A.城鎮(zhèn)數(shù)量猛增B.城市規(guī)模不斷擴(kuò)大【設(shè)計(jì)意圖】通過(guò)讀圖的對(duì)比分析,提高學(xué)生提取信息以及對(duì)比分析問(wèn)題的能力,通過(guò)小組之間的討論,培養(yǎng)合作能力。五、課堂小結(jié)和布置作業(yè)關(guān)于課堂小結(jié),我打算讓學(xué)生自己來(lái)總結(jié),你這節(jié)課學(xué)到了什么。這樣既可以提高學(xué)生的總結(jié)概括能力,也可以讓我在第一時(shí)間內(nèi)獲得它們的學(xué)習(xí)反饋。(本節(jié)課主要學(xué)習(xí)了珠三角的位置和范圍以及改革開(kāi)放以來(lái)珠三角地區(qū)工業(yè)化和城市化的發(fā)展。)關(guān)于作業(yè)的布置,我打算采用分層次布置作業(yè)法。第一個(gè)層次的作業(yè)是基礎(chǔ)作業(yè),要求每一位同學(xué)都掌握,第二個(gè)層次的作業(yè)是彈性作業(yè),學(xué)生可以根據(jù)自己的情況來(lái)選做。整個(gè)這堂課,老師只是作為一個(gè)引導(dǎo)者、組織者的角色,學(xué)生才是課堂上真正的主人,是自我意義的建構(gòu)者和知識(shí)的生成者,被動(dòng)的、復(fù)制式的課堂將離我們遠(yuǎn)去。
為了加強(qiáng)學(xué)生的理解,讓學(xué)生討論以下問(wèn)題。由師生共同總結(jié)。播放一個(gè)短時(shí)視頻,讓學(xué)生認(rèn)識(shí)到水的重要性后,展示節(jié)水標(biāo)識(shí),說(shuō)明由來(lái)。細(xì)胞中的無(wú)機(jī)鹽這部分,我將展示圖表,并列出問(wèn)題:表中哪些成分屬于無(wú)機(jī)鹽?為什么要在運(yùn)動(dòng)員喝的飲料中添加無(wú)機(jī)鹽?無(wú)機(jī)鹽在細(xì)胞的生活中起什么作用?然后展示廣告語(yǔ),讓學(xué)生思考和討論以下問(wèn)題,并得到答案。再閱讀課本,驗(yàn)證自己的答案是否正確。關(guān)于無(wú)機(jī)鹽的作用較難理解,通過(guò)列舉人體生活與健康中的各種實(shí)例來(lái)加深感性認(rèn)識(shí),加強(qiáng)對(duì)理論知識(shí)的理解3、課堂小結(jié),強(qiáng)化認(rèn)識(shí)。(3—5分鐘)課堂小結(jié),可以把課堂傳授的知識(shí)盡快地轉(zhuǎn)化為學(xué)生的素質(zhì);簡(jiǎn)單扼要的課堂小結(jié),可使學(xué)生更深刻地理解理論知識(shí)在實(shí)際生活中的應(yīng)用,并且逐漸地培養(yǎng)學(xué)生具有良好的個(gè)性。4、板書(shū)設(shè)計(jì)我比較注重直觀、系統(tǒng)的板書(shū)設(shè)計(jì),還及時(shí)地體現(xiàn)教材中的知識(shí)點(diǎn),以便于學(xué)生能夠理解掌握。5、布置作業(yè)。
3.甲午中日戰(zhàn)爭(zhēng)中國(guó)戰(zhàn)敗的原因 對(duì)于“中國(guó)戰(zhàn)敗的原因”這一難點(diǎn)的突破,主要通過(guò)設(shè)置問(wèn)題“中國(guó)之?dāng)≡趯?shí)力遜于日本嗎?”通過(guò)幻燈片全方位分析其實(shí)中國(guó)的綜合國(guó)力當(dāng)時(shí)是強(qiáng)于日本的。并且在戰(zhàn)前,日本毫無(wú)取勝的把握。讓學(xué)生結(jié)合剛學(xué)習(xí)過(guò)的戰(zhàn)爭(zhēng)原因和經(jīng)過(guò)進(jìn)行討論,從多方面分析中國(guó)戰(zhàn)敗的原因。經(jīng)過(guò)討論,學(xué)生可以得出以下結(jié)論:避戰(zhàn)自保方針,沒(méi)有積極備戰(zhàn),將領(lǐng)臨陣脫逃,教師肯定并總結(jié)答案進(jìn)行補(bǔ)充。中日對(duì)比:中國(guó)士兵出身農(nóng)民,軍事訓(xùn)練落后,散兵游勇;日本士兵出身武士,訓(xùn)練有素;中國(guó)將領(lǐng)大多臨陣脫逃,并相互猜忌,受當(dāng)時(shí)惡劣的官風(fēng)影響;李鴻章深知北洋海軍實(shí)情,缺乏軍費(fèi),軍備廢弛。為政治資本奉行避戰(zhàn)自保政策,慈禧太后挪用海軍軍費(fèi)過(guò)壽,支持李鴻章。使中方處于被動(dòng)的局面,一再貽誤戰(zhàn)機(jī)。而日本在天皇的帶動(dòng)下,全民備戰(zhàn),做了充分的戰(zhàn)爭(zhēng)準(zhǔn)備。
