The topic of this part is “Write about your festival experience”.During the Listening and Speaking and Talking, students are just asked to say out their festival experiences such as the Spring Festival, Mid-autumn Day, but this part students will be asked to write down their own festival experiences. During the reading part, it introduces the Naadam Festival in Inner Mongolia Autonomous Region, which can give students a good example to imitate. Students not only learn the festival, but touch and feel the Inner Mongolian’s character, the spirit and cultural atmosphere, which can help students form the cultural awareness and learn to enjoy and value the diversity of Chinese culture.Concretely, the dairy tells the experience that the author spent the Naadam Festival in Inner Mongolia Autonomous Region with his/her friend. The structure is clear. In the opening paragraph, it introduces the topic of the Naadam Festival and the whole feeling. Then it introduces the items of the festival like the ceremony, wrestling and horse racing. Finally, it summarizes this experience. Because this part is a travel journal, we must guide students pay more attention to these details: 1. use the first person. 2. use the past tense to tell the past thing and use the present or future tense to describe the scenery. 3. use the timeline to tell the development. 4. be careful for the author’s psychology, emotion and feeling, etc.1. Read quickly to get main idea; read carefully to get the detailed information about Naadam Festival.2. Learn the structure of the reading article and language.3. Write an article about a festival experience4. Learn to use the psychology, emotions and feeling in the writing.1. Write an article about a festival experience.2. Use the structure of the reading article and language.
Listening and Speaking introduces the topic of “talking about how to become an astronaut”. This period is aimed to inform students some details about the requirements of being an astronaut. Students can be motivated and inspired by the astronauts. Teachers ought to encourage students to learn from them and let them aim high and dream big.Listening and Talking introduces the theme of "talk about life in space". This part also informs students more details about life in space and can inspire students to be curious about this job. 1. Guide students to listen for numbers concerning dates, years and ages etc2. Cultivate students' ability to talk about how to become an astronaut and life in space ; 3. Instruct students to use functional sentences of the dialogue such as “ first of all, I am not sure, so what might be .. I guess.. I wonder…I am curious…)appropriately.1. Guide students to understand the content of listening texts in terms of the whole and key details; 2. Cultivate students' ability to guess the meaning of words in listening; discuss with their peers how to become a qualified astronaut and describe the life in space.Part 1: Listening and SpeakingStep 1: Lead inPredictionThe teacher can ask students to predict what the listening text is about by looking at the pictures.About how to become an astronaut./the requirements of an astronautStep 2: Then, play the radio which is about an interview a. And after finishing listening for the first time, the students need to solve the following tasks.
Q4: What is the function of the International exploration ?Having astronauts from different countries on boardQ5: What can you learn from Para 4 ?China has made great achievements in exploring spaceQ6: What is the attitude to the space exploration ?SupportiveStep 6 Post reading---RetellPeople have always wanted to learn more about space. Before the mid-20th century, most people felt (1)_________ (travel) into space was an impossible dream. However, (2)____ the help of scientists, peoplesucceeded in realizing their dream (3) _________ (explore) space. On 4 October 1957, the Sputnik 1 satellite (4) ____________(launch) by the USSR. (5) ________________ scientists try to make sure nothing goes wrong, accidents can still happen. These disasters made everyone(6)___________(disappoint), but people still believe in the importance of (7) ________(carry) on space exploration. In 2003, China became the third country to (8)_____________ (independent) send humans into space. Then Shenzhou 6 and 7 completed (9)____ second manned orbit and the first Chinese spacewalk. In spite of the difficulties, scientists hope future (10)__________ (discovery) will not only enable us to understand the universe but also help us survive well into the future.Answers: 1. travelling 2. with 3. to explore 4. was launched 5. Although6. disappointed 7. carrying 8. independently 9. a 10. discoveriesStep 6 Post reading---Critical thinkingQ1: What do you think of the space exploration ? I think it is beneficial to us. Through further study of space, people will make full use of it in the future, such as the space experiments by Wang Yaping in Tian Gong 1.Q2: If you are determined to be an astronaut, what should you prepare at present ?First of all, I should study hard to get a related college degree. Besides, I must keep mental and physical healthy.Step 7. HomeworkTry to summarize the structure of the article by a mind map.
