1.理解并掌握三角形全等的判定方法——“角边角”“角角边”;(重点)2.能运用“角边角”“角角边”判定方法解决有关问题.(难点) 一、情境导入如图所示,某同学把一块三角形的玻璃不小心打碎成了三块,现在要到玻璃店去配一块完全一样的玻璃,那么最省事的办法是带哪块去?学生活动:学生先自主探究出答案,然后再与同学进行交流.教师点拨:显然仅仅带①或②是无法配成完全一样的玻璃的,而仅仅带③则可以,为什么呢?本节课我们继续研究三角形全等的判定方法.二、合作探究探究点一:全等三角形判定定理“ASA”如图,AD∥BC,BE∥DF,AE=CF,试说明:△ADF≌△CBE.解析:根据平行线的性质可得∠A=∠C,∠DFE=∠BEC,再根据等式的性质可得AF=CE,然后利用“ASA”可得到△ADF≌△CBE.
解析:(1)连接BI,根据I是△ABC的内心,得出∠1=∠2,∠3=∠4,再根据∠BIE=∠1+∠3,∠IBE=∠5+∠4,而∠5=∠1=∠2,得出∠BIE=∠IBE,即可证出IE=BE;(2)由三角形的内心,得到角平分线,根据等腰三角形的性质得到边相等,由等量代换得到四条边都相等,推出四边形是菱形.解:(1)BE=IE.理由如下:如图①,连接BI,∵I是△ABC的内心,∴∠1=∠2,∠3=∠4.∵∠BIE=∠1+∠3,∠IBE=∠5+∠4,而∠5=∠1=∠2,∴∠BIE=∠IBE,∴BE=IE;(2)四边形BECI是菱形.证明如下:∵∠BED=∠CED=60°,∴∠ABC=∠ACB=60°,∴BE=CE.∵I是△ABC的内心,∴∠4=12∠ABC=30°,∠ICD=12∠ACB=30°,∴∠4=∠ICD,∴BI=IC.由(1)证得IE=BE,∴BE=CE=BI=IC,∴四边形BECI是菱形.方法总结:解决本题要掌握三角形的内心的性质,以及圆周角定理.
方法总结:解答此类题目的关键是根据题意构造直角三角形,然后利用所学的三角函数的关系进行解答.变式训练:见《学练优》本课时练习“课后巩固提升” 第7题【类型三】 构造直角三角形解决面积问题在△ABC中,∠B=45°,AB=2,∠A=105°,求△ABC的面积.解析:过点A作AD⊥BC于点D,根据勾股定理求出BD、AD的长,再根据解直角三角形求出CD的长,最后根据三角形的面积公式解答即可.解:过点A作AD⊥BC于点D,∵∠B=45°,∴∠BAD=45°,∴AD=BD=22AB=22×2=1.∵∠A=105°,∴∠CAD=105°-45°=60°,∴∠C=30°,∴CD=ADtan30°=133=3,∴S△ABC=12(CD+BD)·AD=12×(3+1)×1=3+12. 方法总结:解答此类题目的关键是根据题意构造直角三角形,然后利用所学的三角函数的关系进行解答.
问题2、如何用测角仪测量一个低处物体的俯角呢?和测量仰角的步骤是一样的,只不过测量俯角时,转动度盘,使度盘的直径对准低处的目标,记下此时铅垂线所指的度数,同样根据“同角的余角相等”,铅垂线所指的度数就是低处的俯角.活动三:测量底部可以到达的物体的高度.“底部可以到达”,就是在地面上可以无障碍地直接测得测点与被测物体底部之间的距离.要测旗杆MN的高度,可按下列步骤进行:(如下图)1.在测点A处安置测倾器(即测角仪),测得M的仰角∠MCE=α.2.量出测点A到物体底部N的水平距离AN=l.3.量出测倾器(即测角仪)的高度AC=a(即顶线PQ成水平位置时,它与地面的距离).根据测量数据,就能求出物体MN的高度.在Rt△MEC中,∠MCE=α,AN=EC=l,所以tanα= ,即ME=tana·EC=l·tanα.又因为NE=AC=a,所以MN=ME+EN=l·tanα+a.
