想在當(dāng)時(shí)并沒(méi)有實(shí)現(xiàn),因?yàn)樾∩a(chǎn)的物質(zhì)基礎(chǔ)不足以支撐“大同”社會(huì)的運(yùn)轉(zhuǎn),還有搞陰謀、盜竊財(cái)物和作亂等奸邪之事。這種理想在當(dāng)時(shí)雖不能實(shí)現(xiàn),但它具有積極意義,是我們的精神財(cái)富。
三、說(shuō)教學(xué)目標(biāo)基于以上對(duì)教材和學(xué)情的分析,我在研讀新課的要求,閱讀文學(xué)作品時(shí)也有著情感體驗(yàn)說(shuō)感知文章的內(nèi)涵,從中獲得對(duì)自然社會(huì)人生的有益啟示。從三維目標(biāo)三方面制定了如下教學(xué)目標(biāo):1.了解作者的生平與新月派詩(shī)歌“三美”主張,把握詩(shī)歌內(nèi)容2.通過(guò)誦讀法、自主合作探究法,多角度體會(huì)詩(shī)歌的語(yǔ)言美,這也是本節(jié)課的重難點(diǎn)。3,理解作者隱藏在文字下深沉的母愛(ài),體會(huì)生命的美好。四、說(shuō)教法學(xué)法教學(xué)的目的所在,正如葉圣陶先生所說(shuō),教是為了不教,學(xué)是為了會(huì)學(xué),教學(xué)中理應(yīng)靈活處理多種教學(xué)方法,因此,我將多媒體輔助教學(xué)法、提問(wèn)法,點(diǎn)撥法的教法與學(xué)生誦讀品味法、圈點(diǎn)勾畫(huà)法、自主合作探究法的學(xué)法結(jié)合起來(lái),以求達(dá)到事半功倍的效果。
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(huà)畫(huà)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。
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(xiě)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.
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
教學(xué)目標(biāo):1. 掌握本單元一些重點(diǎn)詞匯的寫(xiě)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.”P(pán)art 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.
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.
目標(biāo)導(dǎo)學(xué)三:學(xué)習(xí)綜合運(yùn)用多種表達(dá)方式明確:本文以記敘為主,穿插著議論、抒情。第一部分,作者首先抒發(fā)了自己的親身感受,又以“誰(shuí)是我們最可愛(ài)的人”設(shè)問(wèn)作為記敘、議論的中心,接著用一個(gè)氣勢(shì)磅礴的排比句揭示了志愿軍戰(zhàn)士的精神風(fēng)貌,從意志、品質(zhì)、氣質(zhì)、胸懷四個(gè)方面進(jìn)行高度評(píng)價(jià)和贊美,為文章具體事例的敘述做了思想認(rèn)識(shí)方面的提示和感情的鋪墊。第二部分,文章以記敘為主,具體敘述了三個(gè)典型事例,在敘述完每一個(gè)事例后,文章都穿插了議論、抒情。這些議論抒情,既起到深化主題的作用,又增強(qiáng)了文章的感染力。第三部分,作者告訴人們要珍惜戰(zhàn)士們用鮮血和生命換來(lái)的幸福生活。沒(méi)有用單調(diào)枯燥的說(shuō)教,而是用朋友的懇談來(lái)啟迪人們感受到幸福生活的來(lái)之不易。拓展延伸:收集新時(shí)代“最可愛(ài)的人”典型事跡的資料,準(zhǔn)備舉辦演講會(huì)。
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).
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.
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。
(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.
(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.
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(huà)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).