高一数学必修4教案（精选4篇）
教材是人们为从事教学活动而设计编制的主观性的精神产品, 是人类文化经验结构与学生个体身心结构之间的媒介和桥梁.教材作为学生直接作用的对象, 是促进学生发展的工具和手段.传统教材以传授知识为中心, 教材是“知识仓库”, 强调向学生详尽地传递学科知识, 主要是通过纯文本的方式, 向学生直接呈现事实、概念和原理.这样的教材强调的是教师的教, 很容易导致学生的学习主动性受到压抑, 对所学内容不感兴趣, 不能很好地理解所学的内容.以促进学生的全面发展为宗旨的新课程改革, 不仅重视教材的“知识仓库”功能, 更强调教材是促进学生发展的功能, 教材承载着学生的学和教师的教.
作为新课程改革物化的产物, 人教版高中数学新教材全面体现了新课程高中数学改革的理念和内容, 教材不仅仅是一个信息资源体, 更是一个引导师生教与学, 促进学生全面发展的媒介.新教材通过“思考”“探究”和插入语等特色栏目, 在内容的呈现上, 不拘泥于对数学概念、公式、定理和性质的陈述和解释, 而是注重促进学生学习方式的转变, 注重展现知识获得的过程和方法, 引导学生通过多种多样的主体参与活动, 使学生在独立思考、解决问题的过程中, 自主地获得知识, 自主地获得情感、态度和价值观的体验.本文就人教版高中数学新教材“思考”栏目的教学实践与认识, 谈谈一些体会和看法.
一、新教材“思考”栏目的类型
1.引入型“思考”
“良好的开端是成功的一半”, 新教材在某些章节的开端就设计了精妙的“思考”, 引入学习内容.引入型的“思考”, 可以在第一时间抓住学生的眼球, 引发好奇心, 激发求知欲, 诱导思维动机, 使其产生“愿知其详”的强烈愿望.例如, 在学习“三角函数的诱导公式”时, 新教材数学4是通过“思考”栏目如此引入的:“我们利用单位圆定义了三角函数, 而圆具有很好的对称性, 能否利用圆的这种对称性来研究三角函数的性质呢?例如, 能否从单位圆关于x轴、y轴、直线y=x的轴对称性以及关于原点的中心对称性等出发, 获得一些三角函数的性质呢?”从知识的产生来源入手设计“思考”, 激发了学生的学习兴趣和求知欲, 实现了教师被动教教材到学生主动学教材的转变.新教材的全部内容不再是仅仅呈现结论性知识, 还为展开教学活动以使师生互动产生知识提供范例和素材.
2.总结型“思考”
新教材设计了一些总结性的“思考”, 以问题的形式或者是提供一定的线索, 引导学生对学习内容进行系统整理.例如, 在学完三角函数的诱导公式一至四, 新教材设置了思考:“你能用简洁的语言概括一下公式一至四吗?它们的作用是什么?”在学习正弦函数的图像时, 新教材设置了思考:“在作出正弦函数的图像时, 应抓住哪些关键点?”在这些思考过程中, 使学生对自己的学习活动进行反思, 对知识和方法再认识, 充分调动了学生的学习主体性, 改变了传统的单一以听、记为主的学习方式, 增强了学生对知识的理解和认识.
3.提示型“思考”
教材呈现的知识包括人类实践活动经验和文化精神产物, 数学教材中的知识是人类一代代继承和发展下来的数学产物, 有些数学公式、概念和性质是经过了几代数学家的努力才获得的.新课程倡导多样化的学习方式, 强调学生的主体参与获得知识和方法, 但课堂的时间是有限的, 很多时候当然不能指望学生能在一堂课或两堂课上就能发现这些公式、性质和定理.为此, 新教材为一些新知识的获得通过“思考”栏目进行了提示.比如:“你能从正切函数的图像出发, 讨论它的性质吗?”“你能否从函数图像变换的角度出发, 利用函数y=sinx的图像得到函数y=1+sinx的图像吗?”这些提示为学习提供了方向, 起到了灯塔的作用.