另一方面,其余的人反對(duì)這個(gè)計(jì)劃,因?yàn)樗赡軙?huì)導(dǎo)致一些不好的影響。7.I hold the belief that space exploration not only enable us to understand how the universe began but also help us survived well into the future.我堅(jiān)信探索太空不僅能夠使我們了解宇宙的起源而且能夠幫助我們更好地走進(jìn)未來。8.I think we should spend more time and money exploring space so as to provide new and better solutions to people's shortterm and longterm problems.為了給人類的短期和長(zhǎng)期問題提供更新和更好的解決方法,我認(rèn)為我們應(yīng)該花更多的時(shí)間和金錢來探索太空。9.From my point of view,it is wrong of young people to depend on their telephones too much,which may do harm to both their physical and mental health.在我看來,年輕人過度依賴手機(jī)是不對(duì)的,因?yàn)樗鼈兛赡軙?huì)對(duì)他們的身心健康都有害。最近你班同學(xué)就“人類是否應(yīng)該進(jìn)行宇宙探索”這個(gè)問題進(jìn)行了激烈的討論。有人認(rèn)為,探索宇宙不僅讓人類更好地了解宇宙的發(fā)展,還可以用來指導(dǎo)農(nóng)業(yè)生產(chǎn),以及把一些探索太空的高新技術(shù)用于現(xiàn)實(shí)生活;也有一些人認(rèn)為探索太空花掉了大量的人力物力;影響了人們的生活水平。請(qǐng)你根據(jù)以下情況寫一篇報(bào)告并發(fā)表自己的觀點(diǎn)。注意:1.寫作內(nèi)容應(yīng)包括以上全部要點(diǎn),可適當(dāng)發(fā)揮,使上下文連貫;
Everybody wants to get wealth.In today’s material world,making money or becoming wealthy symbolizes a person’s success and capability. Many people just make every effort, pay any price to attain greater wealth. With money,they can buy nice, large apartments in nice neighborhood. With money they can own luxurious cars. Wealth seems to bring all happiness in life.But is wealth the only road to happiness? Not really. There are many things in the world, which are beyond the means of money, such as friendship, love, health and knowledge. People are so preoccupied with struggling for money that they have no time or would not take the time to form or maintain friendship. What happiness can they feel living as lonely miserable creatures without love or friends in the world even if they accumulate tremendous wealth?In my opinion, people can’t do anything without money, but money is not everything. What money will bring you depends on your personal belief and goal in life. If you are kind enough to help others, especially the poor, money is a good thing to you. With it, you can do much more for the benefit of people and your country, and it will add to your own happiness. If you want money just for your own needs, you’ll never be satisfied or happy. In a word,you should have money spent for more people. Only then can money be the source of your happiness.Step 8 Homework4 students in a group, one acts Roderick, one Oliver, one servant and the fourth one acts Henry Adams, then listen to the tape, pay more attention to the difference between American English and British English in pronunciation, stress, tone.
【參考范文】Narrator:(Henry is smiling as he leaves the restaurant. As he is walking down the street, he sees a sign for a place that cuts hair. He decides to get it cut. )H=Henry;B=Barber;R=rude manH:Good afternoon, I'd like to get a cut, if I may. (The barber looks at Henry's hair and continues cutting another man's hair. )Er, I'd really like a haircut. As you can see it's much too long. B:(in a rude manner) Yes, I can see that. Indeed, I can. H:Fine, well I'll have a seat then. (He sits in one of the barber's chairs. The barber turns to look at Henry. )B:It's quite expensive here, you know!Are you sure you can afford it?H:Yes. I think so. (In comes the rude man. )R:Hey you there. I need a haircut quickly. Can you do me straightaway?B:All right, then, get in the chair and I'll see what I can do. R:Thank you. (sits down in one of the barber's chairs)H:Excuse me, but I was here first. Aren't you going to do my hair first?B:This man's in a hurry. H:Well so am I!I insist that you cut my hair first. B:OK, but I'll have to be quick. This gentleman is waiting. H:Thank you. (They both become quiet. After his hair is cut, the barber tells Henry how much he must pay. Henry shows the barber the bank note. )B:Why, Mr . . . (looks shocked)H:Adams. Henry Adams. I'm sorry, I don't have any change. R:You're that Mr Adams! Well,I'm glad I waited or I might never have known it was you. B:Why, Mr Adams, please don't worry!(wearing a big smile) Nothing to worry about!Nothing at all!Please come back any time, even if you only need too little hairs cut!It will be my honour to serve you!
