新知探究國際象棋起源于古代印度.相傳國王要獎賞國際象棋的發(fā)明者,問他想要什么.發(fā)明者說:“請在棋盤的第1個格子里放上1顆麥粒,第2個格子里放上2顆麥粒,第3個格子里放上4顆麥粒,依次類推,每個格子里放的麥粒都是前一個格子里放的麥粒數(shù)的2倍,直到第64個格子.請給我足夠的麥粒以實現(xiàn)上述要求.”國王覺得這個要求不高,就欣然同意了.假定千粒麥粒的質(zhì)量為40克,據(jù)查,2016--2017年度世界年度小麥產(chǎn)量約為7.5億噸,根據(jù)以上數(shù)據(jù),判斷國王是否能實現(xiàn)他的諾言.問題1:每個格子里放的麥粒數(shù)可以構(gòu)成一個數(shù)列,請判斷分析這個數(shù)列是否是等比數(shù)列?并寫出這個等比數(shù)列的通項公式.是等比數(shù)列,首項是1,公比是2,共64項. 通項公式為〖a_n=2〗^(n-1)問題2:請將發(fā)明者的要求表述成數(shù)學問題.
我們知道數(shù)列是一種特殊的函數(shù),在函數(shù)的研究中,我們在理解了函數(shù)的一般概念,了解了函數(shù)變化規(guī)律的研究內(nèi)容(如單調(diào)性,奇偶性等)后,通過研究基本初等函數(shù)不僅加深了對函數(shù)的理解,而且掌握了冪函數(shù),指數(shù)函數(shù),對數(shù)函數(shù),三角函數(shù)等非常有用的函數(shù)模型。類似地,在了解了數(shù)列的一般概念后,我們要研究一些具有特殊變化規(guī)律的數(shù)列,建立它們的通項公式和前n項和公式,并應用它們解決實際問題和數(shù)學問題,從中感受數(shù)學模型的現(xiàn)實意義與應用,下面,我們從一類取值規(guī)律比較簡單的數(shù)列入手。新知探究1.北京天壇圜丘壇,的地面有十板布置,最中間是圓形的天心石,圍繞天心石的是9圈扇環(huán)形的石板,從內(nèi)到外各圈的示板數(shù)依次為9,18,27,36,45,54,63,72,81 ①2.S,M,L,XL,XXL,XXXL型號的女裝上對應的尺碼分別是38,40,42,44,46,48 ②3.測量某地垂直地面方向上海拔500米以下的大氣溫度,得到從距離地面20米起每升高100米處的大氣溫度(單位℃)依次為25,24,23,22,21 ③
二、典例解析例3.某公司購置了一臺價值為220萬元的設備,隨著設備在使用過程中老化,其價值會逐年減少.經(jīng)驗表明,每經(jīng)過一年其價值會減少d(d為正常數(shù))萬元.已知這臺設備的使用年限為10年,超過10年 ,它的價值將低于購進價值的5%,設備將報廢.請確定d的范圍.分析:該設備使用n年后的價值構(gòu)成數(shù)列{an},由題意可知,an=an-1-d (n≥2). 即:an-an-1=-d.所以{an}為公差為-d的等差數(shù)列.10年之內(nèi)(含10年),該設備的價值不小于(220×5%=)11萬元;10年后,該設備的價值需小于11萬元.利用{an}的通項公式列不等式求解.解:設使用n年后,這臺設備的價值為an萬元,則可得數(shù)列{an}.由已知條件,得an=an-1-d(n≥2).所以數(shù)列{an}是一個公差為-d的等差數(shù)列.因為a1=220-d,所以an=220-d+(n-1)(-d)=220-nd. 由題意,得a10≥11,a11<11. 即:{█("220-10d≥11" @"220-11d<11" )┤解得19<d≤20.9所以,d的求值范圍為19<d≤20.9
情景導學古語云:“勤學如春起之苗,不見其增,日有所長”如果對“春起之苗”每日用精密儀器度量,則每日的高度值按日期排在一起,可組成一個數(shù)列. 那么什么叫數(shù)列呢?二、問題探究1. 王芳從一歲到17歲,每年生日那天測量身高,將這些身高數(shù)據(jù)(單位:厘米)依次排成一列數(shù):75,87,96,103,110,116,120,128,138,145,153,158,160,162,163,165,168 ①記王芳第i歲的身高為 h_i ,那么h_1=75 , h_2=87, 〖"…" ,h〗_17=168.我們發(fā)現(xiàn)h_i中的i反映了身高按歲數(shù)從1到17的順序排列時的確定位置,即h_1=75 是排在第1位的數(shù),h_2=87是排在第2位的數(shù)〖"…" ,h〗_17 =168是排在第17位的數(shù),它們之間不能交換位置,所以①具有確定順序的一列數(shù)。2. 在兩河流域發(fā)掘的一塊泥板(編號K90,約生產(chǎn)于公元前7世紀)上,有一列依次表示一個月中從第1天到第15天,每天月亮可見部分的數(shù):5,10,20,40,80,96,112,128,144,160,176,192,208,224,240. ②
課前小測1.思考辨析(1)若Sn為等差數(shù)列{an}的前n項和,則數(shù)列Snn也是等差數(shù)列.( )(2)若a1>0,d<0,則等差數(shù)列中所有正項之和最大.( )(3)在等差數(shù)列中,Sn是其前n項和,則有S2n-1=(2n-1)an.( )[答案] (1)√ (2)√ (3)√2.在項數(shù)為2n+1的等差數(shù)列中,所有奇數(shù)項的和為165,所有偶數(shù)項的和為150,則n等于( )A.9 B.10 C.11 D.12B [∵S奇S偶=n+1n,∴165150=n+1n.∴n=10.故選B項.]3.等差數(shù)列{an}中,S2=4,S4=9,則S6=________.15 [由S2,S4-S2,S6-S4成等差數(shù)列得2(S4-S2)=S2+(S6-S4)解得S6=15.]4.已知數(shù)列{an}的通項公式是an=2n-48,則Sn取得最小值時,n為________.23或24 [由an≤0即2n-48≤0得n≤24.∴所有負項的和最小,即n=23或24.]二、典例解析例8.某校新建一個報告廳,要求容納800個座位,報告廳共有20排座位,從第2排起后一排都比前一排多兩個座位. 問第1排應安排多少個座位?分析:將第1排到第20排的座位數(shù)依次排成一列,構(gòu)成數(shù)列{an} ,設數(shù)列{an} 的前n項和為S_n。
1.判斷正誤(正確的打“√”,錯誤的打“×”)(1)函數(shù)f (x)在區(qū)間(a,b)上都有f ′(x)<0,則函數(shù)f (x)在這個區(qū)間上單調(diào)遞減. ( )(2)函數(shù)在某一點的導數(shù)越大,函數(shù)在該點處的切線越“陡峭”. ( )(3)函數(shù)在某個區(qū)間上變化越快,函數(shù)在這個區(qū)間上導數(shù)的絕對值越大.( )(4)判斷函數(shù)單調(diào)性時,在區(qū)間內(nèi)的個別點f ′(x)=0,不影響函數(shù)在此區(qū)間的單調(diào)性.( )[解析] (1)√ 函數(shù)f (x)在區(qū)間(a,b)上都有f ′(x)<0,所以函數(shù)f (x)在這個區(qū)間上單調(diào)遞減,故正確.(2)× 切線的“陡峭”程度與|f ′(x)|的大小有關,故錯誤.(3)√ 函數(shù)在某個區(qū)間上變化的快慢,和函數(shù)導數(shù)的絕對值大小一致.(4)√ 若f ′(x)≥0(≤0),則函數(shù)f (x)在區(qū)間內(nèi)單調(diào)遞增(減),故f ′(x)=0不影響函數(shù)單調(diào)性.[答案] (1)√ (2)× (3)√ (4)√例1. 利用導數(shù)判斷下列函數(shù)的單調(diào)性:(1)f(x)=x^3+3x; (2) f(x)=sinx-x,x∈(0,π); (3)f(x)=(x-1)/x解: (1) 因為f(x)=x^3+3x, 所以f^' (x)=〖3x〗^2+3=3(x^2+1)>0所以f(x)=x^3+3x ,函數(shù)在R上單調(diào)遞增,如圖(1)所示