4.拓展延伸型“思考”
引导学生对数学概念、公式、定理和性质等进行横向延伸和纵向推广, 促进了学生对数学知识本质的深刻理解.这样, 不仅纵向深化了所学的知识, 而且横向拓展了学生分析问题、解决问题的能力, 对于开阔学生的数学视野、培养学生的能力、提高学生的数学素养是大有帮助的.例如, “你认为上述求函数y=Asin (ωx+φ) , x∈R及函数y=Acos (ωx+φ) , x∈R周期的方法是否能推广到求一般周期函数的周期上去?即命题‘如果函数y=f (x) 的周期是T, 那么函数y=f (ωx) 的周期是
二、新教材“思考”栏目在教学实践中的认识
首先, “思考”设计合理、科学.“思考”的科学性包括两个方面的含义:一方面是“思考”的设计, 无论是在形式表述上, 还是在内容安排上, 都符合数学学科的特点.表述的语言简练, 没有出现歧义的地方.表述的数学内容严谨, 符合数学的学科性.另一方面, 科学性体现在准确把握高中生的身心发展规律, 立足其认知和情感水平.教材所设计的问题, 难度适中, 既能激起学生的求知欲望, 又能使学生经过努力后有收获, 更进一步加深了学生对知识产生过程的体验, 增强了对公式、概念、性质和定理的理解与掌握.
其次, “思考”转变了学习方式.“思考”栏目使学生的学习不仅仅是记忆与模仿、不仅仅是死记硬背与机械训练, 而是注重激发学生学习的积极性和创造性, 使之真正成为学习的主体, 使学生在学习数学知识的过程中体会数学的创造性、培养自身的数学思维能力和创新能力.
最后, “思考”有利于教师的教学.新教材在重、难点的地方设置问题, 为能引发学生的思考回避了对问题答案的直接呈现, 这样的方式就有利于教师创造性地进行教学, 教师可以根据学生的思考情况, 充分重视作为教学资源的学生, 积极主动地开展教学活动.在这种情况下, 教师个人的知识和师生互动产生的新知识在整个课堂中占有很大比例, 学生在理解和构建教材内容意义的基础上, 获得知识与技能、过程与方法、情感态度与价值观的全面发展.另外, 教材运用了专家们的集体智慧, 在内容重、难点处提出了适当的思考问题, 这也有利于教师的教学不太偏离核心内容的主线.
三、教学建议
1.以学生为主体, 给予学生充分的思考时间
如前所述, 新教材在重、难点的地方设置问题, 引发学生思考, 并且在教材中不呈现问题的答案, 目的是给学生在学习过程中有思考过程.如:“你能用简洁的语言概括一下公式一至四吗?它们的作用是什么?”“能否从单位圆关于x轴、y轴、直线y=x的轴对称性以及关于原点的中心对称性等出发, 获得一些三角函数的性质呢?”很显然, 这些问题都是学习者必须经过的学习环节, 教师不要越位, 不要自问自答, 给学生充分的思考、探究、总结、回答时间, 让学生在思考中提高数学思维, 在顿悟中得到数学知识.
2.要深入钻研和理解教材的主旨, 对“思考”慎加减
引入型“思考”中的素材, 无论是涉及已学知识, 还是现实生活中的实例, 都是立足学生已有认知水平, 引发新问题的思考内容的延伸.不管是哪种类型的思考, 作为探究的前奏, 在各知识点中起到过渡与承上启下的作用.另一方面, 新教材引入“思考”栏目的目的之一就是要转变教学方式以适应新课标的教育教学要求.我们可以立足学生的认知水平, 为学生提供可思考探究的平台, 但不能过多加工, 以免画蛇添足造成偏离学习重点, 更不可在教学过程中为“赶时间”而把这个环节省略掉, 这样缺乏思考的不完整的学习过程也不会达到应有的教学效果.
3.对“思考”要有板书总结
研究表明, 板书对学生的思维具有较大的影响.新教材的部分知识, 通过设置表格、横线等, 让学生思考、自主探究得出结果然后填补上去的.另一方面, 鉴于学生的记忆特征与思维特征, 因此, 思考探究之后的板书总结, 把准确的知识暴露给学生, 是教学中不可忽略的一环.
参考文献
[1]毕华林.教材功能的转变与教师的教科书素养[J].山东师范大学学报 (人文社会科学版) , 2006 (1) .
I．单元教学目标
技能目标 Skill Goals
Talk about body language: cultural differences and intercultural communication
Practise talking about prohibition & warning as well as obligation
Learn to use the -ing form as the Attribute && Adverbial
Learn to write a diary that showing the observation of how body language helps in communication
II． 目标语言
功
能
句
式 Talk about body language
What is the purpose of language?
What do you think “body language” means?
How can you tell if someone is sad or happy even if they do not speak?
How can you communicate a feeling to someone who does not speak your language?
Why do we need to study body language?
Talk about cultural differences && intercultural communication
What do British people often do when they meet strangers?
What do French people often do when they meet people they know?
Why should we be careful about our own body language?
Why is it important to watch others as well as listen to them?
