Unfortunately, I met a math exam just a few days after I entered the class. Because I can't do many things, and the math exam is in the first phase, my mother simply asked me to make up lessons at home and go to class in the second phase of Chinese. A few days later, the math teacher Liu called me into the office and told me about avoiding the exam. Although I don't remember the details she said, it probably means that although I studied a lot less than other students and missed a lot of classes, I couldn't escape the exam! If you take the exam, you may find some knowledge you don't know yet, and then make up for it in a targeted way. I nodded in shame and said that I would never do it again. Later, Mr. Liu called my father and told him about it.
Since then, I have studied harder than before, because I think the teacher is paying attention to me. At home, I do some related exercises besides finishing school homework every day. At school, teachers and classmates also extended a helping hand to me. When I do my homework, if I can't do any questions, the classmates next to me will immediately come around and teach me; Teacher Liu often makes up what I haven't learned before and what I don't understand recently after school.
The trust and help of my classmates and teachers make me work hard and make progress. In class, I try to remember every point the teacher said; When doing my homework, I read the questions carefully and never let go of any conditions; After finishing my homework, I also checked it carefully to see if I could find any mistakes. Slowly, my grades have risen, which is really what my teachers and classmates helped me achieve!
However, I also found some problems in my math study. These problems won't happen because I haven't learned or understood them. For example, when I use proportion to solve problems, I either confuse the former with the latter, or list a meaningless formula; In the equation, if there is an unknown x on both sides of the equation, then sometimes I may not be able to solve it; My calculation ability sometimes becomes a big problem, and sometimes even the formulas of addition and subtraction are not correct; Also, sometimes I do problems carelessly, either I can't see the difference between units or I read the decimal point wrong ... There are still many problems in my math! I have to continue to study hard.
How time flies! I will leave my alma mater and enter junior high school in one month. Recently, our study has become tense. After coming back, I found many problems of my own, and of course I corrected many problems. Recently, a new problem has been discovered, that is, when calculating the surface area of a cylinder, the bottom surface is always calculated too much. I think this is because I always make a comprehensive formula, and it is too complicated to do a few more calculations. Another problem is that the calculation cannot be kept correct.
The graduation exam is coming soon. I think before the exam, I will review better than before, continue to work hard to correct my existing problems, and draw a satisfactory full stop for my three-year life in this primary school. Before graduation, I want to sincerely thank Mr. Liu for his efforts and help. After graduation, I will greet my dear teacher Liu and my lovely classmates with continuous progress.
Erligou Central Primary School Class 1, Grade 6
Helena. Helena
During my six years in primary school, I studied many subjects, such as Chinese, math, English, nature, music … but my favorite subject is math.
Starting from the next semester of Grade Five, the new math teacher in our class, Mr. Liu, led some outstanding students in our class and Class Two to set up math groups in each class.
After the teacher's selection, the math group in our class was finally established. Under the leadership of the group leader, Pei Qi, Zhu Zhengyi, Chi, Wei of our class studied and discussed together.
From the first week of the activity, all team members began to actively participate in the activity. Every week, a team member gives a test question and sends it to each team member as a weekend assignment on Friday. And in the second week, the students who gave the questions put away the papers made by all the students and corrected them. At the same time, at noon on Friday, he will comment on the test paper. This cycle, our math group has been active for half a year.
After a summer vacation, we plunged into intense study again. This semester, our study task is very heavy, because we are about to graduate and step into the middle school gate. Because the members of the math team are the top students in the class, every member wants to be admitted to a key middle school. But in most key middle schools, mathematics is always the main exam, so we must do more math problems. Under the leadership of the group leader Chen Junfeng, we also studied and discussed with the math group in Class Two. From then on, every weekend, our class and Class Two began to give questions in turn. Every test paper in the future is quite difficult, and it is difficult to make it without careful thinking and experiment. All the team members are interested in the math group, because we can learn a lot of knowledge and do a lot of exercises here to improve our math level. Therefore, every time I actively participate in activities, I certify the completion of the weekly paper. In this way, our math group has been active for another half year.