如图,课外数学小组要测量小山坡上塔的高度DE,DE所在直线与水平线AN垂直.他们在A处测得塔尖D的仰角为45°,再沿着射线AN方向前进50米到达B处,此时测得塔尖D的仰角∠DBN=61.4°,小山坡坡顶E的仰角∠EBN=25.6°.现在请你帮助课外活动小组算一算塔高DE大约是多少米(结果精确到个位).解析:根据锐角三角函数关系表示出BF的长,进而求出EF的长,得出答案.解:延长DE交AB延长线于点F,则∠DFA=90°.∵∠A=45°,∴AF=DF.设EF=x,∵tan25.6°=EFBF≈0.5,∴BF=2x,则DF=AF=50+2x,故tan61.4°=DFBF=50+2x2x=1.8,解得x≈31.故DE=DF-EF=50+31×2-31=81(米).所以,塔高DE大约是81米.方法总结:解决此类问题要了解角之间的关系,找到与已知和未知相关联的直角三角形,当图形中没有直角三角形时,要通过作高或垂线构造直角三角形.
方法总结:本题结合三角形内角和定理考查反证法,解此题关键要懂得反证法的意义及步骤.反证法的步骤是:(1)假设结论不成立;(2)从假设出发推出矛盾;(3)假设不成立,则结论成立.在假设结论不成立时要注意考虑结论的反面所有可能的情况.如果只有一种,那么否定一种就可以了,如果有多种情况,则必须一一否定.三、板书设计1.等腰三角形的判定定理:有两个角相等的三角形是等腰三角形(等角对等边).2.反证法(1)假设结论不成立;(2)从假设出发推出矛盾;(3)假设不成立,则结论成立.解决几何证明题时,应结合图形,联想我们已学过的定义、公理、定理等知识,寻找结论成立所需要的条件.要特别注意的是,不要遗漏题目中的已知条件.解题时学会分析,可以采用执果索因(从结论出发,探寻结论成立所需的条件)的方法.
方法总结:绝对值小于1的数也可以用科学记数法表示,一般形式为a×10-n,其中1≤a<10,n为正整数.与较大数的科学记数法不同的是其所使用的是负整数指数幂,指数由原数左边起第一个不为零的数前面的0的个数所决定.【类型二】 将用科学记数法表示的数还原为原数用小数表示下列各数:(1)2×10-7; (2)3.14×10-5;(3)7.08×10-3; (4)2.17×10-1.解析:小数点向左移动相应的位数即可.解:(1)2×10-7=0.0000002;(2)3.14×10-5=0.0000314;(3)7.08×10-3=0.00708; (4)2.17×10-1=0.217.方法总结:将科学记数法表示的数a×10-n还原成通常表示的数,就是把a的小数点向左移动n位所得到的数.三、板书设计用科学记数法表示绝对值小于1的数:一般地,一个小于1的正数可以表示为a×10n,其中1≤a<10,n是负整数.从本节课的教学过程来看,结合了多种教学方法,既有教师主导课堂的例题讲解,又有学生主导课堂的自主探究.课堂上学习气氛活跃,学生的学习积极性被充分调动,在拓展学生学习空间的同时,又有效地保证了课堂学习质量
我来到书房,找到了字典,既想快点知晓答案,和妈妈比个胜负,又想慢点儿,万一又错了怎么办。我紧张地翻开字典,找到了“偌”字的读音。天呐,我是对的,我太开心了!(不足1:缺少动作描写,没有展现出“我”的紧张。修改:我使劲地捏着字典,颤抖着双手,慢慢地打开字典。不足2:结尾缺少人物的语言和神态描写,没有展现出人物开心的心理。修改:我眉飞色舞地大叫道:“天呐,我赢啦!我赢啦!”)我捧着字典,连蹦带跳地来到妈妈面前,欣喜若狂地说:“妈妈,你想不到吧,你一个堂堂初中老师,居然败在拼音不太好的女儿手下。哈哈,我终于报‘仇’了……”此时的我,简直比中了五百万还要开心一百倍。妈妈一听便傻了眼,刚才那坚定的神情已经荡然无存,妈妈连忙接过字典看了又看,生怕我看错了似的。看到字典上的读音,妈妈哑口无言。
(3)推荐男女生代表各一位在全班进行演讲展示。 (4)围绕“讲”和“演”两方面的技巧,点评演讲效果。(生开展演讲活动,师指导)【设计意图】本环节通过集中梳理演讲技巧,并设计演讲技巧进行演讲展示,引导学生将理论知识逐步运用于具体的演讲实践中,提高学生的演讲能力。五、总结存储1.教师总结现代奥林匹克运动的创始人顾拜旦面对世界政治格局剧变的局面,以战略家的视野指出奥林匹克精神的内涵与价值,用诗歌般的语言阐述了奥林匹克平和自信的内涵,提出了奥林匹克运动的宗旨是教育,是面向大众,是促进和平、公平、公正。他激情澎湃地畅想美好前景,确信奥林匹克精神必将如阳光般普照大地。整篇演讲词站位高、格局广,语言庄重、典雅,值得我们用心体会。2.布置作业学校即将举行春季运动会,如果你被邀请在运动会的开幕式上作为学生代表发言,你将如何演讲?结合你对奥林匹克运动的精神的理解,写一篇300字左右的演讲词,并适当设计一些演讲技巧。