教學(xué)目標(biāo):1.知道二次函數(shù)與一元二次方程的聯(lián)系,提高綜合解決問題的能力.2.會(huì)求拋物線與坐標(biāo)軸交點(diǎn)坐標(biāo),會(huì)結(jié)合函數(shù)圖象求方程的根.教學(xué)重點(diǎn):二次函數(shù)與一元二次方程的聯(lián)系.預(yù)設(shè)難點(diǎn):用二次函數(shù)與一元二次方程的關(guān)系綜合解題.☆ 預(yù)習(xí)導(dǎo)航 ☆一、鏈接:1.畫一次函數(shù)y=2x-3的圖象并回答下列問題(1)求直線y=2x-3與x軸的交點(diǎn)坐標(biāo); (2)解方程2x-3=0(3)說出直線y=2x-3與x軸交點(diǎn)的橫坐標(biāo)和方程根的關(guān)系2.不解方程3x2-2x+4=0,此方程有 個(gè)根。二、導(dǎo)讀畫二次函數(shù)y= x2-5x+4的圖象1.觀察圖象,拋物線與x軸的交點(diǎn)坐標(biāo)是什么?2.求一元二次方程x2-5x+4=0的解。3.拋物線與x軸交點(diǎn)的橫坐標(biāo)與一元二次方程x2-5x+4=0的解有什么關(guān)系?(3)一元二次方程ax2+bx+c=0是二次函數(shù)y=ax2+bx+c當(dāng)函數(shù)值y=0時(shí)的特殊情況.二次函數(shù)y=ax2+bx+c的圖象與x軸交點(diǎn)的橫坐標(biāo)與一元二次方程ax2+bx+c=0的根有什么關(guān)系?
解:(1)設(shè)第一次落地時(shí),拋物線的表達(dá)式為y=a(x-6)2+4,由已知:當(dāng)x=0時(shí),y=1,即1=36a+4,所以a=-112.所以函數(shù)表達(dá)式為y=-112(x-6)2+4或y=-112x2+x+1;(2)令y=0,則-112(x-6)2+4=0,所以(x-6)2=48,所以x1=43+6≈13,x2=-43+6<0(舍去).所以足球第一次落地距守門員約13米;(3)如圖,第二次足球彈出后的距離為CD,根據(jù)題意:CD=EF(即相當(dāng)于將拋物線AEMFC向下平移了2個(gè)單位).所以2=-112(x-6)2+4,解得x1=6-26,x2=6+26,所以CD=|x1-x2|=46≈10.所以BD=13-6+10=17(米).方法總結(jié):解決此類問題的關(guān)鍵是先進(jìn)行數(shù)學(xué)建模,將實(shí)際問題中的條件轉(zhuǎn)化為數(shù)學(xué)問題中的條件.常有兩個(gè)步驟:(1)根據(jù)題意得出二次函數(shù)的關(guān)系式,將實(shí)際問題轉(zhuǎn)化為純數(shù)學(xué)問題;(2)應(yīng)用有關(guān)函數(shù)的性質(zhì)作答.
