Do you have any information about the Olympiad in the first and second grades of primary school? thank you

-Winter Vacation Course for Grade Two Primary School (1)

Summary: Intellectual problems, such as chessboard, poker, crossing the bridge, etc., include some basic mathematical ideas and theories, examine students' ability to understand, analyze and solve problems, and also include some simple calculations. As long as you think hard and do it, the answer is right in front of you. Being able to learn math well in games is actually a great learning ability.

Example: 1: There are 10 cards, face up and turn 6 cards at a time. How many times have you turned the cards? Can all the cards face up?

Analysis and solution: You can't find the answer just by your head imagination, so try to find a deck of cards. Here are the zeros on the front and the lows on the back of the card:

(start)

????????????????????????????

??????????????????????????? 1

●●●●●●●●●●●●●● (third round: six zeros)

Example 2: Xiao Zhang bought 24 bottles of soda, and every four empty bottles can be exchanged for 1 bottle of soda. How many bottles of soda can Xiao Zhang drink?

Example 3: One person has 1 rice bowl, two people have 1 vegetable bowl and three people have 1 soup bowl. Now * * * has 1 1 bowl. How many people are there?

Example 4: Plant a tree every 5 meters on one side of the river bank, and plant 10 tree from beginning to end. How long is this river bank?

Example 5: There are 48 students participating in three sports competitions, but the number of participants in each activity is different, and there is a number "6". How many people participated in each of the three sports competitions?

Exercise 1: There are 7 playing cards on the table, all facing up. If you want to turn three cards at a time, how many times must you turn them at least to make all seven cards face down?

Exercise 2: Divide oranges.

Dad gives oranges to everyone in the family 1 and the rest 1. If everyone is divided into two, there will be two less. How many people are there in the family? How many oranges did dad buy?

Solution: 3 people, 4 oranges.

Exercise 3: Chess game

There is a chess game: there is a round or rectangular piece of paper as a chessboard (it is best to use a chessboard), and both parties take turns to play Go on this chessboard. Everyone puts one piece at a time, and every time a new piece is put, it is not allowed to overlap with the piece that has been put in front. Whoever puts the chess piece down first loses.

The question now is: If A is released first, can you predict who will win or lose?

Analysis: In this game, the initiative is also in the hands of the first player. For example, if A puts the first chess piece in the symmetrical center of the chessboard, and then always puts the chess piece in the symmetrical point of the chess piece put in B (symmetrical about the intersection of the center of the circle or the two diagonal lines of the rectangle), A will definitely win. Because as long as B has a place to put it, there must be room for A at the symmetry point where B puts the chess pieces, so A won't encounter a situation where there is no place to put it. It must be B, not A, who first encountered the problem of nowhere to put the chess pieces.

Of course, if the first piece of A is not placed in the symmetrical center of the chessboard, or every piece of A is not placed in the symmetrical point of B in the future, the outcome is unpredictable.

Exercise 4: Water lilies in the pond

The area of water lilies in the pond doubles every day, and the whole pond can grow after 17 days. How many days will it take? Can these water lilies grow half a pond?

Exercise 5: When does the snail climb the well?

A snail accidentally fell into a dry well. It lay at the bottom of the well and began to cry. A toad crawled over and whispered to the snail, "don't cry, little brother!" It's no use crying. The shaft wall is too high. If you fall here, you can only live here. I have been here for many years, and I haven't seen the sun for a long time, let alone want to eat swan meat! "

The snail looked at the old and ugly toad and thought, "What a beautiful world outside the well! I can never live in a dark and cold well like it! " The snail said to the toad, "Uncle toad, I can't live here. I have to climb up! "How deep is this well?" "Ha ha ha ..., are you kidding! The depth of this well is10m. How can you climb up with such a heavy shell at a young age? " "I am not afraid of suffering, not afraid of being tired. I can always climb out after a while every day! "

The next day, the snail ate and drank enough and began to climb the wall. It kept climbing and climbing, and finally climbed 5 meters at night. The snail was very happy and thought, "At this rate, I can climb up tomorrow night." Thinking about it, it fell asleep unconsciously.

