本节课是新版教材人教A版普通高中课程标准实验教科书数学必修1第四章第4.4.3节《不同增长函数的差异》 是在学习了指数函数、对数函数和幂函数之后的对函数学习的一次梳理和总结。本节提出函数增长快慢的问题,通过函数图像及三个函数的性质,完成函数增长快慢的认识。既是对三种函数学习的总结,也为后续导数的学习做了铺垫。培养和发展学生数学直观、数学抽象、逻辑推理和数学建模的核心素养。1.了解指数函数、对数函数、幂函数 (一次函数) 的增长差异.2、经过探究对函数的图像观察,理解对数增长、直线上升、指数爆炸。培养学生观察问题、分析问题和归纳问题的思维能力以及数学交流能力;3、在认识函数增长差异的过程中,使学生学会认识事物的特殊性与一般性之间的关系,培养数学应用的意识,探索数学。 a.数学抽象:函数增长快慢的认识;b.逻辑推理:由特殊到一般的推理;
本节课选自《普通高中课程标准实验教科书数学必修1》5.6.2节 函数y=Asin(ωx+φ)的图象通过图象变换,揭示参数φ、ω、A变化时对函数图象的形状和位置的影响。通过引导学生对函数y=sinx到y=Asin(ωx+φ)的图象变换规律的探索,让学生体会到由简单到复杂、由特殊到一般的化归思想;并通过对周期变换、相位变换先后顺序调整后,将影响图象变换这一难点的突破,让学生学会抓住问题的主要矛盾来解决问题的基本思想方法;通过对参数φ、ω、A的分类讨论,让学生深刻认识图象变换与函数解析式变换的内在联系。通过图象变换和“五点”作图法,正确找出函数y=sinx到y=Asin(ωx+φ)的图象变换规律,这也是本节课的重点所在。提高学生的推理能力。让学生感受数形结合及转化的思想方法。发展学生数学直观、数学抽象、逻辑推理、数学建模的核心素养。
课本从引进函数概念开始就比较注重函数的不同表示方法:解析法,图象法,列表法.函数的不同表示方法能丰富对函数的认识,帮助理解抽象的函数概念.特别是在信息技术环境下,可以使函数在形与数两方面的结合得到更充分的表现,使学生通过函数的学习更好地体会数形结合这种重要的数学思想方法.因此,在研究函数时,要充分发挥图象的直观作用.在研究图象时,又要注意代数刻画以求思考和表述的精确性.课本将映射作为函数的一种推广,这与传统的处理方式有了逻辑顺序上的变化.这样处理,主要是想较好地衔接初中的学习,让学生将更多的精力集中理解函数的概念,同时,也体现了从特殊到一般的思维过程.课程目标1、明确函数的三种表示方法;2、在实际情境中,会根据不同的需要选择恰当的方法表示函数;3、通过具体实例,了解简单的分段函数,并能简单应用.
本节课选自《普通高中课程标准实验教科书数学必修1本(A版)》的第五章的4.5.3函数模型的应用。函数模型及其应用是中学重要内容之一,又是数学与生活实践相互衔接的枢纽,特别在应用意识日益加深的今天,函数模型的应用实质是揭示了客观世界中量的相互依存有互有制约的关系,因而函数模型的应用举例有着不可替代的重要位置,又有重要的现实意义。本节课要求学生利用给定的函数模型或建立函数模型解决实际问题,并对给定的函数模型进行简单的分析评价,发展学生数学建模、数学直观、数学抽象、逻辑推理的核心素养。1. 能建立函数模型解决实际问题.2.了解拟合函数模型并解决实际问题.3.通过本节内容的学习,使学生认识函数模型的作用,提高学生数学建模,数据分析的能力. a.数学抽象:由实际问题建立函数模型;b.逻辑推理:选择合适的函数模型;c.数学运算:运用函数模型解决实际问题;
本章通过学习用二分法求方程近似解的的方法,使学生体会函数与方程之间的关系,通过一些函数模型的实例,让学生感受建立函数模型的过程和方法,体会函数在数学和其他学科中的广泛应用,进一步认识到函数是描述客观世界变化规律的基本数学模型,能初步运用函数思想解决一些生活中的简单问题。1.了解函数的零点、方程的根与图象交点三者之间的联系.2.会借助零点存在性定理判断函数的零点所在的大致区间.3.能借助函数单调性及图象判断零点个数.数学学科素养1.数学抽象:函数零点的概念;2.逻辑推理:借助图像判断零点个数;3.数学运算:求函数零点或零点所在区间;4.数学建模:通过由抽象到具体,由具体到一般的思想总结函数零点概念.重点:零点的概念,及零点与方程根的联系;难点:零点的概念的形成.
