鸽巢问题教学反思

鸽巢问题教学反思
鸽巢问题教学反思

2014年12月大学英语四级考试真题(第二套)

Part I Writing (30 minutes)Directions: For this part, .you are allowed 30 minutes to write a short essay about a course that has impressed you most in college. You should write at least

120 words but No more than 180 words.

Part II Listening Comprehension (30 minutes) Section A

Directions: In this section, you will hear 8 short conversations and 2 long conversations. At the end of each conversation, one or more questions

will be asked about what was said. Both the conversation and the

questions will be spoken only once. After each question there will be a

pause. During the pause, you must read the four choices marked A), B),

C) and D), and decide which is the best answer. Then mark the

corresponding letter on Answer Sheet I with a single line through the

centre.

1. A) She will go purchase the gift herself.

B) The gift should not be too expensive.

C) The man is not good at balancing his budget.

D) They are going to Jane’s house-warming party.

2. A) It takes patience to go through the statistics.

B) He has prepared the statistics for the woman.

C) The woman should take a course in statistics.

D) He is quite willing to give the woman a hand.

3. A) The man wants to make some change in the scripts.

B) The woman does not take the recording seriously.

C) They cannot begin their recording right away.

D) Page 55 is missing from the woman’s scripts.

4. A) A significant event in July.

B) Preparations for a wedding.

C) The date of Carl’s wedding.

D) The birthday of Carl’s bride.

5. A) The man was in charge of scheduling meetings.

B) The man was absent from the weekly meeting.

C) They woman was annoyed at the man’s excuse.

D) The woman forgot to tell the man in advance.

6. A) The woman is a marvelous cook.

B) The man cannot wait for his meal.

C) The woman has just bought an oven.

D) The man has to leave in half an hour.

7. A) Whether the man can keep his job.

B) Where the man got the bad news.

C) What items sell well in the store.

D) How she can best help the man.

8. A) The woman can sign up for a swimming class.

B) He works in the physical education department.

C) The woman has the potential to swim like a fish.

D) He would like to teach the woman how to swim.

Questions 9 to 11 are based on the conversation you have just heard.

9. A) He teaches in a law school.

B) He loves classical music.

C) He is a diplomat.

D) He is a wonderful lecturer.

10. A) Went to see a play.

B) Watched a soccer game.

C) Took some photos.

D) Attended a dance.

11. A) She decided to get married in three years.

B) Her mother objected to Eric’s flying lessons.

C) She insisted that Eric pursue graduate studies.

D) Her father said she could marry Eric right away.

Questions 12 to 15 are based on the conversation you have just heard.

12. A) Editor.

B) Teacher.

C) Journalist.

D) Typist.

13. A) The beautiful Amazon rainforests.

B) A new railway under construction.

C) Big changes in the Amazon valley.

D) Some newly discovered scenic spot.

14. A) In news weeklies.

B) In newspapers’ Sunday editions.

C) In a local evening paper.

D) In overseas editions of U.S. magazines.

15. A) To be employed by a newspaper.

B) To become a professional writer.

C) To sell her articles to news service.

D) To get her life story published soon.

Section B

Directions: In this section, you will hear 3 short passages. At the end of each passage, you will hear some questions. Both the passage and the questions will be

spoken only once. After you hear a question, you must choose the best

answer from the four choices marked A), B), C) and D). Then mark the

corresponding letter on Answer Sheet I with a single line through the

centre.

Passage One

Questions 16 to 18 are based on the conversation you have just heard.

16. A) Nodding one’s head.

B) Waving one’s hand.

C) Holding up the forefinger.

D) Turning the right thumb down.

17. A) Looking away from them.

B) Forming a circle with fingers.

C) Bowing one’s head to them.

D) Waving or pointing to them.

18. A) Looki ng one’s superior in the eye.

B) Keeping one’s arms folded while talking.

C) Showing the sole of one’s foot to a guest.

D) Using a lot of gestures during a conversation.

Passage Two

Questions 19 to 21 are based on the passage you have just heard.

19. A) They had to beg for food after the harvest.

B) They grew wheat and corn on a small farm.

C) They shared a small flat with their relatives.

D) The children walked to school on dirt roads.

20. A) Tour Ecuador’s Andes Mountains.

B) Earn an animal income of $2,800.

C) Purchase a plot to build a home on.

D) Send their children to school.

21. A) The achievements of the Trickle Up Program.

B) A new worldwide economic revolution.

C) Different forms of assistance to the needy.

D) The life of poor people in developing countries.

Passage Three

Questions 22 to 25 are based on the passage you have just heard.

22. A) They are highly sensitive to cold.

B) They are vitally important to our life.

C) They are a living part of our body.

D) They are a chief source of our pain.

23. A) It has to be removed in time by a dentist.

B) It is a rare oral disease among old people.

C) It contains many nerves and blood vessels.

D) It is a sticky and colorless film on the teeth.

24. A) It can change into acids causing damage to their outer covering.

B) It greatly reduces their resistance to the attacks of bacteria.

C) It makes their nerves and blood vessels more sensitive to acid food.

D) It combines with food particles to form a film on their surface.

25. A) Food particles.

B) Gum disease.

C) Unhealthy living habits.

D) Chemical erosion.

Section C

Directions:In this section, you will hear a passage three times. When the passage is read for the first time, you should listen carefully for its general idea.

When the passage is read for the second time, you are required to fill in

the blanks with the exact words you have just heard. Finally, when the

passage is read for the third time, you should check what you have

written.

Stunt people (替身演员) are not movie stars, but they are the hidden heroes of many movies.

They were around long before films. Even Shakespeare may have used them in fight scenes. To be good, a fight scene has to look real. Punches must 26 enemies’jaws. Sword fights must be fought with 27 swords. Several actors arc usually in a fight scene. Their moves must be set up so that no one gets hurt. It is almost like planning a dance performance.

If a movie scene is dangerous, stunt people usually 28 the stars. You may think you see Tom Cruise running along the top of a train. But it is 29 his stunt double. Stunt people must 30 the stars they stand in for. Their height and build should be about the same. But when close-ups are needed, the film 31 the star. Some stunt people 32 in certain kinds of scenes. For instance, a stunt woman named Jan Davis does all kinds of jumps. She has leapt from planes and even off the top of a waterfall. Each jump required careful planning and expert 33 .

Yakima Canutt was a famous cowboy stunt man. Among other stunts, he could ju mp from a second story window onto a horse’s back. He34 the famous trick of sliding under a moving stagecoach. Canutt also 35 a new way to make a punch look real. He was the only stunt man ever to get an Oscar.

Part III Reading Comprehension (40 minutes) Section A

Directions: In this section, there is a passage with ten blanks. You are required to select one word for each blank from a list of choices given in a word

bank following the passage: Read the passage through carefully before

making your choices. Each choice in the bank is identified by a letter.

Please mark the corresponding letter for each item on Answer Sheet 2

with a single line through the centre. You may not use any of the words in

the bank more than once.

Questions 36 to 45 are based on the following passage.

As an Alaskan fisherman, Timothy June, 54, used to think that he was safe from industrial pollutants(污染物) at his home in Haines—a town with a population of 2,400 people and 4,000 eagles, with 8 million acres of protected wild land nearby. But in early 2007, June agreed to take part in a 36 of 35 Americans from seven states. It was a biomonitoring project, in which people’s blood and urine (尿) were tested for 37 of chemicals—in this case, three potentially dangerous classes of compounds found in common household 38 like face cream, tin cans, and shower curtains. The results— 39 in November in a report called “Is It in Us?” by an environmental

group—were rather worrying. Every one of the participants, 40 from an Illinois state senator to a Massachusetts minister, tested positive for all three classes of pollutants. And while the 41 presence of these chemicals does not 42 indicate a health risk, the fact that typical Americans carry these chemicals at all 43 June and his fellow participants.

Clearly, there are chemicals in our bodies that don’t 44 there. A large, ongoing study conducted by the Centers for Disease Control and Prevention has found 148 chemicals in Americans of all ages. And in 2005, the Environmental Working Group found an 45 of 200 chemicals in the blood of 10 new-borns. “Our babies are being born pre-polluted,”says Sharyle Patton of Commonweal, which cosponsored “Is It in Us?”“This is going to be the next big environmental issue after

Section B

Directions: In this section, you are going to read a passage with ten statements attached to it. Each statement contains information given in one of the

paragraphs. Identify the paragraph from which the information is

derived. You may choose a paragraph more than once. Each paragraph

is marked with a letter. Answer the questions by marking the

corresponding letter on Answer Sheet 2.

In Hard Economy for All Ages, Older Isn’t Better... It’s Brutal

[A] Young graduates are in debt, out of work and on their parents’ couches. People in

their 30s and 40s can’t afford to buy homes or have children. Retirees are earning near-zero interest on their savings.

