
Teaching Goal:1. General aims:Talk about recent past events2. Particular aims:A. Language Focus.Talk about recent past events and think of the past events.B. Language goalsHow was….?It was …What did …do over the weekend?C. Language structures:(1). How was your weekend? I was great. Pay attention to no form.(2). What did you do over the weekend? I played soccer. We went to the beach.D. Useful words and phrases:Words: was, did, went, beach, over, project, test, wasn’t, false, number, geography, spend, week, most, mixture, their, had, little, cook, read, saw, change, everyone, sit, sat, no, anythingPhrases: did one’s homework, played soccer, cleaned my room, went to the beach, played tennis, went to the movies, on Saturday morning, over the weekend, cook … for, what about, do some reading, have a party, talk show, go shoppingE. Grammar language:Present simple past tenseRegular and irregular verbsF. Learning strategies:Tour and holidaysG. Interdiscipinary:H. Emotion and manner:Teaching time: 5 periodsTeaching procedures:Period One教學(xué)步驟、時間 教師活動 學(xué)生活動 媒體應(yīng)用Step 1Free talk 3’ Ask some questions like:Who’s on duty today?What’s the weather like? Answer and talk about something.讓同學(xué)們回答下列問題1. Do you like weekend? (Let some students answer)It takes them three minutes to talk about the question.2. Why do you like weekend? (let the students answer) Most of the students like the weekend此時教師用漢語問:“在周末期間問你干了什么?這句話用英語這么回答?Let the students guess.At last the teacher give them right answer3. What did you do over the weekend?(板書、學(xué)習(xí))

所需要用到的句子:Who is that?That is Jack. I like him.Why do you like him?I like him because he is interesting.Task 4: 設(shè)計(jì)理想中的人類Step one: 設(shè)計(jì)理想中的人類的外貌。把全班同學(xué)分成若干小組,學(xué)生可以邊說邊在紙上畫出他們的模樣。Step two: 設(shè)計(jì)理想中人類的性格。學(xué)生們可以把那些能描述性格的單詞寫在圖畫的旁邊。Step three: 每組選出一名同學(xué),其他同組同學(xué)提問,他作簡單回答,并說明原因。所需用到的句子:What does he or she look like?He or she ...What is he or she like?He or she is ...Why?Because ...Task 5: 挑戰(zhàn)性活動調(diào)查性格是天生的還是后天形成的,讓每個同學(xué)回家去調(diào)查一下自己成長過程中性格是否有變化,具體是怎樣的,為什么會這樣? Teaching Aims:1. Enable students to have a general understanding of how to talk about people's physical appearance.2. Enable students to tackle some essential vocabularies and patterns about describing people. Provide them with necessary skills and methods.3. Create various chances for students to describe the persons they're familiar with, such as classmates, family members, teachers, idols, etc.

Period 2 (3a----Section B 2c)Preview(Pre-task): Key points: What laAdd another information about their pen pals----their language on the cardnguage does she/he speak?She/He speaks....Does she/he have any brothers and sisters? Does she/he speak English?Preview(Pre-task): Add another information about their pen pals----their language on the cardKey points: What language does she/he speak?She/He speaks....Does she/he have any brothers and sisters? Does she/he speak English?Step 1 Revision1.Revisionand dictation of the new words 2.Revise the drills they learned yesterday.(by pairwork and grammar exercise)Step 2 Leading-inT has a conversation with one student. The conversation is following:---Do you have a pen pal?---Yes, I do.---What's your pen pal's name? ---His/Her name is....---Where is your pen pal from? ---He/She is from...---Where does he/she live? ---He/She lives in....---What language does he/she speak?He/She speaks...Write the new words on the Bb. They are following: EnglishChineseJapaneseFrenchStep 3 LearnLearn the new words with the whole class.Finish 3a with the students3b Pairwork T still does an example with one student Then the Ss practise in pairs. The example is following:--Curry Muray is my pen pal. He is from the United States.---What language does he speak?