集合的基本运算是人教版普通高中课程标准实验教科书,数学必修1第一章第三节的内容. 在此之前,学生已学习了集合的含义以及集合与集合之间的基本关系,这为学习本节内容打下了基础. 本节内容是函数、方程、不等式的基础,在教材中起着承上启下的作用. 本节内容是高中数学的主要内容,也是高考的对象,在实践中应用广泛,是高中学生必须掌握的重点.课程目标1. 理解两个集合的并集与交集的含义,能求两个集合的并集与交集;2. 理解全集和补集的含义,能求给定集合的补集; 3. 能使用Venn图表达集合的基本关系与基本运算.数学学科素养1.数学抽象:并集、交集、全集、补集含义的理解;2.逻辑推理:并集、交集及补集的性质的推导;3.数学运算:求 两个集合的并集、交集及补集,已知并集、交集及补集的性质求参数(参数的范围);4.数据分析:通过并集、交集及补集的性质列不等式组,此过程中重点关注端点是否含“=”及?问题;
第一节通过研究集合中元素的特点研究了元素与集合之间的关系及集合的表示方法,而本节重点通过研究元素得到两个集合之间的关系,尤其学生学完两个集合之间的关系后,一定让学生明确元素与集合、集合与集合之间的区别。课程目标1. 了解集合之间包含与相等的含义,能识别给定集合的子集.2. 理解子集.真子集的概念. 3. 能使用 图表达集合间的关系,体会直观图示对理解抽象概念的作用。数学学科素养1.数学抽象:子集和空集含义的理解;2.逻辑推理:子集、真子集、空集之间的联系与区别;3.数学运算:由集合间的关系求参数的范围,常见包含一元二次方程及其不等式和不等式组;4.数据分析:通过集合关系列不等式组, 此过程中重点关注端点是否含“=”及 问题;5.数学建模:用集合思想对实际生活中的对象进行判断与归类。
《数学1必修本(A版)》的第五章4.5.2用二分法求方程的近似解.本节课要求学生根据具体的函数图象能够借助计算机或信息技术工具计算器用二分法求相应方程的近似解,了解这种方法是求方程近似解的常用方法,从中体会函数与方程之间的联系;它既是本册书中的重点内容,又是对函数知识的拓展,既体现了函数在解方程中的重要应用,同时又为高中数学中函数与方程思想、数形结合思想、二分法的算法思想打下了基础,因此决定了它的重要地位.发展学生数学直观、数学抽象、逻辑推理和数学建模的核心素养。课程目标 学科素养1.通过具体实例理解二分法的概念及其使用条件.2.了解二分法是求方程近似解的常用方法,能借助计算器用二分法求方程的近似解.3.会用二分法求一个函数在给定区间内的零点,从而求得方程的近似解. a.数学抽象:二分法的概念;b.逻辑推理:运用二分法求近似解的原理;
由于三角函数是刻画周期变化现象的数学模型,这也是三角函数不同于其他类型函数的最重要的地方,而且对于周期函数,我们只要认识清楚它在一个周期的区间上的性质,那么它的性质也就完全清楚了,因此本节课利用单位圆中的三角函数的定义、三角函数值之间的内在联系性等来作图,从画出的图形中观察得出五个关键点,得到“五点法”画正弦函数、余弦函数的简图.课程目标1.掌握“五点法”画正弦曲线和余弦曲线的步骤和方法,能用“五点法”作出简单的正弦、余弦曲线.2.理解正弦曲线与余弦曲线之间的联系. 数学学科素养1.数学抽象:正弦曲线与余弦曲线的概念; 2.逻辑推理:正弦曲线与余弦曲线的联系; 3.直观想象:正弦函数余弦函数的图像; 4.数学运算:五点作图; 5.数学建模:通过正弦、余弦图象图像,解决不等式问题及零点问题,这正是数形结合思想方法的应用.
本节课是正弦函数、余弦函数图像的继续,本课是正弦曲线、余弦曲线这两种曲线的特点得出正弦函数、余弦函数的性质. 课程目标1.了解周期函数与最小正周期的意义;2.了解三角函数的周期性和奇偶性;3.会利用周期性定义和诱导公式求简单三角函数的周期;4.借助图象直观理解正、余弦函数在[0,2π]上的性质(单调性、最值、图象与x轴的交点等);5.能利用性质解决一些简单问题. 数学学科素养1.数学抽象:理解周期函数、周期、最小正周期等的含义; 2.逻辑推理: 求正弦、余弦形函数的单调区间;3.数学运算:利用性质求周期、比较大小、最值、值域及判断奇偶性.4.数学建模:让学生借助数形结合的思想,通过图像探究正、余弦函数的性质.重点:通过正弦曲线、余弦曲线这两种曲线探究正弦函数、余弦函数的性质; 难点:应用正、余弦函数的性质来求含有cosx,sinx的函数的单调性、最值、值域及对称性.
