第一環(huán)節(jié):情境引入內(nèi)容:(一) 情境1實(shí)物投影,并呈現(xiàn)問題:在一望無際的呼倫貝爾大草原上,一頭老牛和一匹小馬馱著包裹吃力地行走著,老牛喘著氣吃力地說:“累死我了”,小馬說:“你還累,這么大的個(gè),才比我多馱2個(gè).”老牛氣不過地說:“哼,我從你背上拿來一個(gè),我的包裹就是你的2倍!”,小馬天真而不信地說:“真的?!”同學(xué)們,你們能否用數(shù)學(xué)知識(shí)幫助小馬解決問題呢?請(qǐng)每個(gè)學(xué)習(xí)小組討論(討論2分鐘,然后發(fā)言).教師注意引導(dǎo)學(xué)生設(shè)兩個(gè)未知數(shù),從而得出二元一次方程.這個(gè)問題由于涉及到老牛和小馬的馱包裹的兩個(gè)未知數(shù),我們?cè)O(shè)老牛馱x個(gè)包裹,小馬馱y個(gè)包裹,老牛的包裹數(shù)比小馬多2個(gè),由此得方程 ,若老牛從小馬背上拿來1個(gè)包裹,這時(shí)老牛的包裹是小馬的2倍, 得方程: .
解:設(shè)甲班的人數(shù)為x人,乙班的人數(shù)為y人,根據(jù)題意,得x+y=93,14x+13y=27,解得x=48,y=45.答:甲班的人數(shù)為48人,乙班的人數(shù)為45人.方法總結(jié):設(shè)未知數(shù)時(shí),一般是求什么,設(shè)什么,并且所列方程的個(gè)數(shù)與未知數(shù)的個(gè)數(shù)相等.解這類問題的應(yīng)用題,要抓住題中反映數(shù)量關(guān)系的關(guān)鍵字:和、差、倍、幾分之幾、比、大、小、多、少、增加、減少等,明確各種反映數(shù)量關(guān)系的關(guān)鍵字的含義.三、板書設(shè)計(jì)列方程組,解決問題)一般步驟:審、設(shè)、列、解、驗(yàn)、答關(guān)鍵:找等量關(guān)系通過“雞兔同籠”,把同學(xué)們帶入古代的數(shù)學(xué)問題情景,學(xué)生體會(huì)到數(shù)學(xué)中的“趣”;進(jìn)一步強(qiáng)調(diào)數(shù)學(xué)與生活的聯(lián)系,突出顯示數(shù)學(xué)教學(xué)的實(shí)際價(jià)值,培養(yǎng)學(xué)生的人文精神;進(jìn)一步豐富學(xué)生數(shù)學(xué)學(xué)習(xí)的成功體驗(yàn),激發(fā)學(xué)生對(duì)數(shù)學(xué)學(xué)習(xí)的好奇心,進(jìn)一步形成積極參與數(shù)學(xué)活動(dòng)、主動(dòng)與他人合作交流的意識(shí).
【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》為題,說一段話,談?wù)勀愕母邢??!驹O(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能。它的毀滅,既是西方侵略者野蠻摧殘人類文化的見證,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!
