Extracurricular knowledge of mathematics in sixth grade

1. Interesting math knowledge after class

2. The sixth grade recommends extracurricular knowledge.

Interesting math knowledge after class 1. Interesting math knowledge is about 20 to 50 words.

Interesting knowledge of mathematics

Number theory part:

1, there is no maximum prime number. Euclid gave a beautiful and simple proof.

2. Goldbach conjecture: Any even number can be expressed as the sum of two prime numbers. Chen Jingrun's achievement is that any even number can be expressed as the sum of the products of one prime number and no more than two prime numbers.

3. Fermat's last theorem: n power of x+n power of y = n power of z, and n> has no integer solution at 2 places. Euler proofs 3 and 4, 1995 were proved by British mathematician andrew wiles.

Topology part:

1. The relationship among points, faces and edges of a polyhedron: fixed point+number of faces = number of edges +2, which was proposed by Descartes and proved by Euler, also known as euler theorem.

2. euler theorem's inference: There may be only five regular polyhedrons, namely regular tetrahedron, regular octahedron, regular hexahedron, regular icosahedron and regular dodecahedron.

3. Turn the space upside down, the left-handed object can be changed into the right-handed, and through Klein bottle simulation, a good mental gymnastics,

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2. Mathematical allusions, numbers, interesting calculations, little knowledge 1 knowledge learned in grade 5 and extracurricular knowledge.

◆ the story of pi1 Zu Chongzhi, the seventh, ranked first in the world, has remained for a thousand years; "The accuracy of calculating pi in a country in history can be used as a symbol to measure the level of mathematical development in that country at that time" (2. 1427, * * * mathematician Al Cassie,16; 1596, Dutch mathematician Rudolf, 35 years old; 1990, with 480 million computers; 65438+February 6, 2002, Tokyo University, 124 1 1 billion.

◆ "0" Roman numeral has no 0; In the fifth century, "0" spread from the East to Rome. At that time, the Pope was very conservative and thought that Roman numerals could be used to remember any number, so "0" was forbidden. A Roman scholar's handbook introduced some usages of 0 and 0, and the Pope tortured them after discovering it. ◆ In the stone statue of an ancient building in Jiaxiang County, Fiona Fang, which is famous for its "rules" and "moments", there are two images of our ancient ancestors deified in ancient times, one is Fuxi and the other is Nu Wa.

The object in Fuxi's hand is a compass, similar to a compass; The object in Nu Wa's hand is called Moment, which is in the shape of a square. China's Ancient Pigeonhole Principle There are many successful examples in China's ancient literature.

For example, in the Song Dynasty Fei Zhou's Records of Liang Man, the pigeon hole principle was used to refute the fallacy of superstitious activities such as "fortune telling". Fei Zhou pointed out that the year, month, day and hour (eight characters) of a person's birth are used as the basis for fortune telling, and the eight characters are used as the "drawer". Only 12 * 360 * 60 = 259200 different drawers.

Taking people in the world as "things", the person who enters the same drawer must be Qian Qian, so the conclusion is that there are many people born at the same time. But since the "eight characters" are the same, "What's the difference between rich and poor?" There are similar words in Qian Daxin's Collection of Thousand Words in Qing Dynasty, Ruan Kuisheng's Tea Guest Talk and Chen Qiyuan's Notes on Yongxianzhai.

But unfortunately, although Chinese scholars have used the pigeon hole principle for the analysis of specific problems for a long time, there is no universal text about the pigeon hole principle in ancient literature, and no one abstracts it as a universal principle. Finally, they had to name this principle after hundreds of years as Dirichlet, a western scholar. The application of pigeon hole principle 1947, Hungarian mathematicians introduced this principle into middle school students' mathematics competition. At that time, there was a question in the Hungarian National Mathematics Competition: "Prove that among any six people, you can find three people who know each other or three people who don't know each other."

At first glance, this question seems incredible. But if you know the principle of pigeon hole, it is very simple to prove this problem.

We use a, b, c, d, e and f to represent six people. Let's choose one of them, such as A, and put the other five people in two drawers: "Know A" and "Don't Know A". According to the pigeon hole principle, there are at least three people in a drawer. Suppose there are three people in the drawer of "Know A". They are b, c and d.