After the end of this semester, we will have a month's holiday. In the past, every holiday's math homework was to do the questions in the math book again. However, this holiday, Mr. Liu thought it was too easy for students in our math group to do the problems in the book, so he assigned a special assignment to my math group-B-level homework for math winter vacation. This set of homework is the problem set of Tsinghua Tongfang Cup and the sample problem of the middle school affiliated to Capital Normal University ... During the winter vacation, all the team members completed this homework seriously.
After returning to school, we will discuss the B-level homework of math winter vacation. If everyone's answers to some questions are consistent, we will pass from generation to generation; If the answers to some questions are controversial, we will have a heated discussion until we get a correct result.
In the six years of primary school life, I learned a lot of knowledge and did a lot of problems in the activities of the math group, which laid a good foundation for my future study. I will study harder in the future, strive for a place in the math competition, and reward my teachers, parents and math team. ...
Erligou Central Primary School Class 1, Grade 6
Jiang jintong
In the math class that day, Teacher Liu said, "The class is wonderful because of mistakes." -short and meaningful.
In the first half of the sixth grade, we learned to solve application problems in proportion. Through the study of several examples in the book, we come to the conclusion that direct scale images all rise or fall linearly. Just as we were about to solve the next problem, Fan asked this question: Why can't it be a broken line that fluctuates up and down, but a straight line? The next time, we spent in answering her puzzles. After arguing for a while, I was a little confused. I found that other students were also slightly confused. The teacher asked Fan to draw a picture on the blackboard, and then we understood what she meant: if the data on the axis are not arranged in order, the image will not rise or fall in a straight line. It turns out that Fan ignores the characteristics of the number axis.
Doesn't this matter verify that sentence? Because of her mistakes in class, the whole class has a deeper understanding of the number axis and positive proportion; Therefore, it also made me realize that mistakes are not terrible. The important thing is to bring it up and let everyone solve it together. From this, I understand that when answering questions, don't hesitate for fear of making mistakes-the class will be wonderful because of mistakes.
Erligou Central Primary School Class 2, Grade 6
plum
In this long journey of life, failures and mistakes are indispensable. The ancients said, "Failure is the mother of success". My personal interpretation of this sentence is to correct the shortcomings after having failed experience. After correcting again and again, you succeeded. In our class, there is one thing that makes all our classmates more prepared for mistakes.
That morning, the second class was math. Teacher Liu reviewed the knowledge of cylindrical cones for us to meet the first unit test.
"Bell ... bell" was accompanied by the bell, and we entered the classroom one after another. It seems that Miss Liu has been waiting for us in the class for a long time. As soon as we sat down, we went straight to the point and began to review the knowledge of cylindrical cones. "Please turn to page 10. Example 6: Wangcun made 100 uncovered iron drums for farmers to carry water. How much tin do you need at least? Who will solve this problem? " Teacher Liu interacts with her classmates by asking questions. One of them quickly raised her hand, but she was Fan Anlin. She didn't like talking in class. Not only I was surprised, but also the teachers and other students seemed to be taken aback. "3. 14 times the diameter, then multiply by the sum of height and radius, and finally multiply by 100." She whipped out a simple formula. "finished?" Teacher Liu asked. Fan nodded and agreed, but it seemed a bit strange. She sat down, Zhou Xiao, Zhang Yuchen and others raised their hands again. The teacher shouted, "Zhou Xiao." "Don't directly calculate the surface area, you must reduce the bottom area." Zhou Xiao corrected it. "ouch!" Fan Anlin covered her mouth and spit out her tongue shyly. Teacher Liu also smiled and said, "Her mistake just reminded everyone that we should carefully examine the questions in the future."