當孩子們由父母陪同時,他們才被允許進入這個運動場。3.過去分詞(短語)作狀語時的幾種特殊情況(1)過去分詞(短語)在句中作時間、條件、原因、讓步狀語時,相當于對應的時間、條件、原因及讓步狀語從句。Seen from the top of the mountain (=When it is seen from the top of the mountain), the whole town looks more beautiful.從山頂上看,整個城市看起來更美了。Given ten more minutes (=If we are given ten more minutes), we will finish the work perfectly.如果多給十分鐘,我們會完美地完成這項工作。Greatly touched by his words (=Because she was greatly touched by his words), she was full of tears.由于被他的話深深地感動,她滿眼淚花。Warned of the storm (=Though they were warned of the storm), the farmers were still working on the farm.盡管被警告了風暴的到來,但農(nóng)民們?nèi)栽谵r(nóng)場干活。(2)過去分詞(短語)在句中作伴隨、方式等狀語時,可改為句子的并列謂語或改為并列分句。The teacher came into the room, followed by two students (=and was followed by two students).后面跟著兩個學生,老師走進了房間。He spent the whole afternoon, accompanied by his mom(=and was accompanied by his mom).他由母親陪著度過了一整個下午。
The grammatical structure of this unit is predicative clause. Like object clause and subject clause, predicative clause is one of Nominal Clauses. The leading words of predicative clauses are that, what, how, what, where, as if, because, etc.The design of teaching activities aims to guide students to perceive the structural features of predicative clauses and think about their ideographic functions. Beyond that, students should be guided to use this grammar in the context apporpriately and flexibly.1. Enable the Ss to master the usage of the predicative clauses in this unit.2. Enable the Ss to use the predicative patterns flexibly.3. Train the Ss to apply some skills by doing the relevant exercises.1.Guide students to perceive the structural features of predicative clauses and think about their ideographic functions.2.Strengthen students' ability of using predicative clauses in context, but also cultivate their ability of text analysis and logical reasoning competence.Step1: Underline all the examples in the reading passage, where noun clauses are used as the predicative. Then state their meaning and functions.1) One theory was that bad air caused the disease.2) Another theory was that cholera was caused by an infection from germs in food or water.3) The truth was that the water from the Broad Street had been infected by waste.Sum up the rules of grammar:1. 以上黑體部分在句中作表語。2. 句1、2、3中的that在從句中不作成分,只起連接作用。 Step2: Review the basic components of predicative clauses1.Definition
Step 7: complete the discourse according to the grammar rules.Cholera used to be one of the most 1.__________ (fear) diseases in the world. In the early 19th century, _2_________ an outbreak of cholera hit Europe, millions of people died. But neither its cause, 3__________ its cure was understood. A British doctor, John Snow, wanted to solve the problem and he knew that cholera would not be controlled _4_________ its cause was found. In general, there were two contradictory theories 5 __________ explained how cholera spread. The first suggested that bad air caused the disease. The second was that cholera was caused by an _6_________(infect) from germs in food or water. John Snow thought that the second theory was correct but he needed proof. So when another outbreak of cholera hit London in 1854, he began to investigate. Later, with all the evidence he _7_________ (gather), John Snow was able to announce that the pump water carried cholera germs. Therefore, he had the handle of the pump _8_________ (remove) so that it couldn't be used. Through his intervention,the disease was stopped in its tracks. What is more, John Snow found that some companies sold water from the River Thames that __9__________________ (pollute) by raw waste. The people who drank this water were much more likely _10_________ (get) cholera than those who drank pure or boiled water. Through John Snow's efforts, the _11_________ (threaten) of cholera around the world saw a substantial increase. Keys: 1.feared 2.when 3. nor 4.unless 5.that/which 6.infection 7.had gathered 8.removed 9.was polluted 10.to get 11. threat
Step 5: After learning the text, discuss with your peers about the following questions:1.John Snow believed Idea 2 was right. How did he finally prove it?2. Do you think John Snow would have solved this problem without the map?3. Cholera is a 19th century disease. What disease do you think is similar to cholera today?SARS and Covid-19 because they are both deadly and fatally infectious, have an unknown cause and need serious public health care to solve them urgently.keys:1. John Snow finally proved his idea because he found an outbreak that was clearly related to cholera, collected information and was able to tie cases outside the area to the polluted water.2. No. The map helped John Snow organize his ideas. He was able to identify those households that had had many deaths and check their water-drinking habits. He identified those houses that had had no deaths and surveyed their drinking habits. The evidence clearly pointed to the polluted water being the cause.3. SARS and Covid-19 because they are both deadly and fatally infectious, have an unknown cause and need serious public health care to solve them urgently.Step 6: Consolidate what you have learned by filling in the blanks:John Snow was a well-known _1___ in London in the _2__ century. He wanted to find the _3_____ of cholera in order to help people ___4_____ it. In 1854 when a cholera __5__ London, he began to gather information. He ___6__ on a map ___7___ all the dead people had lived and he found that many people who had ___8____ (drink) the dirty water from the __9____ died. So he decided that the polluted water ___10____ cholera. He suggested that the ___11__ of all water supplies should be _12______ and new methods of dealing with ____13___ water be found. Finally, “King Cholera” was __14_____.Keys: 1. doctor 2. 19th 3.cause 4.infected with 5.hit 6.marked 7.where 8.drunk 9.pump 10.carried 11.source 12.examined 13.polluted 14.defeatedHomework: Retell the text after class and preview its language points
This happens because the dish soap molecules have a strong negative charge, and the milk molecules have a strong positive charge. Like magnets, these molecules are attracted to each other, and so they appear to move around on the plate, taking the food coloring with them, making it look like the colors are quickly moving to escape from the soap.Listening text:? Judy: Oh, I'm so sorry that you were ill and couldn't come with us on our field trip. How are you feeling now? Better?? Bill: Much better, thanks. But how was it?? Judy: Wonderful! I especially liked an area of the museum called Light Games.it was really cool. They had a hall