寫作背景這首詩(shī)寫于普希金被沙皇流放的日子里,是以贈(zèng)詩(shī)的形式寫在他的鄰居奧希泊娃的女兒葉甫勃拉克西亞·尼古拉耶夫娜·伏里夫紀(jì)念冊(cè)上的。那里俄國(guó)革命正如火如荼,詩(shī)人卻被迫與世隔絕。在這樣的處境下,詩(shī)人卻沒有喪失希望與斗志,他熱愛生活,執(zhí)著地追求理想,相信光明必來,正義必勝。(三)、問題探究1、“假如生活欺騙了你”指的是什么?指在生活中因遭遇艱難困苦甚至不幸而身處逆境。作者寫這首詩(shī)時(shí)正被流放,是自己真實(shí)生活的寫照。2、詩(shī)人在詩(shī)中闡明了怎樣的人生態(tài)度?請(qǐng)結(jié)合你感受最深的詩(shī)句說說你曾有過的體驗(yàn)。詩(shī)中闡明了這樣一種積極樂觀的人生態(tài)度:當(dāng)生活欺騙了你時(shí),不要悲傷,不要心急;在苦惱的時(shí)候要善于忍耐,一切都會(huì)過去,我們一定要永葆積極樂觀的心態(tài);生活中不可能沒有痛苦與悲傷,歡樂不會(huì)永遠(yuǎn)被憂傷所掩蓋,快樂的日子終會(huì)到來。
1. First, ... then, ... next, ... finally, ...首先,……然后,……接著,……最后,……這是英語(yǔ)中表達(dá)做某事的步驟的一種說法。如果步驟較多,還可以說:first-next-after that-later on-finally/at last通常你會(huì)聽到說英語(yǔ)國(guó)家的人在說 first, next, then, finally 和后面的內(nèi)容時(shí),他們會(huì)做一些停頓。這樣就能提前告訴聽者接下來講的是一系列的步驟。這一點(diǎn)在朗讀和聽力中應(yīng)特別注意。2. how many, how much均為疑問詞,同是“多少”,但用法不同。請(qǐng)看:how many修飾可數(shù)名詞復(fù)數(shù),how much修飾不可數(shù)名詞。但在用法上,同學(xué)們常犯如下錯(cuò)誤:1) [誤] How many are there bananas on the table?[正] How many bananas are there on the table?[析] how many, how much 中的many,much是形容詞,常修飾名詞作定語(yǔ),故后面跟名詞。2) [誤]How much tea are there on the table?[正]How much tea is there on the table?[析] how much修飾不可數(shù)名詞時(shí),謂語(yǔ)動(dòng)詞用單數(shù)。how many與how much的區(qū)別可簡(jiǎn)記為:前how many:?jiǎn)枴岸嗌佟保瑥?fù)數(shù)名詞后面跑;how much問“多少”,不可數(shù)名詞單數(shù)好。前者答語(yǔ)用基數(shù)詞,后者答語(yǔ)用數(shù)量關(guān)系。
“Go for it!” is based on “Task-Based Language Teaching”. It adheres to “The authenticity principle”, “The form-function principle”, “The task dependency principle” and “The principle of learning by doing”. These principles all accord with the demands of curriculum focus.In and of Grade Seven (II), “Go for it!”, students have learned “The Simple Past Tense”. And it appears again in of Grade Eight (I). teaches students more about how to talk about events in the past. In addition, it gives affirmative and negative statements in the past tense, such as the sentence patterns “Did you see …?” “Were there …?” “Did you go …?” As the first part of Unit 8, Section A opens with a picture presenting the last school trip in the aquarium and continues with several step-by-step practice activities, which are all good for students to master “The Simple Past Tense”. Doing well in Section A will help students integrate the new target language with that in Section B. Thus, they can describe the events in the past freely and foster their own ability of reflecting and practicing. II. Teaching ObjectivesTeaching objective is the beginning and aim of teaching activities. According to the overall goal of the English elementary course--- improve students' synthetic ability of language application, which should be based on the development of students’ “Language knowledge”, “Language skills”, “Character building”, “Learning strategies” and “Cross-cultural awareness”. The teaching objectives are described as follows(I). Knowledge objectivesi. Master the simple past tense of regular and irregular verbsii. Recite the new words and expressions about the last school trip in the aquarium, including their pronunciation and intonation
Step 3 (3b)First, tell the students when we talk about our future plans, we often use: I’m+verb+ing When we talk about what we must do, we use have to. Ask the students to fill in the blanks in 3b. The answers are: shopping, go to see, a test, I’m going, my family. Step 4 (3c)Let the students write an e-mail message to a friend. Say why you can’t visit next. Before the exercise, ask the students to give some possible answers and write them on the blackboard. So the students will feel easy to finish the writing exercise. After they finish it, Let them to correct it in groups first. Each group chooses theirs best one to read in front of the whole class. Step 5 ( planning a party )First read the conversation in the box together. Then ask the students to turn to page 88.Write down everything you have to do next week. Write in all the things you have to do . Ask the students to look at the list. Ask them “What day are you free?” This is when you can have your party. Step 6 (Self check 1 )Let the students to fill in the blanks with the words given. Change the forms of the words if possible. Then make their own sentences. The answers are: visit, playing, have to, study, comeStep 7 (Self check 2)Imagine you are Marie. Read the information and look at your schedule. Write replies to the invitation.