[B] In the current listless(缺乏活力的) economy, every generation has a claim to

having been most injured. But the Labor Department’s latest jobs reports and other recent data present a strong case for crowning baby boomers (二战后生育

高峰期出生的人) as the greatest victims of the recession and its dreadful consequences.

[C] These Americans in their 50s and early 60s—those near retirement age who do

not yet have access to Medicare and Social Security—have lost the most earnings power of any age group, with their household incomes 10 percent below what they made when the recovery began three years ago, according to Sentier Research, a data analysis company. Their retirement savings and home values fell sharply at the worst possible time: just before they needed to cash out. They are supporting both aged parents and unemployed young-adult children, earning them the unlucky nickname “Generation Squeeze”.

[D] New research suggests that they may die sooner, because their health, income

security and mental well-being were battered(重创) by recession at a crucial time in their lives. A recent study by economists at Wellesley College found that people who lost their jobs in the few years before becoming qualified for Social Security lost up to three years from their life expectancy(预期寿命), largely because they no longer had access to affordable health care.

[E] Unemployment rates for Americans nearing retirement are far lower than those for

young people, who are recently out of school, with fewer skills and a shorter work history. But once out of a job, older workers have a much harder time finding another one. Over the last year, the average duration of unemployment for older people was 53 weeks, compared with 19 weeks for teenagers, according to the Labor Department’s jobs report released on Friday.

[F] The lengthy process is partly because older workers are more likely to have been

laid off from industries that are downsizing, like manufacturing. Compared with the rest of the population, older people are also more likely to own their own homes and be less mobile than renters, who can move to new job markets.

[G] Older workers are more likely to have a disability of some sort, perhaps limiting

the range of jobs that offer realistic choices. They may also be less inclined, at least initially, to take jobs that pay far less than their old positions.

[H] Displaced boomers also believe they are victims of age discrimination, because

employers can easily find a young, energetic worker who will accept lower pay and who can potentially stick around for decades rather than a few years.

[I] In a survey of older workers who were laid off during the recession, just one in six

had found another job, and half of that group had accepted pay cuts. 14% of the re-employed said the pay in their new job was less than half what they earned in their previous job. “I just say to myself: ‘Why me? What have I done to deserve this?’”said John Agati, 56, whose last full-time job, as a product developer, ended four years ago when his employer went out of business. That position paid $90,000, and his resume lists jobs at companies like American Express, Disney and USA Networks. Since being laid off, though, he has worked a series of part-time, low-wage, temporary positions, including selling shoes at Lord & Taylor and making sales calls for a car company.

[J] The last few years have taken a toil not only on his family’s finances, but also on his feelings of self-worth. “You just get sad,”Mr. Agati said. “I see people getting up in the morning, going out to their careers and going home. I just wish I was doing that. Some people don’t like their jobs, or they have problems with their jobs, but at least they’re working. I just wish I was in their shoes.” He said he cannot afford to go back to school, as many younger people without jobs have done. Even if he could afford it, economists say it is unclear whether older workers like him benefit much from more education.

[K] “It just doesn’t make sense to offer retraining for people 55 and older,”said Daniel Hamermesh, an economics professor. “Discrimination by age, long-term unemployment, and the fact that they’re now at the end of the hiring queue just don’t make it sensible to invest in them.”

[L] Many displaced older workers are taking this message to heart and leaving the labor force entirely. The share of older people applying for Social Security early rose quickly during the recession as people sought whatever income they could find. The penalty they will pay is permanent, as retirees who take benefits at age

62 will receive as much as 30% less in each month’s check for the rest of their

lives than they would if they had waited until full retirement age (66 for those born after 1942).

[M] Those not yet qualified for Social Security are increasingly applying for another, comparable kind of income support that often goes to people who expect never to work again: disability benefits. More than one in eight people in their late 50s is now on some form of federal disability insurance program, according to Professor Mark Duggan at the University of Pennsylvania’s Wharton School.

[N] The very oldest Americans, of course, were battered by some of the same ill winds that tormented (折磨) those now nearing retirement, but at least the most senior were cushioned by a more readily available social safety net. More important, in a statistical twist, they may have actually benefited from the financial crisis in the most fundamental way: longer lives.

[O] Death rates for people over 65 have historically fallen during recessions, according to a November2011 study by economists at the University of California, Davis. Why? The researchers argue that weak job markets push more workers into accepting relatively undesirable work at nursing homes, leading to better care for residents.

46. Greater mobility puts younger people at an advantage in seeking new jobs.

47. Many of the older workers laid off during the recession had to accept lower pay in

their new jobs.

48. Those who lose their jobs shortly before retirement age live a shorter-than-average

life.

49. Seniors at nursing homes could benefit from the weak job market.

50. Age discrimination in employment makes it pointless retraining older workers.

51. According to recent reports and data analyses, boomers suffer most from the weak

economy.

52. Unemployed boomers are at a disadvantage in job-hunting because employers

tend to hire younger workers.

53. People in their fifties and early sixties bear the heaviest family burdens.

54. People who take benefits from Social Security before official retirement age will

get much less for the rest of their lives.

55. Older workers’ choice of jobs can be limited because of disability.

Section C

Directions:There are 2 passages in this section. Each passage is followed by some questions or unfinished statements. For each of them there are four

choices marked A), B), C) and D). You should decide on the best choice

and mark the corresponding letter on Answer Sheet 2 with a single line

through the centre.

Passage One

Questions 56 to 60 are based on following passage.

New Yorkers are gradually getting used to more pedaling (骑车的) passengers on those shining blue Citi Bikes. But what about local bike shops? Is Citi Bike rolling up riders at their expense?

At Gotham Bikes in Tribeca, manager W. Ben said the shop has seen an increase in its overall sales due to the bike-share program. “It’s getting more people on the road,” he said. James Ryan, an employee at Danny’s Cycles in Gramercy also said Citi Bike is a good option for people to ease into biking in a city famed for its traffic jams and aggressive drivers. “They can try out a bike without committing to buying one,” he said.

Rentals are not a big part of the business at either Gotham Bikes or Danny’s Cycles. But for Frank’s Bike Shop, a small business on Grand St., the bike-share program has been bad news. Owner Frank Arroyo said his rental business has decreased by 90% since Citi Bike was rolled out last month. Arroyo’s main rental customers are European tourists, who have since been drawn away by Citi Bikes.

However, Ben said the bike-share is good for bike sales at his shop. “People have used the bike-share and realized how great it is to bike in the city, then decide that they want something nicer for themselves,” he noted.

Christian Farrell of Waterfront Bicycle Shop, on West St. just north of Christopher St., said initially he was concerned about bike-share, though, he admitted, “I was happy to see people on bikes.”

Farrell’s early concerns were echoed by Andrew Crooks, owner of NYC Velo, at 64 Second Ave. “It seemed like a great idea, but one that would be difficult to implement,” Crooks said of Citi Bike. He said he worried about inexperienced riders’lack of awareness of biking rules and strong negative reaction from non-cyclists. However, he said, it’s still too early to tell if his business has been impacted.

While it’s possible bike-share will cause a drop in business, Crooks allowed that the idea is a positive step forward for New York City.

56. What is the author’s chief concern about the increasing use of Citi Bikes in New

York?

A) How non-cyclists will respond to it.

B) Whether local bike shops will suffer.

C) Whether local bike businesses will oppose it.

D) How the safety of bike riders can be ensured.

57. What happened to Gotham Bikes as a result of the bike-share program?

A) It found its bike sales unaffected.

B) It shifted its business to rentals.

C) It saw its bike sales on the rise.

D) It rented more bikes to tourists.

58. Why is the bike-share program bad news for Frank’s Bike Shop?

A) It cannot meet the demand of the bike-share program.

B) Its customers have been drawn away by Citi Bikes.

C) Its bike prices have to be lowered again and again.

D) It has to compete with the city’s bike rental shops.

59. Why did Andrew Crooks think that the bike-share program would be difficult to

execute?

A) Inexperienced riders might break biking rules.

B) Conflicts might arise among bike rental shops.

C) Traffic conditions might worsen in the downtown area.

D) There are not enough lanes to accommodate the bikes.

60. What is the general attitude of local bike shops towards Citi Bike?

A) Wait-and-see.

B) Negative.

C) Indifferent.

D) Approving.

Passage Two

Questions 61 to 65 are based on the following passage.

Various studies have shown that increased spending on education has not led to measurable improvements in learning. Between 1980 and 2008, staff and teachers at U.S. public schools grew roughly twice as fast as students. Yet students showed no additional learning in achievement tests.

Universities show similar trends of increased administration personnel and costs without greater learning, as documented in Richard Arum and Josipa Roksa’s recent book Academically Adrift: Limited Learning on College Campuses.