4,教師重點(diǎn)點(diǎn)撥以下幾個(gè)問(wèn)題⑴廊坊戰(zhàn)役:義和團(tuán)浴血奮戰(zhàn),對(duì)敵人毫不退縮, 其勝利,挫敗了西摩爾聯(lián)軍進(jìn)犯北京的計(jì)劃,沉重打擊了侵略者的氣焰,粉碎了所謂“西方軍隊(duì)無(wú)敵”的神話。這是對(duì)學(xué)生進(jìn)行愛(ài)國(guó)主義的重要素材之一,教師重點(diǎn)點(diǎn)撥突出其情感教育的重要作用。⑵讓學(xué)生(閱讀教材小字和材料,結(jié)合插圖,認(rèn)清八國(guó)聯(lián)軍對(duì)中國(guó)人民犯下的滔天罪行。)并讓學(xué)生分組探討自己的看法,一方面培養(yǎng)學(xué)生的語(yǔ)言表訴能力,另一方面通過(guò)學(xué)生的訴說(shuō)激發(fā)學(xué)生的愛(ài)國(guó)情感,樹(shù)立落后就要挨打的觀念.⑶指導(dǎo)學(xué)生通過(guò)對(duì)條約主要內(nèi)容進(jìn)行了分析,并自然得出結(jié)論:清政府完全成為帝國(guó)主義統(tǒng)治中國(guó)的工具,中國(guó)完全陷入半殖民地半封建社會(huì)。讓學(xué)生逐步學(xué)會(huì)分析和歸納能力(4)進(jìn)行拓展訓(xùn)練出示中國(guó)近代史上列強(qiáng)的大規(guī)模的侵華戰(zhàn)爭(zhēng)和中國(guó)人民的反抗斗爭(zhēng)
f.有絲分裂的意義(討論分析教學(xué)),首先引導(dǎo)學(xué)生結(jié)合所學(xué)知識(shí)討論有絲分裂的的作用,最后有教師歸納總結(jié),并要求學(xué)生在理解的基礎(chǔ)上記憶。g.無(wú)絲分裂(圖形直觀教學(xué)、簡(jiǎn)介),本部分內(nèi)容不是教學(xué)的重點(diǎn),內(nèi)容也相對(duì)簡(jiǎn)單,所以我的教學(xué)方法是直接給學(xué)生展示掛圖,再進(jìn)行簡(jiǎn)短介紹,讓學(xué)生了解即可。h.引出減數(shù)分裂的概念,為第五章學(xué)習(xí)打下基礎(chǔ)。小結(jié):新課講完以后由教師對(duì)本節(jié)內(nèi)容進(jìn)行總結(jié)鞏固和反饋:進(jìn)行一些課堂練習(xí)達(dá)到鞏固和反饋的作用。最后布置作業(yè),各種難度的作業(yè)題目均設(shè)置一些,其中簡(jiǎn)單題比重大,難題要求學(xué)生選作,這樣提高學(xué)生學(xué)習(xí)積極性。2教學(xué)媒體程序設(shè)計(jì): 細(xì)胞周期的概念(多媒體課件演示周期動(dòng)畫(huà))植物細(xì)胞有絲分裂(多媒體課件演示分裂各期動(dòng)畫(huà))動(dòng)植物細(xì)胞有絲分裂異同點(diǎn)(多媒體課件演示分裂各期動(dòng)畫(huà))有絲分裂過(guò)程中DNA和染色體數(shù)量的變化規(guī)律(掛圖演示,包括表格和函數(shù)圖象)
(3)v. 給:提出;展現(xiàn),顯現(xiàn)present sb. with sth. ; present sth. to sb. 把. . 交給;頒發(fā);授予present sth. (for sth. )/present sth. to sb. e. g. Om his birthday, his friends presented him a collection of stamps. 在他生日時(shí),他的朋友們送給他一套郵票作為禮物。The sword was presented by the family to the museum. 這家人把寶劍捐贈(zèng)給了博物館。The committee will present the final report to Parliament in June. 委員會(huì)將在六月向議會(huì)提交最后的報(bào)告。You need to present yourself better. 你需要更善于展現(xiàn)自己。It is essential that we present a united front. 至關(guān)重要的是我們要表現(xiàn)得更加團(tuán)結(jié)。Step 4 ConsolidationT:Now that we have got a general idea of these words and phrases. Lets make up some sentences using them to master them. Suggested sentences:1. Your duties include typing letters and answering the telephone. 2. It is one of the greatest roles that she has played. 3. A large number of people have applied for the job. 4. The number of the panda is declining. 5. I'11 go there, even if I have to walk. 6. He came up to me to ask for a light. 7. The novel is about a family who can't communicate with each other. 8. He based his plan on interests of most people. 9. Why doesn't he make use of his singing talent?Step 5 Summary and homeworkT:Today we dealt with several new words and phrases. After class I hope that youcan read them again and again to keep them in mind. That's all for today. You aredismissed.