If B, C and D don't know each other, then we have found three people we don't know. If two of B, C and D know each other, for example, B and C know each other, then A, B and C are three people who know each other. In either case, the conclusion of this question is valid.

Because of its novel form and ingenious solution, this test quickly spread all over the world, making many people know this principle. In fact, the pigeon hole principle is not only useful in mathematics, but also plays a role everywhere in real life, such as enrollment, employment arrangement, resource allocation, job title evaluation and so on. It is not difficult to see the function of pigeon cage principle.

Have you ever heard of the question "Chicken and rabbit in the same cage"? This question is one of the famous and interesting questions in ancient China. About 1500 years ago, this interesting question was recorded in Sun Tzu's calculation.

The book describes it like this: "There are chickens and rabbits in the same cage today, with 35 heads on the top and 94 feet on the bottom. The geometry of chicken and rabbit? These four sentences mean: there are several chickens and rabbits in a cage, counting from the top, there are 35 heads; It's 94 feet from the bottom. How many chickens and rabbits are there in each cage? Can you answer this question? Do you want to know how to answer this question in Sunzi Suanjing? The answer is this: If you cut off the feet of every chicken and rabbit in half, then every chicken will become a "one-horned chicken" and every rabbit will become a "two-legged rabbit".

In this way, the total number of feet of (1) chickens and rabbits changed from 94 to 47. (2) If there is a rabbit in the cage, the total number of feet is more than the total number of heads 1. So the difference between the total number of feet 47 and the total number of heads 35 is the number of rabbits, that is, 47-35= 12 (only).

Obviously, the number of chickens is 35- 12=23. This idea is novel and strange, and its "foot-cutting method" has also amazed mathematicians at home and abroad.

This way of thinking is called reduction. Reduction method means that when solving a problem, we do not directly analyze the problem first, but deform and transform the conditions or problems in the problem until it is finally classified as a solved problem.

Pucsok's interesting topic Pucsok is a famous mathematician in the former Soviet Union. 195 1 wrote a book, Math Teaching Methods in Primary Schools.

There is an interesting question in this book. This shop sold 1026 meter cloth in three days.

The sales volume of the second day is twice that of the first day; On the third day, it sold three times as much as the next day. How much rice cloth do you want to sell in three days? The problem can be thought of this way: the number of meters sold on the first day is regarded as 1 serving.

You can draw the following line chart: the first day 1 copy; The second day is twice as much as the first day; The third day is three times that of the second day and two times that of the first day. Comprehensive calculation shows that the number of cloth sold on the first day is1026 ÷ (l+2+6) =1026 ÷ 9 =114 (meters) and1/kloc-.

Please do the problem in this way. Four people donated money for disaster relief.

B's donation is twice that of A, C's donation is three times that of B, and D's donation is four times that of C. They made a total donation of 132 yuan.

How much do you want each of the four people to donate? There was a general named Han Xin in the Han Dynasty. Every time he * * * troops, he only asked his men to count off at l~3, 1~5, 1~7, and then reported the remainder of each team's count off, so he knew how many people had arrived.

His ingenious algorithm is called "Ghost Valley Calculation", "Partition Calculation", or "Han Xin Point Soldiers", while foreigners call it "Ghost Valley Calculation".

3. Extracurricular mathematics knowledge

1. Goldbach conjecture 1742 Goldbach in Germany wrote a letter to Euler, a great mathematician living in Petersburg, Russia at that time. In the letter, he raised two questions: First, can every even number greater than 4 be expressed as the sum of two odd prime numbers? Such as 6 = 3+3, 14 = 3+ 1 1 and so on. Second, can every odd number greater than 7 represent the sum of three odd prime numbers? Such as 9=3+3+3, 15=3+5+7, etc. This is the famous Goldbach conjecture. This is a famous problem in number theory, which is often called the jewel in the crown of mathematics.