一、 教學(xué)內(nèi)容Section A 1a----1c二、 教學(xué)目標(biāo)1.學(xué)習(xí)詞匯do the dishes, make the bed, take out the trash, fold the clothes, do the laundry, sweep the floor, clean the living room.2.句型 Could you please clean your room? Yes, sure.三、 教學(xué)準(zhǔn)備 學(xué)生預(yù)習(xí)本單元所有的詞匯多媒體課件 活動(dòng)表 獎(jiǎng)品四、 教學(xué)過程Pre-task1. Warming upEnjoy ourselves. Watch cartoon Cinderella. 看動(dòng)畫片段《灰姑娘》導(dǎo)如入本課話題和新詞匯“chores”美麗善良的鬼姑娘因繼母的嫉妒,每天得做所有的家務(wù)。片段的主題使學(xué)生聯(lián)想到本課的話題。2. learn new words and phrasesLook! What is she / he dong? 看圖學(xué)習(xí)動(dòng)詞詞組do chores, do the dishes, make the bed, take out the trash, fold the clothes, do the laundry, clean the living room.3. Guessing game.What is she doing ? 4. Pair work. 1a, Do you do these things at home? Write “Y” for “yes” and “N” for “no”.5. Listening . 1b , Peter’s chores or Mom’s chores?理解目標(biāo)語(yǔ)Could you please clean your room? Yes, sure.Write “M” for Mom’s chores, “P” for Peter’s chores in the chart.6. PairworkLook at the picture,Ask your partner to do the chores that you see. 7. Interview Who is the most able at home? 1) What chores do you do at home? How often do you do the chores? Work in four, interview each of the students in the group, fill in the chart.
Step Ⅶ Role play ( Work on 1b)1. First ask two students to read the dialogue to the class.Sa: How do you get to school?Sb: Well, I ride my bike to the subway station. Then I take the subway.2. Now work with a partner.Suppose you use two kinds of transportation to get to school \Hangzhou\Beijing... (bus, train, subway, walking, bike, etc.) Tell how you get there. You may use the phrases in 1a.3. Then ask different pairs of students to present their conversations to the class.Step ⅧListening1. Work on 2a(1) First ask students to read the list of information that Thomas wants to know.…where Nina lives.…h(huán)ow far from school she lives.…h(huán)ow long it takes to get to school.…h(huán)ow she gets to school.…what she thinks of the transportation.(2) Tell students what transportation and bus stop mean.bus stop 汽車站 transportation n. 運(yùn)送;運(yùn)輸Then tell students we'll hear a recording. Please put a checkmark in front of each thing that Thomas wants to know.(3) Now play the recording for students.( Have students pay attention to the sample answer.) (4) Then correct the answers.
Teaching goals : 1. Words & phrases: babysit ,get back , fishing , rent , think about , decide(on) , tourist etc. 2. How to talk about future plans . 3. 現(xiàn)在進(jìn)行時(shí)表示將來計(jì)劃或行動(dòng). 4. 特殊疑問句(where , when , how long引導(dǎo)) Important and difficult points : Drills :What are you doing for vacation ? I’m watching TV . When are you going ? I’m going … . How long are you staying ? We’re staying for five days . Teaching aids : cards and a tape ,a large wall calendar . Period 1 Teaching procedures : Step 1Leading in1. Free talk . 2. Put up the wall calendar . T: I’m staying home on Saturday (pointing to next Saturday ).Ss repeat . Ss: I’m staying home on Saturday . T: OK. Today we’ll learn how to talk about future plans. Step 2Pre-task SB Page 13 , 1a . 1. Look at the picture carefully and tell what you see in the picture . 2. Write the activities from the pictures in the box and add some more . 3. Practice reading . Step 3While-task1. Using the activities we write in 1a to make conversations .For example :What are you doing for vacation ? I’m visiting my uncle . 2. Pairwork .Practice in pairs . 3. 用第三人稱練習(xí)對(duì)話.