In this step, give students a few minutes to read the passage . While they are reading, I will write some key words of the text on the blackboard. Then ask students to retell the passage according to the key words.By retelling, students can improve their ability of language organization and have an overall understanding of the article.Step 4 Group discussionIn this step, students will be divided into groups of 4 to discussion the following question: What qualities make a great person?After their discussion, invite a few groups to make a report to the class.This group discussion can practice students’ oral English and cultivate their abilities of cooperation and communication.Step 5. HomeworkLet students write a short passage to introduce a great person he or she admires.The homework can consolidate the knowledge the students have learned and cultivate their writing ability. Part 6 Blackboard Design(板書(shū)設(shè)計(jì))That’s all my teaching procedures. Finally, I’d like to say sth about part 6 blackboard design. On the top is the title. On the left, there will be some new words and expressions. In the middle of the blackboard, I will write some useful sentence structures so that the students can know clearly what they’ve learned and then try to master the knowledge.OK. That’s all for my presentation. Thank you for your attention.
5.5癌癥的預(yù)防作為本節(jié)最重要內(nèi)容,且與生活息息相關(guān),我采用老師引導(dǎo)、學(xué)生討論總結(jié)的方法進(jìn)行教學(xué)。從生活各方面總結(jié)出保健良方 ,既對(duì)知識(shí)有很好應(yīng)用,又體現(xiàn)對(duì)生命的熱愛(ài)。此時(shí),本節(jié)課達(dá)到高潮,同學(xué)們意氣風(fēng)發(fā),熱烈討論,實(shí)現(xiàn)本節(jié)課的教學(xué)目標(biāo)。5.6 癌癥的治療通過(guò)講述癌癥治療方法的副作用,激發(fā)學(xué)生探究生物學(xué)欲望,激勵(lì)學(xué)生立志除癌。 在此,我選用一則關(guān)于一名癌癥晚期病人運(yùn)用心理療法成功戰(zhàn)勝癌癥的故事,在于對(duì)不同層次的學(xué)生進(jìn)行多方面啟發(fā)教育,體現(xiàn)面向全體學(xué)生的課程理念。5.7 愉悅總結(jié),及時(shí)反饋本節(jié)知識(shí)點(diǎn)零散,我將帶領(lǐng)學(xué)生回憶瀏覽本節(jié)內(nèi)容,使零散知識(shí)點(diǎn)系統(tǒng)化。在課堂反饋環(huán)節(jié),我通過(guò)簡(jiǎn)單練習(xí)采用分組競(jìng)答的方式把握學(xué)生對(duì)知識(shí)的掌握程度,并給予表現(xiàn)突出的學(xué)生適當(dāng)獎(jiǎng)勵(lì),這是本節(jié)課第三個(gè)亮點(diǎn)。競(jìng)答既使課堂顯得緊湊、集中,又有利于形成學(xué)生的競(jìng)爭(zhēng)意識(shí),還使得學(xué)生的知識(shí)得以鞏固應(yīng)用。