【教学理念】 1.整体感知课文内容,理清文章思路。2.培养学生筛选信息能力,了解纳米的有关知识和应用前景。3.激发科学兴趣,培养学生勇于大胆想象的科学精神。【教学流程】一、谈话引入,激发兴趣。1.今天我们来学习一篇新课文《纳米技术就在我们身边》(板书课题)。2.以前听说过“纳米技术”吗?你了解纳米技术吗?是怎么了解到的?预设:我通过预习课文了解到“纳米技术”就是研究小小物质新奇特性的一门学问。预设:我是通过查找资料了解什么是纳米,什么是纳米技术的。二、通读课文,了解大意。1.检查课文朗读。出示课文中的科技术语和句子。先组内相互听读纠正,然后全班交流。词语:除臭技术 纳米缓释技术 长度单位 纳米涂层 碳纳米管 纳米吸波材料 探测雷达波。句子:纳米技术就是研究并利用这些特性造福于人类的一门新学问。2.自由交流:读了课文,你知道了什么?
一、图片导入,激发兴趣。1.导语:大家还记得在科幻世界里那些随意消失变化的人吗?还记得在神话世界里,孙悟空的七十二变吗?现在所有这一切都不是在疯狂的科幻世界里,不是在神奇的神话里,而是在离我们也许只有几年之遥的纳米时代!那么什么是纳米?什么是纳米技术?大家想不想了解有关这方面的知识?2.展示图片:【课件出示2】图1.纳米机器人(描述的是一个纳米机器人在清理血管中的有害堆积物。由于纳米机器人可以小到在人的血管中自由地游动,对于像脑血栓、动脉硬化等病灶,它们可以非常容易地予以清理,而不再用进行危险的开颅、开胸手术。)图2.纳米技术制作的中国地图(这是中国科学院化学所的科技人员,利用纳米加工技术在石墨表面,通过搬迁碳原子而绘制出的世界上最小的中国地图。这幅地图到底有多小呢?打个比方吧,如果把这幅图放大到一张一米见方的中国地图大小的尺寸,就相当于把该幅地图放大到中国辽阔的领土的面积。)
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教学步骤、时间 教师活动 学生活动 媒体应用Step 1Free talk 3’ Ask some questions like:Who’s on duty today?What’s the weather like? Answer and talk about something.让同学们回答下列问题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此时教师用汉语问:“在周末期间问你干了什么?这句话用英语这么回答?Let the students guess.At last the teacher give them right answer3. What did you do over the weekend?(板书、学习)
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: 设计理想中的人类Step one: 设计理想中的人类的外貌。把全班同学分成若干小组,学生可以边说边在纸上画出他们的模样。Step two: 设计理想中人类的性格。学生们可以把那些能描述性格的单词写在图画的旁边。Step three: 每组选出一名同学,其他同组同学提问,他作简单回答,并说明原因。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: 挑战性活动调查性格是天生的还是后天形成的,让每个同学回家去调查一下自己成长过程中性格是否有变化,具体是怎样的,为什么会这样? 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. (板书,教读)教师把这些句子板书在黑板上,并请学生大声整齐地读祈使句和“can’t”句型,并让学生注意两种句型表达形式的不同和转换,“Don’t …=You can’t…”;并对学生说:These are our school rules. (板书,教读) You can’t break the school rules. Don’t break the school rules.(板书,教读)步骤3 :Practicea. T: Now, each of the students is breaking one of these rules.Please finish 1a.学生看图,完成1a的内容,检查答案并大声朗读校规。b. 听录音,完成1b,选出四位学生都违反了哪条校规;听之前,学生要读会英文名。c. 请两位学生朗读1c部分的句型;要求学生两人一组对话表演,SA扮演外校转来新生,SB告知本校校规。(学生可经过讨论,多说出他们想到的校规,不必只限于书上;教师应给予帮助)2) 第二课时(2a~4)步骤1 :warming up of revisionT: What are the rules at your school?学生使用“can”或祈使句表达各条校规;其中老师可引出“eat in the cafeteria outside”的表达。步骤2 :Practicea.T: Christina is an exchange student. She doesn’t know the rules. Let’s listen, what activities they’re talking about?学生听第一遍时,完成2a;第二遍时,完成2b;b. 请学生领读2c部分,看着2a完成的表格,理解2c活动的要求;分成小组针对2a进行问答;
