I saw such a problem in the "two-color class for primary school students" this afternoon.

The bottom radius of the cone is 8 decimeters, and the ratio of height to bottom radius is 3: 2. What is the volume of this cone?

Analysis: This is a proportional application problem ... "

I figured it out on this issue without reading the analysis, huh? I haven't learned how to calculate the area of a cone. Then how can I solve this problem? I sighed, ready to continue to watch the analysis, and then I thought, will I be in the sixth grade soon after this summer vacation? If you can't even do the questions in this course. What kind of Olympics class am I? Is it not worthy of the name? Yes, I have to solve it myself.

As usual, I must build a model in my mind before this kind of problem, but I am very cautious about this problem for fear of making mistakes. I drew a perspective effect of a cone on the paper. Take a closer look, huh? Isn't this figure the same as a triangle if it is a plane figure? Isn't the cubic area of this cone 1 of the area of a cylinder with the same base and height? I am ecstatic. The original cone area is also easy to find. As long as you know the height and bottom area of the cone, can't you get it? Back to this question, its condition tells you the radius of the bottom, which is equivalent to telling the area of the bottom. It says that the ratio of height to bottom radius is 3: 2, which means that the length of bottom radius is two-thirds of height. Isn't that height just radius ×3÷2= height? Therefore, the height is 12 decimeter, the bottom area is 200.96 cubic decimeter, and the cone area is 200.96×12 ÷ 2 =1205.76 cubic decimeter.

"Wow, I finally solved it." I heaved a sigh of relief. Through this question, I also found that there are many things in mathematics, just like the area of a cone and the area of a triangle. In fact, you don't need to know all the calculation formulas, as long as you can understand them, you can also solve problems.

2. Five 500-word math stories and feelings

Gauss discovered the mathematical theorem at the age of eight: from one plus to one hundred and seven, Gauss entered St. Catherine's primary school. When I was about ten years old, my teacher had a difficult problem in arithmetic class: "Write down the integers from 1 to 100 and add them up! Whenever there is an exam, they have this habit: the first person who finishes it puts the slate face down on the teacher's desk, and the second person puts the slate on the first slate, thus falling one by one. Of course, this question is not difficult for people who have studied arithmetic progression, but these children are just beginning to learn arithmetic! The teacher thinks he can have a rest. But he was wrong, because in less than a few seconds, Gauss had put the slate on the lecture table and said, "Here's the answer! Other students added up the numbers one by one, sweating on their foreheads, but Gauss sat quietly, ignoring the contemptuous and suspicious eyes cast by the teacher. After the exam, the teacher checked the slate one by one. Most of them were wrong, so the students were whipped. Finally, Gauss's slate was turned over and there was only one number on it: 5050 (needless to say, this is the correct answer. The teacher was taken aback, and Gauss explained how he found the answer:1+100 =1,2+99 =10/,3+98 =/kloc-. A * * * has 50 pairs, and the sum is 10 1, so the answer is 50× 10 1=5050. It can be seen that Gauss found the symmetry of arithmetic progression, and then put the numbers together in pairs like the general arithmetic progression summation process. Hua is a native of Jintan County, Jiangsu Province, and was born on. He comes from a poor family and is determined to study hard. When I was in middle school, in a math class, the teacher gave the students a famous question: "There is a number, three places, and two;" 5 digits, 5 numbers, and the remaining 3; There are seven places in seven, and there are two left. What's the number of this? " While everyone was thinking, Hua stood up and said, "23". His answer surprised the teacher and won his praise. When I was a child, I studied hard. However, Hua was called to see that shop (the one that sells cotton). For an internationally famous China, a woman once went to buy cotton. Hua is solving a math problem. How much does the lady say it costs to pack cotton? However, diligent Hua didn't hear it, so she answered the calculated answer. The woman screamed, "Why is it so expensive?" At this time, Hua knew that someone was coming to buy cotton and said the price. The woman bought a bag of cotton and left. When Hua was about to sit down and continue to calculate, he found that the toilet paper that had just been calculated was taken away by the woman. This time, Hua was anxious to catch up desperately. A master Huang Bao met Professor Hua, a modern mathematician in China who enjoys a high reputation in the world. I let him take the bus (because they knew each other) and finally caught up with him. Hua said shyly, "Aunt, please … please give me back the toilet paper. The woman said angrily, "I paid the money, but it wasn't from you." Seeing that he was in a hurry, Hua said, "How about this! I paid for it. When Hua reached out for money, the woman seemed to be moved by the child. "！ He not only asked for money, but also returned the toilet paper to Hua. At this time, HuaCai slightly relieved, after returning home, he calculated again. ...