2. A long time ago, there was a man named Caesar in India. He carefully designed a game for the king, which is now 64-square chess. The king was very satisfied with the game and decided to give it to Cesar. The king asked Cesar what he needed. Cesar pointed to the small squares on the chessboard and said, "Just give me the first square 1 grain of wheat, the second square with 2 grains of wheat and the third square with 4 grains of wheat. At this rate, the wheat in each square is twice as much as that in the previous one. Your Majesty, give me all the 64 tablets that fill the chessboard like this. " The king readily agreed to Cesar's request without thinking. However, after calculation, ministers found that it was not enough to give Cesar all the wheat harvested in one year. Cesar is right. His demands can't really be met. According to the calculation, the total number of wheat in 64 squares on the chessboard will be a 19 digit, which is about 200 billion tons by weight. The king has supreme power, but he interprets the profoundness of knowledge with his ignorance.

3. How did the wise men in ancient Greece measure the height of the pyramids? First, a bamboo pole is erected on the ground, and the length of the shadow of the bamboo pole and the shadow of the pyramid are measured at the same time when the sun is shining, and then the ratio of the length of the bamboo pole to the shadow of the bamboo pole is calculated, that is, the ratio of the height of the pyramid to the length of the shadow of the pyramid. Using this ratio and the shadow length of the pyramid, the height of the pyramid can be calculated.

4. Interesting mathematical knowledge, about 300 words, for handwritten newspaper,

It takes 1 hour to burn a rope from one end. Now you need to use this rope and a box of matches to measure the time for half an hour without looking at your watch. You may think it's easy. You just need to make a mark in the middle of the rope, and then measure the time it takes for the rope to burn half. Unfortunately, however, this rope is uneven, thick in some places and thick in others. So this kind of rope burns at different speeds in different places. Maybe it takes only 5 minutes for half of the rope to burn, but it takes 55 minutes for the other half to burn. Faced with this situation, it seems impossible to accurately measure 30 minutes with the rope above, but this is not the case. You can solve the above problem in an innovative way. This method is to ignite at the same time from both ends of the rope. The rope must take 30 minutes to burn out. The two trains run in opposite directions along the same track, and each train runs at 50 miles per hour. When the distance between the two trains is 100 mile, a fly begins to fly from train A to train B at a speed of 60 miles per hour. After it meets the B train, it immediately turns around and flies to the A train, and so on until the two trains collide. We know that the distance between two cars is 100 miles, and the speed of each car is 50 miles per hour. This means that each car has traveled 50 miles, that is, two cars collided one hour later. During the short time from the train to the collision, the fly kept flying at 60 miles per hour, so when the two cars collided, the fly flew 60 miles. Whether the fly flies in a straight line, in a "Z" shape or tumbling in the air. The result is the same. Flipping a coin on the eighth floor is not the fairest way to make a decision. People think that this method is fair to both sides, because they think that the probability of coins upside down and upside down is the same, both of which are 50%. Interestingly, this very popular idea is not correct. First of all, although it is unlikely that a coin will fall and stand on the ground, this possibility exists. Secondly, even if this small possibility is ruled out, the test results show that if you flick the coin in the conventional way, that is, with your thumb, the probability that the coin will still face up when you start throwing is about 5 1%. The reason why this happens is that when you flick it with your thumb, sometimes the coin doesn't turn over, but just rises like a trembling flying saucer. Next time, if you want to choose which side of the coin in the coin thrower's hand is facing up, you should look at which side is facing up first, so that you have a greater chance of guessing correctly. But if that person is holding coins and turning his fists one by one, then you should choose the opposite from the beginning.

Extracurricular knowledge is recommended for grade six 1. Must-read bibliography for grade six.

Scientific Discovery Guo Zhengyi and others China Children's Publishing House 2000 Edition Popular Science Fairy Tales People's Literature Publishing House 2000 Edition The Story of Elements (Su) According to The Folk Tales of China Translated by Ni Khayev and Teng Diping Hunan Education Publishing House (1999 Edition), the dialogue between Nobel Prize winners and China Friendship Publishing House children (2000 Edition) Sanlian Bookstore (June 2003 Edition). Poems of a Thousand Families edited by Chen Bixiang are edited by Kipling of Nankai University Press (1995 edition), Alice in Wonderland by Children's Publishing House (1996 edition), Alice in Wonderland by Xu Pu (English), and Chen Bochui by Shanghai Science and Technology Education Press (1). Wang Quangen translated Mark Twain's The Adventures of Tom Sawyer (200 1 version), Zhong Lei edited Wamba's Diary of a Troublemaker (2000 version), Simin translated St. Exupery's The Little Prince (2003 version), and Ma Zhen hired him to translate it. Harry Potter and the Sorcerer's Stone, People's Literature Publishing House, May 2000 (English) joko Rowling People's Literature Publishing House, The Code of Life in 2000, Tan, Hunan Children's Publishing House, If Give Me Three Days of Light in 2000, Helen Keller, Li, Chinese Publishing House, Father and Son, Great Writer Snoopy in 2002 (2002

2. The sixth grade of primary school must read extracurricular books.

Must-read bibliography for sixth-grade students

"Scientific Discovery" Guo Zhengyi waiting for China Children's Publishing House, 2000.