教学过程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、教学建议第一课时: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.
1 Each group choose one place to describe and what you are doing in it Choose one place, and describe what they are doing 2 Move around the room and give suggestions Talk about it and write it down 3 Ask one to show their works and act it Choose one of each group to make a report 4 Evaluate the best group and the best reporter Choose the best one Homework Ask your friends their ideal place and write about it教学反思:新课程标准中强调学生在课堂中的主体地位,在综合课中他们的主体地位就更加突出。在各个活动中给不同程度的学生不同层次的任务,让各层面的学生都有表现发挥的机会,从而产生对英语的兴趣。使用照片图片多媒体来辅助教学,效果更好。同时让了解其他国家风景,风俗的同学介绍ideal place,增加学生的背景知知识,实现跨学科交流的目的。教案点评:采用任务型教学模式,在各个活动中给不同程度的学生不同层次的任务,让各层面的学生都有表现发挥的机会,从而产生对英语的兴趣。使用照片图片多媒体来辅助教学,效果更好。让了解其他国家风景,风俗的同学介绍ideal place,增加学生的背景知识,实现跨学科交流的目的。
2.1Match the country with the language.Step II Reading3a? let the students read the letter fast and answer the questions.? Let the students ask more questions about the letter as possible as the can.Step III Writing3b.Step IV. Pairwork2cStep V Listening2a, 2bStep V. HomeworkExercises book(1) P3Exercises book (2) P3Period FourStep I . Dictate the words and sentences in Unit1.Step II. Self-checkStep III. Check the answers for Exercises book in the unit.Step IV. Home workRevise and preparation for unit 2.教学反思:通过本单元的学习,学生基本可以谈论人们的国籍,居住城市及其所说的语言,通过书信方式去介绍自己并寻找笔友。但在涉及到国外的一些城市时,学生对这方面的知识相对欠缺,能介绍的城市并不多,也反应出学生课前预习不充分,这跟学生学习条件也有关,大多数学生无法通过网络获取所需信息。因此,在以后的教学中要多指导学生通过计算机网络获取信息,拓宽知识面。
五、教学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.说明:这一步旨在让学生运用已有的语言知识谈论对事物的看法和意见,并简单阐明理由,培养学生的主动思维能力和运用英语的能力。六、教学拓展调查电视节目的收视率任务:调查你周围的人对现在各种电视节目的反响。活动过程:1.教师布置任务,让学生调查周围的人(包括他的亲戚朋友和邻居)喜欢收看哪方面的电视节目。2.学生进行调查活动,运用本单元所学的句型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.记录下排在前10位的TV Program,填写调查表,比较其收视率。