3. Mathematics Thesis Who can write me an article of about 500 words at the fifth grade level of primary school?

An Olympic math teacher once said: learning mathematics is like a fish like a net; Knowing how to solve a problem is like catching a fish and mastering the method to solve the problem, just like having a net; So the difference between "learning math well" and "learning math well" lies in whether you have a fish or a net. Mathematics, a thoughtful course, is very logical, so it always gives people the illusion. Geometry in mathematics is very interesting. Each number is interdependent, but it also has its own advantages. Such as a circle. The formula for calculating the area of a circle is S=∏r2. Because of different radii, we often make some mistakes. For example, "A pizza with a radius of 9 cm and a pizza with a radius of 6 cm are equal to a pizza with a radius of 15 cm". Proposition, this topic first confuses everyone and gives people an illusion. Using the formula of circular area skillfully makes people have a wrong balance. Actually, a pizza with a radius of 9 cm and a pizza with a radius of 6 cm are not equal to a pizza with a radius of 15 cm, because the area of a pizza with a radius of 9 cm and a pizza with a radius of 6 cm is S = ∏ R2 = 92 ∏+62 =1/kloc-0. I felt relaxed at first, but the higher I climbed, the steeper the peak became, which made people feel scared. At this time, only those who really like mathematics will have the courage to continue climbing. Therefore, people who stand at the peak of mathematics all like mathematics from the heart. Remember, people standing at the foot of the peak can't see the summit.

4. Tales of famous mathematicians (500 words)

When Lenin was eight years old, one day, his parents took Lenin to visit his aunt's house. Brothers and sisters there are very much looking forward to Lenin playing hide-and-seek with them at home. This time, Lenin was arrested, and everyone hid from Lenin. Lenin found a little friend. He hid behind the sofa. Lenin continued his search and found another one. He hid in the cupboard, which was still a little empty. Lenin searched and searched, and finally found him in a box. While they were having fun, one thing made them lose interest in playing, that is, I don't know who touched the vase underground. My aunt, who was cooking in the kitchen, came over and asked anxiously, "Are you all hurt?" They said, "We didn't hurt our aunt, but we hit a vase you love!" " "Nothing, my aunt said.

I want to ask who broke the vase. They all hung their heads and said, "Not me!" Lenin also lowered his head and said, "I didn't break the vase." Aunt said: "Pay attention to safety when playing in the future!" Partners and Lenin said, "We remember!" Lenin went home and lay in bed. His mother came up to him and asked him, "What's the matter, son?" Lenin told the story to his mother.

Mother said, "Then write a letter to your aunt!" " "Lenin wrote a letter, and a few days later, I wrote back to menstruation. The letter said: "Lenin, you are an honest boy! " "

5. Ask for 500 words in the fifth grade of mathematics thesis.

Mathematical paper

About "0"

0, can be said to be the earliest human contact number. Our ancestors only knew nothing and existence at first, and none of them was 0, so 0 isn't it? I remember the primary school teacher once said, "Any number minus itself is equal to 0, and 0 means there is no number." This statement is obviously incorrect. As we all know, 0 degrees Celsius on the thermometer indicates the freezing point of water (that is, the temperature of ice-water mixture at standard atmospheric pressure), where 0 is the distinguishing point between solid and liquid water. Moreover, in Chinese characters, 0 means more as zero, such as: 1) fragmentary; A small part. 2) The quantity is not enough for a certain unit ... At this point, we know that "no quantity is 0, but 0 not only means no quantity, but also means the difference between solid and liquid water, and so on."

"Any number divided by 0 is meaningless." This is a "conclusion" about 0 that teachers from primary school to middle school are still talking about. At that time, division (primary school) was to divide a copy into several parts and figure out how many there were in each part. A whole cannot be divided into 0 parts, which is "meaningless". Later, I learned that 0 in a/0 can represent a variable with zero as the limit (the absolute value of a variable is always smaller than an arbitrarily small positive number in the process of change) and should be equal to infinity (the absolute value of a variable is always larger than an arbitrarily large positive number in the process of change). From this, another theorem about 0 is obtained: "A variable whose limit is zero is called infinitesimal".

"Room 203 105 in 2003", although all of them are zeros, they are roughly similar in appearance; They have different meanings. 0 indicator vacancy of 105 and 2003 cannot be deleted. 0 in Room 203 separates "Building (2)" from "House Number". (3) "(that is, Room 8 on the second floor) can be deleted. 0 also means that ...

Einstein once said: "I always think it is absurd to explore the meaning and purpose of a person or all living things." I want to study all the numbers of "existence", so I'd better know the number of "non-existence" first, so as not to become what Einstein called "absurd". As a middle school student, my ability is limited after all, and my understanding of 0 is not thorough enough. In the future, I hope (including action) to find "my new continent" in the "ocean of knowledge".