of mirrors where I could see myself reflected thousands of times!? Bill: A hall of mirrors can be a lot of fun. What else did they have?? Judy: Well, they had an experiment where we looked at a blue screen for a while, and then suddenly we could see tiny bright lights moving around on it. You'll never guess what those bright lights were!? Bill: Come on, tell me!? Judy: They were our own blood cells. For some reason, our eyes play tricks on us when we look at a blue screen, and we can see our own blood cells moving around like little lights! But there was another thing I liked better. I stood in front of a white light, and it cast different shadows of me in every color of the rainbow!? Bill: Oh, I wish I had been there. Tell me more!? Judy: Well, they had another area for sound. They had a giant piano keyboard that you could use your feet to play. But then, instead of playing the sounds of a piano, it played the voices of classical singers! Then they had a giant dish, and when you spoke into it, it reflected the sound back and made it louder. You could use it to speak in a whisper to someone 17 meters away.? Bill: It all sounds so cool. I wish I could have gone with you? Judy: I know, but we can go together this weekend. I'd love to go there again!? Bill: That sounds like a great idea!
You have no excuse for not going.你沒有理由不去。He was punished for not having finished his homework.他因未完成作業(yè)而受到懲罰。2.動詞ing形式復合結(jié)構(gòu)由物主代詞或人稱代詞賓格、名詞所有格或普通格加動詞ing,即“sb./sb.'s+doing”構(gòu)成。動詞ing形式的復合結(jié)構(gòu)實際上是給動詞ing形式加了一個邏輯主語。動詞ing形式的復合結(jié)構(gòu)有四種形式:①形容詞性物主代詞+動詞ing②名詞所有格+動詞ing③代詞賓格+動詞ing④名詞+動詞ingHer coming to help encouraged all of us.她來幫忙鼓舞了我們所有人。The baby was made awake by the door suddenly shutting.這個嬰兒被突然的關門聲吵醒了。Can you imagine him/Jack cooking at home?你能想象他/杰克在家做飯的樣子嗎?無生命名詞無論是作主語還是作賓語都不能用第②種形式。Tom's winning first prize last year impressed me a lot.湯姆去年得了一等獎使我印象深刻。Do you mind my/me/Jack's/Jack leaving now?你介意我/杰克現(xiàn)在離開嗎?Excuse me for my not coming on time.很抱歉我沒能按時來。His father's being ill made him worried.他父親病了,他很擔心。We are looking forward to the singer's/the singer to give us a concert.我們盼望著這位歌手來給我們舉辦一場演唱會。
The grammar of this unit is designed to review noun clauses. Sentences that use nouns in a sentence are called noun clauses. Nominal clauses can act as subject, object, predicate, appositive and other components in compound sentences. According to the above-mentioned different grammatical functions, nominal clauses are divided into subject clause, object clause, predicate clause and appositive clause. In this unit, we will review the three kinds of nominal clauses. Appositive clauses are not required to be mastered in the optional compulsory stage, so they are not involved.1. Guide the students to judge the compound sentences and determine the composition of the clauses in the sentence.2. Instruct students to try to learn grammar by generalizing grammar rules, controlling written practice, and semi-open oral output.3. Inspire the students to systematize the function and usage of noun clause1.Instruct students to try to learn grammar by generalizing grammar rules, controlling written practice, and semi-open oral output.2.Inspire the students to systematize the function and usage of noun clauseStep1: The teacher ask studetns to find out more nominal clauses from the reading passage and udnerline the nominal clauses.