教學(xué)目標(biāo)1.知識(shí)目標(biāo):(1)學(xué)習(xí)What are you going to be when you grow up?/How are you going to do that?句式。(2)學(xué)會(huì)用英語(yǔ)描述有關(guān)職業(yè)的表達(dá)法。2.能力目標(biāo):(1)能夠談?wù)摓閷?shí)現(xiàn)理想所做出的打算和安排。(2)能夠談?wù)撐磥碜约号c他人理想的職業(yè)及原因。(3)能用英語(yǔ)描述課余時(shí)間的活動(dòng)安排,最終具備表達(dá)綜合信息的能力。3.情感目標(biāo):新學(xué)期到來之際,讓他們?cè)趯W(xué)習(xí)、體育、飲食、特長(zhǎng)、讀書等方面制定計(jì)劃,教育學(xué)生合理安排自己的課外生活,思考自己的理想職業(yè)及適合自己的職業(yè)。教學(xué)重點(diǎn)、難點(diǎn)本單元的重點(diǎn)為“be going to”表將來,want to be, what,where, when,how引導(dǎo)的特殊疑問句。難點(diǎn)是語(yǔ)言目標(biāo)的實(shí)現(xiàn)。教材分析本單元以I am going to be a basketball player為話題,共設(shè)計(jì)了三部分的內(nèi)容:一、Section A該部分有4個(gè)模塊。第一模塊圍繞Do you think these jobs are interesting?這一話題展開思維(1a)、聽力(1b)、口語(yǔ)(1c)訓(xùn)練;
1 交通工具的比較此活動(dòng)為小組活動(dòng)。學(xué)生通過討論找出到達(dá)某一城市可乘坐的各種交通工具,并選擇最佳出行方式。Teacher:We’re going to Shanghai. How many ways can we use to get there? Yes, there are four ways: by bus, by plane, by train, by ship. Please discuss how you are going to get there.操作建議:(1)學(xué)生以小組為單位展開活動(dòng),談?wù)摫窘M所選擇的交通工具。(2)各組選代表向全班匯報(bào),闡述本組所選擇的交通工具的利和弊。完成任務(wù)所需要的語(yǔ)言結(jié)構(gòu):We can go there by ship. It’s more comfortable and cheaper than any other transportation.We can go there by bus. It’s cheaper but it takes longer time.2 哪個(gè)城市更合適?此活動(dòng)具有挑戰(zhàn)性。假設(shè)中國(guó)要舉行2014年世界杯足球賽,分別從歷史,人文,天氣等方面對(duì)各城市(北京,大連,上海,昆明)進(jìn)行比較,選擇最佳舉辦城市。T: Imagine China is holding the 2014 FIFA World Cup. Which city do you think is the best for the World Cup, Beijing, Dalian, Shanghai or Kunming? Let’s work in groups. If you choose Beijing, please join the Team Red. If you chose Dalian, please join the Team White. If you choose Shanghai, please join the Team Blue. If you choose Kunming, please join the Team Green. Please show us its advantages. Then let’s see which team will win.