A survey shows that 63% of employers say that recent college graduates don’t have the skills they need to succeed and 25% of employers say that entry-level writing skills are lacking.

Some simplistically attribute the decline in our public education system to the drain of skilled students by private schools, but far more significant events were at work.

Public schools worked well until about the 1970s. In fact, until that time, public schools provided far better education than private ones. It was the underperforming students who were thrown out of public schools and went to private ones.

A prominent reason public schools did well was that many highly qualified women had few options for working outside the house other than being teachers or nurses. They accepted relatively low pay, difficult working conditions, and gave their very best.

Having such a large supply of talented women teachers meant that society could pay less for their services. Women’s liberation opened up new professional opportunities for women, and, over time, some of the best left teaching as a career option, bringing about a gradual decline in the quality of schooling.

Also around that time, regulations, government, and unions came to dictate pay, prevent adjustments, and introduce bureaucratic (官僚的) standard for advancement. Large education bureaucracies and unions came to dominate the landscape, confusing activity with achievement. Bureaucrats regularly rewrite curricula, talk nonsense about theories of education, and require ever more administrators. The end result has been that, after all the spending, students have worse math and reading skills than both their foreign peers and earlier generations spending far less on education—as all the accumulating evidence now documents.

61. What do we learn from various studies on America’s public education?

A) Achievement tests have failed to truly reflect the quality of teaching.

B) Public schools-lack the resources to compete with private schools.

C) Little improvement in education has resulted from increased spending.

D) The number of students has increased much faster than that of teachers.

62. How do some people explain the decline in public education?

A) Government investment does not meet schools’ needs.

B) Skilled students are moving to private schools.

C) Qualified teachers are far from adequately paid.

D) Training of students’ basic skills is neglected.

63. What was a significant contributor to the past glory of public schools?

A) Well-behaved students.

B) Efficient administration.

C) Talented women teachers.

D) Generous pay for teachers.

64. Why did some of the best women teachers leave teaching?

A)N ew career opportunities were made available to them by women’s liberation.

B) Higher academic requirements made it difficult for them to stay in their jobs.

C) They were unhappy with the bureaucratic administration in their schools.

D) The heavy teaching loads left them little time and energy for family life.

65. What does the author think is one of the results of government involvement in

education?

A) Increasing emphasis on theories of education.

B) Highly standardized teaching methods.

C) Students’ improved academic performance.

D) An ever-growing number of administrators.

Part IV Translation (30 minutes) Directions:For this part, you are allowed 30 minutes to translate a passage from Chinese into English. You should write your answer on Answer Sheet 2.

中国的互联网社区是全世界发展最快的。2010年,中国约有 4.2亿网民(netizen),而且人数还在迅速增长。互联网的日渐流行带来了重大的社会变化。中国网民往往不同于美国网民。美国网民更多的是受实际需要的驱使。用互联网为工具发电子邮件、买卖商品、做研究、规划旅程或付款。中国网民更多是出于社交原因使用互联网,因而更广泛地使用论坛、博客、聊天室等。

《鸽巢问题》教学设计

《鸽巢问题》教学设计 【教学内容】 人教版课标教材小学数学六年级下册第五单元数学广角第70-71页。 【教学目标】 1.通过操作、观察、比较、分析、推理、抽象概括,引导学生经历抽屉原理的探究过程,初步了解抽屉原理,会用抽屉原理解释生活中的简单问题。 2.在探究的过程中,渗透模型思想,培养学生的推理和抽象思维能力。 3.使学生感受数学的魅力,培养学习的兴趣。 【教学重点】 经历抽屉原理的探究过程,初步了解抽屉原理,会用抽屉原理解释生活中的简单问题。 【教学难点】 理解抽屉原理,并对一些简单的实际问题加以模型化。 【教学过程】 一、开门见山,引入课题。 承接课前谈话内容,直接揭示课题。 二、经历过程,构建模型。 (一)研究“4个小球任意放进3个抽屉”存在的现象。 1.出示结论:4个小球放进3个抽屉里,不管怎么放,总有一个抽屉里面至少放2个小球。 让学生说说对这句话的理解。 2.验证结论的正确性。 让学生用长方形代替抽屉,用圆代替小球画一画,看有几种不同的放法。 3.全班交流。 学生汇报后,教师引导观察每种放法,通过横向、纵向比较,找到每种放法中放得最多的抽屉,然后从最多数里找最少数,发现不管哪种放法,都能从里面找到这样的一个抽屉,里面至少有2个小球。从而理解并证明了“不管怎么放,总有一个抽屉里至少放2个小球”这个结论是正确的。 (二)研究“5个小球任意放进4个抽屉”存在的现象,找到求至少数的简便方法。 1.猜测:根据刚才的研究经验猜一猜:把5个小球放进4个抽屉里,不管怎么放,总有一个抽屉至少放几个小球? 2.验证。 学生以小组为单位共同研究:先画出不同的放法。然后观察分析每种放法, 1 / 3

新人教版六年级数学下册 5.1《鸽巢原理》教学设计

《鸽巢原理》教案设计 教学目标 1.初步了解“鸽巢原理”,学会简单的“鸽巢原理”分析方法,运用“鸽巢原理”的知识解决简单的实际问题。 2.使学生逐步理解和掌握“鸽巢原理”,经历将具体问题数学化的过程,培养学生的模型思想。 3.通过对“鸽巢原理”的灵活运用,感受数学的魅力,体会数学的价值,提高学生解决问题的能力和兴趣。 教学重点 理解鸽巢原理,掌握列举法”和尽量“平均分”的方法。 教学难点 理解“总有”“至少”的意义,理解“至少数=商数+1”。 课前准备 教师准备PPT课件一副扑克牌 学生准备4支铅笔3个笔筒 教学过程 ⊙游戏导入 1.组织学生玩“抽扑克牌”游戏。 (1)准备一副扑克牌,取出大王、小王。 (2)选出5名同学,请他们任意抽取一张扑克牌并记在心里,把牌收好。 (3)教师猜测“在这5张扑克牌里,至少有2张是同一花色的。” (4)学生把扑克牌拿出来验证教师的猜测。 2.引入新课。(板书课题:鸽巢原理) 设计意图:通过“抽扑克牌”游戏,使学生初步体验从一副4种花色的扑克牌中任意抽取5张扑克牌,不管怎么抽,都至少有2张扑克牌是同一花色的,为新知的探究作铺垫。 ⊙探究新知 1.教学例1。

(1)出示题目:把4支铅笔放进3个笔筒中,有几种不同的放法? (2)探究放法。 ①自主摆放并汇报放法及发现。 预设 生1:我用数字表示放法:(4,0,0),(3,1,0),(2,2,0),(2,1,1)。 生2:我用式子表示放法:4=4+0+0,4=3+1+0,4=2+2+0,4=2+1+1。 生3:我用数的分解表示放法: 4400431042204211 生4:我发现不管怎么放,总有一个笔筒中至少有2支铅笔。 ②直接摆放。 a.引导学生找到一种更为直接的方法,只摆一种情况就能得到上面的结论。 预设 生:可以采用平均分的方法。4÷3=1……1,每个笔筒中各放1支,剩下的1支无论放进哪个笔筒中,总有一个笔筒中至少有2支铅笔。 b.组织学生小组合作探究。 把5支铅笔放进4个笔筒中,把6支铅笔放进5个笔筒中,把7支铅笔放进6个笔筒中,各会出现什么情况?找到其中的规律。 预设 生:铅笔的支数比笔筒数多1,用平均分的方法直接计算就可以发现:不管怎么放,总有一个笔筒中至少有2支铅笔。 (3)总结“鸽巢原理”(一)。 把m个物体任意分放进n个鸽巢中(m>n,m和n是非0自然数),那么一定有一个鸽巢中至少放进了2个物体。 2.教学例2。 (1)出示思考题目。 ①把7本书放进3个抽屉,不管怎么放,总有一个抽屉里至少放进几本书?