Don’t fight. =You can’t fight. (板書,教讀)教師把這些句子板書在黑板上,并請學(xué)生大聲整齊地讀祈使句和“can’t”句型,并讓學(xué)生注意兩種句型表達(dá)形式的不同和轉(zhuǎn)換,“Don’t …=You can’t…”;并對學(xué)生說:These are our school rules. (板書,教讀) You can’t break the school rules. Don’t break the school rules.(板書,教讀)步驟3 :Practicea. T: Now, each of the students is breaking one of these rules.Please finish 1a.學(xué)生看圖,完成1a的內(nèi)容,檢查答案并大聲朗讀校規(guī)。b. 聽錄音,完成1b,選出四位學(xué)生都違反了哪條校規(guī);聽之前,學(xué)生要讀會英文名。c. 請兩位學(xué)生朗讀1c部分的句型;要求學(xué)生兩人一組對話表演,SA扮演外校轉(zhuǎn)來新生,SB告知本校校規(guī)。(學(xué)生可經(jīng)過討論,多說出他們想到的校規(guī),不必只限于書上;教師應(yīng)給予幫助)2) 第二課時(2a~4)步驟1 :warming up of revisionT: What are the rules at your school?學(xué)生使用“can”或祈使句表達(dá)各條校規(guī);其中老師可引出“eat in the cafeteria outside”的表達(dá)。步驟2 :Practicea.T: Christina is an exchange student. She doesn’t know the rules. Let’s listen, what activities they’re talking about?學(xué)生聽第一遍時,完成2a;第二遍時,完成2b;b. 請學(xué)生領(lǐng)讀2c部分,看著2a完成的表格,理解2c活動的要求;分成小組針對2a進(jìn)行問答;

教學(xué)過程Step 1: warming-up Sing a song---------“food and drink” Step 2: Revision1 Dictation2 Revise: What kind of noodles would you like?I’d like …What size bowl of noodles would you like?I’d like…Step 3: Presentation1 show pictures of food, ask students say the words.2 Students read the newspaper ad in 3a. Fill in blanks with words in the box. Then read the ad together, the teacher explains some difficult language points.3 Check the answers Step 4 PracticeAsk students to finish 3b in the same way according to 3a. Students read the short passage and fill in the blanks .At last, check the answers.Step 5 productionAsk students to write their own ad for dumplings, noodles, drinks, and other foods they know. Then ask students to read their partner’s ad. Then order food and drink from their partner.Step 6 Home workGroup work – make an ad about “food and drink”

三、教學(xué)建議第一課時:1. Lead in (Vocabulary)A) Before class, teacher should collect some pictures of working places. For example: Bank, TV Station, Restaurant, Police Station, Hospital ...B) In class, show students the pictures (PowerPoint, OHP). Ask students to tell the name of the working places and the name of the jobs.Shop assistant, doctor, actor, reporter, police office, waiter, bank clerk, studentC) Do exercise 1a and 3a.2. Bingo GameAsk groups of students to make up pairs of cards with a job on one and the related workplace on the other. For example, waiter / restaurant, teacher / school, doctor / hospital. Encourage students to use both the job / workplace combinations in the book and the ones that students came up during class discussions. Be sure they have twice as many sets of cards as there are students in the group. They can make two sets of cards for a single job / workplace, if necessary. Then have each group mix up its set of cards and hand their cards out in random order. Each time a student gets a pair of cards that match, he or she can lay these cards down. The goal is to have no cards in your hand at the end.3. Task OneA) Ask students to work in pairs and ask the partner what does he / she want to be in the future.e. g. :What do you / does he / does she want to be?I want to be a.Why?Because it's (adj).B) Vocabulary: Section B, 1a4. Homework 1.2.