教學(xué)重點(diǎn)和難點(diǎn):運(yùn)用所掌握的語(yǔ)言描述,比較不同地點(diǎn)的特點(diǎn)。在練習(xí)中學(xué)習(xí)掌握英語(yǔ)比較級(jí)和最高級(jí)的用法。課前準(zhǔn)備分配小組,每組五至六人。通過上網(wǎng)或翻閱報(bào)刊雜志等方法,確定旅游線路,做出基本的旅游計(jì)劃。教學(xué)設(shè)計(jì):本節(jié)課流程圖 學(xué)法指導(dǎo):1.由于這是一堂新課,在教學(xué)中應(yīng)注意面向全體,發(fā)揮學(xué)生的主體性,引導(dǎo)學(xué)生積極參與,激發(fā)學(xué)生的求知欲和學(xué)習(xí)積極性,指導(dǎo)學(xué)生積極思維,主動(dòng)獲取知識(shí),養(yǎng)成良好的學(xué)習(xí)方法。逐步學(xué)會(huì)獨(dú)立解決問題??傊M可能調(diào)動(dòng)學(xué)生的非智力因素促進(jìn)智力因素的發(fā)展。教法選擇:1.電化教學(xué)法2.課堂討論法3.任務(wù)型教學(xué)法采用這些方法的目的是為了充分調(diào)動(dòng)學(xué)生的學(xué)習(xí)積極性,使學(xué)生變被動(dòng)學(xué)習(xí)為主動(dòng)學(xué)習(xí)。通過電腦形象的演示,加強(qiáng)印象,提高興趣,突破難點(diǎn),提高教學(xué)效率,進(jìn)而增大教學(xué)的容量和信息量。充分體現(xiàn)教師為主導(dǎo),學(xué)生為主體的教學(xué)原則。
She shouldn’t go to the party tonight.Step7. TaskT: You know, there are lots of problems in our life. If you are a doctor, please tell us how to solve the problem. I will divide you into 9 groups. Please work in groups. And then choose one of you to report your ideas.The following are the problems:I have a toothache.I am hungry. I have a sore throat.I am stressed out. I have a sore back.I am tired. I can’t sleep.I have a cold. I have a headache.Report: If you have a headache, you should go to bed early. You should see the doctor. You should eat some medicine. You shouldn’t wash your face with cold water.You shouldn’t sleep late.You shouldn’t swim.…..T encourages the students to give advice as much as possible.Homework:1. Chose one of the problems, and write down your advice2. Copy the new words這一步是用于熱身的,同時(shí)也可以讓他們復(fù)習(xí)一部分的表示人體部位的單詞,擴(kuò)充知識(shí).學(xué)習(xí)語(yǔ)言的過程也是一個(gè)不斷積累的過程,復(fù)習(xí)舊知識(shí),增添新知識(shí).通過小游戲,強(qiáng)化學(xué)生對(duì)Does she/he have…這個(gè)句子的運(yùn)用能力.通過復(fù)習(xí),自然的引到下面新知識(shí)的學(xué)習(xí)。充分利用表格,由句子到對(duì)話,再到文章,讓學(xué)生循序漸進(jìn). 提高學(xué)生的綜合語(yǔ)言運(yùn)用能力,運(yùn)用以前學(xué)過的知識(shí)來解決身邊的問題.Period 5 (Section B 3a—3c, selfcheck)教學(xué)內(nèi)容與分析:
第五環(huán)節(jié):課堂小結(jié)內(nèi)容:師生相互交流總結(jié)解二元一次方程組的基本思路是“消元”,即把“二元”變?yōu)椤耙辉保?解二元一次方程組的第一種解法——代入消元法,其主要步驟是:將其中的一個(gè)方程中的某個(gè)未知數(shù)用含有另一個(gè)未知數(shù)的代數(shù)式表示出來,并代入另一個(gè)方程中,從而消去一個(gè)未知數(shù),化二元一次方程組為一元一次方程.解這個(gè)一元一次方程,便可得到一個(gè)未知數(shù)的值,再將所求未知數(shù)的值代入變形后的方程,便求出了一對(duì)未知數(shù)的值.即求得了方程組的解.目的:鼓勵(lì)學(xué)生通過本節(jié)課的學(xué)習(xí),談?wù)勛约旱氖斋@與感受,加深對(duì) “溫故而知新” 的體會(huì),知道“學(xué)而時(shí)習(xí)之”.設(shè)計(jì)效果:學(xué)生能夠在課堂上暢所欲言,并通過自己的歸納總結(jié),進(jìn)一步鞏固了所學(xué)知識(shí).第六環(huán)節(jié):布置作業(yè)課本習(xí)題5.2教學(xué)設(shè)計(jì)反思1.引入自然.二元一次方程組的解法是學(xué)習(xí)二元一次方程組的重要內(nèi)容.教材通過上一小節(jié)的實(shí)際問題,比較一元一次方程的列法和解法,從而自然引入二元一次方程組的代入消元解法.