小学数学学科教学指导

《小学数学学科教学指导》应知应会试卷A 一、填一填。 1.数学课程应致力于现实主义教育阶段的培养目标,面向全体学生,适应学生(个性发展)的需要,使得人人都能获得(良好的数学)教育,不同的人在数学上得到(不同的发展 )。 2.高效的课堂法教学要发挥教师的主导作用,唤醒学生的(主体意识),落实学生的(主体地位),实现(先学后教)以学定教,(少教多学)顺学而导的教学理念,促进师生智慧的共同发展。 3.教学反思是教师(自我认识)(自我分析)(自我提高)的过程。 4.备课要做到“三备”即:(备课标)(备学生)(备教材),在此基础上设计教学过程和板书。 5.布置作业绝不是灵机一动、信手拈来,而是一项充满(创造性)和(艺术性)的行为。 6.教师教学应该以(学生)的认知发展水平和(已有的经验)为基础。面向全体学生,注重启发式和(因材施教)。 7.教学设计不仅是一门(科学),也是一门(艺术)。作为一门科学它必须遵循一定的(教育)、(教学)规律; 8.教学设计依次三个基本问题所组成。首先是(“我去哪里”)即教学目标的制定;然后是(“我如何去那里”);最后是“我怎么判断我已到了那里”即(“教学的评价”)。 二、选择。 1.课程内容要反映社会的需要、数学的特点,要符合学生的认知规律。它包括((1)(2)(3))。 (1)数学的结果(2)数学结果的形成过程(3)数学思想方法(4)数学技能 2.数学备课的基本原则((1)(2)(3)) (1)面向全体(2)因材施教(3)创造性(4)独立性 3.小学数学的作业基本原则包括((1)(2)(3)(4)(5)) (1)科学性(2)趣味性(3)层次性(4)规范性(5)激励性 4.小学数学课堂教学评价基本要素包括((1)(2)(3)(4)(5)(6)(7)(8)) (1)教学目标(2)教学内容(3)教学方法(4)教学过程(5)教师行为(6)学生活动(7)教学效果(8)教学特色 三、简答。 1.义务教育数学课程标准(2011年版)将数学课程的总目标表述是哪三点?(书第三页) 答:1. 获得适应社会生活和进一步发展所必需的数学的基础知识、基本技能、基本思想、基本活动经验。 2. 体会数学知识之间、数学与其他学科之间、数学与生活之间的联系,运用数学的思维方式进行思考,增强发现和提出问题的能力、分析和解决问题的能力。 3. 了解数学的价值,提高学习数学的兴趣,增强学好数学的信心,养成良好的学习习惯,具有初步的创新意识和科学态度。 2.第一学段图形的运动的具体要求是什么?(书9页) 答:1. 结合实例,感受平移、旋转、轴对称现象。2. 能辨认简单图形平移后的图形。 3. 通过观察、操作,初步认识轴对称图形。

部编人教版六年级数学下册 《鸽巢问题(2)》优质教案【新版】

鸽巢问题(2) 教学导航: 【教学内容】 “鸽巢问题”的具体应用(教材第70页例3)。 【教学目标】 1.在了解简单的“鸽巢问题”的基础上,使学生会用此原理解决简单的实际问题。 2.培养学生有根据、有条理的进行思考和推理的能力。 3.通过用“鸽巢问题”解决简单的实际问题,激发学生的学习兴趣,使学生感受数学的魅力。 【重点难点】 引导学生把具体问题转化为“鸽巢问题”,找出这里的“鸽巢”有几个,再利用“鸽巢问题”进行反向推理。 【教学准备】 课件,1个纸盒,红球、蓝球各4个。 教学过程: 【情景导入】 教师讲《月黑风高穿袜子》的故事。 一天晚上,毛毛房间的电灯突然坏了,伸手不见五指,这时他又要出去,于是他就摸床底下的袜子,他有蓝、白、灰色的袜子各一双,由于他平时做事随便,袜子乱丢,在黑暗中不知道哪些袜子颜色是相同的。毛毛想拿最少数目的袜子出去,在外面借街灯配成相同颜色的

一双。你们知道最少拿几只袜子出去吗? 在学生猜测的基础上揭示课题。 教师:这节课我们利用鸽巢问题解决生活中的实际问题。 板书:“鸽巢问题”的具体应用。 【新课讲授】 1.教学例3。 盒子里有同样大小的红球和蓝球各4个,要想摸出的球一定有2个同色的,最少要摸出几个球? (出示一个装了4个红球和4个蓝球的不透明盒子,晃动几下)师:同学们,猜一猜老师在盒子里放了什么? (请一个同学到盒子里摸一摸,并摸出一个给大家看) 师:如果这位同学再摸一个,可能是什么颜色的?要想这位同学摸出的球,一定有2个同色的,最少要摸出几个球? 请学生独立思考后,先在小组内交流自己的想法,验证各自的猜想。 指名按猜测的不同情况逐一验证,说明理由。 摸2个球可能出现的情况:1红1蓝;2红;2蓝 摸3个球可能出现的情况:2红1蓝;2蓝1红;3红;3蓝 摸4个球可能出现的情况:2红2蓝;1红3蓝;1蓝3红;4红;4蓝 摸5个球可能出现的情况:4红1蓝;3蓝2红;3红2蓝;4蓝1红;5红;5蓝

鸽巢原理教学设计优质课

《鸽巢原理》教学设计 教学内容:义务教育教科书六年级下册第68、69页。 教学目标: 1.知识与能力目标:经历“鸽巢原理”的探究过程,初步了解“鸽巢原理”,会用“鸽巢原理”解决简单的实际问题。通过猜测、验证、观察、分析等数学活动,建立数学模型,发现规律。 2.过程与方法目标:经历从具体到抽象的探究过程,提高学生有根据、有条理地进行思考和推理的能力。 3.情感、态度与价值观目标:通过“鸽巢原理”的灵活应用,提高学生解决数学问题的能力和兴趣,感受到数学文化及数学的魅力。 教学重点:经历“鸽巢原理”的探究过程,初步了解“鸽巢原理”。 教学难点:理解“鸽巢原理”,并应用这一原理解决实际问题。 教学准备:多媒体课件、纸杯、铅笔、书。 教学过程: 一、游戏激趣,初步体验。 1、游戏:猜扑克牌。请5位同学,每人随意抽一张扑克牌。 2、教师猜:在5张扑克牌里至少有2张的花色是一样的。 3、引入学习内容。 二、操作探究,发现规律。 1.自主猜想,初步感知。 把4枝铅笔放进3个笔筒中。不管怎么放,总有一个笔筒至少放进()枝铅笔。让学生猜测“至少会是”几枝? 2.验证结论。

小组合作:学生借助实物进行操作,(摆一摆、画一画、写一写)来验证结论,并做好记录。 3、指名学生汇报 (1)根据学生汇报的情况,教师适时演示,同时教师根据学生的回答板书所有的情况。(4,0,0)(3,1,0)(2,2,0)(2,1,1)(明确这是枚举法) (2)观察摆一摆、画一画、写一写的结果,你发现了什么?(把4枝铅笔放进3个笔筒中。不管怎么放,总有一个笔筒里至少有2枝铅笔) 4、思考:“总有”、“至少”是什么意思? 5、提出问题:不用一一列举,想一想还有其它的方法来证明这个结论吗?在学生汇报的基础上,教师小结:假如把4枝铅笔中的3枝平均放到3个笔筒中,每个笔筒放1枝铅笔,剩下的1枝铅笔不管怎样放,总有一个笔筒里至少有2枝铅笔。(明确这是假设法) 6、初步观察规律。 教师继续提问:把5支铅笔放进4个笔筒里会出现什么情况? 把5支铅笔放进4个笔筒里会出现什么情况? 把7支铅笔放进6个笔筒里呢? 把8枝笔放进7个笔筒里呢?…… 100支铅笔放进99个笔筒呢? 教师引导学生进行比较:你发现什么? (笔的枝数比笔筒数多1,不管怎么放,总有一个笔筒里至少有2枝铅笔。) 7、看有关鸽巢原理资料,让学生感受古代数学文化。 8、学习例2:把7本书放进3个抽屉,不管怎么放,总有一个抽屉至少放进3本书。为什么?

鸽巢原理教学反思

《鸽巢问题》教学反思 武汉市光谷豹澥第一小学马战勇《鸽巢原理》就是以前是的教学内容《抽屉原理》,新教材把这一部分内容纳入了数学广角。当第一次看到《鸽巢问题》成为必学内容时,老师们都很困惑:什么是鸽巢问题?这么难的内容学生能理解吗?我的印象里《抽屉原理》也是非常坚深难懂的。为了上好这一内容,我搜集学习了很多资料,文中对“抽屉原理”作了深入浅出的分析,使我对“抽屉原理”有了新的认识,也终于理出了头绪。抽屉原理是教给我们一种思考方法,也就是从“最不利”的情况来思考问题,所以要让学生充分体会什么是“最不利”。 兴趣是学习最好的老师。所以在本节课我就设计了“抢凳子”游戏来导入新课,在上课伊始我就说:“同学们:在上新课之前,我们来做个“抢凳子”游戏怎么样?想参与这个游戏的请举手。叫举手的一男一女两个同学上台,然后问,老师想叫三位同学玩这个游戏,但是现在已有两个,你们说最后一个是叫男生还是女生呢?”同学们回答后,老师就说:“不管是男生还是女生,总有二个同学的性别是一样的,你们同意吗?”并通过三人“抢凳子”游戏得出不管怎样抢“总有一根凳子至少有两个同学”。相机引入本节课的重点“总有……至少……”。这样设计使学生在生动、活泼的数学活动中主动参与、主动实践、主动思考、主动探索、主动创造;使学生的数学知识、数学能力、数学思想、数学情感得到充分的发展,从而达到动智与动情的完美结合,全面提高学生的整体素质。