词
汇 1． 四会词汇
major, local, represent, curious, Columbia, introduce, approach, touch, cheek, stranger, spoken, express, action, Jordan, nod, general, avoid, comedy, misunderstand, similar, facial, expression, agreement, yawn, chest, gesture, adult, punish
2． 认读词汇
Garcia, Julia, learned, unspoken, posture, Ahmed Aziz, Coulon, Muslim, frown, threaten
3． 词组
be likely to, at ease, an exciting experience for, not all ..., introduce oneself to sb
语
法 4． 重点词汇
represent, introduce, approach, touch, express, nod, avoid, misunderstand, punish, general, curious, similar, expression, agreement, gesture, action
The -ing form as the attribute && adverbial
Finding out in the reading text sentences with present participle(s) used as the attribute or adverbial.
1. The -ing form as the attribute
They are visitors coming from several other countries, ...
His nose touches Mr. Cook’s moving hand, ...
This is an exciting experience for you, ...
2. The -ing form as the adverbial
... so you stand watching and listening.
Four people enter looking around in a curious way.
You see her step back appearing surprised, and take a few steps away from Mr. Garcia.
The visitor from Japan comes in smiling at the same time as George Cook from Canada.
重 点 句 子 1. They will be meeting at a major hotel with local business people and people who represent the Chinese government. P25
2. The first person who arrives is Mr. Garcia from Columbia, closely followed by Julia Smith from Britain. P26
3. You think that there may have been a mistake. P26
4. Not all cultures greet each other the same way, nor are they comfortable touching strangers or being too close or too far away. P26
5. In the same way that people communicate with spoken language, they also express their feelings using unspoken “language” through keeping physical distance, actions or posture. P26
6. People from places like Spain, Italy or ... others closely and are more likely to touch them. P26
7. ... nodding the head shows agreement, while shaking
the head means that you do not agree, ... P30
Ⅲ． 教材分析和教材重组
1． 教材分析
本单元以Body Language--“体态语”为中心话题，具体涉及什么是“体态语”，如何理解“体态语”，以及“体态语”的跨文化性等。本单元的语言技能和语言知识也都是围绕“体态语”这一中心话题设计的，旨在通过单元教学，用听、说、读、写、做(表演)等多种形式，让学生正确认识和掌握“体态语”在交际中的作用和意义，使学生明确“体态语”在人类交际中的重要性，了解“体态语”在不同民族、不同文化交际中的多样性；使学生在今后的日常生活、学习、工作和交往中尽量减少或避免运用“体态语”时可能产生的误解，提高他们的“语言交际”能力和“非语言交际”能力。
1.1 WARMING UP 以列表对比（填充及增补）的形式，并通过WARMING UP的活动，让学生了解有声语言与“体态语”的对应关系，了解语言意义与行为意义（“体态语”）在交际中具有同等重要的作用。同时，学生在听、说、做（即表演“体态语”的动作）中能够增进对语言交际的感性认识，为他们在阅读过程中上升到对语言交际的理性认识打下基础。
1.2 PRE-READING 通过提供三个关于不同文化背景下“体态语”的问题，启发学生思考我们所学习的“语言”的目的、形式、功能。通过引导学生联系自己日常生活的实际，提高学生努力学习英语的积极性和自觉性；同时培养学生留心社会、关注生活的洞察力，为引导学生进一步“阅读”作好准备。
1.3 READING 是一篇介绍性（记叙文）体裁的文章，主要介绍了各种文化背景下的“体态语”的异同，为学生提供了来自不同国度、不同语言文化背景的“体态语”及其在交际中的异同和影响的具体例证。学生也可以结合自己在语言交际中所遇到的实际例子来进一步理解“交际，毫无问题可言吗？”这一主题。
1.4 COMPREHENDING 包括八个问题（前5个旨在检查学生对阅读材料细节的理解，6~7旨在引导学生对“体态语”的意义及文化差异的思考，第8个检查学生能否通过细节进行推理判断），通过对来自不同国度、不同语言文化背景的六个角色对待男女不同性别所使用的“体态语”异同的（学生在老师指导下的自我或小组讨论后的）归纳，进一步熟悉和掌握“体态语”在不同语言文化交际中的作用和意义。
1.5 LEARNING ABOUT LANGUAGE 分词汇和语法两部分。词汇部分由“本单元重点词汇英文释义”，“词语填空”和“词性变换”三项内容构成，语法部分由两大方面组成：一是让学生自己通过在课文中寻找相关语法的句子并按其语法功能分类，二是根据学生的认知规律安排该语法项目的练习让学生进行操练。整个项目通过三个练习和一个游戏，以及语法结构讲练，进一步巩固本单元所学词汇（尤其是课文中的黑体字），学习“现在分词”结构用作定语和状语，并通过操练，以收到“学以致用”、“熟练生巧”的效果。