Gao Shiqi Popular Science Fairy Tales, Gao Shiqi People's Literature Publishing House, 2000.

The Story of Elements (Su), translated by Ni Khayev and Teng Diping, Hunan Education Press, 1999.

Selected Folk Stories of China, China Friendship Publishing House, Ren Xuan, 2000.

Dialogue between Nobel Prize Winners and Children, Sanlian Bookstore, June 2003.

Five Thousand Years of the World, edited by Duan Wanhan, Gu and Chen Bixiang, Children's Publishing House 199 1 edition.

Three-character Classics, Hundreds of Surnames, Thousands of Poems, edited by Xinxia of Nankai University Press, 1995.

The Legend of the Jungle by Kipling, translated by Xu Pu, Children's Publishing House, 1996.

Alice in Wonderland by lewis carroll, translated by Chen Bochui, Shanghai Science and Technology Education Edition 1996.

The Goose Journey (Sweden) is written by Lagrov, translated by Wang Quangen, Beijing Children's Publishing House, 200 1 edition.

The Adventures of Tom Sawyer, Mark Twain, edited by Zhong Lei, Harbin Publishing House, 2000.

Wanba's Diary of a Troupe (Italian), translated by Simin, China Social Publishing House, 2003.

The Little Prince (France) by Saint Exupery, translated by Ma Zhen, People's Literature Publishing House, May 2000.

Harry Potter and the Sorcerer's Stone (English): Joko Rowling People's Literature Publishing House, 2000.

The Code of Life, written by Tan Zhu, Hunan Children's Publishing House, 2000.

If you give me three days of light, translated by Helen Keller Lee, Chinese Publishing House, 2002.

Father and Son (Germany) and Austria Braun, edited by Hu Paige, Yilin Press, 200 1 edition.

Snoopy, the Great Writer (America), Monte Schultz CITIC Publishing House, 2003.

Goodbye, Crewe (Japan), Yuan Qiu Liangping Nanhai Publishing House, 2003.

3. What extracurricular books (to enrich extracurricular knowledge) are most suitable for sixth-grade primary school students?

When my brother was in the sixth grade, she read the magic garden, Niels' Goose Riding Travel, If you give me three days of light, China for five thousand years and other extracurricular books, which were also requested by their teachers.

Go to the bookstore to find those famous books for teenagers, all around 10 yuan, which are easy to understand. Pick something interesting to read. Reading more books is very helpful to improve the level of composition.

I read the following.

Lu Xun's "Morning Flowers and Evening Picks"

How the Steel Was Tempered

Rickshaw Boy

Notre Dame Cathedral

Camille

Sister Carrie

The Count of Monte Cristo

Anna Karenine

Jane Eyre

War and Peace

I am in the second grade, and these are all things I have read, including Lu Xun's Flowers in the Morning and Picking Up in the Evening.

"How Steel was Tempered" and "Camel Xiangzi" are all required reading for teachers, and so is childhood.

A little experience, I hope it will help you.

4. What extracurricular books are suitable for sixth grade students?

The Arabian Nights, Andersen's Fairy Tales, The Adventures of Tom Sawyer's Robinson Crusoe, The Little Prince, I am a cat, If you give me three days of light, How the steel was tempered, The Romance of the Three Kingdoms and The Education of Love are all suitable for reading.

The sixth grade of primary school is the key time to cultivate children's correct three views, so the following books can play a certain role in cultivating children's good quality. There are many books about sports, painting and piano, which can also cultivate children's interest and increase their vitality.