提問:1.怎樣判斷兩種相關聯(lián)的量是否成正比例?用字母怎樣表示正比例關系? 2.判斷下面兩種量是否成正比例?為什么? (1)時間一定,行駛的路程和速度 (2)除數(shù)一定,被除數(shù)和商 3.單價、數(shù)量和總價之間有怎樣的關系?在什么條件下,兩種量成正比例? 4.導入新課: 如果總價一定,單價和數(shù)量的變化有什么規(guī)律?這兩種量存在什么關系?今天,我們就來研究這種變化規(guī)律。
三、說教學目標基于這樣的背景,綜合漢字教學的一般規(guī)律,識字教學的基本要求,我對這一課的教學目標定位如下:1.學習“天、地、人、你、我、他”這六個生字,會讀、能辨認字形。2.借助圖片、故事、漢字演變過程幫助學生牢記漢字形狀,理解漢字意思。3.通過游戲、情景設置激發(fā)學生學習漢字的情感,調(diào)動學習興趣。四、說教學重難點1.通過聽讀、觀察圖畫、聯(lián)系生活等方法,認識生字。(重點)2.讀準“人、你、我”的字音。五、說教法學法為了突出重點,化解難點,完成教學目標,選擇行之有效的教學方法十分關鍵。根據(jù)新課標的具體要求,結(jié)合本節(jié)課的特點,我主要采用游戲激趣法、圖文結(jié)合,利用多媒體課件調(diào)動學生學習的積極性。學生則通過游戲,聯(lián)系生活實際,小組合作等方法學習6個生字。
一、說教材《下課啦》是北師大一年級上冊第二單元的內(nèi)容。本節(jié)課是學生在學習比大小、比多少基礎上進行學習的。比高矮、長短對于學生而言并不陌生,這節(jié)課的內(nèi)容難在學生初步掌握比高矮、長短的方法。因此,我把本節(jié)課的目標預設為:1、在比一比的活動中,通過直觀地比較物體的高矮、長短、初步感知幾個物體之間的高矮、長短。2、知道在比較高矮、長短時需要在同一起點進行。3、通過與他人合作交流,掌握比較的方法,獲得成功的體驗,增強自信心。教學重點通過觀察、比較、讓學生獲得高矮、長短等比較活動的方法。教學難點讓學生用自己的語言組織比較的方法。二、說學情本節(jié)內(nèi)容的教學主要是比較物體的高矮、長短,學生對這一方面的知識已經(jīng)有一定的生活經(jīng)驗,但層次參差不齊,需要教師知識性的梳理。因此在教學中應結(jié)合學生年齡特點、生活背景等具體情況的基礎上進行教學。
一、說教材本課選自北師大小學數(shù)學實驗教材一年級上冊《上下》,它屬于“空間與圖形”中的內(nèi)容,為以后學習“方向與位置”及“方向與路線”做好鋪墊。在這一課時里我充分利用學生已有的生活經(jīng)驗,把這一知識的學習融入到找家的活動,讓學生在活動中認識上下的位置關系。依據(jù)新課標精神和學生實際,結(jié)合教材我確定了如下教學目標(1)知識與技能目標:體驗上下的位置關系,能用準確的數(shù)學語言表達出來。(2)能力目標:培養(yǎng)學生觀察、分析、概括的能力及想象力,發(fā)展學生的空間觀念。(3)、情感目標:在有趣的課堂活動中體驗數(shù)學與生活的緊密聯(lián)系及數(shù)學學習的快樂,并養(yǎng)成熱情好客尊敬長輩的行為習慣。4、教學重、難點:重點是學生會用自己的的語言描述上下位置關系,難點是體會上下位置關系的相對性。依據(jù)一年級學生的年齡特點,為了激發(fā)學生的學習興趣,培養(yǎng)學生自主學習的能力,我是這樣實施教學的。