五、教學(xué)Section B-2c1. Pair work: What do you think of the belt/sunglasses/…? What does your father/mother/… think of your scarf/belt…?2. Group work(1). Teacher shows some different kinds of school uniforms (制服)and asks : “ What do you think of your school uniforms? If you have a chance to choose your school uniforms, what kind would you like to choose?”(2). Discuss in groups.(3).Get some Ss to report in class.說明:這一步旨在讓學(xué)生運(yùn)用已有的語言知識談?wù)搶κ挛锏目捶ê鸵庖?,并簡單闡明理由,培養(yǎng)學(xué)生的主動思維能力和運(yùn)用英語的能力。六、教學(xué)拓展調(diào)查電視節(jié)目的收視率任務(wù):調(diào)查你周圍的人對現(xiàn)在各種電視節(jié)目的反響?;顒舆^程:1.教師布置任務(wù),讓學(xué)生調(diào)查周圍的人(包括他的親戚朋友和鄰居)喜歡收看哪方面的電視節(jié)目。2.學(xué)生進(jìn)行調(diào)查活動,運(yùn)用本單元所學(xué)的句型What do you think of….? (Why?)What's your favorite game shows?What do you think of talk show?I doesn’t mind it.I like it.I love it.I can’t stand it.3.記錄下排在前10位的TV Program,填寫調(diào)查表,比較其收視率。

句型: Where did you go on vacation? I went to summer camp.Did she go to Central Park?Yes,she did.No, she didn’t語法:一般過去時特殊疑問句、一般疑問句及肯、否定回答。課時安排4課時第一課時:Section A:la,1b,lc,2a,2b,2c 第二課時:Section A:3a,3b,4第三課時:Section B:1,2a,2b,2c第四課時:Section B:3a,3b,3c,4 and Self Check第一課時教學(xué)目標(biāo)掌握描寫假期生活的形容詞。假期里自己所做事情的簡單表達(dá)。談?wù)摷倨谧龅氖虑榧爱?dāng)時情況。談?wù)摷倨跁r旅游的天氣,旅游者以及食物等。教學(xué)過程一、導(dǎo)入播放一首英文歌曲:Let’s travel 說明:通過讓學(xué)生聽節(jié)奏歡快迪斯尼英語歌曲Let’s travel.引入本節(jié)課談?wù)摰脑掝}vacation and travel. 讓歌曲使學(xué)生的思維活躍,增強(qiáng)課堂氣氛,激發(fā)學(xué)生提高學(xué)習(xí)英語的興趣。T:How is the trip ?Ss : It’s pretty good/ happy/exciting /relaxing/busy/dangerous/ fantastic說明:這個問題是為了操練形容詞。建議讓多個Ss作答。鼓勵他們用不同的形容詞。上述個別形容詞本應(yīng)在第二課時中出現(xiàn),但可以在warming-up中第一次非正式出現(xiàn)。這些形容詞也可在老師的評價語中適時出現(xiàn),以加深學(xué)生對詞匯的印象。

單元整體說明(一)單元教材分析本單元的核心話題是描述動物和表達(dá)個人喜好,以及句式why do you like…? Because…。這也是本單元的教學(xué)重點(diǎn)。通過本單元的學(xué)習(xí),學(xué)生應(yīng)能較流利地運(yùn)用所學(xué)詞匯和句型描述動物,表達(dá)個人喜好。(二)單元知識結(jié)構(gòu)1.詞匯動物名稱 tiger, elephant, koala, dolphin, etc.詞匯描述性形容詞: smart, cute, ugly, clever, shy, etc.國家名: Australia, South Africa2.句型Why do you like koala hears? Because they are cute.Where are pandas from? They're from China.What animals do you like? I like dolphins.(三)單元整體目標(biāo)1.Master the vocabulary2.Master and use: Why do you like koalas? Because they am cute.Where are pandas from? They're from China.What animals do you like? I like dolphins.(四)單元教學(xué)重難點(diǎn)一覽(五)單元學(xué)情分析學(xué)生此前已經(jīng)學(xué)過由why, where, what 引導(dǎo)的特殊疑問句句型,具有了學(xué)習(xí)本單元知識的認(rèn)知前提。形形色色的動物能激發(fā)學(xué)生的好奇心,產(chǎn)生了解它們的欲望,這有利于本單元知識的教學(xué)和學(xué)生學(xué)習(xí)興趣的培養(yǎng)。

