The title is the general title of the paper and the epitome of the basic content of the article. The ancients said, "It is the epigram of the whole article." Therefore, the title should be short, clear, concise and eye-catching, not too long, nor too general and confusing; It is necessary to prevent the article from being irrelevant, and to prevent the article from being irrelevant, and to avoid pursuing novelty, vagueness and no actual content.
Generally, it includes the significance, contents and methods, achievements or values of this study, so that readers can quickly understand the general situation of the full text. Therefore, the abstract should be concise, fascinating, comprehensive, focused and independent.
Preface, also known as introduction or introduction, generally includes the background or starting point of this study, the problems to be studied, the methods and means of the study, and the significance or value of the study. It should be noted that the significance or value of research should be realistic and should not be exaggerated, belittled or overly modest.
The main body of the paper, as a part of expressing the author's personal research results, occupies a large space, and sometimes it must be supplemented by necessary subtitles. We should strive for clear concepts, clear arguments, rigorous arguments, sufficient arguments, scientific accuracy, innovation, clear organization and concise writing.
The conclusion is to synthesize the problems analyzed and demonstrated in this paper and summarize the basic viewpoints, which is the answer to the questions. Conclusion, as the logical development of theoretical analysis and experiment, is the generalization and sublimation from local to general, from concrete facts and experiences to theoretical generalization, and it is the destination of the whole paper. Therefore, we should try our best to be complete, accurate and distinctive, and also point out the scope and significance of application of this theory, as well as the unsolved problems in this paper and the direction of further research.
References are the basis to reflect the author's serious scientific attitude and research work, including books (author's name, title, edition, number of pages, publishing house and publication year) or periodicals (author's name, title, publication name, volume or period, number of pages and year) referred to in this paper. 2. The first step in the writing process of primary school mathematics papers is to select topics and materials. What content of an article you want to write, whether it is theoretical discussion, teaching materials, teaching methods and skills, and summary of teaching experience, you must know the depth and breadth of the problem and have a clear purpose and subjectivity.
No matter which content and specific theme you choose, you should strive for advancement, pertinence and practicality. To do this, first of all, you should consult as much information as possible according to the method of literature retrieval and master the latest research trends at home and abroad. Secondly, in-depth study of these documents to see if we can get further inspiration and have new insights. Although the topics may be repeated and there are many similar topics, we can also write some new ideas according to different objects and different examples from different sides, so as to make the viewpoints clearer, the methods more effective, and more advanced, targeted and practical. Third, the topic selection should proceed from reality, and the size of the topic and the depth and breadth of the subject matter should be appropriate. The second step is to sketch and write. After choosing a topic, you should pay attention to writing an outline, which is the basis of writing a good article. First of all, we should lay out the content and structure, draw up a writing outline, and prepare to divide it into several parts, each of which revolves around several issues. The relationship between these parts and the problem needs to be further carefully designed to make its structure clear, scientific and reasonable. Secondly, we should pay attention to the characteristics of various articles. To write a theoretical article, it is best to determine the size of the title again, so as to make the argument clear and credible and easy for others to learn from; When writing teaching material analysis's articles, we should compare them and put forward suggestions for improvement or problems worthy of further study. The third step is to revise the final version. Revision is a process after the completion of the first draft of the article, including the revision of the text of the paper and scientific scrutiny. After the first draft of the paper is formed, you should read it repeatedly from beginning to end and scrutinize it sentence by sentence to check whether the arguments in the paper are clear, sufficient, reasonable, rigorous and correct. A good primary school mathematics composition should be full of articles. That is to say, there must be good mathematical content and good written expression.
Therefore, writing efforts are very important for mathematics papers. In the math paper, you should be concise and use less floating words, so as not to dilute the center of the article. Words should be easy to understand, concise and to the point, words should be accurate and concise, expression should be complete, especially the central content must be explained thoroughly. In addition, the writing should be standardized, and the title number, drawing number and punctuation should be correct. Revision is a meticulous work. Only by repeatedly scrutinizing and revising the manuscript can we eliminate undue mistakes. Only after repeated revision and processing, the quality of the article will continue to improve.
I once heard an Olympic math teacher say: learning math 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 half diameter 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. In fact, 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. The area of a pizza with a radius of 15cm is S=∏r2= 152 ∏=225∏, so a pizza with a radius of 9cm and 6cm is not equal to a pizza with a radius of 15cm.
Mathematics is like a mountain peak, soaring into the sky. 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.
The world is full of wonders, and there are many interesting things in our mathematics kingdom. For example, in my ninth exercise book, there is a thinking question that reads: "A bus goes from Dongcheng to Xicheng at a speed of 45 kilometers per hour and stops after 2.5 hours. At this time, it is just 18 km away from the center of the east and west cities. How many kilometers is it between East and West? When Wang Xing and Xiaoying solve the above problems, their calculation methods and results are different. Wang Xing's mileage is less than Xiao Ying's, but xu teacher said that both of them were right. Why is this? Have you figured it out? You can also calculate the calculation results of both of them. " In fact, we can quickly work out a method for this problem, which is 45 × 2.5 = 1 12.5 (km),112.5+18 =130.5 (km).