Discuss these questions in groups.Q1: Have you ever been to a place that has a diverse culture ? What do you think about the culture diversity ?One culturally diverse place that I have been to is Harbin, the capital city of Heilongjiang Province. I went there last year with my family to see the Ice and Snow Festival, and I was amazed at how the culture as different to most other Chinese cities. There is a big Russian influence there, with beautiful Russian architecture and lots of interesting restaurants. I learnt that Harbin is called “the Oriental Moscow” and that many Russians settled there to help build the railway over 100 years ago.Q2: What are the benefits and challenges of cultural diversity ?The benefits: People are able to experience a wide variety of cultures, making their lives more interesting, and it can deepen the feelings for our national culture, it is also helpful for us to learn about other outstanding culture, which helps improve the ability to respect others. The challenges: People may have trouble communicating or understanding each other, and it may lead to disappearance of some civilizations and even make some people think “The western moon is rounder than his own.”Step 7 Post reading---RetellComplete the passage according to the text.Today, I arrived back in San Francisco, and it feels good (1) _____(be) back in the city again. The city succeeded in (2)_________ (rebuild) itself after the earthquake that (3)________ (occur) in 1906, and I stayed in the Mission District, enjoying some delicious noodles mixed with cultures. In the afternoon, I headed to a local museum (4)____ showed the historical changes in California. During the gold rush, many Chinese arrived, and some opened up shops and restaurants in Chinatown to earn a (5)_____ (live). Many others worked on (6)______ (farm), joined the gold rush, or went to build the railway that connected California to the east. The museum showed us (7)____ America was built by immigrants from (8)________ (difference) countries and cultures. In the evening, I went to Chinatown, and ate in a Cantonese restaurant that served food on (9)________(beauty) china plates. Tomorrow evening, I’m going to (10)__ jazz bar in the Richmond District. 答案:1. to be 2. rebuilding 3. occurred 4. that 5.living6. farms 7.how 8. different 9. beautiful 10. a
The theme of this unit focuses on “space exploration.” Students will learn about the training and experience needed to become an astronaut. The text is mainly about the development of space exploration. On the one hand, the text helps students to have a good understanding about the great feats humans have achieved, on the other hand, they will further understand the contributions that we Chinese have achieved, and feel confident and proud about our homeland and strengthen their love for our country. The teacher should instruct students to aim high and study harder to make great progress in the space career if possible.1. Read about the development and value of space exploration.2. Explore the mysteries of the universe and the achievements in space exploration.3. Skillfully use the vocabulary of this text to cultivate self-study ability 4. Develop cooperative learning ability through discussion.1. Enable the Ss to talk about the development and value of space exploration.2. Guide the Ss to summarize the main idea of each paragraph as well as the main idea of the text.3. Help Ss comprehend the main reasons for space exploration. Multi-media, textbook, notebooks.Step 1: Warming up and predictionLook at the title and the pictures of the text and predict what the text will be about?2. What are the main reasons for space exploration?
4. A:We’d like to have someone to say a word at the beginning to welcome the group.B:↙Who?A:We thought that you or Dr.Johnson might do it.B用降调说Who,其意思是问,对方想让谁在开场时致欢迎词。Step 6 Pronunciation---Practice1. Listen to the short conversation and mark the intonation with ↗, ↙ or ↙, ↗. Then discuss with a partner what they intend to convey by using different intonation.Owner: You know what ?↗ It’s a million-pound bank note↙.Waiter 1: Really ?↗(question)Waiter 2: Really !↙(unbelievable and surprised)Waiter 3: Really ?!↙↗(first question then surprised)2. Listen to the conversations. Underline the parts that are stressed and mark the intonation. Then talk about the implied meanings of the responses with different intonations. Listen again and repeat.1) Henry: It’s a nice suit.Owner: Oh, it’s perfect!↙(The intonation means it is very suitable for Henry.)2) Henry: Well, that’s very kind of you.Owner: Kind, sir ?↗(what you said is not right) No, it’s kind of you. You must come whenever you want and have whatever you like. Just having you sit here is a great honour !!↙(welcome you to come again)3)Henry:Well, to be honest, I have none. Oliver:(happily) What luck!(excited) Brother↗, what luck!↙(It means “Didn’t you hear it?”)Henry: Well, it may seem lucky to you but not to me!↗(angry) If this is your idea of some kind of joke, I don’t think it’s very funny. Now if you’ll excuse me, I ought to be on my way.↙(If so, I would leave.)Roderick: Please don’t go↙...(hope Henry can wait for a moment)Part B Viewing and Talking---Describe people’s changing attitudes in a film clipStep 1 Before-listening---Tell the filmYou are going to watch part of the film The Million Pound Bank Note. Look at these photos and guess what happens in the film.
