How to solve the math problems in primary schools;

In primary school mathematics teaching, the teaching of applied problems occupies an important position. How to teach this part of knowledge well, here are some of my practices and experiences.

First, cultivate students' habit of carefully examining questions and understand the meaning of questions is the premise of accurately answering application questions. Therefore, in teaching, students can first find out the direct and indirect conditions in the problem according to the requirements of solving the problem, construct the relationship between the conditions and the problem, and determine the quantitative relationship. In order to analyze the dependence between the known quantity and the unknown quantity in the problem, students can be asked to think while reading the problem, draw the conditions and problems with different symbols or express the known conditions and problems with line graphs.

In order to cultivate children's habit of carefully examining questions, I often put some confusing questions together for students to analyze and calculate. For example: ① There are 3000 science and technology books and story books in the library, and the number of science and technology books is 2/3 of story books. How many science and technology books are there? There are 3000 story books in the library, and the number of science and technology books is 2/3 of that of story books. How many science and technology books are there? There are 3000 volumes in question 1, and the 3000 volumes in question 2 are the same, so the calculation method is different. If you practice this kind of exercises often, it is easy to form the habit of carefully examining the questions.

Second, teach students the common reasoning methods for analyzing application problems. In the process of solving problems, students are often used to imitating the answers of teachers and examples and completing them mechanically. Therefore, it is very important to teach students the reasoning method of analyzing application problems and help them clear up their thinking of solving problems. Analytical method and synthesis method are commonly used analytical methods. The so-called analysis method is to analyze the desired problem in the application problem. First consider what conditions are needed to solve the problem, which of these conditions are known and which are unknown, until the unknown conditions can be found in the problem. For example, a car transports 300 kilograms of coal at a time, and b car transports 50 kilograms more than a car. How many kilograms of coal do these two cars carry at a time? Instruct students to dictate how many kilograms of coal two cars need to transport at a time. According to the meaning of the question, which two conditions (car A and car B) must be known? Which of the conditions listed in the question is known (A car transport) or unknown (B car transport), which should be sought first (B car transport 300+50=350)? What do you want (how many kilograms of coal do two cars share, 300+350=650)? The synthesis method is based on the known conditions of the application problem, and the required problems in the problem are deduced through analysis. For example, guide students to think like this: given that car A contains 300 kilograms of coal and car B uses 50 kilograms more than car A, the weight of coal in car B can be calculated (300+50=350). How many kilograms of coal can two cars hold under this condition? (300+350=650)。 Through the two solutions to the above problems, we can see that both analytical method and comprehensive method should combine the known conditions of application problems with the questions asked. The questions asked are the thinking direction, and the known conditions are the basis for solving problems.

Third, the comparative analysis of confusing problems Some related and confusing application problems can guide students to make comparative analysis, such as how much is a fraction of a number and a fraction of a known number, and the application problems of this number often confuse students. First, they can't tell whether to use multiplication or division; Second, there is no need to add parentheses when calculating. So you can arrange the following group of questions for comparative teaching. ① There are 240 pear trees in the orchard, and apple trees account for 1/3 of the pear trees. How many apple trees are there? ② There are 240 pear trees in the orchard, accounting for 1/3 of the apple trees. How many apple trees are there? ③ There are 240 pear trees in the orchard, with fewer apple trees than pear trees 1/3. How many apple trees are there? ④ There are 240 pear trees in the orchard, less than apple trees 1/3. How many apple trees are there? ⑤ There are 240 pear trees in the orchard, and there are more apple trees than pear trees 1/3. How many apple trees are there? There are 240 pear trees in the orchard, more than apple trees 1/3. How many apple trees are there? When comparing two numbers, the latter number is the standard number and the former number is the comparison number, that is, who is the standard number compared with (usually the standard number is 1). Given a number, find its score and the score of the known number, and find this number. The similarities between these two types of application problems are: (1) the fraction of the known comparison number to the standard number; The difference is that the former seeks the comparison number from the known standard number, while the latter seeks the standard number from the known comparison number. Questions 1, 3 and 5 are all comparisons between apple trees and pear trees. The number of pear trees is the standard number, the number of apple trees is the comparison number, and the number of pear trees is already known. Therefore, they belong to the former category through multiplication. Questions ②, ④ and ⑥ are all comparisons between pear trees and apple trees. The number of apple trees is standard, the number of pear trees is comparative, the number of apple trees is standard, the number of pear trees is comparative, and the number of apple trees is unknown. Therefore, it belongs to the latter category according to the division. The scores of comparison numbers in 1 and 2 questions in the standard number are known, so "brackets" are not used in the calculation, and the scores of comparison numbers in 3, 4, 5 and 6 questions in the standard number are unknown. You need to add the score of 1 and subtract the score of 1 to get it, so "brackets" are needed in the calculation.