In the morning, the snail was awakened by a purr. At first glance, it turned out that Uncle Tu was still sleeping. It was surprised: "How come I am so close to the bottom of the well?" It turned out that this snail slipped 4 meters from the borehole wall after falling asleep. The snail sighed, gritted his teeth and began to climb again. At night, it climbed another 5 meters, but at night the snail slipped another 4 meters. Climb and climb, and finally the strong snail climbed up the well platform.

Children, can you guess how many days it will take a snail to climb the drilling platform?

Exercise 6: Finding Parts

There are 100 pieces in total, which are packed in 10 bags, and each bag contains 10 pieces. Among them, the parts in 9 bags are 5 kg each, and the parts in 1 bag are 4 kg each. This 10 package is mixed together, and the defective products are not visible to the naked eye. Can you find a bag with 4 kilograms of parts only once?

Analysis and solution: Because it can only be weighed once, it must be related to all bags this time. We might as well number this 10 bag first: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. Then take out 1 part from 1 bag, 2 parts from the second bag, 3 parts from the third bag ... take out 10 parts from 10 bag, thus taking out 1+2+3+4+5+6. Put these 55 parts on the scale, the total weight should be less than 5× 55 = 275 (kg).

If 1 kg is missing, 1 bag is what you are looking for;

If it is less than 2 kg, the second bag is what you are looking for;

If it is less than 3 kg, the third bag is what you are looking for;

……

If 10 kg is missing, the 10 package is what you are looking for.

Simple logical thinking

-Winter Vacation Course for Grade Two Primary School (2)

Summary: Logical thinking mainly means that we think about a thing through the information collected by means of eyes and ears, and gradually infer the story hidden behind the known conditions through the known conditions, which requires us to have rich practical experience in life. This is a compulsory course for studying Olympic Mathematics.

Example 1: Longlong and Liangliang go to the park to play and want to buy tickets, but they don't have enough money. Longlong lacks 4 yuan by 80 points, and Liangliang lacks 1 point. The sum of their money is still not enough. How much is the park ticket?

Example 2: It takes three minutes for three people to eat three tomatoes at the same time, and how many minutes for six people to eat six tomatoes at the same time?

Example 3: A rectangular colored paper has four corners. How many corners are left after cutting off one corner along a straight line? (Drawing representation)

Ex. 4: The power went out at night. Xiaowen lit eight candles at home. First, 1 candle was blown out by the wind, and then two candles were blown out by the wind. How many candles are left at last?

Example 5: To plant 9 trees, it is required to plant 3 trees per row, which is exactly 10 row. How should I plant it? Can you help plant it?

Exercise 1: cross the river skillfully

The hunter wants to take a wolf, a sheep and a basket of cabbage from the left bank of the river to the right bank, but his ferry is too small to carry only one at a time. Because wolves eat sheep, sheep eat cabbage, wolves and sheep, sheep and cabbage can't get along without supervision. Ask the hunter how to achieve his goal.

Solution: With a little thought, you can get the way to cross the river, as follows:

The first time:

The second time:

The third time:

The fourth time:

Exercise 2: Crossing the Bridge

An overseas Chinese crossed the river from east to west, and it took him five minutes. There is a pavilion in the middle of the bridge. There is a night watchman in the pavilion. He comes out every three minutes. When you see someone passing by, tell him to go back and not go there. A clever man who crossed the bridge from east to west thought of a clever way and finally crossed the bridge. Excuse me: How did the wise man think of crossing the bridge?

Exercise 3: Three safes

Mr. Zhao is the director of the accounting office of a company.

One day, the accounting office bought three safes. Mr. Zhao intends to allocate these three safes to three staff members.

"I'll leave these three safes to you," Mr. Zhao said to the three staff in front of him, putting a bunch of keys on his desk. "Every safe has two keys."

"Does everyone use the safe alone?" A staff member asked.

"No," Zhao Liang shook his head. "You three use it together, and ask each person to open three safes and not the other two."

"That is to say, each of us should have three keys to the safe," another worker said to himself. "But now there are only two keys in each safe, which is difficult to distribute. ! "

"Mr. Director," asked the third staff member, "can you give each safe another key?"

"No, no!" Mr. Zhao waved his hand again and again. "For the sake of safety, you are not allowed to take keys."