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. 以上黑体部分在句中作表语。2. 句1、2、3中的that在从句中不作成分,只起连接作用。 Step2: Review the basic components of predicative clauses1.Definition
当孩子们由父母陪同时,他们才被允许进入这个运动场。3.过去分词(短语)作状语时的几种特殊情况(1)过去分词(短语)在句中作时间、条件、原因、让步状语时,相当于对应的时间、条件、原因及让步状语从句。Seen from the top of the mountain (=When it is seen from the top of the mountain), the whole town looks more beautiful.从山顶上看,整个城市看起来更美了。Given ten more minutes (=If we are given ten more minutes), we will finish the work perfectly.如果多给十分钟,我们会完美地完成这项工作。Greatly touched by his words (=Because she was greatly touched by his words), she was full of tears.由于被他的话深深地感动,她满眼泪花。Warned of the storm (=Though they were warned of the storm), the farmers were still working on the farm.尽管被警告了风暴的到来,但农民们仍在农场干活。(2)过去分词(短语)在句中作伴随、方式等状语时,可改为句子的并列谓语或改为并列分句。The teacher came into the room, followed by two students (=and was followed by two students).后面跟着两个学生,老师走进了房间。He spent the whole afternoon, accompanied by his mom(=and was accompanied by his mom).他由母亲陪着度过了一整个下午。
4.That was an experience that frightened everyone. →That was _____________________. 答案:1. taking 2. being discussed 3. in the reading room 4. a frightening experienceStep 6 The meaning and function of V-ing as the predicative动词-ing形式作表语,它通常位于系动词后面,用以说明主语“是什么”或“怎么样”一种表示主语的特质、特征和状态, 其作用相当于形容词; 另一种具体说明主语的内容, 即主语等同于表语, 两者可互换。The music they are playing sounds so exciting. 他们演奏的音乐听起来令人激动。The result is disappointing. 结果令人失望。Our job is playing all kinds of music. 我们的工作就是演奏各种音乐。Seeing is believing. 眼见为实。Step 7 Practice1. It is ________(amaze) that the boy is able to solve the problem so quickly.2. Buying a car is simply _______(waste) money. 3. Please stop making the noise—it’s getting ________(annoy). 4. complete the passage with the appropriate -ing form.La Tomatina is a festival that takes place in the Spanish town Bunol every August. I think many food festivals are __________ because people are just eating. however, this festival is _________ because people don't actually eat the tomatoes. Instead, they throw them at each other! the number of people ________ part in this tomato fight, can reach up to 20,000, and it is a very __________ fight that lasts for a whole hour. The _______ thing is how clean Bunol is after the tomatoes are washed away after the fight. this is because the juice form tomatoes is really good for making surfaces clean!答案:1. amazing 2. wasting 3. annoying4. boring interesting taking exciting amazing
The topic of this part is “Discover the reasons for festivals and celebrations.The Listening & Speaking & Talking part aims at talking about the experiences and feelings or emotions about the festivals and celebrations. This section aims at detecting the reason why the people celebrate the festivals, the time, the places, the types and the way of celebrations. It also explains why some traditions in the old celebrations are disappearing, like the firecrackers in the big cities and some new things are appearing like the prosperity of business or commerce. 1. Students can talk about what festivals they know and the reasons and the way of celebrating them.2. Students should learn the reading skills such as the headline and get the topic sentences, the structures of articles.3. Students can understand the past, the present situation of some festival around the world and why there are some changes about them. 4. Students can have the international awareness about the festivals.1. Students should learn the reading skills such as the headline and get the topic sentences, the structures of articles.2. Students can understand the past, the present situation of some festival around the world and why there are some changes about them.Step 1 Lead in---Small talkWhat festival do you like best ? Why ?I like the Spring Festivals because I can set off the fireworks, receive the lucky money and enjoy the Gala with my families.Step 2 Before reading---Pair workWhy do people celebrate different festivals ?The Spring Festivals is to celebrate the end of winter and the coming of spring and new life.The Mid-autumn Day is to celebrate the harvest and admire the moon.