只有学生主动参与到学习活动中,才是有效的教学。在教学过程中,充分利用学具操作,如把4支小棒放入3个杯子学习中,把5支小棒放入4个杯子学习中等,都是让学生自己操作,这为学生提供主动参与的机会,让学生想一想、圈一圈,把抽象的数学知识同具体的实物结合起来,化难为易,化抽象为具体,让学生体验和感悟数学。 通过直观例子,借助实际操作,引导学生探究“鸽巢问题”,初步经历“数学证明“的过程,并有意识的培养学生的“模型思想。为学生营造宽松自由的学习氛围和学习空间,能让学生自己动脑解决一些实际问题,从而更好的理解鸽巢问题。在教学过程中能够及时地去发现并认可学生思维中闪亮的火花。 不足之处在于教学过程中所设置的问题应具有针对性,应更多的关注学生的思维活动,及时的给予认可和指导,使教学能够面向全体学生。

鸽巢问题的教学反思

六年级数学下册《鸽巢问题》教学反思 大花岭小学孙立群 数学广角的教学是为了丰富学生解决问题的方法和策略,使学生感受到数 学的魅力。本节课我让学生经历探究“鸽巢原理”的过程,初步了解了“鸽巢 原理”,并能够应用于实际,学会思考数学问题的方法,培养学生的数学思 维。 一、情境导入,初步感知 兴趣是学习最好的老师。所以在本节课我就设计了表演魔术的游戏来导入 新课,在上课开始我就说:我给大家表演一个“魔术”。一副扑克牌,去掉大 小王,还剩52张,你们5人每人随意抽一张,我知道至少有2张牌是同花色的。相信吗?想参与这个游戏的请举手。同学们踊跃参加,然后叫举手的两组同学 上台抽牌。同学们发现抽的牌中至少有2张牌是同花色的,接着引出了课题。 相机引入本节课的重点“总有……至少……”。这样设计使学生在生动、活泼的数 学活动中主动参与、主动实践、主动思考、主动探索、主动创造;使学生的数 学知识、数学能力、数学思想、数学情感得到充分的发展,从而达到动智与动 情的完美结合,全面提高学生的整体素质。这个游戏虽简单却能真实的反映 “鸽巢原理”的本质。通过小游戏,一下就抓住学生的注意力,有效地调动和 激发学生的学习主动性和兴趣,让学生觉得这节课要探究的问题,好玩又有意义。 二、活动中恰当引导,建立模型 采用列举法,让学生把4枝铅笔放入3个笔筒中的所有情况通过摆一摆、 画一画或写一写等方式都列举出来,运用直观的方式,发现并描述,理解最简 单的“鸽巢原理”即“铅笔数比笔筒数多1时,总有一个笔筒里至少有2枝笔”。在例2的教学时,让学生借助直观操作发现列举法适用于数字较小时,有局限性,而假设法应用范围广,假设把书尽量多的“平均分”到各个抽屉, 看每个抽屉能分到多少本书,剩下的书不管放到哪个抽屉里,总有一个抽屉比 平均分得的本数多1本,可以用有余数的除法这一数学规律来表示。大量列举 之后,再引导学生总结归纳这一类“鸽巢原理”的一般规律,让学生借助直观 操作、观察、表达等方式,让学生经历从不同的角度认识鸽巢原理。特别是通 过学生归纳总结的规律:到底是“商+余数”还是“商+1”,引发学生的思 维步步深入,并通过讨论和说理活动,使学生经历了一个初步的“数学证明” 的过程,培养了学生的推理能力和初步的逻辑能力。 三、通过练习,解释应用 适当设计形式多样化的练习,可以引起并保持学生的练习兴趣。如“从扑 克牌中去掉两张王牌,在剩下的52张中任意抽出18张,至少有几张是同花色的。任意抽出20张,至少有几张是数字相同的。把红白两种球各10个放在同 一个盒子里,要保证有两个球的颜色相同,至少要摸出几个球?(3个球), 要保证摸出的球有一个是红色的,至少要摸出多少个球?(11个球)。15只鸽子飞回4个鸽舍中,至少有()只鸽子飞回同一个鸽舍,为什么?教会

鸽巢问题教学设计公开课

数学广角——鸽巢问题教案 朱小姜松 一、教学目标: 1、经历“鸽巢问题”的探究过程,初步了解“鸽巢问题”,会用“鸽巢问题”解决简单的实际问题。 2、通过操作发展学生的类推能力,形成比较抽象的数学思维。 3、培养学生有根据、有条理地进行思考和推理的能力。 4、通过“鸽巢问题”的灵活应用感受数学的魅力;提高学生解决问题的能力和兴趣。 二、教学重点: 经历“鸽巢问题”的探究过程,初步了解“鸽巢问题”。 三、教学难点: 理解“鸽巢问题”,并对一些简单实际问题加以“模型化”。 四、教材说明: 这部分教材通过几个直观例子,借助实际操作,向学生介绍“鸽巢问题”,使学生在理 解“鸽巢问题”这一数学方法的基础上,对一些简单的实际问题加以“模型化”,会用“抽屉原理”加以解决。 在数学问题中有一类与“存在性”有关的问题。例如,任意13人中,至少有两人的出生月份相同。任意367名学生中,至少存在两名学生,他们在同一天过生日。在这类问题中,只需要确定某个物体(或某个人)的存在就可以了,并不需要指出是哪个物体(或哪个人),也不需要说明是通过什么方式把这个存在的物体(或人)找出来。这类问题依据的理论,称之为“鸽巢问题”。“鸽巢问题”的理论本身并不复杂,甚至可以说是显而易见的。例如,要把三个苹果放进两个抽屉,至少有一个抽屉里有两个苹果。这样的道理对于学生来说,也是很容易理解的。但“鸽巢问题”的应用却是千变万化的,用它可以解决许多有趣的问题,并且常常能得到一些令人惊异的结果。因此,“鸽巢问题”在数论、集合论、组合论中都得到了广泛的应用。 五、教学设计 课前谈话: 1、同学们,今年是2016年,很多预言家都曾预言2012年是世界末日,可是没能成真,他们的预言准确 吗?知道吗?姜老师也是一位预言家,你不信?请你在纸上写三位你的好朋友的名字,我预言你的三位好朋友中至少有两位是同性,对不对?我还能预言我们全班34位同学,总有一个月份至少有3位同学出生(学生起立验证)。 2、你想不想当一名预言家?谁来试试?从一副扑克牌中抽出大小王,还剩下52张,任意抽取5张牌,谁

参赛《鸽巢原理》教学设计(1)知识讲解

《鸽巢原理》教学设计 修水二小向娟红 一、教材内容:人民教育出版社小学数学六年级下册第68至69页 二、教学目标: 1.经历“鸽巢原理”的探究过程,初步了解“鸽巢原理”,会用“鸽巢原理”解决简单的实际问题。 2.通过操作发展学生的类推能力,形成比较抽象的数学思维。 3.通过“鸽巢原理”的灵活应用感受数学的魅力。 教学重点:经历“鸽巢原理”的探究过程初步了解“鸽巢原理。 教学难点:理角“鸽巢原理”并对一些简单简单的实际问题加以“模型化。 三、教学过程 (一)情境导入 1.创设情境: 师:这有一副牌(抽掉大、小王),老师用它变一个魔术,想看吗?这个魔术的名字叫“猜花色”。老师请5名同学每人随意抽一张牌,我能猜到,至少有两位同学的手中的花色是相同的,你们信吗? 师:谁能猜一猜,我是用什么方法知道的结果? 2.揭示课题,板书“鸽巢原理” 师:刚才老师和这5名同学合作展示了鸽巢原理中最简单的一种问题。鸽巢原理很神奇,我们用它可以解决很多有趣的的问题,这节课我们就一起来探究这个神秘的原理。

(设计意图:通过一个学生感兴趣的展示生活中的一种简单的“鸽巢原理”问题,激发学生的好奇心和学习欲望,为原本枯燥的数学课注入活力。) (二)合作探究建立原理模型 1. 小组合作探究,初步感知“鸽巢原理” (1)课件出示简化后的例题1(将3支笔放进两个笔筒里,你有几种放法? 同时出示小组合作要求:学生拿出准备的3枝笔,2个笔筒,摆一摆,想一想共有有几种放法?然后小组内说一说,你有什么发现? (2)小组汇报展示 学习小组派代表到台前展示成果。要求学生边摆边说,老师同时在黑板上画出草图。可能会出现以下几种放法: 放法1 或 (引导学生明确虽然摆放的顺 序不一样,但是同一种放法) 放法或 师:还有别的放法吗? 生:没有了。 师:是的,就这两种放法。除找到不同的放法之外,哪个小组还有其它的发现? 引导学生得出:不管怎么放,总有一个盒子里至少有2枝笔。 问题: (1)“总有”是什么意思?(一定有) (2)“至少”有2枝什么意思?(不少于两只,可能是2枝,也可能是多于2枝?) 教师引导学生总结规律:我们把3枝笔放进2个盒子里,不管怎么放,