Recognize the facts
Erligou Central Primary School Liu (2)
The math problem in school is not difficult. You can do all the questions, but there are not many times to get full marks. You either didn't see the division and combination clearly, or forgot to write the name of the unit, or you made a mistake, so one or two points will always be deducted. Ask my classmates, many people are in the same boat with me-I was careless when I answered the questions, and I regretted it after I handed them out. In the final analysis, the problem is-not serious!
Calculations and exams are a tough nut to crack, so the teacher has made great efforts. For example, in order for us to find the unit "1" when doing the percentage problem, the teacher racked his brains to come up with a good method: first, judge whether "1" is known or indirect, if it is known, use multiplication, if it is unknown, use division or equation, try word for word, and mark the places that are easy to make mistakes. This method has been implemented for several days, which has greatly improved the examination of questions. However, the good times did not last long. Because it was too much trouble, I delayed the time. In a few days, I began to make old mistakes again and again. No matter what the teacher told me, many students still stumbled. Because there are few mistakes in the exam after all, everyone always takes chances and always wants to finish it quickly and not to fall behind. "Slow work makes fine work", as soon as the speed is fast, mistakes will follow. In fact, there is plenty of time for the exam, so you can do it seriously. Even in normal times, grades are not very important, but at least be serious. Our teachers all circle the questions, not to mention us. Teachers often say, "Being earnest can make up for many shortcomings in us." It's really true. Maybe some students who didn't study very well gave themselves more chances to succeed because they were serious, and lost a lot of points, while those of us who are "smart-aleck" sentenced ourselves to death while doing problems.
Success belongs to those who are prepared. In order to meet success, let's start by doing math problems, and from now on, learn to be a man and be a serious person!
Experience of joining a math group
Wei Weibo, Class 1, Grade 6, Erligou Central Primary School
In the fifth grade, our math teacher organized a math group. Up to now, our math group has a whole year's history. The members of our math group are: Chen Junfeng, Wang Siyu, Zhu Zhengyi, Zhu Ziqi, Zhang Tiancheng, Li Mengya and me. Every week, a person will give a question in the group. Let's do it. So, on Friday, we will comment collectively. Through such a math group, I learned a lot:
1, because the five questions given each week are of different types, some will, some will not, some have studied, and some have not. What I have learned can help me to consolidate my previous instructions. If you haven't learned it, take it out and learn it.
If I want to do a problem by myself, I may only come up with one or two methods at most, while seven people in our math group will do it together, and there will be at least seven methods. So the math group has cultivated my spirit of finding problem-solving skills in various ways.
3. Because our math group has a discussion once a week, everyone will say that my oral expression ability is not good, so I call this opportunity. I not only finished the problem carefully, but also figured out how to explain it to them. In this way, I have exercised my oral expression ability.
4. Let me know the gap between myself and some good classmates through the explanations of good classmates in the math group, thus giving me the motivation to study hard and try to catch up with them.
This math group has given me so many valuable things, isn't it?
happy
The number 1+ 1=2.
interest
Cui Xinzi, Class 1, Grade 6, Erligou Central Primary School
Mathematics is my favorite subject, but before the fourth grade, I was not interested in it. Later, the teachers and classmates around me made me interested in it!
I was not very good at math, but my grades almost soared in the fifth grade! Of course, besides your own efforts, it is also important to have a good teacher. She is the female teacher who has taken over our class since the fifth grade-Miss Liu. She won't tell us the problems in the book unnecessarily in class, but link the problems with the content of life and arouse the enthusiasm of students. We listen carefully! The grades have naturally improved!
There is a person who has made greater progress than us, and even I admire him a little!