說明:在幫Li Lei提建議的同時,教育學(xué)生如何學(xué)好英語。第三課時教學(xué)目標(biāo)1. 語言目標(biāo):a) 詞匯: Original, in style, haircut, the same as.b) 語言結(jié)構(gòu):My friend wears the same clothes and has the same haircut as I do.2. 能力目標(biāo):大多數(shù)學(xué)生能夠談?wù)撟约合矚g哪種服裝,提高查找信息的能力。3. 情感目標(biāo):學(xué)會如何與朋友相處,要有自己對時尚的看法。教學(xué)重點(diǎn)掌握一些重要詞匯。教學(xué)難點(diǎn)學(xué)會談?wù)搯栴},并能提出書面建議?!艚虒W(xué)突破首先針對Erin的問題,提出個人的建議,模仿2c部分的對話展開雙人交際Pair-work;聽老師誦讀3a部分的信件,并找出LEFT OUT的問題所在;學(xué)生完成3b部分的內(nèi)容,給Left Out提出書面的建議;學(xué)以口頭形式提出自己目前存在的某個問題,講給大家聽,讓同學(xué)們給自己提出一個建議,并作筆錄;學(xué)生兩、三個人分成一組,隨意性地進(jìn)行口語交際,談?wù)揚(yáng)14的第4部分的某個問題,相互交換意見。

區(qū)分賓語從句、定于從句和狀語從句賓語從句和狀語從句,都叫做主從復(fù)合句。賓語從句主要是中考必考的,是初中階段必掌握的從句,賓語從句主要是掌握三要素,所謂賓語從句,就是賓語在主從復(fù)合句當(dāng)中充當(dāng)賓語的一個句子,叫做賓語從句。主句的謂語動詞是及物動詞,后面如果是詞或者是短語的話,是簡單句,如果是句子的話,肯定是賓語從句。I know that he good at English.就是賓語從句,三要素,一要素是要注意連詞,連詞一共學(xué)了三類連詞,一類連詞是that口語當(dāng)中可以省略,就像剛才說的那一句,I hear he is good at English.還有疑問代詞、疑問副詞,how where when,疑問代詞、疑問副詞。還有一類連詞weather是否的意思,不是狀語從句當(dāng)中的如果,這一定要和如果區(qū)分開,這是是否。I don't know if he interested at English。賓語從句要注意if是連詞。第二要素是語序,要用陳述舉語序。比如說你家有幾口人,我們都說How many people are there in you family?但是這是簡單句,一旦說成賓語從句,你可以告訴我你家有幾口人嗎?Could you tell me how many people there are in you family ?

"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!請做一下自我介紹。認(rèn)識一下你的新同學(xué)?!蓖ǔT谡n上老師會這樣說。你會說什么呢?“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話。“王楠是一個很棒的乒乓球運(yùn)動員,不是嗎?”“我希望自己能認(rèn)識她,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)這個單元吧,下次在英語課上,你會發(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。)

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.

(一).知識方面: 1.培養(yǎng)學(xué)生能運(yùn)用過去進(jìn)行時來描述、談?wù)撨^去某個時間正在發(fā)生的事情或動作的意識和能力,能就過去某個時間正在發(fā)生的動作做出正確的描述。 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^去的時間和講述一個故事),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)行時的有關(guān)知識。Was/were+現(xiàn)在分詞,是該時態(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。