1.6 USING LANGUAGE 通过增加阅读篇目“Showing Our Feelings”来拓展学生在“体态语”方面的知识视野，并通过“True” or “False”判断练习和问题讨论，使学生进一步明确“体态语”对人们在日常交际中了解对方情感、思想、态度等方面所起的作用。同时要让学生认真对待自己的“体态语”，并在日常交际中“听其言”（Listen to them）、“观其行”（Watch them）。此外，该部分还通过听、说、读、写四个方面来巩固本单元所学内容和语言交际项目。
1.7 SUMMING UP 师生从话题、词汇和结构三个方面来共同总结本单元所学的单词和短语，语言及语法项目，总结本单元所学的主要内容和收获。
1.8 LEARNING TIPS 建议学生关注实用交际技巧，学会“体态语”；建议学生在看英语电影时或与以英语为母语的人士交谈时，观察对方面部表情和体态姿势，观察对方的“言”、“行”，进而形成有效的口笔头语言及“体态语”的交际能力。
2. 教材重组
2.1 听力：Using language中的Listening, Workbook中的Listening和Listening Task这三部分的任务及话题较为接近，将这三个部分整合在一起上一堂听力课。
2.2 口语：Warming up, Using language中的Reading and Talking, Speaking和Workbook中的Talking，Speaking Task以及Learning about language中的Discovering useful words and expressions 4, “Play a game in group of four”均紧扣本单元话题，同时涉及到本单元的功能句，教师可指导学生通过“说”（用英语发出与“体态语”相关的指令）与“做”（用“体态语”表达指令）结合来进行口语训练，这将是一节生动有趣的口语课。
2.3 精读：把Pre-reading，Reading和Comprehending三部分整合为一节阅读课。
2.4 泛读：把Using Language中的Reading和Workbook中的Reading Task整合为一节拓展学生视野的泛读课。
2.5 语言学习：深入处理Learning about language中的Discovering useful words and expressions, Discovering useful structures; Workbook中的Using Words and Expressions和Using Structures。重点学习Discovering useful structures中“-ing (现在分词)”在句中做定语和状语的用法。
2.6 语言运用：处理Using Language中的Reading and Writing和Workbook中的Writing Task。指导学生写一篇有关“The Body Language I Know”短文，反映其在不同文化背景、不同语言环境中的运用情况，及所造成的理解上的困难、障碍甚至误解等。
3． 课型设计与课时分配
1st period Speaking
2nd period Reading (I)
3rd period Reading（II）
4th period Language Study
5th period Listening
6th period Writing
Ⅳ． 分课时教案
The First Period Speaking
Teaching goals 教学目标
1. Target Language目标语言
a. 重点词汇和短语
misunderstand, similar, facial, expression, agreement, yawn, chest, gesture, adult, punish
b. 重点句型或交际用语
Act out the following meanings, please.
Please guess what I mean.
Please show the actions, using body language.
Now it is your turn to show the action / gesture.
Please use either spoken words or body language to express your ideas.
Please use both spoken words and body language to express your ideas.
2. Ability goals能力目标
a. Enable the students to understand what a certain gesture of the body language means in a given situation.
b. Enable the students to act out some meanings, requirements, requests or situations given in the target language.
c. Enable the students to express with the target language the meanings given in body language.
3. Learning ability goals 学能目标
a. Help the students learn how to express themselves in body language when needed.
b. Help the students understand others when body language is being used.
Teaching important points教学重点
a. Teach the students how to understand body language used in different countries or cultures as well as in different occasions.
b. Teach the students how to use body language in the most appropriate occasions.
Teaching difficult points 教学难点
a. Enable the students to realize the importance of body language in communication so that little or no misunderstanding may occur.
b. Let the students know that there is both positive body language and negative body language.
Teaching methods教学方法
a. Individual work, pair work and group work.
b. Acting out by imitation, mime or with gestures and body movement.
Teaching aids教具准备
A computer, a projector and some pictures.
Teaching procedures & ways教学过程与方式
Step I Lead-in
The teacher shows some pictures on screen. These pictures are from the Evening Party Celebrating the coming Lunar New Year of the Rooster of .
Ss: Yes, Thousands of Hands Kwan-yin.