2. let the Ss complete the forms paragraph by paragraph. Purpose here is to help Ss to get the habit of reading a passage as a whole, and pay attention to the organization of the text, as a result the Ss will fully understand the whole passage.3. ask Ss to retell the passage with the help of the key words in the form.Since the Ss in the class are in different levels, so I let them to fill in the blank to understand the meaning of the words and phrases better. ( That’s all for the while-reading. Now let’s move to the fifth step.)Step V: Post-reading (10mins) ---DiscussionIn this part students are asked to discuss in groups and list Wang Kun’s and Wang Wei’s attitudes about the trip. After that, Ss are encouraged to express their attitudes with the whole class. Collect their answers and don’t forget to praise them even if their answers may not be perfect.In this activity, discussion provides a vivid and active learning environment for Ss to communicate in English with newly learned language items. (Finally it comes to the homework.)StepⅥ: Homework (1min)1. Ss are required to read the text again after class and figure out the meaning of some complex sentences.2. Do the exercises on P19; This can help Ss to consolidate what they’ve learnt and make preparation for the next lessonPart4. Blackboard design.(說(shuō)板書(shū)設(shè)計(jì))On the top, there is the title of this lesson. On the left, there are main ideas for each paragraph. On the right, there are some new words and expressions.Unit 3 Travel journalJourney down the MekongMain idea of each para.:Para1: deciding to take a great bike trip along the Mekong river.Para2: Different attitudes between Wang kun and Wang wei.
Step 7 Language points 1.Vocabulary (1) go through (2) set down (3) a series of (4) on purpose (5) in order to (6)at dusk (7)entirely (8)face to face 2.Important sentences (1)…I’ve grown so crazy about everything to do with nature. (2)There was a time when … (3)I stayed awake on purpose until … (4)It was the first time … that I’d seen the night … (5)It’s no pleasure looking through … Purpose: 1.Master the required vocabulary and sentence structures. 2.Use them freely. Step 8 Consolidation 1.Find out the topic sentences 2.Retell the text according to the topic sentences Purpose: I want to know if my students understand the text. Step 9 Discussion Imagine you have to go into hiding like Anne and her family, what would you miss most? Giveyour reasons. Purpose: Train Ss’ oral English ability. Step 10 Homework Write an article on Friends. Purpose: 1. Improve the Ss’ writing ability. 