歡快的音樂像小朋友在做游戲,舒緩溫柔的音樂像春姑娘在翩翩起舞。這些充滿童趣的語言,讓他們在感受音樂中豐富了想象,在想象中又進(jìn)行了樂感的培養(yǎng)。接著,我讓學(xué)生分小組為這段旋律填寫春天的歌詞,這喚起并促進(jìn)兒童潛在的音樂本能。讓孩子們感受到音樂是自已生活中的需要。學(xué)生在一起進(jìn)行創(chuàng)作,發(fā)揮集體協(xié)作精神,我再讓小組展示自己的創(chuàng)作,并進(jìn)行互評。這樣的創(chuàng)作活動無論是過程還是結(jié)果,孩子們在心理上都得到滿足、肯定、愉悅。最后,我采用情景陶冶法,用多媒體技術(shù)把教室創(chuàng)設(shè)成一個美麗的大草地,在春天圖案的背景下,在優(yōu)美的樂曲聲中,學(xué)生分組進(jìn)行游戲活動。在輕松快樂自由的氛圍中學(xué)生知道了春天到底藏在哪里?它,在溫暖的陽光里,在嫩綠的枝頭上,在大家的歌聲里,在老師的笑臉上,在我們的心里,在美好的生活里。孩子們感受到了春天的無處不在,從而更加熱愛大自然。珍惜幸福生活。

學(xué)生A回答:我會學(xué)習(xí)張米亞老師的無私奉獻(xiàn)精神,去幫助大家,去挽救更多的生命。學(xué)生B回答:我會盡我所能去就我能救得每一個人。學(xué)生C回答:我會從現(xiàn)在開始,多學(xué)習(xí)有關(guān)地震方面的知識,萬一遇上,可以合理指揮現(xiàn)場,把損失降到最小。教師總結(jié):總而言之,在災(zāi)難來臨之時,我們要學(xué)習(xí)張米亞老師身上無私奉獻(xiàn)的精神,勇于挺身而出。這一環(huán)節(jié)的設(shè)置,使學(xué)生積極主動,合作交流,在思考和討論中加深理解和體驗(yàn),有所感悟,從而收到情感熏陶獲得思想啟迪,進(jìn)而解決了教學(xué)重點(diǎn),突破了教學(xué)難點(diǎn)。第四環(huán)節(jié)拓展延伸知識遷移請同學(xué)們閱讀課本36頁的相關(guān)鏈接文章《冰雪為容玉作胎》,結(jié)合本課內(nèi)容談?wù)勀愕淖x后感。本環(huán)節(jié)的設(shè)置拓展了學(xué)生的知識面和閱讀范圍,使學(xué)生學(xué)以致用,培養(yǎng)了學(xué)生的應(yīng)用探究能力。第五環(huán)節(jié) 歌聲陶冶振奮精神全班齊聲合唱韋唯的著名歌曲《愛的奉獻(xiàn)》結(jié)束全課。

第四結(jié)束環(huán)節(jié):表演歌曲,我主要采用創(chuàng)編練習(xí)的方法來完成。1、請孩子們帶上自己做的臉譜,以及發(fā)出短音哼唱的。對孩子們的制作表示贊賞,對特別有創(chuàng)意和制作特別精美的臉譜的孩子獎勵。2、當(dāng)然,由于時間的緊迫,學(xué)生們的創(chuàng)編在這一節(jié)音樂課上不可能一一的展現(xiàn)出來,我將選擇其中較好的小組的創(chuàng)編在本節(jié)課上進(jìn)行當(dāng)眾表演,并鼓勵其它組創(chuàng)編的形式,課后進(jìn)行再加工,下一節(jié)音樂課為老師和同學(xué)進(jìn)行表演。這樣的設(shè)計(jì),不僅使本節(jié)課的教學(xué)得到了適時的拓展,而且,還將這一內(nèi)容擴(kuò)大到了課后,為下次的音樂課教學(xué)做了很好的鋪墊作用??傊?,我設(shè)計(jì)的這節(jié)針對小學(xué)五年級學(xué)生的音樂課,體現(xiàn)了新課標(biāo)要求,遵循了基本的教育原則,并在單元目標(biāo)的總體規(guī)劃下,體現(xiàn)了音樂課獨(dú)特的施教特點(diǎn),完成了教學(xué)內(nèi)容,達(dá)到了授課目標(biāo)。