Arabian Nights is a collection of folk stories, also known as Arabian Nights. According to legend, there was a Sasan kingdom between ancient India and China. King Ruyal was cruel and jealous, so he killed the queen because of her bad behavior. After that, he married a girl every day and killed her the next morning as revenge.

Scheherazade, the daughter of the Prime Minister, volunteered to marry the king to save the innocent woman and attract the king by telling stories. Every night, at dawn, the king couldn't bear to kill her and allowed her to continue talking the next night. Her story has been told for 1001 nights, and the king was finally moved to grow old with her.

Gorky praised it as "the most magnificent monument" in the history of world folk literature because of its rich content and large scale. Andersen's Fairy Tales The collection of fairy tales created by Danish writer Andersen consists of 166 stories.

Those who * * * clearly hate, but enthusiastically praise the working people, praise their good and pure character; Ruthlessly expose and criticize the stupidity, incompetence, greed and cruelty of princes and nobles. The Adventures of Tom Sawyer is a novel published by American novelist Mark Twain in 1876.

It tells the story of an ordinary town on the Mississippi River in the United States in the first half of the19th century. Tom sawyer, the protagonist, and his companions took some absurd adventures near St. Petersburg, a rural town along the Mississippi River.

Robinson Crusoe is a novel by British writer daniel defoe. It tells the story that the protagonist Robinson Crusoe was born in a middle-class family and devoted his life to traveling around the world.

Once, I was caught in a storm on my way to Africa, drifted to an uninhabited desert island alone, and began to live in isolation. With strong will and unremitting efforts, he survived tenaciously on a desert island and returned to his hometown after 28 years and 2 months 19 days.

The Little Prince is a famous short story of children's literature written by French writer Antoine de Saint-Exupé ry in 1942. It tells all kinds of adventures that the little prince from another planet experienced when he set off from his own planet to the earth.

With the childlike eyes of the little prince, the author reveals the emptiness, blindness, stupidity and rigidity of adults, and writes the lonely and rootless fate of human beings in simple and childish language. At the same time, it also expresses the author's criticism of the relationship between money and eulogizes the truth, goodness and beauty.

If you give me three days of light, the masterpiece of American contemporary writer Helen Keller's prose. The first half mainly describes Helen's life after blindness and deafness, and the second half introduces Helen's study career.

At the same time, it also introduces her different colorful life experiences and her charity activities. From the perspective of a weak woman who is physically disabled and determined, she warns people who are physically healthy to cherish life and cherish everything given by the creator.

"How Steel was Tempered" is a novel by Nikolai ostrovsky, a writer of the former Soviet Union, written in 1933. It tells the story that pavel korchagin, the hero, became a strong steel (referring to the spirit) from an ignorant teenager to a Bolshevik soldier loyal to the revolution to a blind but unyielding novel.

I am a cat is a novel written by Japanese writer Natsume Soseki. This paper takes a poor teacher's cat as the protagonist and observes human psychology from the perspective of this anthropomorphic cat.

This is a cat who is good at thinking, knowledgeable, full of sense of justice and literati temperament, but has never learned to catch mice until his death. It vividly reflects the thoughts and life of Japanese petty bourgeoisie in the early 20th century, and sharply exposes and criticizes the "civilized" capitalist society in Meiji period.

Romance of the Three Kingdoms is a novel written by Luo Guanzhong, one of China's classical Four Great Classical Novels. This paper describes the historical situation of nearly a hundred years from the end of the Eastern Han Dynasty to the beginning of the Western Jin Dynasty, mainly describing the war, and tells the story of the warlord melee, the political and military struggle among Wei, Shu and Wu countries in the end of the Eastern Han Dynasty, and finally Sima Yan unified the three countries and established the Jin Dynasty.

It reflects the transformation of various social struggles and contradictions during the Three Kingdoms period, summarizes the historical changes of this era, and shapes a group of heroes of the Three Kingdoms. The Education of Love is a diary novel by the Italian writer Edmund de Amicis.

It tells the life of Amrico, a fourth-grade primary school student, in a school year, interspersed with "stories" told by teachers every month and many inspirational articles written by parents for him. It is a children's literature aimed at education. It preaches great patriotism and praises the lofty feelings of unity and friendship between people.

Children's books or reading materials refer to literary works, knowledge books, comics and games that children read. Child development (child development) The changing process of children's physiology and psychology in time.