2 Train the Ss’ ability of self—teaching and looking up information by themselves. Part 5 Blackboard design(說(shuō)板書(shū)設(shè)計(jì))Unit 1 Friendship Reading Anne’s Best Friend 1.Main idea of each paragraph: Para. 1 Anne made her diary her best friend. Para .2 Anne wrote her feelings in her diary. Para .3 Anne missed nature. Para.4 Anne saw the night face to face Para.5 Anne wanted to experience nature outdoors. 2.Listening: Exx.1 P3 3.Discussion: Exx.3 P3 Purpose: 1.Make Ss familiar with the passage 2.Make the design inductive, instructive and artistic.
一、說(shuō)教材本節(jié)課選自于人教版語(yǔ)文必修二第二單元詩(shī)三首中的一首詩(shī)歌,它是陶淵明歸隱后的作品。寫(xiě)的是田園之樂(lè),實(shí)際表明的是作者不愿與世俗同流合污的心聲,甘愿守著自己的拙志回歸田園。學(xué)習(xí)該詩(shī),有助于學(xué)生了解山水田園詩(shī)的特點(diǎn),感受者作者不同流俗的高尚情操,同時(shí)可以培養(yǎng)學(xué)生初步的鑒賞古典詩(shī)歌的能力。
科學(xué)是人類認(rèn)識(shí)世界的重要工具,閱讀科普說(shuō)明文不僅可以啟迪心智,了解更多知識(shí)。而且更夠激發(fā)學(xué)生對(duì)科學(xué)的興趣。學(xué)習(xí)這些文章要注重學(xué)生科學(xué)精神的培養(yǎng),關(guān)注科學(xué)探索的過(guò)程,感受科學(xué)家在科學(xué)探索中表現(xiàn)的人格魅力。我們知道一些科學(xué)家就是因?yàn)殚喿x了相關(guān)的科普文章才對(duì)某一學(xué)科產(chǎn)生興趣,從而走上成功之路的。我們?cè)谥v解的時(shí)候可以跟學(xué)生列舉一些例子,讓學(xué)生認(rèn)識(shí)到一篇好的科普文章的重大意義。
培養(yǎng)學(xué)生合作交流意識(shí)和探究問(wèn)題的能力,這一部分知識(shí)層層遞進(jìn),符合學(xué)生由特殊到一般、由簡(jiǎn)單到復(fù)雜的認(rèn)知規(guī)律。4、互動(dòng)探究(1)極限思想的滲透讓學(xué)生閱讀“思考與討論”小版塊.培養(yǎng)學(xué)生的自學(xué)和閱讀能力提出下列問(wèn)題,進(jìn)行分組討論:a、用課本上的方法估算位移,其結(jié)果比實(shí)際位移大還是?。繛槭裁??b、為了提高估算的精確度,時(shí)間間隔小些好還是大些好?為什么?針對(duì)學(xué)生回答的多種可能性加以評(píng)價(jià)和進(jìn)一步指導(dǎo)。讓學(xué)生從討論的結(jié)果中歸納得出:△t越小,對(duì)位移的估算就越精確。滲透極限的思想。通過(guò)小組內(nèi)分工合作,討論交流,培養(yǎng)學(xué)生交流合作的精神,以及搜集信息、處理信息的能力;通過(guò)小組間對(duì)比總結(jié),使學(xué)生學(xué)會(huì)在對(duì)比中發(fā)現(xiàn)問(wèn)題,在解決問(wèn)題過(guò)程中提高個(gè)人能力;
設(shè)計(jì)意圖:幾道例題及練習(xí)題,其中例1小車由靜止啟動(dòng)開(kāi)始行駛,以加速度 做勻加速運(yùn)動(dòng),求2s后的速度大?。窟M(jìn)而變式到:小車遇到紅燈剎車……,充分體現(xiàn)了“從生活到物理,從物理到社會(huì)”的物理教學(xué)理念;例題及練習(xí)題由淺入深、由易到難、各有側(cè)重,體現(xiàn)新課標(biāo)提出的讓不同的學(xué)生在物理上得到不同發(fā)展的教學(xué)理念。這一環(huán)節(jié)總的設(shè)計(jì)意圖是反饋教學(xué),內(nèi)化知識(shí)。(6) 小結(jié)歸納,拓展深化我的理解是,小結(jié)歸納不應(yīng)該僅僅是知識(shí)的簡(jiǎn)單羅列,而應(yīng)該是優(yōu)化認(rèn)知結(jié)構(gòu),完善知識(shí)體系的一種有效手段,為充分發(fā)揮學(xué)生的主題作用,從學(xué)習(xí)的知識(shí)、方法、體驗(yàn)是那個(gè)方面進(jìn)行歸納,我設(shè)計(jì)了這么三個(gè)問(wèn)題:① 通過(guò)本節(jié)課的學(xué)習(xí),你學(xué)會(huì)了哪些知識(shí);② 通過(guò)本節(jié)課的學(xué)習(xí),你最大的體驗(yàn)是什么;③ 通過(guò)本節(jié)課的學(xué)習(xí),你掌握了哪些學(xué)習(xí)物理的方法?