T: But do you know who she is? Yes, she was the leading dancer of the program. Her name is Tai Lihua（邰丽华）. She is called a Fairy of Peach blossom(桃花仙子) by people. You know she is a deaf girl, but she is a wise, diligent, charming and energetic girl. She studied very hard and got two degrees of bachelors in university. She was famous as an artist for her wonderful performance. She is deaf and dumb. But how did she get that great achievement and became a successful person? She loves life very much. We should learn from her spirit. Besides her hard working, body language plays a very important part in her life. We are all healthy people, sometimes we can use body language to express ourselves. So we should pay more attention to learning body languages.
Step II Introduction
T: Now let’s do some TPR (Total Physical Response) activities together, I hope you will enjoy them and have fun as well.
Touch your head / face / eyes / nose / mouth / ears / cheeks / forehead / shoulders / stomach / legs / feet / toes ...
Shake your head / arm / hand ...
Wave your arm / hand ...
Open your eyes / arms /mouth ...
Close your eyes / mouth ...
Twist your wrist / waist.
Cross your arms / fingers.
Nod your head. Bow your head.
Make a face to each other.
Bend / cry / shout / scream / smile / laugh ...
T: All right. Now let’s do them a little bit difficult. Let’s play a game together. Those who fail to follow the rule of the game will be dropped out. The game is: “Simon says”. For example, if I say “Simon says, touch your head”, then you touch your head. If not, you shouldn’t touch your head but remain still. Clear? Ready? Now let’s start.
3 or 5 minutes for the game.
T: Ok. It’s time to take up the lesson. Please look at the screen. Let’s take a look at the following gestures:
Gesture Action Meaning
A handshake You are welcome.
A clap of hand Come on; be cheerful.
A V-shape of the fore-finger and middle finger May you succeed!
Or congratulations on your success!
A half-closed hand with thumb down I am not in favor of your idea or I’ll have to refuse you.
A wrinkling of the brow in thought or displeasure or a scowl She is worried.
Tears coming out of his eyes. He is very sad.
All smiles on her face She is very happy.
Waving their hands They are waving goodbye to people around.
A hand stretched out forward with strength He is stopping a tank.
People jump with their both hands stretched open in the air. They are cheering for the victory.
T: What are the actions of the above gestures? What do they mean?
S4: The first gesture is a handshake, which means “You’re welcome”.
S5: The second is a handclap, which means “Come on” or “Be cheerful” or something like that.
S6: The third one is a V-shaped posture of the first finger and the middle finger, which suggests a wish for the other or others to succeed.
S7: The fourth is a half-closed hand with the thumb down. It means the one who gives this gesture is against the other’s idea or simply refuses the request.
S8: The fifth is a worried look of a woman. She wrinkles her brows or frowns. It also seems that she scowls. It shows that she is worried or sad. In other words, she is unhappy.
S9: The sixth is a man shedding tears. Tears were running down his cheeks. He is very sad for losing his relatives or sad for his failure.
S10: The seventh is a smiling face. It is easy to see that she is very happy.
S11: The eighth is a gesture of waving hands. They are waving goodbye to people who are around to see them off.
S12: The ninth is a hand stretched out forward with great strength. The boy is trying to stop a tank from entering into his homeland.
S13: The tenth is hands stretched out upward. They are all very cheerful. They are wild with joy; maybe they have just won a game. So we can see that they are cheering for their victory.
T: You have all done a good job. So you see that there are many cases or situations in which body language can convey meanings as well as spoken or written languages. If you want to know more about it, let’s come to Unit 4 Body Language.
Step Ⅲ Practice
T: Look at the chart on Page 25. Here is a list. On the left side are feelings or ideas. You are asked to add three of your own. Make notes on the right side of the chart and then act them out to see how you would make someone understand these feelings and ideas without speaking. Do it with your partner first. And then some of you will be asked to the front of the classroom to act them out.
Meaning Action
1. You are welcome. A smile and a handshake.
2. I am worried. A frowned or upset look.
3. I ate too much Putting a hand on the stomach, patting or rubbing.
4. I am sorry that I did something wrong. Drooping or hanging the head.
5. I’m so happy. A loud laughter with a shining face or smiling with arms open and head back.
6. You did a good job. A thumb up.
7. You are angry. Turning your back to someone on purpose.
8. Stop here. Putting the left palm on the forefinger of the right hand.
Demonstration:
The students can be allowed to act out the feelings or ideas without following the order in the chart so that it may be more challenging as well as more interesting.
Step Ⅳ Time for Fun
T: Now let’s play a game in groups of four. One thinks of a situation and asks the others to show some actions using body language. When the one chooses the action that is most likely, it is his or her turn to think of some other situation for the others to show the actions so that the game may go on for a few rounds. Clear?
Ss: Yes. That’s funny!
T: Try to make the situations as interesting and enjoyable as you can. And show the situation as lively as possible. Besides, make sure that everyone has a turn.