6. The mathematical story about the circle, more than 500 words.

Xiao Ming asked: Why are wheels round? Xiao Qiang drew a circle with a compass and said, "We measured the distance from any point on the circumference to the center of the circle and found that they were all equal. This is called radius. Make the wheel into a circle, put the axle on the center of the circle, and the distance between the axle and the ground is always equal to the radius of the wheel, so that the wheel can roll smoothly on the ground. If the wheel is square or triangular, and the distance from the rim to the center of the circle is not equal, the car will vibrate up and down when walking. Therefore, the wheel is round. " After that, Xiao Ming understood. He said with deep feelings: "It seems that mathematics is indispensable everywhere!"

7. math diary, Grade Five, 3 articles of 500 words.

February 14 Saturday sunny.

Today is another sunny day. I was wandering in the street when I suddenly saw a lot of people gathered not far away. I ran for a year, and the result was a prize-winning game. "Hum, what's fun about winning the prize?" I was bored when the person next to me quickly said, "It's not fun to grab the prize, but there is a big prize that can attract people." I asked eagerly, "What is it!" "50 yuan money." The man with big eyes said. I'm very excited to hear that. "I have to try anything for such an attractive prize." Then I asked the shopkeeper how to grasp the rules. The shopkeeper said, "This is 24 Mahjong, and it says 12 5, 12 10. You can only catch 12 mahjong at a time. If the total number of 12 mahjong targets is 60, then you can win the 50 yuan Prize. " Without rolling up my sleeves, I took out 5 yuan money from my pocket and gave it to the shopkeeper.

Although I won 10 times, I still didn't win the grand prize.

When I got home, I thought about it and felt something was wrong. I think, to get 60 points, all 12 mahjong should be marked with 5. In the best case, the first 1 second catch 1 5, the second catch of two 5 s and the third catch of three 5 s will cost at least 6 yuan money. But what if the target number of mahjong is 10 or the sum of the two is the same, how many times will it cost?

Finally, after some consideration, I finally figured it out. I rushed to the street to look for an account, but I ran away without a trace.

Saturday, February 28th is fine.

When I read the newspaper today, I saw such a topic: Find the surface area of a cone.

[Title] A cone, the diameter of the bottom surface is 6 meters, and the length from the apex of the cone to any point on the circumference of the bottom surface is 5 meters. Find the surface area of this cone.

Although I have never learned to calculate the surface area of a cone, I have learned the surface area of a cylinder. By solving the surface area of cylinder, I know that the surface area of cylinder is equal to one side plus two bottom areas, while the surface area of cone is one lateral area plus one bottom area, and the side is a sector. Although I haven't studied it, I have checked the data and know that the area of a sector is: the area of a sector = arc length × circle radius × 1/2. The topic has told us that the length from the apex of the cone to any point on the circumference of the bottom surface is 5m, while the arc length is 3. 14×6= 18.84 (m), and the sector area is18.84× 5×1/2 = 47./kloc.

Mathematics is the gymnastics of thinking. As long as we study hard and think hard, we will certainly overcome the problems and embark on the road to success!

Tuesday, 2 March

Every time I go to Tomb-Sweeping Day, there will be a sea of people on the giant mountain, so some swindlers come up with some deceptive tricks, such as gambling on something on a plate.

Prop is very simple, draw a big circle on a board, and fix a rotatable pointer in the center of the big circle with a nail. The great circle is divided into 24 equal squares, and the needles in the squares can rotate. The box says 1-24 equal numbers, which are worthless in the odd box, but almost all even numbers are valuable.

The gameplay is also very simple. Set the pointer to 1 first, then you dial the pointer again, and the pointer will start to rotate and finally stop in a grid. Then press the number marked on the grid where the pointer is located and dial the pointer again. N- 1 grid, where n is the number marked on the grid.

This is just a little math game. In fact, no matter which box you dial, you can only lose money, not make money. Because when the pointer turns to an odd cell, the number of cells dialed is odd-1= even, and odd+even is only equal to odd, so it is impossible to turn to an even cell and nothing valuable can be obtained. If the pointer turns to an even grid and the number of grids dialed is even-1= odd, and odd+even = odd, then you won't get anything of value.

Friday May 12

Calculate wages

At noon, my father came back from work, humming a ditty, and happily stepped into the house. I greeted him and asked, "Dad, what's so happy today?" Dad said, "I got a raise this month." I asked, "How much salary do you get now?" Dad thought about it and smiled and said, "My salary is higher than * * *. Our monthly salary adds up to 2800, and the monthly salary difference is 100. How much do you think I get a month? "

After listening to my father's words, I began to draw line drawings on paper to help me understand:

Through observation and thinking, I quickly worked out the answer and told my father. First of all, mom's salary is as much as dad's, so mom and dad's monthly salary is (2800+ 100)=2900 yuan, and then the total monthly salary is divided into two parts, and 1 part is dad's monthly salary. The formula is: (2800+ 100)÷2= 1450 yuan.