(1)一個(gè)快落山的太陽(yáng),跟大家講的,更多的是自己一生奮斗過來的體會(huì)。指61歲的老人。(2)加入人家說我是權(quán)威,也許還馬馬虎虎。作者自謙的說法,指成績(jī)還過得去。(3)明明是一個(gè)過去時(shí)態(tài),大家誤認(rèn)為是現(xiàn)在時(shí)態(tài)。指作者認(rèn)為自己不適合再做權(quán)威了。(4)扶植年輕人我覺得是一種歷史的潮流,當(dāng)然我們要?jiǎng)?chuàng)造條件,就是把他們推到需要刺激的風(fēng)口浪尖上。比喻重要的崗位或市場(chǎng)的前沿。【感悟精彩句子】1.所以我知道自己是一個(gè)下午四五點(diǎn)鐘的太陽(yáng)。各位呢,上午八九點(diǎn)鐘的太陽(yáng),這是本科生;碩士生呢,九十點(diǎn)鐘的太陽(yáng);博士生呢,十點(diǎn)十一點(diǎn)鐘的太陽(yáng)。比喻,拉近了與聽眾的距離,倍感親切、期望和鼓舞。2.所以1992年前電視臺(tái)采訪我,我基本上都拒絕了。透過細(xì)節(jié),體現(xiàn)了堅(jiān)持不懈的科研精神。
材料說明了什么?探究二:材料分析:2005年12月13日至18日,WTO第六次部長(zhǎng)級(jí)會(huì)議在香港召開。會(huì)議經(jīng)過談判通過了《部長(zhǎng)宣言》,規(guī)定發(fā)達(dá)成員和部分發(fā)展中成員2008年前向最不發(fā)達(dá)國(guó)家所有產(chǎn)品提供免關(guān)稅、免配額的市場(chǎng)準(zhǔn)入;發(fā)達(dá)成員2006年取消棉花的出口補(bǔ)貼, 2013年年底前取消所有形式農(nóng)產(chǎn)品出口補(bǔ)貼。材料體現(xiàn)了世界貿(mào)易組織在國(guó)際經(jīng)濟(jì)貿(mào)易領(lǐng)域中發(fā)揮哪些作用?探究三:P97:A、這些圖示,反映出我國(guó)利用外資哪些特點(diǎn)?。B、能為我國(guó)提高外資利用水平提出些建議嗎?探究四:材料展示:我國(guó)是人口眾多的發(fā)展中大國(guó),全國(guó)居民每天消費(fèi)總額達(dá)到37億元。每天消費(fèi)糧食75萬噸,相當(dāng)于一個(gè)縣級(jí)商品糧基地的全年產(chǎn)量;每天消耗豬肉6萬噸,食油1萬噸,糖1.6萬噸,鮮蛋1.8萬噸。每天購(gòu)買雜志600多萬冊(cè),報(bào)紙5000多萬份,需要400量中型載貨汽車才能裝載。
思考提示在階級(jí)社會(huì)中,社會(huì)基本矛盾的解決主要是通過階級(jí)斗爭(zhēng)實(shí)現(xiàn)的,階級(jí)斗爭(zhēng)是推動(dòng)階級(jí)社會(huì)發(fā)展的直接動(dòng)力,當(dāng)舊的生產(chǎn)關(guān)系嚴(yán)重阻礙生產(chǎn)力發(fā)展,需要進(jìn)行變革時(shí),代表舊的生產(chǎn)關(guān)系的沒落階級(jí)卻不會(huì)自動(dòng)退出歷史舞臺(tái),利用舊的上層建筑維護(hù)自己的統(tǒng)治,只有代表新生產(chǎn)力發(fā)展方向的階級(jí)通過社會(huì)革命,推翻沒落的階級(jí)統(tǒng)治,才能解放生產(chǎn)力,推動(dòng)社會(huì)向前發(fā)展。所以,階級(jí)社會(huì)的進(jìn)步往往是通過激烈的社會(huì)革命實(shí)現(xiàn)的。但是,社會(huì)主義社會(huì)與階級(jí)社會(huì)不同,這是因?yàn)?,社?huì)主義社會(huì)中,生產(chǎn)力和生產(chǎn)關(guān)系、經(jīng)濟(jì)基礎(chǔ)和上層建筑之間的矛盾是一種非對(duì)抗性矛盾,不需要通過一個(gè)階級(jí)推翻另一個(gè)階級(jí)的階級(jí)斗爭(zhēng)的方式來解決,只能通過改革實(shí)現(xiàn)社會(huì)的發(fā)展,通過對(duì)生產(chǎn)關(guān)系和上層建筑進(jìn)行改革,實(shí)現(xiàn)社會(huì)主義的自我完善,從而促進(jìn)社會(huì)的發(fā)展。所以,我國(guó)經(jīng)濟(jì)體制改革是在堅(jiān)持社會(huì)主義制度的前提下,改革生產(chǎn)關(guān)系和上層建筑中不適應(yīng)生產(chǎn)力發(fā)展的一系列相互聯(lián)系的環(huán)節(jié)和方面。