Ss: All right.
S1: What are you likely to do if it rains?
(Actions) S2: reads a book;
S3: puts on a raincoat;
S4: cleans the house.
S1: Ok. I think S3 seems the most likely, so it is his turn.
S3: What are you likely to do if the river floods?
(Actions) S1: runs away as fast as he can;
S2: helps the younger or elder to escape as soon as possible;
S4: climbs on to a tree.
S3: Ok. I think S2 seems the most likely, so it is her turn.
S2: What are you likely to do if the house catches fire?
(Actions) S1: fetches some water;
S3: tries to put it out with blooms;
S4: runs away as quickly as he can.
S2: Ok. I think S4 seems the most likely, so it is his turn.
S4: What are you likely to do if you meet with a fierce dog?
(Actions) S1: remains where he is and bends down, looking at the dog;
S3: tries to scare it away with small stones;
S4: runs away as quickly as possible.
S2: Ok. I think S1 seems the most likely, so we all have done a good job.
T: Yes. I couldn’t agree with you. Now, one more group.
Step V Talking
Get the students to work in pairs. The situation is that you are worried about Lin Pei, who is not friendly any more, and does not want to talk to you or her other friends. She seems to be sad. She stays alone. She is not doing her homework and the teacher is not pleased with her. She doesn’t seem to care about how she looks and behaves.
T: Now class, work in pair. Discuss Lin Pei’s behavior. Think about the problems she might have. Describe her “body language” or the behavior that shows how she feels. Three minutes for you.
T: All right, who’d like to describe or act out Lin Pei’s behavior?
S1: I think there is something wrong with her. When I saw her recently, she would turn away from me and would not speak to me. (Miming the action)
S2: Yes, when I saw her in class, she looked as if she had been crying. And she would not even look at me. She just looked straight out of the window. She seemed as if she could see nobody in her eyes. (Miming the action)
S3: I quite agree. When I met her at the school gate and tried to have a word with her, she just bent down her head and passed me as if she hadn’t noticed me. (Miming the action)
S4: I couldn’t agree with you more! This morning, when I went close to her, trying to start a conversation between us, she crossed her arms in front of her and didn’t look at me. And then she turned away immediately. (Miming the action)
T: Good job. Now class, let’s try to think of a way to help her out, OK?
Ss: Yes, Sir.
Step Ⅵ Role Play (Speaking task on P67)
T: Now, there’s still a little time left. Let’s come to Speaking Task on Page 67. We’re given two situations. For each situation, prepare a role-play with your partner. Use both spoken words and body language to express your ideas. Then explain to the class what the differences are in Western and Chinese languages, and what they mean. The first two sentences have been given in the text.
Work in pairs
1. You fall and hurt your foot while you are hiking on a
lonely path. You need help, and see someone in the distance.
S1-You, S2-Passer-by
S1: Help! Help! Please come over here! (waving and crooking your hand toward the place where you are lying)
S2: What do you want? I can’t hear you! (hand behind your ear)
S1: Can you see me? Please come here! (waving and crooking your hand again toward the place where you are lying)
S2: Why? I can’t understand you. (with a forefinger on the right side of the head)
S1: I hurt my foot when I fell. (pointing to your injured foot)
S2: All right. I am coming! (running)
Work in group of three
2. You are visiting a strange city and need to buy some tea and oranges. You only know a little English and want to know where you can get them and how much they cost.
S1-You, S2-Passer-by, S3-Shopkeeper
S1: Can you help me please? I need some tea and some oranges. (smiling and leaning forward)
S2: Pardon? What do you need?
S1: Tea (taking out the little sample) and oranges (using thumb and the forefinger to form a round shape). Where can I get some? (miming the question)
S2: Oh, this is tea. And some oranges, right?
S1: (Nodding your head) Yes. Where can I buy some? (repeating the mime)
S2: (Showing the way) This way, please.
S1: Thanks. (acting out the Chinese way to show thanks)
S2: Here you are.
(They are entering the grocery store.)
S3: Can I help you?
S2: He wants to buy some tea and oranges.
S3: No problem. (To S1) How much tea do you need? And how many oranges?
S1: (Sticking out five fingers to show half kilo of tea, and two hands to show ten oranges)
S3: Here you are.
S1: How much are they? ( drawing the sign of the US dollar-$)
S3: (Working on the calculator) $9 in all including taxes.
S1: Here is ten dollars. (handing the ten-dollar note)
S3: Here is the change.
S1: Thanks. (nodding your thanks) Bye!
Step Ⅶ Homework
1. Team work: Discuss the importance of body language.
2. Go over the Reading:
1) Communication: No Problem?