This is Wang Jiaxi. She sits on my left. She transferred to America in the second grade and came back in the fifth grade. Education there is much simpler than ours. In the United States, her study has always been top-notch, but her grades have been much worse since she came back, but she has never given up and has become a good example for me. Sometimes I encounter a difficult math problem and don't know how to think seriously. I just "patronize" other people's answers, and when I saw her, she was frowning and thinking hard. Although there is an eye-catching red dot next to the topic after it was handed down, it is actually much more glorious than the fake hook on my paper. Sometimes when I encounter a multi-digit calculation problem, I don't work hard on the draft book, but secretly take out a calculator that Teacher Liu won't let me use. But when I looked at Wang Jiaxi, when she was also troubled by this problem, she was trying to draft a book. At this moment, I seem to feel that there are tens of millions of needles on that small calculator, which makes me put it back in my schoolbag. Faced with the wrong question, I just said, "lend me your math exercise book!" " "She changed the question back, but she asked me modestly. However, sometimes I didn't make it clear, and she didn't stop there and continued to ask other students. She always makes every question clear. And I ... maybe you will think that I study much better than her when you look at our grades, but my serious attitude is far from her ... really, I really learned a lot from her. I no longer copy homework that my classmates can't do, but think as hard as her. I don't use that prick the hand calculator anymore. I gave it to my aunt, who is an accountant. I want to calculate those complicated figures carefully in the draft of Rainbow's Family Jubilee. In the face of doing something wrong, I will think seriously first like her, and never say "lend me your math exercise book" again. Instead, I will learn from her and say modestly, "May I ask you this question?" ……
Not only her, but also Li Jia, Li Ao and Zhu Zhengyi. These classmates around me have inspired me a lot. Their love for learning and mathematics awakened me who was not interested in mathematics. Now, I not only love learning, but also love math, and even regard it as an indispensable good partner in my life. I always find some extracurricular math exercises to do, and they always accompany me, just like my twin sister! When it comes to math, I no longer have a headache. Now, doing math problems is no longer a torment, but like a game, like life, it will accompany me through my childhood growth and life ...
6 graduates from Class 06, Erligou Central Primary School, Haidian District. ( 1)
Li Mengya
I have to do the problem again, and I need a troublesome cylindrical area. Alas, it is not easy to find the surface area. We need to find the bottom area and the side area, and then add them up. If we are not careful, we will make mistakes. Is there any good way to put it all together? I was thinking. Look at the bottom area and lateral area's formula!
S-bottom =πr2, which has two bottoms, namely 2πr2. Let's look at lateral area's formula: S-side =2πrh, add them together, extract the similar term: 2πr, and form a new formula: S-table =2πr(r+h) by using the law of multiplicative association. A new formula was born. With this formula, just multiply it once and everything will be fine!
I used a formula to find the area of a ring: s ring =π(R2-r2). Come to think of it, this is actually a combination of formulas! Subtract two circles, extract π and * * *, and get a new formula.
The birth of these new formulas is attributed to flexibility and laziness! If it was not too much trouble, there would be no such formula. In fact, it is also important to use the formula flexibly. Sometimes, the questioner steals a lazy person and misses a condition, so we can ask for more. However, we need to be lazy in some places, and we can't be lazy.
There is a problem: there is an inscribed circle in a big square, and the area of the big square is 20 square centimeters. Find the area of a circle.
According to common sense, we should first find the side length of a big square, which is D, then R, and finally the area. However, in this problem, how can we find R&D? Unless a prescription is prescribed, it will be troublesome and will certainly be inexhaustible. What should I do? At this time, it is necessary to use the formula flexibly. Since the area formula of a circle is πr2, it is ok to find r2 instead of R! At this time, we can regard it as a whole a, that is, we only need to find aπ. How to ask? The area of a square should be (2r)2, which is 4r2 after simplification, that is, 4a. So we can use 20÷4=5(cm2) to find a, and then use 5×π≈ 15.7(cm2). The area of the circle is about 15.7cm2, so the area of the circle aπ can be solved without roots.
Many formulas can be combined with each other to form a simple and practical new formula.
As long as we innovate, we are actually kneading the steamed bread eaten by the giants into a ball and making new rolls. Is this not good?