【例3】本例中“p是q的充分不必要條件”改為“p是q的必要不充分條件”,其他條件不變,試求m的取值范圍.【答案】見(jiàn)解析【解析】由x2-8x-20≤0得-2≤x≤10,由x2-2x+1-m2≤0(m>0)得1-m≤x≤1+m(m>0)因?yàn)閜是q的必要不充分條件,所以q?p,且p?/q.則{x|1-m≤x≤1+m,m>0}?{x|-2≤x≤10}所以m>01-m≥-21+m≤10,解得0<m≤3.即m的取值范圍是(0,3].解題技巧:(利用充分、必要、充分必要條件的關(guān)系求參數(shù)范圍)(1)化簡(jiǎn)p、q兩命題,(2)根據(jù)p與q的關(guān)系(充分、必要、充要條件)轉(zhuǎn)化為集合間的關(guān)系,(3)利用集合間的關(guān)系建立不等關(guān)系,(4)求解參數(shù)范圍.跟蹤訓(xùn)練三3.已知P={x|a-4<x<a+4},Q={x|1<x<3},“x∈P”是“x∈Q”的必要條件,求實(shí)數(shù)a的取值范圍.【答案】見(jiàn)解析【解析】因?yàn)椤皒∈P”是x∈Q的必要條件,所以Q?P.所以a-4≤1a+4≥3解得-1≤a≤5即a的取值范圍是[-1,5].五、課堂小結(jié)讓學(xué)生總結(jié)本節(jié)課所學(xué)主要知識(shí)及解題技巧
本章通過(guò)學(xué)習(xí)用二分法求方程近似解的的方法,使學(xué)生體會(huì)函數(shù)與方程之間的關(guān)系,通過(guò)一些函數(shù)模型的實(shí)例,讓學(xué)生感受建立函數(shù)模型的過(guò)程和方法,體會(huì)函數(shù)在數(shù)學(xué)和其他學(xué)科中的廣泛應(yīng)用,進(jìn)一步認(rèn)識(shí)到函數(shù)是描述客觀世界變化規(guī)律的基本數(shù)學(xué)模型,能初步運(yùn)用函數(shù)思想解決一些生活中的簡(jiǎn)單問(wèn)題。1.了解函數(shù)的零點(diǎn)、方程的根與圖象交點(diǎn)三者之間的聯(lián)系.2.會(huì)借助零點(diǎn)存在性定理判斷函數(shù)的零點(diǎn)所在的大致區(qū)間.3.能借助函數(shù)單調(diào)性及圖象判斷零點(diǎn)個(gè)數(shù).?dāng)?shù)學(xué)學(xué)科素養(yǎng)1.數(shù)學(xué)抽象:函數(shù)零點(diǎn)的概念;2.邏輯推理:借助圖像判斷零點(diǎn)個(gè)數(shù);3.數(shù)學(xué)運(yùn)算:求函數(shù)零點(diǎn)或零點(diǎn)所在區(qū)間;4.數(shù)學(xué)建模:通過(guò)由抽象到具體,由具體到一般的思想總結(jié)函數(shù)零點(diǎn)概念.重點(diǎn):零點(diǎn)的概念,及零點(diǎn)與方程根的聯(lián)系;難點(diǎn):零點(diǎn)的概念的形成.
(4)“不論m取何實(shí)數(shù),方程x2+2x-m=0都有實(shí)數(shù)根”是全稱量詞命題,其否定為“存在實(shí)數(shù)m0,使得方程x2+2x-m0=0沒(méi)有實(shí)數(shù)根”,它是真命題.解題技巧:(含有一個(gè)量詞的命題的否定方法)(1)一般地,寫(xiě)含有一個(gè)量詞的命題的否定,首先要明確這個(gè)命題是全稱量詞命題還是存在量詞命題,并找到其量詞的位置及相應(yīng)結(jié)論,然后把命題中的全稱量詞改成存在量詞,存在量詞改成全稱量詞,同時(shí)否定結(jié)論.(2)對(duì)于省略量詞的命題,應(yīng)先挖掘命題中隱含的量詞,改寫(xiě)成含量詞的完整形式,再依據(jù)規(guī)則來(lái)寫(xiě)出命題的否定.跟蹤訓(xùn)練三3.寫(xiě)出下列命題的否定,并判斷其真假:(1)p:?x∈R,x2-x+ ≥0;(2)q:所有的正方形都是矩形;(3)r:?x∈R,x2+3x+7≤0;(4)s:至少有一個(gè)實(shí)數(shù)x,使x3+1=0.【答案】見(jiàn)解析【解析】(1) p:?x∈R,x2-x+1/4<0.∵?x∈R,x2-x+1/4=(x"-" 1/2)^2≥0恒成立,∴ p是假命題.