Generally speaking, it refers to the process from birth to maturity (early youth), and some scholars began to study it from fetal period. The development of children's physiology is manifested in the changes of body length, weight, structure and function of bones, muscles and nervous system.

The development of children's psychology is mainly manifested as follows: psychological activities develop from simple and concrete to complex and abstract; The randomness and consciousness of psychological activities are constantly improving; From being born with only some quality differences to gradually forming personality. Children's psychological development has stages and continuity.

Stage means that children of a certain age have some common psychological development characteristics. For example, what preschool children have in common is that various psychological processes are obviously concrete and arbitrary.

According to the comprehensive characteristics of children's development (activity form, intelligence level, personality, physical development and speech level, etc.). ), children's development is generally divided into the following stages: lactation (from birth to 1 year) and infancy (1 year).

5. Extracurricular knowledge of sixth grade Chinese.

1. Look at the words below and fill in the blanks as required. (2 points)

Xiaojing, Aosuding Town

In alphabetical order, the order of these six words is from small to large according to the number of strokes.

2. Pay attention to the following polyphonic words. (5 points)

Plant () a good watermelon and then plant () a good watermelon.

B, this evil person is really hateful ().

C. How do you pay () or not pay () my money?

D, Xiaoxing 'anling contains () rich treasures ().

There will be a meeting here tomorrow.

3. crossword puzzles. (4 points)

A, the top is just a horizontal line, and the bottom is a little missing. ( )

B, the word Lin is more than half, so don't guess the word Sen. ()

C, ninety-nine ()

D, 1.1 horizontal length, roll to the west. Two trees are planted side by side on a stone. ( )

4. Put the following words in a certain order. (3 points)

Night, midnight, morning, sunset, dawn and noon.

5. Fill in the brackets with 12 Chinese Zodiac to form 12 Chinese Zodiac Xiehouyu. (6 points)

() Out of the hole-look in all directions () Your Majesty was moved-awesome.

() * * *-Don't touch () Take the mouse-Mind your own business.

() Eat grass-speak hesitatingly () Eat Chili-scratch your ears.

It's too late to mend ()-I don't know the length of the hole ().

Blind people ride blind ()-trespassing () Eight quit to wear flowers-smelly people

() Pulling carts-jumping around () Paying New Year greetings to weasels-flattering them.

6. Fill in the name of a part of the human body in the following () to form a four-word idiom. (5 points)

() Gun () Sword Sleeve () It is difficult for a person to make a sound ().

Flexibility () can be counted as () success () should be counted as ()

() () Quote () hang () promote () talk about ()

Single-handedly ()

7. Fill in the blanks with comprehensive knowledge. (20 points)

A. Xu Xiake, a geographer in the late Ming Dynasty, said: "When the Five Mountains return, they don't look at the mountains, and when Huangshan returns, they don't look at the mountains." Excuse me, the five mountains refer to Mount Tai, Mount Tai, Mount Tai, Mount Tai, Mount Tai, Mount Tai.

B. "Three Friends in Cold Year" means:,,.

Four Treasures of the Study means:,,,.

D "Four Great Inventions" means:,,,.

E who are the three people in the romance of the three kingdoms who said "taoyuan became sworn"?

F. The author of the novel The Legend of the Condor Heroes is: You know that all the characters in the novel are like this.

Attach the answer by the way.

According to the strokes, small, concave, simple, true, ding and Jing.

Two, 1 third sound, fourth sound. 2, the fourth sound of e, the fourth sound of Wu. 3, Hai Er Sheng, Huan Er Sheng 4, Cang Er Sheng, Zang Si Sheng. 5, the fourth, the fourth.

I can't stand by and do nothing. I can't count my fingers.

Have a heart-to-heart talk

Dongyue Taishan

Xiyue Huashan

Nanyue Hengshan

Bei heng yue shan

Zhongyue Songshan

Three friends are cold, pine, bamboo and plum blossoms.

Four great inventions: compass, gunpowder, papermaking and printing.

Four Treasures of the Study paper, ink, pen and inkstone.

Taoyuan Jieyi Zhangbei Guan Yu

Guo Rong, the hero of Jin Yong's works, is the author of sculpture.

There were also questions and answers about Olympic knowledge in 2008.