2) Showing our feeling.
T: I think you must have known something about these pictures. Yes, they are from a program of CCTV, the Evening Party Celebrating the Spring Festival of 2005, the coming Lunar New Year of the Rooster. I think that was the best program. Do you remember the name of this program?
详细内容请订阅
1.函数 的定义域是
A. B. C. D.
2.如果幂函数 的图象经过点 ,则 的值等于
A、B、C、D、
3.已知 是单调函数 的一个零点，且 则
A. B.
C. D.
4.下列表示同一个函数的是
A. B.
C. D.
5.函数 的图象为
A. B. C. D.
6.若偶函数 在 上是减函数，则下列关系中成立的是
A. B
C D
7. 下面不等式成立的是
A. B.
C. D.
8.定义在R上的偶函数 满足 ，且当 时 ，则 等于
A. B. C. D.
9. 函数 是定义在 上的偶函数，则 在区间 上是
A. 增函数 B. 减函数
C. 先增后减函数 D.先减后增函数
10.若函数 在区间 上是减函数，则 的取值范围是
A. B. C. D.
选择题答案
题号 1 2 3 4 5 6 7 8 9 10
答案
二、填空题(每小题5分，共20分)
11.已知 在映射 下的对应元素是 ，则 在映射 下的对应元素是 ;
12.设 为定义在R上的奇函数，且当 时， ，则 时 的解析式为_____________ __
14.方程 的解的个数为 个.
15. =
三、解答题：本题共5小题，共40分。
16.计算(6分)
17. (8分)已知函数 的定义域为 ， 的定义域为集合 ;集合 ，若 ，求实数a的取值集合。
18.(8分)f(x)定义在R上的偶函数，在区间 上递增，且有 ,求a的取值范围.
19.(8分)设某旅游景点每天的固定成本为 元，门票每张为 元，变动成本与购票进入旅游景点的人数的算术平方根成正比。一天购票人数为 人时，该旅游景点收支平衡;一天购票人数超过 人时，该旅游景点需另交保险费 元。设每天的购票人数为 人，赢利额为 元。
⑴求 与 之间的函数关系;
⑵该旅游景点希望在人数达到 人时即不出现亏损，若用提高门票价格的措施，则每张门票至少要多少元(取整数)?
注：①利润=门票收入—固定成本—变动成本;
②可选用数据： ， ， 。
(1)求 值;
(2)判断并证明该函数在定义域 上的单调性;
(3)若对任意的 ，不等式 恒成立，求实数 的取值范围;
数学必修一过关检测(2)
一、选择题：本大题共10小题，每小题4分，共40分
1.函数 的定义域是：
2.全集U={0,1,3,5,6,8｝,集合A={ 1，5, 8 }, B ={2},则集合 ：
A.{0,2,3,6} B.{ 0,3,6} C. {2,1,5,8} D.
3.已知集合 ：
A. ( 2, 3 ) B. [-1,5] C. (-1,5) D. (-1,5]
4.下列函数是偶函数的是：
A. B. C. D.
5.化简： =：
A. 4 B. C. 或4 D.
6.在同一直角坐标系中，函数 与 的图像只能是：
7.下列说法正确的是：
A.对于任何实数 ， 都成立
B.对于任何实数 ， 都成立
C.对于任何实数 ，总有
D.对于任何正数 ，总有
8.如图所示的曲线是幂函数 在第一象限内的图象.已知 分别取 ，l， ，2四个值，则与曲线 、、、相应的 依次为：
A.2，1， ， B.2， ，1，
C. ，1，2， D. ，1，2，
9.函数 的零点所在区间为：
A. B. C. D.
10.若指数函数 在[-1，1]上的值与最小值的差是1，则底数 为：
A. B. C. D.
选择题答案
题号 1 2 3 4 5 6 7 8 9 10
答案
二、填空题：本大题共5个小题，每小题4分，共20分.
11. =
12.已知 ，则 .
13.已知 ，则 .
14. 方程 的解是 .
15. 关于下列命题：
①若函数 的定义域是{ ，则它的值域是
② 若函数 的定义域是 ，则它的值域是 ;
③若函数 的值域是 ，则它的定义域一定是 ;
④若函数 的值域是 ，则它的定义域是 .
其中不正确的命题的序号是_____________( 注：把你认为不正确的命题的序号都填上).
三、解答题(本大题共5小题，共40分.解答应写出文字说明，证明过程或演算步骤.)
16.(每小题满分6分)
不用计算器求下面式子的值:
;
17.(本小题满分8分)
已知全集 ， ， ， .