How to distribute the six keys of these three safes? Three staff members, you look at me, I look at you, with a sad face.

Children, would you please do something for them?

Answer: The three safes are numbered 1, 2, 3, and each of the three staff members takes a key from one of them. Then put a key to cabinet 2 in cabinet 1, a key to cabinet 3 in cabinet 2 and a key to cabinet 1 in cabinet 3. In this way, each staff member can open three safes without others.

Exercise 4: Four students, A, B, C and D, have different numbers printed on their jerseys. Zhao said, "A is number two, and B is number three." Qian said, "C is number four, and B is number two." Sun said, "Ding is number two and C is number three." Li said, "Ding is number one, and B is number three."

Overlapping problem

-Winter vacation course for the second grade of primary school (3)

Summary: knowledge points: queuing problem: from the front, from the back, Lily ranks sixth. How many people are there in this row? Lily counts twice here, and sometimes we call this kind of problem overlap. This kind of question must be analyzed in calculation, and don't be confused by simple requirements, and don't take it for granted to get the answer. In fact, the key to solve this problem is to draw a picture or observe it with the help of physical objects, and connect it with the reality of life, and the answer will be clear at a glance.

Example 1: Put eight handkerchiefs washed on a rope to dry, and the same clamp will hold both sides of two adjacent handkerchiefs. How many clips do you need to do this?

Analysis: As can be seen from the picture, one side of the two handkerchiefs is overlapped, and three clips are used. Three handkerchiefs have overlapping edges. With four clips, we find that the number of clips is always more than the number of handkerchiefs 1, so eight handkerchiefs need nine clips.

Example 2: Every two pictures are nailed to the wall. How many thumbtacks do you need for five pictures now?

Analysis: Each row of two paintings needs 6 pushpins, each row of three paintings needs 8 pushpins, and each row of four paintings needs 10 pushpins. As you can see, every time you add a picture, you will add two pushpins, so five pictures need 12 pushpins.

Example 3: There are two boards of the same length, nailed together. If each board is 25 cm long and the one nailed together in the middle is 5 cm long, how long is this long board now?

Analysis: nail two boards together, and the length of the place where they are nailed together is the overlapping part. The current total length is the sum of the original two total lengths minus the overlap. Formula: 25+25-5=45 (cm), so now the board is 45 cm long.

Exercise 1: Teacher Zhang gave two questions. 13 people answered the first question correctly, 22 people answered the second question correctly, and 8 people answered both questions correctly. How many people are there in this class?

Analysis: Among the 13 people who answered the first question correctly, 8 people also answered the second question correctly, so these 8 people who answered the second question are counted again, so add up the number of people who answered the first question correctly and the number of people who answered the second question correctly, and then subtract these 8 people who got the duplicate number. Formula: 13+22-8=27 (people), so there are 27 people in this class.

Exercise 2: Four 8 cm long ropes are tied together to form a long rope. No matter how long the knot is, the knot length of each rope is 1 cm. How long is this long rope now?

Analysis: Two ropes have one knot, three ropes have two knots, so four ropes have three knots. One knot needs1+1= 2cm, then three knots need 2+2+2 = 6cm, and the total length of the rope is 8+8+8+8 = 32cm, minus the knotted 6cm, and 32-6=26. Now this long rope is 26 cm.

Age problem

-Winter vacation course for the second grade of primary school (4)

Summary: The age problem in the Olympic Mathematics is to compare the age of two people and the difference product quotient relationship to determine the age of a specific person. For example, my father is 30 years older than my son this year. Three years later, the father was four times older than his son. How old is my son this year? The age difference is the same, they are all 30 years old. Three years later, the father is four times as big as his son, which is a differential relationship. Then the age of the son is 30/(4- 1)= 10, and the father is 10*4=40. So this year, the son 10-3=7 years old and the father 40-3=37 years old.

This kind of problem should pay attention to two similarities: first, the age difference between two people is always the same; Second, two people increase or decrease at the same age. It is easy to find the answer by drawing a line segment.

Example 1: The sum of four people's ages is 77 years old, and the youngest 10 years old. The sum of the ages of the oldest and youngest people is seven years older than that of the other two. How old is the oldest person?