(2)綜合運用圖畫、語言、音樂,再創(chuàng)情境。(教師描述)如果現(xiàn)在是夜晚,我們一起坐在院子里,抬頭看天空,藍天上有星星,有月亮。這彎彎的月亮,它多像一艘小船呀!(播放背景音樂)現(xiàn)在請大家聽著音樂 輕輕擺,慢慢地閉上眼睛。想著,想著,你是不是坐在月亮上了?是不是飛上藍天了?(此時學生會情不自禁說自己已經(jīng)飛上藍天,已經(jīng)坐在月亮上了。)當學生睜開眼睛,(師播放課件)哈,小朋 友現(xiàn)在我們已經(jīng)飛上天了,已經(jīng)坐在小船里了,讓我們在月亮上愉快地唱起《小小的船》(播放兒童歌曲《小小的船》),伴隨著歌聲的響起,學生就會進入美妙的境界。教師隨即出示句式:我看見了____________________________________。引導學 生說出:宇宙飛船上天,航天飛機登上月球等。接著再用“藍藍的天”進行說話訓練。例如藍藍的天上有什么?我在藍藍的天上干什么?不難看出,在理解重點句子時,根據(jù)創(chuàng)設的情境,讓學生充分展開想象的翅膀,學生往往為此而興奮不已,學生情緒為之高漲,進入一個高潮。此舉極大地豐富了課文內(nèi)容,學生的學就樂在其中,悟也在其中。
二、說教學目標1.認識“時、候、覺”等11個生字,會寫“自、己、衣”三個生字。2.能正確、流利、有感情地朗讀課文。3.理解課文內(nèi)容,體驗長大的快樂。三、說教學重難點1.學會本課生字詞,能正確、流利、有感情地朗讀課文。(重點)?2.理解課文內(nèi)容,體驗長大的快樂。(難點)四、說教法和學法語文課程標準提出:“努力建設開放而有活力的語文課程。”所以本節(jié)課主要采用媒體演示、自主讀書,自主識字、合作學習、合作解疑的方法。學生在教師的引導下動腦、動手、動口。通過自己的勞動獲取知識,變被動學習為主動學習。體現(xiàn)“以教師為主導,學生為主體,訓練為主線”的原則。
(二)合作探究,解疑釋困。1.你能用什么辦法記住“蝸”這個字嗎?? 2.結(jié)合插圖認識“芽、草、莓、蘑、菇”五個生字。?【設計意圖】低年級學生形象思維占主導地位,用圖片對所學的漢字進行理解和記憶,分散了學生識字的難度,完成了課后練習二。? 33.同桌互讀課文,要求:讀準字音,讀通句子。如果他都讀對了,你就夸夸他;如果他讀錯了,你就幫幫他。?4.認讀句子和詞語。?(1)認讀句子。?課件出示:①小蝸牛爬呀,爬呀,好久才爬回來。②“孩子,到小樹林里去玩吧,小樹發(fā)芽了。”③“媽媽,草莓沒有了,地上長著蘑菇,樹葉全變黃了?!?(2)認讀詞語:住在?好久?蝸牛?玩吧?爬呀爬? 5.再讀課文,一邊讀一邊找,小蝸牛和媽媽一共進行了幾次對話?你是怎么找到的?引導學生認識冒號、引號,并簡單了解用法。? 6.它們說了什么呢?蝸牛媽媽的話用“?_____”畫出來;小蝸牛的話用“~~?”畫出來。7.他們的第一次對話在第幾自然段?這次對話講述的是什么時候?蝸牛媽媽讓小蝸牛去哪干什么?? 8.看第一幅圖,觀察小蝸牛和蝸牛媽媽在一起時的表情和姿態(tài),想象一下,這對母子感情怎么樣?蝸牛媽媽會怎樣對小蝸牛說話呢?? 指名朗讀,注意聲音要輕柔,語速可以稍慢,讀出媽媽對小蝸牛的疼愛。