等式性質(zhì)與不等式性質(zhì)是高中數(shù)學(xué)的主要內(nèi)容之一,在高中數(shù)學(xué)中占有重要地位,它是刻畫(huà)現(xiàn)實(shí)世界中量與量之間關(guān)系的有效數(shù)學(xué)模型,在現(xiàn)實(shí)生活中有著廣泛的應(yīng),有著重要的實(shí)際意義.同時(shí)等式性質(zhì)與不等式性質(zhì)也為學(xué)生以后順利學(xué)習(xí)基本不等式起到重要的鋪墊.課程目標(biāo)1. 掌握等式性質(zhì)與不等式性質(zhì)以及推論,能夠運(yùn)用其解決簡(jiǎn)單的問(wèn)題.2. 進(jìn)一步掌握作差、作商、綜合法等比較法比較實(shí)數(shù)的大?。?3. 通過(guò)教學(xué)培養(yǎng)學(xué)生合作交流的意識(shí)和大膽猜測(cè)、樂(lè)于探究的良好思維品質(zhì)。數(shù)學(xué)學(xué)科素養(yǎng)1.數(shù)學(xué)抽象:不等式的基本性質(zhì);2.邏輯推理:不等式的證明;3.數(shù)學(xué)運(yùn)算:比較多項(xiàng)式的大小及重要不等式的應(yīng)用;4.數(shù)據(jù)分析:多項(xiàng)式的取值范圍,許將單項(xiàng)式的范圍之一求出,然后相加或相乘.(將減法轉(zhuǎn)化為加法,將除法轉(zhuǎn)化為乘法);5.數(shù)學(xué)建模:運(yùn)用類比的思想有等式的基本性質(zhì)猜測(cè)不等式的基本性質(zhì)。
本節(jié)課是三角函數(shù)的繼續(xù),三角函數(shù)包含正弦函數(shù)、余弦函數(shù)、正切函數(shù).而本課內(nèi)容是正切函數(shù)的性質(zhì)與圖像.首先根據(jù)單位圓中正切函數(shù)的定義探究其圖像,然后通過(guò)圖像研究正切函數(shù)的性質(zhì). 課程目標(biāo)1、掌握利用單位圓中正切函數(shù)定義得到圖象的方法;2、能夠利用正切函數(shù)圖象準(zhǔn)確歸納其性質(zhì)并能簡(jiǎn)單地應(yīng)用.數(shù)學(xué)學(xué)科素養(yǎng)1.數(shù)學(xué)抽象:借助單位圓理解正切函數(shù)的圖像; 2.邏輯推理: 求正切函數(shù)的單調(diào)區(qū)間;3.數(shù)學(xué)運(yùn)算:利用性質(zhì)求周期、比較大小及判斷奇偶性.4.直觀想象:正切函數(shù)的圖像; 5.數(shù)學(xué)建模:讓學(xué)生借助數(shù)形結(jié)合的思想,通過(guò)圖像探究正切函數(shù)的性質(zhì). 重點(diǎn):能夠利用正切函數(shù)圖象準(zhǔn)確歸納其性質(zhì)并能簡(jiǎn)單地應(yīng)用; 難點(diǎn):掌握利用單位圓中正切函數(shù)定義得到其圖象.
(2)l的傾斜角為90°,即l平行于y軸,所以m+1=2m,得m=1.延伸探究1 本例條件不變,試求直線l的傾斜角為銳角時(shí)實(shí)數(shù)m的取值范圍.解:由題意知(m"-" 1"-" 1)/(m+1"-" 2m)>0,解得1<m<2.延伸探究2 若將本例中的“N(2m,1)”改為“N(3m,2m)”,其他條件不變,結(jié)果如何?解:(1)由題意知(m"-" 1"-" 2m)/(m+1"-" 3m)=1,解得m=2.(2)由題意知m+1=3m,解得m=1/2.直線斜率的計(jì)算方法(1)判斷兩點(diǎn)的橫坐標(biāo)是否相等,若相等,則直線的斜率不存在.(2)若兩點(diǎn)的橫坐標(biāo)不相等,則可以用斜率公式k=(y_2 "-" y_1)/(x_2 "-" x_1 )(其中x1≠x2)進(jìn)行計(jì)算.金題典例 光線從點(diǎn)A(2,1)射到y(tǒng)軸上的點(diǎn)Q,經(jīng)y軸反射后過(guò)點(diǎn)B(4,3),試求點(diǎn)Q的坐標(biāo)及入射光線的斜率.解:(方法1)設(shè)Q(0,y),則由題意得kQA=-kQB.∵kQA=(1"-" y)/2,kQB=(3"-" y)/4,∴(1"-" y)/2=-(3"-" y)/4.解得y=5/3,即點(diǎn)Q的坐標(biāo)為 0,5/3 ,∴k入=kQA=(1"-" y)/2=-1/3.(方法2)設(shè)Q(0,y),如圖,點(diǎn)B(4,3)關(guān)于y軸的對(duì)稱點(diǎn)為B'(-4,3), kAB'=(1"-" 3)/(2+4)=-1/3,由題意得,A、Q、B'三點(diǎn)共線.從而入射光線的斜率為kAQ=kAB'=-1/3.所以,有(1"-" y)/2=(1"-" 3)/(2+4),解得y=5/3,點(diǎn)Q的坐標(biāo)為(0,5/3).