Dad listened and nodded with satisfaction. At this time, my mother, who was cooking, said to me, "Do you have any other methods?" "Is there any other way?" I said in surprise. I stopped to observe and think curiously. I found that the key to this problem is to find out who is the standard. Different standards have different methods. So, I have a second method: taking mom's salary as the standard, assuming mom and dad's salary is the same, then the sum of their monthly salary is (2800- 100)=2700 yuan, and then divide the sum of monthly salary into two parts on average. 1 part is mom's monthly salary, and finally it is more than mom's 100. The formula is (2800-100) ÷ 2+100 =1450 yuan.

After listening to the second method I introduced, mom and dad both laughed. ...

It will be sunny on Wednesday March 24th.

The electric fan factory plans to produce 1600 electric fans within 20 days. After five days of production, due to the improvement of technology, the work efficiency has increased by 25%. How many days will it take to complete this task?

Analysis: This problem can be solved by direct proportion method through transformation. If the original efficiency is "1", then the actual efficiency is (1+25%)=5/4, and the ratio of actual efficiency to original efficiency is 5/4: 1 = 5: 4, because efficiency is inversely proportional to time.

It will take x days to complete this plan.

4∶5 = X∶20-5

5X=4× 15

X= 12

A: It takes 12 days to complete the plan.

Saturday, March 27th is fine.

I was bored today, so I took out a math newspaper, and suddenly a very special topic attracted me.

[Title] There is a rectangular iron sheet, which can be made into a cylinder by cutting off the shadow in the picture. The radius of the bottom of this cylinder is 2 decimeters, so what is the area of the original rectangular iron sheet?

[Analysis and Problem Solving] Look carefully at the right. The width of the shadow rectangle can't be the circumference of the bottom of the cylinder, so the circumference of the bottom of the cylinder is the length of the shadow rectangle. In addition, we can also find the width of the rectangular iron sheet, that is, the height of the cylinder is twice the diameter of the cylinder bottom, and the diameter of the cylinder bottom+the perimeter of the cylinder bottom is equal to the length of the rectangular iron sheet. Therefore, the length of rectangular iron sheet is 2× 2+2× 3.14× 2 =16.56 (decimeter) and the width is 2×2×2=8 (decimeter). The area of the original rectangular iron sheet is 16.56×8= 132.48 (decimeter).

Saturday, March 27th is fine.

Think about the problem in combination with reality.

Think about it, where is he wrong?

[Title] There are two cylindrical wooden columns in a hall. The diameter of the bottom of the wooden column is 0.6m, and the height of the column is 6m. If you want to paint their surface, how many square meters is the painted part?

After reading this question, Xiao Qiang felt very simple. He quickly listed the formula and worked out how many square meters the paint area was.

3.14× (0.6÷ 2 )× (0.6÷ 2)+3.14× 0.6× 6× 2 = 23.7384 (square meter). A careful analysis of the meaning of the problem reveals that Xiao Qiang's idea is completely wrong, and the reason for the mistake is that he didn't think about the problem in combination with reality. Although the wooden column is cylindrical, as far as practical problems are concerned, the painted part does not include the upper bottom surface and the lower bottom surface. Therefore, it is necessary to draw part of the area to find the side area of these two cylindrical wooden columns. The formula should be: 3. 14×0.6×6×2=22.608 (square meter). A: The area of the painted part is 22.608 square meters. Give you a few more articles for your reference.

8. 500-word interesting math story in grade five

During the war of liberation, after two scouts of our army obtained important information, the large troops set out long ago. In order to send the information to the army leaders in time, they must cut corners and head on.

The shortcut is a vast desert without people. According to the local people, it takes 10 days to cross the desert, but according to the climatic characteristics and human load of the desert, only 8 Jin of food and 8 Jin of water can be brought every day at most, and each person should consume at least 1 kg of food and 1 kg of water every day. In this way, the last two days will be buried in the desert because they can't get food and water supplement.

Although migrant workers can be found in the local area, each migrant worker can only bring 8 Jin of grain and 8 Jin of water, which is not enough for his own consumption.

What are we doing? I'm so anxious that two scouts scratch their heads.

The two men pondered over the solution.

"Yes, you can!" Suddenly a team member came up with a wonderful method. A total of two people is really feasible.

So the two men successfully passed through the desert and successfully completed the task.

What did they think of?