Erligou Central Primary School Class 2, Grade 6
Li hengsha
Mathematics is difficult to learn because we are often confused by the complicated problem-solving process. Especially when you meet the wrong answer in the book, you will be miserable! It would be better if you accepted it without doubt. If you doubt this answer, it will make you eat badly, sleep badly, and your head swell as big as basketball. This happened to me in the fifth grade.
That's what I did when I was studying in the Olympic Mathematics training class. One day when I was solving a problem, I was stumped by a question: 0.99...× 10 =? Let me see, cyclic decimal multiplication! It's too difficult. Let's read the notes. To my surprise, the note actually said: Because 1-0.99 … = 0.00 … = 0, so 0.99 … = 1. What the hell is going on here? I'm confused. On second thought, this seems to be the right way, but look at 0.99 ... and 1. They really don't look alike. How can values be equal? That night, I stared at the ceiling and couldn't sleep. There are always two numbers floating in front of me: 0.99 ... and 1. I didn't fall asleep until midnight.
The next day, I brought this strange phenomenon to the classroom and invited Zhang Yuchen, a math expert in our class, to discuss the answer to this question. This time, even the best Zhang Yuchen was at a loss, only to see him with his chin in his hand, frowning and helpless.
Is there no other proof except subtraction? "Yes!" Zhang Ruoxi said, "0.33 ... =1/3,1/3x3 = 3/3 =1= 0.33x3 = 0.99, 0.99 ... =1".But Teacher Liu is not so. If 0.99... 1, the difference between them must be 0.00... 1, but this number does not exist at all, and there is no result in the end.
Since we couldn't discuss it, we searched the Internet and clicked the mouse, and the result was: 0.99...≠ 1. Their values are different, and no one can tell the difference, because both numbers are irrational. It turns out that the answer in the book is wrong.
Through this problem solving, I learned to discuss, understand irrational numbers and how to deal with mistakes in books. I think, when you find the answer is unreasonable, don't be superstitious about books, otherwise you may never find the right answer. Also, any difficult math problem, as long as you think hard and are not ashamed to ask questions, will always find the correct answer.
The fruit you grow tastes sweet. In fact, mathematics is quite interesting, especially when you get the correct answer through hard work. I will explore and discover in the castle of mathematics in the future, and constantly experience the happiness brought by success.
Failure and mistakes are the foundation of success.
Li er Li Gou central primary school class 2, grade 6
In this long journey of life, failures and mistakes are indispensable, and success can only be achieved through repeated failures.
The ancients said, "Failure is the mother of success". My personal interpretation of this sentence is that after you fail, you should correct your shortcomings. After correcting it again and again, you are the son of failure-success.
There are many examples to show that failure will not make people unsuccessful forever. You must have a strong will and overcome all kinds of difficulties to succeed. For example, during Sun Yat-sen's uprising, after numerous failures, the Republic of China was established and the Qing Dynasty was overthrown.
Of course, mistakes don't necessarily make people bid farewell to success. For example, during the Spring and Autumn Period and the Warring States Period, the King of Qin was in urgent need of talents in order to win state affairs. At that time, a famous philosopher named Han Fei was persuaded by Li Si, the minister, and Han Fei voted for Qin. But the king of Qin did not value him. Instead, he advised the king of Qin and captured Zhao. And Reese is a villain, jealous of Han Fei, and forced Han Fei to death with poisoned wine. The King of Qin knew that he was wrong, and he used villains, so he finally unified China with Han Fei's thoughts in 22 1 BC.
In either case, it is proved that failure and mistakes are the foundation of success.
In our class, there is one thing that makes all our classmates more prepared for mistakes.
That morning, the second class was math. Teacher Liu reviewed the knowledge of cylindrical cones for us to meet the first unit test.
"Bell ... bell" was accompanied by the bell, and we entered the classroom one after another. It seems that Miss Liu has been waiting for us in the class for a long time.