The theme of this section is “Talk about festival activities and festival experiences”.Festival and holiday is a relaxing and interesting topic for students. This part talks about the topic from the daily life of students’. In the part A ---Listening and Speaking, there are three conversations among different speakers from three countries(Japan, Rio and China), where the speakers are participating in or going to participate in the festivals and celebrations. So listening for the relationship among them is a fundamental task. Actually, with the globalization and more international communication, it is normal for Chinese or foreigners to witness different festivals and celebrations in or out of China. In the Conversation 1, a foreign reporter is interviewing a Japanese young girl who just had participated in the ceremony of the Coming-of-Age Day on the street and asking her feeling about the ceremony and the afterwards activities. Conversation 2, Chinese girl Li Mei is witnessing the Rio Carnival for the first time, and her friend Carla gives her some advice on the costumes which enables her to match with the carnival to have a good time. Conversation 3, a Chinese guide is showing a group of foreign visitors around the Lantern Festival and introducing the customs of the festival to them. The three conversations have a strong vitality and insert the festival and cultural elements from different countries. So perceiving the festivals and cultures from different countries is the second task. At the same time, the scripts also insert the targeted grammar --- v-ing as attributive and predicative, which students can perceive and experience in a real context and make a road for the further study. That is the third task. In the Part B--- Listening and Talking, the theme is “Talk about festival experience”, which is the common topic in our daily conversations. During the conversation, Song Lin, a Chinese student, asked Canadian friend Max about how to spend Christmas. In the conversation, Song Lin talked about experience and the feelings during the Chinese Spring Festival, during which there are not only some enjoyable things but some unpleasant things. After the listening, perhaps students find there are some similarities between Christmas and the Chinese Spring Festival as there are some differences in the origins and celebrations. For example, people always visit friends and relatives, decorate their houses, have a big dinner together, chat and give presents to each other.
1. 表示时间。Hearing these stories, I’m skeptical about the place. = When I heard these stories. . . 2. 表示原因。Not knowing his address, I can’t send this book to him. = Because/Since/As I don’t know his address. . . 3. 表示结果。His father died, leaving him a lot of money. =. . . and left him a lot of money4. 表示条件。Going straight down the road, you will find the department store. = If you go straight down the road. . . 5. 表示让步。Being tired, they went on working. =Although they were tired. . . 6. 表示行为方式、伴随情况或补充说明。He lay on the grass, staring at the sky for a long time. =. . . and stared at the sky for a long time注意:非谓语动词作状语时, 如所提供的动词不能和句子中的主语保持一致, 动词-ing形式必须有自己的逻辑主语, 通常由名词或代词来担任, 这就是独立主格结构。The last bus having gone, we had to walk home. (having gone的逻辑主语是the last bus, 而不是we)Weather permitting, the football match will be played on Friday. (permitting的逻辑主语是time, 而不是the football match)Step 7 Practice1. ________(study) hard, you are sure to get first prize. 2. People use plastic in their daily life, _______(leave) large amounts of waste. 3. ________(work) hard at your lessons, you are to succeed. 4. The old man, ____________(work) abroad for twenty years, is on the way back to his motherland. 5. ______________(finish) his homework, he was playing on the playground. Answers: 1. Studying 2. leaving 3. Working 4.having worked 5. Having finishedStep 8 HomeworkFinish the homework on Page 22.
The topic of this part is “Learn to make choices in life”.The Listening & Speaking & Talking part aims at the moral dilemmas, and this part is about making choices in life. The heroin is Lin Qiaozhi, a famous medical scientist, made a great contribution to our country’s medical care. Most importantly, her life experience can inspire our students whether in studying or the development of career. she had moral dilemmas and life choices, which are similar to the students who will step into society. Besides, Lin has quite good virtues like kindness, self-improvement, insistence, job-loving , generosity and responsibility, which is worth being learned.Concretely, this article is a biography about Lin Qiaozhi. The article tells her whole life according the timeline, among which the life choices is emphasized. For example, whether married or chased her dream, returned home or stayed abroad, family or public, her choices all reflected her faith, spirit, responsibility and devotion.1. Fast reading to get the detailed information about Lin Qiaozhi; careful reading to do the deductive information.2. Learn the reading skills--deductive judgement according the context.3. Study the structure features and language features. 4. Communicate about Lin’s life choices and reflect their own life choices.1. Learn the reading skills--deductive judgement according the context.2. Study the structure features and language features.3. Communicate about Lin’s life choices and reflect their own life choices.Step 1 Lead in---Small talkWhat are some important life choices?Importance choices: university study, jobs and marriage partners. Because they can determine our future.