在探究估算方法的時(shí)候,教師要注重適時(shí)的引導(dǎo),以免讓學(xué)生無從下手.在教學(xué)過程中一定要讓學(xué)生體會(huì)估算的實(shí)用價(jià)值,了解到“數(shù)學(xué)既來源與生活,又回歸到生活為生活服務(wù)”.(二)課堂評(píng)價(jià)的一些思考在教學(xué)中要多鼓勵(lì)學(xué)生用自己的語(yǔ)言表達(dá)他們的想法,在估算的過程中多給予適當(dāng)?shù)囊龑?dǎo)和評(píng)價(jià),讓學(xué)生逐步把握估算的方法,找到解決問題的信心.比如對(duì)“畫能掛上去嗎”這個(gè)問題情境,學(xué)生可能提出不同的看法,有些學(xué)生可能認(rèn)為可以掛上去,因?yàn)槿诉€有身高,完全可以彌補(bǔ)梯子穩(wěn)定擺放的高度和掛畫位置的高度之間的差距,有些學(xué)生可能認(rèn)為,人不可能爬到梯子的頂部,加上人如果本來比較矮,畫就不能掛上去等等想法,教師都應(yīng)該給予肯定,這樣才能激發(fā)學(xué)生思考問題的熱情,調(diào)動(dòng)學(xué)生探究問題的積極性.作為教師,一定要尊重學(xué)生的個(gè)體差異,滿足多樣化的學(xué)習(xí)需要,鼓勵(lì)探究方式、表達(dá)方式和解題方法的多樣化.
2.法解二元一次方程組,是提升學(xué)生求解二元一次方程的基本技能課,在例題的設(shè)置上充分體現(xiàn)化歸思想.2.在學(xué)習(xí)二元一次方程組的解法中,關(guān)鍵是領(lǐng)會(huì)其本質(zhì)思想——消元,體會(huì)“化未知為已知”的化歸思想.因而在教學(xué)過程中教師通過對(duì)問題的創(chuàng)設(shè),鼓勵(lì)學(xué)生去觀察方程的特點(diǎn),在過手訓(xùn)練中提高學(xué)生的解答正確率和表達(dá)規(guī)范性,提升學(xué)生學(xué)會(huì)數(shù)學(xué)的信心,激發(fā)學(xué)習(xí)數(shù)學(xué)的興趣.3.通過精心設(shè)計(jì)的問題,引導(dǎo)學(xué)生在已有知識(shí)的基礎(chǔ)上,自己比較、分析得出二元一次方程組的解法,在鞏固訓(xùn)練活動(dòng)中,加深學(xué)生對(duì)“化未知為已知”的化歸思想的理解.特別是如何由代入消元法到加減消元法,過渡自然。讓學(xué)生深刻的體會(huì)到二元一次方程是一元一次方程的拓展,二元一次方程組又要通過“消元”,轉(zhuǎn)化為一元一次方程求解,這樣的轉(zhuǎn)化,不僅有助于學(xué)生掌握知識(shí)、技能和方法,提高學(xué)習(xí)效率,而且還加深了對(duì)數(shù)學(xué)中通性和通法的認(rèn)識(shí),體會(huì)學(xué)習(xí)數(shù)學(xué)和研究數(shù)學(xué)的規(guī)律,提升數(shù)學(xué)思維能力.