Example 2: On my father's 50th birthday, my brother said, "When I grow to my brother's present age, the sum of my brother and I will be equal to my father's then age." So how old is my brother this year?

Example 3: The average age of Party A, Party B and Party C is 42 years old. If Party A's age is increased by 7 years, Party B's age is doubled, and Party C's age is reduced by half, which is equal. How old is Party A?

Ex. 4: In a family, the total age of all members is now 73 years old. There are father, mother, daughter and son at home. My father is three years older than my mother, and my daughter is two years older than my son. Four years ago, the total age of all the people in the family was 58. How old is each member of the family now?

Exercise 1: 10 years ago, Wu Hao was seven times older than his son. 15 later, Wu Hao is twice as old as his son. How old are the father and son now?

Exercise 2: My grandfather is six times as old as Xiao Ming this year, five times as old as Xiao Ming in a few years, and four times as old as Xiao Ming in a few years. How old is grandpa this year?

The chicken and the rabbit are in the same cage.

-Winter vacation course for the second grade of primary school (5)

Summary: This is a typical Olympic math problem, which is simple and complicated (RMB, problem solving and other variations). Starting with simple problems, we can understand such problems in many ways. It can be used as graph method, list complete enumeration method, foot lifting method, hypothesis method, equation method and so on.

Example 1: There are rabbits and chickens in the cage. Count 36 legs, 1 1 head. How many rabbits and chickens do you ask?

Example 2: There are 100 chickens and rabbits. Rabbits have 40 more feet than chickens. How many chickens and rabbits are there?

Example 3: two models of 17 boxes put 99 yuan, each large box 12 yuan, each small box 5 yuan, which is just enough. How many pieces are there in each big box and small box?

Example 4: The math contest paper * * has 10 questions. Do a right question, 10, do a wrong question, 2 points. Xiaoming got 76 points in the final exam. Ask him how many questions he did right and how many questions he did wrong.

Exercise 1: A chicken has a two-legged head and a rabbit has a four-legged head. If the chickens and rabbits in a cage have 10 and 26 feet, do you know how many chickens and rabbits are in the cage?

Exercise 2: A bicycle has two wheels and a tricycle has three wheels. There are 10 bicycles and tricycles in the carport, with 26 wheels. How many bicycles and tricycles are there?

Exercise 3: Crickets have only six legs and spiders have eight. There are currently 10 crickets and spiders, and * * * has 68 legs. How many crickets and spiders are there?

Exercise 4: chickens and rabbits have 140 feet; If the number of chickens and rabbits are exchanged, the number of feet becomes 160 feet; How many chickens and rabbits are there?

Exercise 5: Xiaohua takes part in a math contest, and * * * has 10 questions. It is stipulated that the correct answer is given ten points, and the wrong answer is deducted five points. Xiaohua answered all ten questions and got 85 points. How many questions did Xiaohua answer correctly?

Exercise 6: Xiaoli has 100 coins in her piggy bank. She changed all twenty cents into five cents, and the total number of coins became 73. Then she changed a penny into an equivalent nickel, and the total number of coins became 33. So how much money is in her piggy bank?

Exercise 7: A math test paper with only 25 multiple-choice questions. Get 4 points for doing a right question, and deduct 1 point for doing a wrong question; If you don't do it, you won't score or deduct points. If Xiaoming got 78 points, how many questions did he get right, how many questions did he get wrong and how many questions did he not do?

Clock problem

-Winter vacation course for the second grade of primary school (6)

Summary: There are various clock problems in primary schools, but there is always one thing: first, find the position of the hour hand and the minute hand in the clock, that is, draw a picture for analysis; Second, pay attention to the fact that the hour hand and the minute hand are dynamic.

Example 1: Xiaohong sees in the mirror that the clock is 9 o'clock. What is the real time?

Analysis and solutions: First, look at the back of the paper; The second is to use 12: 00 to reduce the time seen by the mirror.

Example 2: A clock turns to 3600. How many degrees does the minute hand walk in one minute and the hour hand walk in one hour? What is the angle between the hour hand and the minute hand on the clock face at 2 o'clock? What's the temperature at half past two?

Is it okay? These are all for my teaching. What's more, add me if you want! !