(2)歷史課本中歷朝歷代的文化發(fā)展。(3)政治生活中關(guān)于綜合國(guó)力競(jìng)爭(zhēng)的相關(guān)知識(shí)。(4)了解文化產(chǎn)業(yè)的發(fā)展,深入體會(huì)知識(shí)經(jīng)濟(jì)、文化經(jīng)濟(jì)現(xiàn)象。五、【方法點(diǎn)津】:(1)堅(jiān)持理論聯(lián)系實(shí)際的方法,感悟文化現(xiàn)象,理解文化內(nèi)涵,分析文化的作用,增強(qiáng)文化學(xué)習(xí)的自覺性。(2)自學(xué)探究。以課本的簡(jiǎn)單提示為線索,深入探究文化與經(jīng)濟(jì)、政治的相互交融,探究文化在綜合國(guó)力競(jìng)爭(zhēng)中的地位和作用。(3)集體討論。針對(duì)當(dāng)前國(guó)際競(jìng)爭(zhēng)的實(shí)質(zhì),探討我國(guó)應(yīng)如何發(fā)展文化產(chǎn)業(yè)、發(fā)展文化生產(chǎn)力、增強(qiáng)文化競(jìng)爭(zhēng)力;討淪為更好地應(yīng)對(duì)文化競(jìng)爭(zhēng),作為中學(xué)生目前應(yīng)做好哪些準(zhǔn)備。六、【課文導(dǎo)語(yǔ)】:文化,一個(gè)我們十分熟悉的詞匯。然而“熟知并非真知”。有人說,文化是知識(shí);有人說,文化是藝術(shù)。究竟什么是“文化”?只要在社會(huì)生活中細(xì)細(xì)體味,我們就能真切地感悟“文化”的內(nèi)涵與文化的力量。
A生產(chǎn)方式是人類社會(huì)存在和發(fā)展的基礎(chǔ)人要生存必須有吃、穿、住、用等物質(zhì)生活資料,只有生存問題解決了才能談得上社會(huì)的存在和發(fā)展,才能從事其他的活動(dòng)(教育、藝術(shù)、體育、政治)。而要獲得物質(zhì)生活資料,必須從事物質(zhì)資料的生產(chǎn)勞動(dòng)。在這一活動(dòng)中,形成了現(xiàn)實(shí)的生產(chǎn)力和生產(chǎn)關(guān)系,即生產(chǎn)方式?!舅枷虢逃柯浜蟊厝话ご?,我國(guó)大力發(fā)展經(jīng)濟(jì),就是為了發(fā)展生產(chǎn)力。發(fā)展是硬道理,中國(guó)解決一切問題的關(guān)鍵在與自己的發(fā)展。要積極支持改革開放,積極投身于經(jīng)濟(jì)建設(shè)中去。現(xiàn)在學(xué)好知識(shí)將來教育育人,為社會(huì)培養(yǎng)更多的合格人才。B生產(chǎn)方式?jīng)Q定著社會(huì)的性質(zhì)和面貌社會(huì)生活紛繁復(fù)雜,包括經(jīng)濟(jì)生活、政治生活、精神生活、婚姻家庭生活等許多方面。這些方面都受生產(chǎn)方式的制約,有什么樣的生產(chǎn)方式,就有什么樣的社會(huì)結(jié)構(gòu);不同的生產(chǎn)方式,表現(xiàn)為不同性質(zhì)的社會(huì)形態(tài)。社會(huì)的整個(gè)面貌只能從生產(chǎn)方式中得到科學(xué)的說明?!九e例】家庭聯(lián)產(chǎn)承包責(zé)任制的產(chǎn)生與推廣1958年的人民公社化運(yùn)用曾使中國(guó)農(nóng)民在勞動(dòng)和分配上都實(shí)行絕對(duì)的平均主義,大鍋飯的結(jié)果是飯?jiān)匠栽缴?,人越過越窮。
1.澳大利亞混合農(nóng)業(yè)地域在生產(chǎn)結(jié)構(gòu)、經(jīng)營(yíng)方式、科技應(yīng)用、農(nóng)業(yè)專業(yè)化和地域化等方面有哪些特點(diǎn)?2.在澳大利亞混合農(nóng)業(yè)地 域形成的過程中,有哪些區(qū)位因素在起作用?學(xué)生發(fā)言,教師適當(dāng)引導(dǎo)、評(píng)點(diǎn)并作講解。[教師提問]:那么,澳大利亞的墨累—達(dá)令盆地的區(qū)位因素有什么不足之處?知識(shí)拓展:課件展示澳大利亞大分水嶺的雨影效應(yīng)的形成原理及東水西調(diào)示意圖。