多媒體讓學(xué)生直觀地掌握好音高,鞏固歌曲旋律的掌握,積累讀譜經(jīng)驗(yàn)。六、創(chuàng)造表現(xiàn)-----享受過程在學(xué)生能熟練演唱的基礎(chǔ)上,讓學(xué)生選擇豎笛為歌曲伴奏,還可以讓學(xué)生邊唱邊即興表演。讓學(xué)生自由組合分成打擊樂器組、演唱表演組和豎笛組,調(diào)動學(xué)生多種感官參與音樂體驗(yàn)和表現(xiàn),加深了對這一音樂作品的感受,獲得審美體驗(yàn)。這里我啟發(fā)學(xué)生用自己喜歡的各種方式來表現(xiàn)歌曲,可以是身體語言、也可以是打擊樂器。門德爾松說過一首我喜愛的樂曲,所傳給我的思想和意義是不能用語言表達(dá)的。通過充分的音樂實(shí)踐培養(yǎng)學(xué)生的能力,提高音樂素養(yǎng)。從目標(biāo)的提出、到過程的安排、學(xué)習(xí)方法的確定、乃至學(xué)習(xí)成果的呈現(xiàn),都讓學(xué)生有更大的自主性、更多的實(shí)踐性、更濃的創(chuàng)造性,讓學(xué)生的音樂課堂更加豐富,教學(xué)成效更加明顯。

最富趣味的是荷蘭藝術(shù)家埃舍爾,他到西班牙旅行參觀時,對一種名為阿罕拉的建筑物有很深的印象,這是一種十三世紀(jì)皇宮建筑物,其墻身、地板和天花板由摩爾人建造,而且鋪了種類繁多、美侖美奐的馬賽克圖案。Escher用數(shù)日的時間復(fù)制了這些圖案,并得到了啟發(fā),創(chuàng)造了各種并不局限于幾何圖案的密鋪圖案,這些圖案包括人、青蛙、魚、鳥、蜥蜴,甚至是他憑空想象的物體。他創(chuàng)作的藝術(shù)作品,結(jié)合數(shù)學(xué)與藝術(shù),給人留下深刻的印象,更讓人對數(shù)學(xué)產(chǎn)生了另一種看法。欣賞埃舍爾的藝術(shù)世界:2、動手創(chuàng)作。(小小設(shè)計(jì)師)看了大藝術(shù)家的作品,你現(xiàn)在是不是也有了創(chuàng)作的沖動?下面,請你選一種或幾種完全一樣的圖形進(jìn)行密鋪,可以自己設(shè)計(jì)顏色,比一比,誰的設(shè)計(jì)更美觀、更新穎。(交流,展示)四、總結(jié):談收獲體會我們今天只是研究了一些規(guī)則圖形的簡單的密鋪。生活中還有各種各樣的密鋪現(xiàn)象。同學(xué)們可以到生活中去觀察,也可以上網(wǎng)瀏覽。

密鋪的歷史背景1619年——數(shù)學(xué)家奇柏(J.Kepler)第一個利用正多邊形鋪嵌平面。1891年——蘇聯(lián)物理學(xué)家弗德洛夫(E.S.Fedorov)發(fā)現(xiàn)了十七種不同的鋪砌平面的對稱圖案。 1924年——數(shù)學(xué)家波利亞(Polya)和尼格利(Nigeli)重新發(fā)現(xiàn)這個事實(shí)。最富趣味的是荷蘭藝術(shù)家埃舍爾(M.C. Escher)與密鋪。M.C. Escher于1898年生于荷蘭。他到西班牙旅行參觀時,對一種名為阿罕伯拉宮(Alhambra)的建筑有很深刻的印象,這是一種十三世紀(jì)皇宮建筑物,其墻身、地板和天花板由摩爾人建造,而且鋪上了種類繁多、美輪美奐的馬賽克圖案。Escher 用數(shù)日復(fù)制了這些圖案,并得到啟發(fā),創(chuàng)造了各種并不局限于幾何圖形的密鋪圖案,這些圖案包括魚、青蛙、狗、人、蜥蜴,甚至是他憑空想像的物體。他創(chuàng)造的藝術(shù)作品,結(jié)合了數(shù)學(xué)與藝術(shù),給人留下深刻印象,更讓人對數(shù)學(xué)產(chǎn)生另一種看法。
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