鸽巢问题教学反思

六年级数学下册《鸽巢问题》教学反思 云鹤镇中心小学夏春林 数学广角的教学是为了丰富学生解决问题的方法和策略,使学生感受到数学的魅力。本节课我让学生经历探究“鸽巢原理”的过程,初步了解了“鸽巢原理”,并能够应用于实际,学会思考数学问题的方法,培养学生的数学思维。 一、情境导入,初步感知 兴趣是学习最好的老师。所以在本节课我就设计了表演魔术的游戏来导入新课,在上课开始我就说:我给大家表演一个“魔术”。一副扑克牌,去掉大小王,还剩52张,你们5人每人随意抽一张,我知道至少有2张牌是同花色的。相信吗?想参与这个游戏的请举手。同学们踊跃参加,然后叫举手的两组同学上台抽牌。同学们发现抽的牌中至少有2张牌是同花色的,接着引出了课题。相机引入本节课的重点“总有……至少……”。这样设计使学生在生动、活泼的数学活动中主动参与、主动实践、主动思考、主动探索、主动创造;使学生的数学知识、数学能力、数学思想、数学情感得到充分的发展,从而达到动智与动情的完美结合,全面提高学生的整体素质。这个游戏虽简单却能真实的反映“鸽巢原理”的本质。通过小游戏,一下就抓住学生的注意力,有效地调动和激发学生的学习主动性和兴趣,让学生觉得这节课要探究的问题,好玩又有意义。 二、活动中恰当引导,建立模型 采用列举法,让学生把4枝铅笔放入3个笔筒中的所有情况通过摆一摆、画一画或写一写等方式都列举出来,运用直观的方式,发现并描述,理解最简单的“鸽巢原理”即“铅笔数比笔筒数多1时,总有一个笔筒里至少有2枝笔”。 在例2的教学时,让学生借助直观操作发现列举法适用于数字较小时,有局限性,而假设法应用范围广,假设把书尽量多的“平均分”到各个抽屉,看每个抽屉能分到多少本书,剩下的书不管放到哪个抽屉里,总有一个抽屉比平均分得的本数多1本,可以用有余数的除法这一数学规律来表示。 大量列举之后,再引导学生总结归纳这一类“鸽巢原理”的一般规律,让学生借助直观操作、观察、表达等方式,让学生经历从不同的角度认识鸽巢原理。特别是通过学生归纳总结的规律:到底是“商+余数”还是“商+1”,引发学生的思维步步深入,并通过讨论和说理活动,使学生经历了一个初步的“数学证明”的过程,培养了学生的推理能力和初步的逻辑能力。 三、通过练习,解释应用 适当设计形式多样化的练习,可以引起并保持学生的练习兴趣。如“从扑克牌中去掉两张王牌,在剩下的52张中任意抽出18张,至少有几张是同花色的。任意抽出20张,至少有几张是数字相同的。把红白两种球各10个放在同一个盒子里,要保证有两个球的颜色相同,至少要摸出几个球?(3个球),要保证摸出的球有一个是红色的,至少要摸出多少个球?(11个球)。15只鸽子飞回4个鸽舍中,至少有()只鸽子飞回同一个鸽舍,为什么?教会学生用算式来说明理由,简洁明了,因为15÷4=4……3 4+1=5,所以15只鸽子飞回4个鸽舍,总有5只鸽子飞进同一个鸽笼。六年级4班由67个同学,总有多少个同学的属相相同?学校有367个同学,总有各位同学同一天过生日?练习内容紧密联系生活,让学生体会数学来源于生活。练习由易到难,层层递进,符合学生的认知规律。在练习中,学生兴趣盎然,达到了预期的效果。 不足之处是学生的语言表达能力还有待提高。课堂中,数学语言精简性直接影响着学生对新知识的理解与掌握。例如,教材中“不管怎么放,总有一只抽屉

鸽巢问题教学反思

《鸽巢问题》教学反思 我在设计鸽巢原理教学时,课堂上,我首先采用游戏导入、小组活动的形式,使学生集中注意力,把心思马上放到课堂上,让学生觉得这节课探究的问题既好玩又有意义。但这部分内容属于奥数知识范畴,真正理解对于学生来说有一定的难度。在教学中我通过实际案例培养学生有根据、有条理地进行思考和推理的能力,从而解决实际问题,初步感受数学的魅力。本堂课注重为学生提供自主探索的空间,引导学生通过探索,初步了解“鸽巢原理”,会用“鸽巢原理”解决实际问题。 在本节课中,我非常注重学生的自主探索精神,让学生在学习中,经历猜想、验证、推理、应用的过程。 1、采用列举法,让学生把4枝笔放入3个笔筒中的所有情况都列举出来,运用直观的方式,发现并描述、理解最简单的“鸽巢原理”即“铅笔数比笔筒数多1时,总有一个抽屉里至少有2枝笔”。 2、让学生借助直观操作发现,把笔尽量多的“平均分”给各个笔筒,看每个笔筒能分到多少枝笔,剩下的笔不管放到哪个笔筒里,总有一个笔筒比平均分得的枝数多1,可以用有余数的除法这一数学规律来表示。 3、大量例举之后,再引导学生总结归纳这一类“鸽巢问题”的一般规律,让学生借助直观操作、观察、表达等方式,让学生经历从不同的角度认识鸽巢原理。 在这堂课的难点突破处,也就是让学生借助直观操作发现,把笔尽量多的“平均分”到各个笔筒,看每个笔筒能分到多少枝笔,剩下的笔不管放到哪个笔筒里,总有一个笔筒比平均分得的枝数多1,我还可以对教学环节进行再安排,让学生体会到多余的物体只要不超过抽屉的个数,总有一个抽屉至少放2个物体,这样学生对“鸽巢原理”规律会更清晰更明了。同时,我们要明确,教学知识不光是让学生按照公式来套用公式,这样很容易造成学生的思维定势,所以在让学生充分说理的基础上,明确把什么当作“抽屉数”,把什么当作“物体数”是相当重要的。 在这节课里部分学生判断不出谁是“物体”,谁是“抽屉”。因此,在今后的教学中,多下些功夫,以求在课堂上让学生更好地理解、消化所授知识。课后还要让多做相关的练习加以巩固。

最新人教版六年级数学下册《鸽巢问题一》公开课优秀教案

《鸽巢问题一》 一、教学目标 (一)知识与技能 通过数学活动让学生了解鸽巢原理,学会简单的鸽巢原理分析方法。(二)过程与方法 结合具体的实际问题,通过实验、观察、分析、归纳等数学活动,让学生通过独立思考与合作交流等活动提高解决实际问题的能力。 (三)情感态度和价值观 在主动参与数学活动的过程中,让学生切实体会到探索的乐趣,让学生切实体会到数学与生活的紧密结合。 二、教学重难点 教学重点:理解鸽巢原理,掌握先“平均分”,再调整的方法。 教学难点:理解“总有”“至少”的意义,理解“至少数=商数+1”。 三、教学准备 多媒体课件。 四、教学过程 (一)游戏引入 出示一副扑克牌。

教师:今天老师要给大家表演一个“魔术”。取出大王和小王,还剩下52张牌,下面请5位同学上来,每人随意抽一张,不管怎么抽,至少有2张牌是同花色的。同学们相信吗? 5位同学上台,抽牌,亮牌,统计。 教师:这类问题在数学上称为鸽巢问题(板书)。因为52张扑克牌数量较大,为了方便研究,我们先来研究几个数量较小的同类问题。 【设计意图】从学生喜欢的“魔术”入手,设置悬念,激发学生学习的兴趣和求知欲望,从而提出需要研究的数学问题。 (二)探索新知 1.教学例1。 (1)教师:把3支铅笔放到2个铅笔盒里,有哪些放法?请同桌二人为一组动手试一试。 教师:谁来说一说结果? 预设:一个放3支,另一个不放;一个放2支,另一个放1支。(教师根据学生回答在黑板上画图表示两种结果) 教师:“不管怎么放,总有一个铅笔盒里至少有2支铅笔”,这句话说得对吗? 教师:这句话里“总有”是什么意思? 预设:一定有。 教师:这句话里“至少有2支”是什么意思?