[教師講解]:澳大利亞東南部受大分水嶺的影響,降水集中于大分水嶺的東側(cè),在其西側(cè)形成山地的雨影效應(yīng),降水豐富地區(qū)與農(nóng)業(yè)生產(chǎn)地區(qū)分布不一致,灌溉成為澳大利亞農(nóng)牧業(yè)發(fā)展的限制性條件。因此,澳大利亞對(duì)水利工程建設(shè)很 重視,東水西調(diào)促進(jìn)了墨累—達(dá)令盆地農(nóng)牧業(yè)的發(fā)展。[課堂小結(jié)]:這節(jié)課我們學(xué)習(xí)了農(nóng)業(yè)區(qū)位選擇的基本原理。 通過學(xué)習(xí)我們了解到,農(nóng)業(yè)的區(qū)位選擇實(shí)質(zhì)上就是對(duì)農(nóng)業(yè)土地的合理利用。
一、知識(shí)與技能1、知道伽利略的理想實(shí)驗(yàn)及其主要推理過程和推論,知道理想實(shí)驗(yàn)是科學(xué)研究的重要方法2、理解牛頓第一定律的內(nèi)容及意義;理解力和運(yùn)動(dòng)的關(guān)系,知道物體的運(yùn)動(dòng)不需要力來維持。3、理解慣性的概念,知道質(zhì)量是慣性大小的量度;會(huì)用慣性解釋一些現(xiàn)象。二、過程與方法1、觀察生活中的慣性現(xiàn)象,了解力和運(yùn)動(dòng)的關(guān)系2、通過實(shí)驗(yàn)加深對(duì)牛頓第一定律的理解3、理解理想實(shí)驗(yàn)是科學(xué)研究的重要方法三、情感態(tài)度與價(jià)值觀1、通過伽利略和亞里士多德對(duì)力和運(yùn)動(dòng)關(guān)系的不同認(rèn)識(shí),了解人類認(rèn)識(shí)事物本質(zhì)的曲折性2、感悟科學(xué)是人類進(jìn)步的不竭動(dòng)力[教學(xué)重點(diǎn)]1、理解力和運(yùn)動(dòng)的關(guān)系2、對(duì)牛頓第一定律和慣性的正確理解3、理想實(shí)驗(yàn)[教學(xué)難點(diǎn)]1、力和運(yùn)動(dòng)的關(guān)系2、慣性和質(zhì)量的關(guān)系[課時(shí)安排]1課時(shí)[教學(xué)過程][引入]
一、知識(shí)與技能1、知道伽利略的理想實(shí)驗(yàn)及其主要推理過程和推論,知道理想實(shí)驗(yàn)是科學(xué)研究的重要方法2、理解牛頓第一定律的內(nèi)容及意義;理解力和運(yùn)動(dòng)的關(guān)系,知道物體的運(yùn)動(dòng)不需要力來維持。3、理解慣性的概念,知道質(zhì)量是慣性大小的量度;會(huì)用慣性解釋一些現(xiàn)象。二、過程與方法1、觀察生活中的慣性現(xiàn)象,了解力和運(yùn)動(dòng)的關(guān)系2、通過實(shí)驗(yàn)加深對(duì)牛頓第一定律的理解3、理解理想實(shí)驗(yàn)是科學(xué)研究的重要方法三、情感態(tài)度與價(jià)值觀1、通過伽利略和亞里士多德對(duì)力和運(yùn)動(dòng)關(guān)系的不同認(rèn)識(shí),了解人類認(rèn)識(shí)事物本質(zhì)的曲折性2、感悟科學(xué)是人類進(jìn)步的不竭動(dòng)力[教學(xué)重點(diǎn)]1、理解力和運(yùn)動(dòng)的關(guān)系2、對(duì)牛頓第一定律和慣性的正確理解3、理想實(shí)驗(yàn)[教學(xué)難點(diǎn)]1、力和運(yùn)動(dòng)的關(guān)系2、慣性和質(zhì)量的關(guān)系
l Toteach the story and understand the story.l Ss can act out the conversation anduse the main sentences.l Train them to form a concept ofcooperation Help them to improve their interest of Englishlearning
l To teach the consonant sounds [t]and for letters t respectively.To teach the consonant sounds [d] and for letters d respectively.