As soon as we sat down, we went straight to the point and began to review the knowledge of cylindrical cones.
"Please turn to page 10. Example 6: Wangcun made 100 uncovered iron drums for farmers to carry water. How much tin do you need at least? Who will solve this problem? " Teacher Liu interacts with her classmates by asking questions.
One of them lifted it up quickly, but she was Fan Anlin, and she didn't like to talk much in class. Not only I was surprised, but also the teachers and other students seemed to be taken aback.
"3. 14 times the diameter, then multiply by the sum of height and radius, and finally multiply by 100." She whipped out a simple formula.
"finished?" Teacher Liu's question
Fan nodded and agreed, but it seemed a bit strange.
She sat down, Zhou Xiao, Zhang Yuchen and others raised their hands again. The teacher shouted, "Zhou Xiao."
"Don't directly calculate the surface area, you must reduce the bottom area." Zhou Xiao corrected it.
"ouch!" Fan Anlin covered her mouth as if she knew the mistake.
Teacher Liu also smiled and said, "Her mistake just reminded everyone. Don't make any mistakes in the future. "
After class, Teacher Liu also said, "The class is wonderful because of mistakes." This sentence seems to contain a great moral.
Life is to have failures and mistakes to add color. Edison said, "Failure is what I need, and it is as valuable to me as success." Kepler said, "Failure is the beginning of a new brilliant fantasy." Dostoevsky said, "If you don't make ten mistakes, you won't get a truth." Hugo also said: "Every step of failure is a step closer to success." ……
Whether it's famous sayings or aphorisms, I always believe that failure and mistakes are the foundation of success.
Skillful mastery and flexible application in mathematics learning.
Erligou Central Primary School Class 2, Grade 6
If the difference between a number and b number is equal to b number, then b number must be a number. On the surface, this is a very simple question, and the answer is 1/2 or 50%, but Zhang Yuchen's answer is different from most people's answer. He thinks that B must be the divisor of A. At first glance, some people may think that this answer is right, and I almost walked into it. When the teacher asked me what this topic had to do, I couldn't remember the names of such topics. It took me a while to answer the teacher's question-the answer was "divisible". After that, Teacher Liu gave us a Chinese fill-in-the-blank question: How to master and apply mathematical knowledge? I soon thought of mastering it skillfully and using it flexibly, and my classmates agreed with this answer. But think about it, have we really achieved these two points? No, we didn't. Just like Zhang Yuchen's mistake today and the time I spent answering questions and thinking, we can see that none of us mastered it skillfully. This sentence is the method and goal of my future study. I must "master it skillfully and use it flexibly."
There are no real problems in the world:
I remember that it was a very funny thing, and I still remember it in retrospect.
In the third grade, Mr. Chen gave us a very simple question: 20 apples, ate 4, how many are left? I quickly worked out the answer in my notebook: 16. But after a while, I didn't see the teacher continue to lecture, so I wondered: Is there any "ambush" on this question? Let's have a look. I snapped my fingers and counted loudly: "I ate seventeen ... ah!" Sure enough, there is an ambush, and there are seventeen left! " I was as happy as if I had discovered a new continent and told this "secret" to Zhang Yuchen.
He also agreed with me and unified the "front". When the teacher began to lecture and asked everyone what the answer was, two voices of seventeen broke the harmony of sixteen, and everyone stared at me and Zhang Yuchen in amazement. After a "war of words", we were finally persuaded. We just found out that this question is so simple.
Although I was wrong that time, I learned not to think of simple problems as complicated. Before seeing every math problem, don't think it is complicated and cause psychological pressure. Secondly, I want to have a good attitude: in fact, there are no problems in the world, only what we can do now and what we won't do for the time being, and the problems we do will be solved as long as we are willing to use our brains.
……
In mathematics learning, there are many interesting or educational things. If we think about it carefully, these things will definitely tell us some learning methods, or let us understand the truth.
A class is wonderful because of mistakes.