(1)求 ;
(2)求 .
18.(本小题满分8分)
已知函数 是定义在R上的偶函数，且当 ≤0时， .
(1)现已画出函数 在y轴左侧的图像，如图所示，请补出完整函数 的图像，并根据图像写出函数 的增区间;
(2)写出函数 的解析式和值域.
19.(本小题满分8分)
已知 ，求函数 的值和最小值.
20.(本小题满分10分)
已知函数 .
(1)求函数 的定义域;
(2)判断 的奇偶性;
(2)理解在给定集合中一个子集的补集的含义，会求给定子集的补集;(3)能用Venn图表达集合的关系及运算，体会直观图示对理解抽象概念的作用。
课 型：新授课
教学重点：集合的交集与并集、补集的概念;
教学难点：集合的交集与并集、补集“是什么”，“为什么”，“怎样做”;
教学过程：
六、引入课题
我们两个实数除了可以比较大小外，还可以进行加法运算，类比实数的加法运算，两个集合是否也可以“相加”呢?
思考(P9思考题)，引入并集概念。
七、新课教学
1. 并集
一般地，由所有属于集合A或属于集合B的元素所组成的集合，称为集合A与B的并集(Union)
记作：A∪B
Venn图表示： 读作：“A并B” 即： A∪B={x|x∈A，或x∈B}说明：两个集合求并集，结果还是一个集合，是由集合A与B的所有元素组成的集合(重复元素只看成一个元素)。
问题：在上图中我们除了研究集合A与B的并集外，它们的公共部分(即问号部分)还应是我们所关心的，我们称其为集合A与B的交集。
2. 交集
一般地，由属于集合A且属于集合B的元素所组成的集合，叫做集合A与B的交集(intersection)。
记作：A∩B
读作：“A交B” 即： A∩B={x|∈A，且x∈B}
交集的Venn图表示
说明：两个集合求交集，结果还是一个集合，是由集合A与B的公共元素组成的集合。 拓展：求下列各图中集合A与B的并集与交集
集
3. 补集
全集：一般地，如果一个集合含有我们所研究问题中所涉及的所有元素，那么就称这个集合为全集(Universe)，通常记作U。
A
说明：当两个集合没有公共元素时，两个集合的交集是空集，而不能说两个集合没有交补集：对于全集U的一个子集A，由全集U中所有不属于集合A的所有元素组成的集合称为集合A相对于全集U的补集(complementary set),简称为集合A的补集，
记作：CUA
即：CUA={x|x∈U且x∈A}
补集的Venn图表示
说明：补集的概念必须要有全集的限制
4. 求集合的并、交、补是集合间的基本运算，运算结果仍然还是集合，区分交集与并集的
关键是“且”与“或”，在处理有关交集与并集的问题时，常常从这两个字眼出发去揭示、挖掘题设条件，结合Venn图或数轴进而用集合语言表达，增强数形结合的思想方法。
5. 集合基本运算的一些结论：
A∩B?A，A∩B?B，A∩A=A，A∩?=?,A∩B=B∩A
A?A∪B，B?A∪B，A∪A=A，A∪?=A,A∪B=B∪A
(CUA)∪A=U，(CUA)∩A=?
若A∩B=A，则A?B，反之也成立
若A∪B=B，则A?B，反之也成立
若x∈(A∩B)，则x∈A且x∈B
若x∈(A∪B)，则x∈A，或x∈B
6. 课堂练习
(1)设A={奇数}、B={偶数}，则A∩Z=A，B∩Z=B，A∩B=?
(2)设A={奇数}、B={偶数}，则A∪Z=Z，B∪Z=Z，A∪B=Z
(3)集合A?{n|nm?1?Z}，B?{m|?Z}，则A?B?__________22
5(4)集合A?{x|?4?x?2}，B?{x|?1?x?3}，C?{x|x?0，或x? 2
那么A?B?C?_______________,A?B?C?_____________;
八、作业布置：(1) 已知X={x|x2+px+q=0，p2-4q>0},A={1,3,5,7,9},B={1,4,7,10}，且
X?A??,X?B?X，试求p、q;
(2) 集合A={x|x2+px-2=0},B={x|x2-x+q=0},若A?B={-2，0，1}，求p、q;
【高一数学必修4教案】推荐阅读：
高一数学必修一总结09-14
高一数学必修1应该怎么学好07-09
高一必修二数学知识点11-29
高一数学必修三第三单元知识点09-24
高一英语必修4单词表11-10
高一数学函数教案10-23
高一数学第二课堂教案05-27
高一数学第二章第一节教案11-21
高一历史必修一教案06-15