解析:本題是要求兩個(gè)未知數(shù),即3和4的權(quán).所以應(yīng)把平均數(shù)與方程組綜合起來,利用平均數(shù)的定義來列方程,組成方程組求解.解:設(shè)投進(jìn)3個(gè)球的有x人,投進(jìn)4個(gè)球的有y人,由題意,得3x+4y+5×2=3.5×(x+y+2),0×1+1×2+2×7+3x+4y=2.5×(1+2+7+x+y).整理,得x-y=6,x+3y=18.解得x=9,y=3.答:投進(jìn)3個(gè)球的有9人,投進(jìn)4個(gè)球的有3人.方法總結(jié):利用平均數(shù)的公式解題時(shí),要弄清數(shù)據(jù)及相應(yīng)的權(quán),避免出錯(cuò).三、板書設(shè)計(jì)平均數(shù)算術(shù)平均數(shù):x=1n(x1+x2+…+xn)加權(quán)平均數(shù):x=(x1f1+x2f2+…+xnfn)f1+f2+…fn通過探索算術(shù)平均數(shù)和加權(quán)平均數(shù)的聯(lián)系與區(qū)別,培養(yǎng)學(xué)生的思維能力;通過有關(guān)平均數(shù)問題的解決,提升學(xué)生的數(shù)學(xué)應(yīng)用能力.通過解決實(shí)際問題,體會(huì)數(shù)學(xué)與社會(huì)生活的密切聯(lián)系,了解數(shù)學(xué)的價(jià)值,增進(jìn)學(xué)生對(duì)數(shù)學(xué)的理解和增加學(xué)好數(shù)學(xué)的信心.
探究點(diǎn)三:函數(shù)的圖象洗衣機(jī)在洗滌衣服時(shí),每漿洗一遍都經(jīng)歷了注水、清洗、排水三個(gè)連續(xù)過程(工作前洗衣機(jī)內(nèi)無水).在這三個(gè)過程中,洗衣機(jī)內(nèi)的水量y(升)與漿洗一遍的時(shí)間x(分)之間函數(shù)關(guān)系的圖象大致為()解析:∵洗衣機(jī)工作前洗衣機(jī)內(nèi)無水,∴A,B兩選項(xiàng)不正確,淘汰;又∵洗衣機(jī)最后排完水,∴D選項(xiàng)不正確,淘汰,所以選項(xiàng)C正確,故選C.方法總結(jié):本題考查了對(duì)函數(shù)圖象的理解能力,看函數(shù)圖象要理解兩個(gè)變量的變化情況.三、板書設(shè)計(jì)函數(shù)定義:自變量、因變量、常量函數(shù)的關(guān)系式三種表示方法函數(shù)值函數(shù)的圖象在教學(xué)過程中,注意通過對(duì)以前學(xué)過的“變量之間的關(guān)系”的回顧與思考,力求提供生動(dòng)有趣的問題情境,激發(fā)學(xué)生的學(xué)習(xí)興趣,并通過層層深入的問題設(shè)計(jì),引導(dǎo)學(xué)生進(jìn)行觀察、操作、交流、歸納等數(shù)學(xué)活動(dòng).在活動(dòng)中歸納、概括出函數(shù)的概念,并通過師生交流、生生交流、辨析識(shí)別等加深學(xué)生對(duì)函數(shù)概念的理解.
1.細(xì)講概念、強(qiáng)化訓(xùn)練要想讓學(xué)生正確、牢固地樹立起算術(shù)平方根的概念,需要由淺入深、不斷深化的過程.概念是由具體到抽象、由特殊到一般,經(jīng)過分析、綜合去掉非本質(zhì)特征,保持本質(zhì)屬性而形成的.概念的形成過程也是思維過程,加強(qiáng)概念形成過程的教學(xué),對(duì)提高學(xué)生的思維水平是很有必要的.概念教學(xué)過程中要做到:講清概念,加強(qiáng)訓(xùn)練,逐步深化.“講清概念”就是通過具體實(shí)例揭露算術(shù)平方根的本質(zhì)特征.算術(shù)平方根的本質(zhì)特征就是定義中指出的:“如果一個(gè)正數(shù) 的平方等于 ,即 ,那么這個(gè)正數(shù) 就叫做 的算術(shù)平方根,”的“正數(shù) ”,即被開方數(shù)是正的,由平方的意義, 也是正數(shù),因此算術(shù)平方根也必須是正的.當(dāng)然零的算術(shù)平方根是零.