六年级数学《鸽巢原理》教学设计说明

数学广角—鸽巢问题 【教学容】 人教版小学数学六年级下册《数学广角--抽屉原理》。 【学情分析】 抽屉原理是学生从未接触过的新知识,难以理解抽屉原理的真正含义,发现有相当多的学生他们自己提前先学了,在具体分的过程中,都在运用平均分的方法,也能就一个具体的问题得出结论。但是这些学生多数只“知其然,不知其所以然”,为什么平均分能保证“至少”的情况,他们并不理解。有时要找到实际问题与“抽屉原理”之间的联系并不容易,即使找到了,也很难确定用什么作为“抽屉”,要用几个“抽屉”。 1.年龄特点:六年级学生既好动又敛,教师一方面要适当引导,引发学生的学习兴趣,使他们的注意力始终集中在课堂上;另一方面要创造条件和机会,让学生发表见解,发挥学生学习的主体性。 2.思维特点:知识掌握上,六年级的学生对于总结规律的方法接触比较少,尤其对于“数学证明”。因此,教师要耐心细致的引导,重在让学生经历知识的发生、发展和过程,而不是生搬硬套,只求结论,要让学生不知其然,更要知其所以然。 【教学方法】 1.借助学具,学生自主动手操作、分析、推理、发现、归纳、总结原理。 2. 适时引导学生对枚举法和假设法进行比较,并通过逐步类推,使学生逐步理解“抽屉问题”的“一般化模型”。 3.引导学生构建解决抽屉原理类问题的模式:明确“待分的物体”→哪是“抽屉”→平均分→商+1 4.完善评价体系,进行小组捆绑,激励学生全员参与,体验成功的乐趣。 5.师生课前准备:①学生:每组5根小棒、4个杯子;课件②学生记录自己是哪一个月出生的。③教师准备1副牌。 【教学目标】 知识目标:初步了解抽屉原理,会用抽屉原理解决简单的实际问题。

新人教版六年级下册第五单元《数学广角鸽巢问题》教学设计

(5)2015新人教版六年级下册第五单元《数学广角- 鸽巢问题》教学设计 第五单元数学广角——鸽巢问题 单元要点分析 一、单元教材分析: 本教材专门安排“数学广角”这一单元,向学生渗透一些重要的数学思想方法。和以往的义务教育教材相比,这部分内容是新增的内容。本单元教材通过几个直观例子,借助实际操作,向学生介绍“鸽巢问题”,使学生在理解“鸽巢问题”这一数学方法的基础上,对一些简单的实际问题加以“模型化”,会用“鸽巢问题”加以解决。在数学问题中,有一类与“存在性”有关的问题。在这类问题中,只需要确定某个物体(或某个人)的存在就是可以了,并不需要指出是哪个物体(或人)。这类问题依据的理论我们称之为“抽屉原理”。“抽屉原理”最先是19世纪的德国数学家狄利克雷运用于解决数学问题的,所以又称“狄利克雷原理”,也称之为“鸽巢问题”。“鸽巢问题”的理论本身并不复杂,甚至可以说是显而易见的。但“鸽巢问题”的应用却是千变万化的,用它可以解决许多有趣的问题,并且常常能得到一些令人惊异的结论。因此,“鸽巢问题”在数论、集合论、组合论中都得到了广泛的应用。 二、单元三维目标导向: 1、知识与技能:(1)引导学生通过观察、猜测、实验、推理等活动,经历探究“鸽巢原理”的过程,初步了解“鸽巢原理”的含义,会用“鸽巢原理”解决简单的实际问题。 2、过程与方法:经历探究“鸽巢原理”的学习过程,体验观察、猜测、实验、推理等活动的学习方法,渗透数形结合的思想。 3、情感态度与价值观:(1)体会数学与生活的紧密联系,体验学数学、用数学的乐趣。(2)理解知识的产生过程,受到历史唯物注意的教育。(3)感受数学在实际生活中的作用,培养刻苦钻研、探究新知的良好品质。 三、单元教学重难点

六年级下册《鸽巢问题》教案知识分享

“鸽巢问题”教案 教学内容:教材第68-70页例1、例2,及“做一做”。 学习目标: 1、知识与技能:了解“鸽巢问题”的特点,理解“鸽巢原理”的含义。使学生学会用此原理解决简单的实际问题。 2、过程与方法:经历探究“鸽巢原理”的学习过程,体验观察、猜测、实验、推理等活动的学习方法,渗透数形结合的思想。 3、情感态度与价值观:通过用“鸽巢问题”解决简单的实际问题,激发学生的学习兴趣,使学生感受数学的魅力。学习重点:引导学生把具体问题转化成“鸽巢问题”。 学习难点:找出“鸽巢问题”解决的窍门进行反复推理。教具准备:多媒体课件。 学习过程: 一、创设情境,导入新知 老师组织学生做“抢椅子”游戏(请3位同学上来,摆开2条椅子),并宣布游戏规则。 其实这个游戏中蕴藏着一个非常有趣的数学原理,这节课我们就一起来研究这类问题。-----出示课题《鸽巢问题》“鸽巢原理”又称“抽屉原理”,最先是由19世纪的德

国数学家狄利克雷提出来的,所以又称“狄利克雷原理”,这一原理在解决实际问题中有着广泛的应用。“抽屉原理”的应用是千变万化的,用它可以解决许多有趣的问题,并且常常能得到一些令人惊异的结果。下面我们就来研究这一原理。 二、合作交流,探究新知 1、教学例1(课件出示例题1情境图) 思考问题:把4支铅笔放进3个笔筒中,不管怎么放,总有1个笔筒里至少有2支铅笔。为什么呢? 问题:“总有”和“至少”是什么意思? 学生通过操作发现规律→理解关键词的含义→探究证明→认识“鸽巢问题”的学习过程来解决问题。 (1)操作发现规律:通过把4支铅笔放进3个笔筒中,可以发现:不管怎么放,总有1个笔筒里至少有2支铅笔。 (2)理解关键词的含义:“总有”和“至少”是指把4支铅笔放进3个笔筒中,不管怎么放,一定有1个笔筒里的铅笔数大于或等于2支。这里的“总有”指的是“一定有”或“肯定有”的意思;而“至少”指的是最少,即在所有方法中,放的鸽子最多的那个“笼子”里鸽子“最少”的个数。 (3)探究证明。个人调整意见 方法一:用“分解法”证明。把4分解成3个数。由图

最新人教版六年级下册数学《数学广角——鸽巢问题》教案

数学广角——鸽巢问题 【教学目标】 1.知识与技能:了解“鸽巢问题”的特点,理解“鸽巢原理”的含义。使学生学会用此原理解决简单的实际问题。 2.过程与方法:经历探究“鸽巢原理”的学习过程,体验观察、猜测、实验、推理等活动的学习方法,渗透数形结合的思想。 3.情感、态度和价值观:通过用“鸽巢问题”解决简单的实际问题,激发学生的学习兴趣,使学生感受数学的魅力。 【课时安排】 3课时 【第一课时】 【教学重难点】 1.引导学生把具体问题转化成“鸽巢问题”。 2.找出“鸽巢问题”解决的窍门进行反复推理。 【教学准备】 课件 【教学过程】 一、探究新知: 1.教学例1.(课件出示例题1情境图) 思考问题:把4支铅笔放进3个笔筒中,不管怎么放,总有1个笔筒里至少有2支铅笔。为什么呢?“总有”和“至少”是什么意思? 学生通过操作发现规律→理解关键词的含义→探究证明→认识“鸽巢问题”的学习过程来解决问题。 操作发现规律:通过吧4支铅笔放进3个笔筒中,可以发现:不管怎么放,总有1鸽笔筒里至少有2支铅笔。 理解关键词的含义:“总有”和“至少”是指把4支铅笔放进3个笔筒中,不管怎么放,一定有1个笔筒里的铅笔数大于或等于2支。 探究证明。