In fact, we have neglected a very important condition here, that is, the word "Li" mentioned in the condition is "just 18 km from the center of the east and west cities", and it does not say whether it has not yet reached the midpoint or exceeded the midpoint. If the distance from the midpoint is less than 18km, the formula is the previous one; If it is greater than 18km, the formula should be 45× 2.5 = 1 12.5 (km), 1 12.5-65448. Therefore, the correct answer should be: 45× 2.5 =112.5 (km)12.5+18 =130.5, (km)/kloc-0. (km) 45× 2.5 = 1 12.5 and (km),112.5-18 = 94.5 (km) 94.5× 2 =/kloc-0. Two answers, that is to say, Wang Xing's answer and Xiaoying's answer are comprehensive.
In daily study, there are often many math problems with multiple solutions, which are easily overlooked in practice or examination. This requires us to carefully examine the problem, awaken our own life experience, scrutinize it carefully, and fully and correctly understand the meaning of the problem. Otherwise, it is easy to ignore other answers and make a mistake of generalizing. About "0" 0, it can be said that it is the earliest number that human beings have come into contact with. 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. The division of time (in primary school) is to divide a copy into several parts and find out how many there are in each part. A whole cannot be divided into 0 parts, "nothing is meaningful". 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 much 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". On the tiled floor or wall, adjacent floor tiles or tiles are evenly attached together, and there is no gap on the whole floor or wall.
For example, a triangle. A triangle is a plane figure composed of three line segments that are not on the same line. Through experiments and research, we know that the sum of the inner angles of a triangle is 180 degrees, and the sum of the outer angles is 360 degrees. The ground can be covered by six regular triangles. Look at the regular quadrangle, which can be divided into two triangles. The sum of internal angles is 360 degrees, the degree of an internal angle is 90 degrees, and the sum of external angles is 360 degrees. The ground can cover four regular quadrangles. What about regular pentagons? It can be divided into three triangles, the sum of internal angles is 540 degrees, the degree of one internal angle is 108 degrees, and the sum of external angles is 360 degrees. It cannot cover the ground. Hexagon can be divided into four triangles, the sum of internal angles is 720 degrees, the degree of one internal angle is 120 degrees, and the sum of external angles is 360 degrees. The ground can cover three regular quadrangles. A heptagon can be divided into five triangles. The sum of internal angles is 900 degrees, the degree of internal angles is 900/7 degrees, and the sum of external angles is 360 degrees. It cannot cover the ground. From this, we come to the conclusion. N- polygon can be divided into (n-2) triangles, the sum of internal angles is (n-2)* 180 degrees, the degree of one internal angle is (n-2)* 180÷2 degrees, and the sum of external angles is 360 degrees. If (n-2)* 180÷2 can be divisible by 360, then it can be used to pave the way; If not, it can't be used to pave the road. We can not only cover the ground with a regular polygon, but also cover the ground with two or three graphic combinations. For example: regular triangle and square, regular triangle and hexagon, square and octagon, regular pentagon and octagon, regular triangle and square and hexagon ... In real life, we have seen various patterns composed of regular polygons. In fact, many patterns are often composed of irregular basic graphics.
During the "Eleventh" period, many shopping malls are offering discounts. Taking this good opportunity, I went to the "Lin Wan" market with my parents. On the second floor, we took a fancy to a suit, and its price tag was 520 yuan. The salesman said, "It's just eleven now. Over 200, you can choose to get a 20% discount or return to 160. Both are similar. " Is it really similar? I have such a problem in my mind. If you choose a 20% discount, you need 520× 0.8 = 4 16.
(yuan). And if it exceeds 200, it will return to 160? We have to pay 520 yuan first, and then we will get a coupon of 160× 2 = 320 (yuan), so we actually spent 520-320=200 (yuan). Compared with 200,416, the second one is of course better. But after getting the coupon? If you buy something from 320 yuan again, you can return it to 160 yuan, and the rebate of this 160 yuan is only 200- 160 = 40 yuan. If you fill in this 40 yuan shopping form, you can return it to 160 yuan. Don't you have a crush? But if you really do this, you will fall into a bottomless pit and spend 200 times 160, 200 times 160 ... you will never spend the rest of the money. Merchants really try their best to make money.
During the National Day holiday, my mother and I went shopping in the supermarket to find kilograms and grams. Walking into the supermarket, we first came to the biscuit cabinet. Among so many dazzling cookies, I chose my favorite casual cookie. I looked at it carefully and finally found the "net content100g" in the corner, indicating that the weight of this packet of biscuits excluding the bag is100g. So if there is 10 package of such cookies, it is 1 kg. Then we went to the place where we bought rice, and I found that a bag of rice cost 10 kg. If our family eats 2 Jin a day, our family will eat 60 Jin a month, which is six bags of rice. Later, I saw that there were 16 eggs, about 65436.