方法一:用“枚举法”证明。 方法二:用“分解法”证明。 把4分解成3个数。 由图可知,把4分解成3个数,与枚举法相似,也有4中情况,每一种情况分得的3个数中,至少有1个数是不小于2的数。 方法三:用“假设法”证明。 通过以上几种方法证明都可以发现:把4只铅笔放进3个笔筒中,无论怎么放,总有1个笔筒里至少放进2只铅笔。 认识“鸽巢问题” (1)像上面的问题就是“鸽巢问题”,也叫“抽屉问题”。在这里,4支铅笔是要分放的物体,就相当于4只“鸽子”,“3个笔筒”就相当于3个“鸽巢”或“抽屉”,把此问题用“鸽巢问题”的语言描述就是把4只鸽子放进3个笼子,总有1个笼子里至少有2只鸽子。 这里的“总有”指的是“一定有”或“肯定有”的意思;而“至少”指的是最少,即在所有方法中,放的鸽子最多的那个“笼子”里鸽子“最少”的个数。 小结:只要放的铅笔数比笔筒的数量多,就总有1个笔筒里至少放进2支铅笔。 (2)如果放的铅笔数比笔筒的数量多2,那么总有1个笔筒至少放2支铅笔;如果放的铅笔比笔筒的数量多3,那么总有1个笔筒里至少放2只铅笔…… 小结:只要放的铅笔数比笔筒的数量多,就总有1个笔筒里至少放2支铅笔。 归纳总结: 鸽巢原理(一):如果把m个物体任意放进n个抽屉里(m>n,且n是非零自然数),那么一定有一个抽屉里至少放进了2个物体。 2.教学例2(课件出示例题2情境图) 思考问题: (1)把7本书放进3个抽屉,不管怎么放,总有1个抽屉里至少有3本书。为什么呢? (2)如果有8本书会怎样呢?10本书呢? 学生通过“探究证明→得出结论”的学习过程来解决问题(一)。 探究证明。 方法一:用数的分解法证明。 把7分解成3个数的和。把7本书放进3个抽屉里,共有如下8种情况: 由图可知,每种情况分得的3个数中,至少有1个数不小于3,也就是每种分法中最多那个数最小是3,即总有1个抽屉至少放进3本书。

《鸽巢原理(1)》教案

《鸽巢原理(1)》名师教案 一、学习目标 (一)学习内容 《义务教育教科书数学》(人教版)六年级下册第五单元第68~69页的例1、2。“抽屉原理”是一类较为抽象和艰涩的数学问题,对全体学生而言具有一定的挑战性。为此,教材选择了一些常见的、熟悉的事物作为学习内容,经历将具体问题“数学化”的过程。 (二)核心能力 经历将具体问题“数学化”的过程,初步形成模型思想,发展抽象能力、推理能力和应用能力。 (三)学习目标 1.理解“鸽巢原理”的基本形式,并能初步运用“鸽巢原理”解决相关的实际问题或解释相关的现象。 2.通过操作、观察、比较、说理等数学活动,经历鸽巢原理的形成活动,初步形成模型思想,发展抽象能力、推理能力和应用能力。 (四)学习重点 了解简单的鸽巢问题,理解“总有”和“至少”的含义。 (五)学习难点 运用“鸽巢原理”解决相关的实际问题或解释相关的现象。 (六)配套资源 实施资源:《鸽巢原理(1)》名师课件 二、学习设计 (一)课堂设计 1.谈话导入 师:我这里有一副扑克牌,去掉了两张王牌,还剩52张,我请一位同学任意抽5张,不要让我看到你抽的是什么牌。但是老师却知道,其中至少有两张牌是同种花色的,再找一个学生再次证明。 师:看来我两次都猜对了。谢谢你们。老师为什么能料事如神呢?到底有什么秘诀呢?学习完这节课以后大家就知道了。

2.问题探究 (1)呈现问题,引出探究 出示例1:小明说“把4支铅笔放进3个笔筒里。不管怎么放,总有一个笔筒里至少放进2支铅笔”,他说得对吗?请说明理由。 师:“总有”是什么意思?“至少”有2支是什么意思? 学生自由发言。 预设:一定有 不少于两只,可能是2支,也可能是多于2支。 就是不能少于2支。 (2)体验探究,建立模型 师:好的,看来大家已经理解题目的意思了。那么把4支铅笔放进3个笔筒里,可以怎样放?有几种不同的摆法?(我们用小棒和纸杯分别表示铅笔和笔筒)请大家摆摆看,看有什么发现? 小组活动:学生思考,摆放。 ①枚举法 师:大部分同学都摆完了,谁能说说你们是怎么摆的。能不能边摆边给大家说。 预设1:可以在第一个笔筒里放4支铅笔,其它两个空着。 师:这种放法可以记作:(4,0,0),这4支铅笔一定要放在第一个笔筒里吗? (不一定,也可能放在其它笔筒里。) 师:对,也可以记作(0,4,0)或者(0,0,4),但是,不管放在哪个笔筒里,总有一个笔筒里放进4支铅笔。还可以怎么放? 预设2:第一个笔筒里放3支铅笔,第二个笔筒里放1支,第三个笔筒空着。 师:这种放法可以记作(3,1,0) 师:这3支铅笔一定要放在第一个笔筒里吗? (不一定) 师:但是不管怎么放——总有一个笔筒里放进3支铅笔。 预设3:还可以在第一个笔筒里放2支,第二个笔筒里也放2支,第三个笔

鸽巢原理的教学反思

鸽巢原理的教学反思 教学内容: 《义务教育教科书数学》(人教版)六年级下册第70-71页。 教材和学情分析: 1、理解教材: 在数学问题中,有一类与“存在性”有关的问题,如任意367名学生中,一定存在两名学生,他们在同一天过生日。在这类问题中,只需要确定某个物体(或某个人)的存在就可以了,并不需要指出是哪个物体(或哪个人),也不需要说明通过什么方式把这个存在的物体(或人)找出来。这类问题依据的理论,我们称之为“抽屉原理”。 本课时的教学内容为例1和例2。 例1介绍了较简单的“抽屉问题”:只要物体数比抽屉数多,总有一个抽屉里至少放进2个物体。它意图让学生发现这样的一种存在现象:不管怎样放,总有一个杯子里至少放进2根小棒。例1呈现的是2种思维方法:一是枚举法,罗列了摆放的所有情况。二是假设法,用平均分的方法直接考虑“至少”的情况。通过例1两个层次的探究,让学生理解“平均分”的方法能保证“至少”的情况,能用这种方法在简单的具体问题中解释证明。 例2在例1的基础上说明:只要物体数比抽屉数多,总有一个抽屉里至少放进(商+1)个物体。因此我认为例2的目的是使学生进一步理解“尽量平均分”,能用有余数的除法算式表示思维的过程。 2、分析学生: 通过调查,发现有相当多的学生以前的奥数班已经解除了抽屉原理,他们在具体分得过程中,都在运用平均分的方法,也能就一个具体的问题得出结论。但是这些学生中大多数只“知其然,不知其所以然”,为什么平均分能保证“至少”的情况,他们并不理解。 还有部分学生完全没有接触,所以他们可能会认为至少的情况就应该是“1”。 设计理念: 1、用具体的操作,将抽象变为直观。 “总有一个笔筒中至少放进3枝笔”这句话对于学生而言,不仅说起来生涩拗口,而且抽象难以理解。怎样让学生理解这句话呢?我觉得要让学生充分的操作,一在具体操作中理解“总有”和“至少”,二在操作中理解“平均分”是保证

新人教版小学数学六年级下册《鸽巢问题》教学设计

“鸽巢问题”教学设计 【教学内容】 人教版课标教材小学数学六年级下册第五单元数学广角第68-69页。 【教学目标】 1.通过操作、观察、比较、分析、推理、抽象概括,引导学生经历抽屉原理的探究过程,初步了解抽屉原理,会用抽屉原理解释生活中的简单问题。 2.在探究的过程中,渗透模型思想,培养学生的推理和抽象思维能力。 3.使学生感受数学的魅力,培养学习的兴趣。 【教学重点】 经历抽屉原理的探究过程,初步了解抽屉原理,会用抽屉原理解释生活中的简单问题。 【教学难点】 理解抽屉原理,并对一些简单的实际问题加以模型化。 【教学过程】 一、开门见山,引入课题 承接课前谈话内容,直接揭示课题。 二、经历过程,构建模型 (一)研究“4个小球任意放进3个抽屉”存在的现象。

1.出示结论:4个小球放进3个抽屉里,不管怎么放,总有一个抽屉里面至少放2个小球。 让学生说说对这句话的理解。 2.验证结论的正确性。 让学生用长方形代替抽屉,用圆代替小球画一画,看有几种不同的放法。 3.全班交流。 学生汇报后,教师引导观察每种放法,通过横向、纵向比较,找到每种放法中放得最多的抽屉,然后从最多数里找最少数,发现不管哪种放法,都能从里面找到这样的一个抽屉,里面至少有2个小球。从而理解并证明了“不管怎么放,总有一个抽屉里至少放2个小球”这个结论是正确的。 (二)研究“5个小球任意放进4个抽屉”存在的现象,找到求至少数的简便方法。 1.猜测:根据刚才的研究经验猜一猜:把5个小球放进4个抽屉里,不管怎么放,总有一个抽屉至少放几个小球? 2.验证。 学生以小组为单位共同研究:先画出不同的放法。然后观察分析每种放法,看看哪种猜测是正确的。 3.全班交流。 小组汇报研究结果。 教师追问:通过验证,我们发现5个小球放进4个抽屉里,不管

相关文档
最新文档