Fourthly, it is an important link to guide students to make their own application problems, let them know the structure of application problems and attach importance to the teaching of self-made application problems. When teaching simple application problems in lower grades, let students know that the general problem of an application problem consists of two parts: known conditions and questions to be asked, so that they can fill in the blanks. For example, there are (1) female athletes in the school sports meeting 153, and there are 37 more male athletes than female athletes. (Fill in the blanks) (2) The school held a sports meeting with 153 female athletes. How many people are there? (Fill in the appropriate conditions) Senior students should be guided to write their own application problems, so that students can understand and master the structural characteristics of various application problems through their own writing. For example, 1, according to the specified formula: for example, according to the formula 240× 1/3=? Make up an application problem. 2. Adapting one application question into another: If there are 45 students in my class and girls account for 2/5, how many girls are there? Turn it into an application problem of finding the score of a given number. 3. Specify the topic type and compile the topic, such as compiling inverse proportion application questions. How to teach children to solve math application problems in primary schools? Li Yin, Luohan Central Primary School, my method has been verified by my niece. I have taught her this method since her fourth grade, saying that this method can benefit her from the first grade. Generally speaking, girls have poor logical thinking, and mathematics is more difficult for them, but it is precisely because of my method that her mathematics has always been among the best in the class, and she herself has repeatedly expressed her gratitude for my method.

Now my nephew is in the fourth grade of primary school, and he starts asking me math questions in this field. I began to teach my nephew in this way. The following two questions were asked by him tonight. I will take these two topics as examples to talk about my method.

Question 1: There are 60 more female employees than male employees in a shopping mall, and the female employees are three times as many as male employees. How many men and women employees are there in this shopping center? Question 2: The father is 27 years older than his son. Four years later, the father is four times older than his son. How old is father now? I told my nephew that you treat "Bi" and "Yes" as =, "More" and "Big" as+,"Less" and "Small" as-and "Several Times" as "Several Times". Then list the relationships step by step in words according to the meaning of the question.

For example, in the first question, "there are 60 more female employees than male employees" can be written as "female employees = male employees +60" and abbreviated as "female = male+60"; "The number of female employees is three times that of male employees" can be written as "the number of female employees = the number of male employees ×3 times" and abbreviated as "female = male× 3". In this way, we easily listed two relationships in the first question: female = male +60 (1) and female = male× 3 (2), and then taught him to substitute (2) into (1) to get: male× 3 = male +60 (3), and then taught him. Available: 2 male =60 (4) solution: male =30 (5) and then substitute (5) into (1) or (2), available: female =90 (6), so that the topic can be easily explained to him. The second question is only slightly changed, and the explanation is similar. There are two main points in my method: First, take "Bi" and "Yes" as "=", "Duo" and "Da" as "+","Shao" and "Xiao" as "-"and "times" as "X". Second, list the mathematical relations in words. In fact, the difficulty in the application of mathematics in primary schools lies in these two points. First, the meaning of the question is not easy to understand. Sometimes they don't know whether "many" and "big" should be "+"or "-"; Whether "less" and "small" should be "-"or "+"; "Several times" should be "X" or "∫"; The unknowns before and after "Bi" and "Yes" are reversed. Second, they have never studied algebra, or only learned to solve an unknown number-the equation of "X", and can't enumerate relationships. If we teach them to set the unknown quantities as "x", "y" and "z", they will be very incomprehensible and unacceptable. But if we directly use the words in the title to list the mathematical relations (that is, directly use the words "father", "son", "female worker" and "male worker" in the title as unknowns to list the mathematical relations), they will naturally understand. Then teach them simple equation solving skills, and the equation solving of elementary school math application problems is generally very simple. The second point of my method-"listing mathematical relations in words" can be said to be the intermediate transition stage of mathematical application problems from arithmetic solution to algebraic solution, but this link is missing in the teaching of mathematical application problems in our primary school. It is precisely because of the lack of this link that it is difficult for our teachers to explain clearly the reasons and solving process of arithmetic solutions to such mathematical application problems, which makes it difficult for our students to understand some arithmetic solutions, not only for students, but also for parents who are "adults". However, when our parents are faced with such questions raised by their children, it is easy to solve them with the algebra method of senior one, but it is difficult to explain the arithmetic method clearly. The arithmetic methods listed are usually evolved from algebraic methods, that is, in the process of solving "x" and "y" by algebraic methods, only derivation is carried out without calculus operation, and the final derivation is used as the arithmetic solution.

And using my above method to explain to children can let children have an adaptive process from arithmetic solution to algebraic solution. In fact, the biggest failure in the teaching of mathematical application problems in our primary school is the lack of the link of "enumerating mathematical relations in words" It is difficult for students to use arithmetic, but it is easy to use algebra to solve it. This is a teaching method that completely tortures students, but it is euphemistically called training children's logical thinking ability. Children's logical thinking ability is not this kind of practice method, but a progressive process from arithmetic method to word method to algebra method. This method of mine is a method that I realized under the torment of the algorithmic solution of mathematical application problems in primary schools and the method of learning algebra in senior one. I call on parents and teachers to teach your children in this way to make up for a big defect in our primary school mathematics education. I also hope that the Ministry of Education can accept this way and let it enter the classroom to reduce the torture to our children and parents. How to teach children to solve math application problems in primary schools? Li Yin, Luohan Central Primary School, my method has been verified by my niece. I have taught her this method since her fourth grade, saying that this method can benefit her from the first grade. Generally speaking, girls have poor logical thinking, and mathematics is more difficult for them, but it is precisely because of my method that her mathematics has always been among the best in the class, and she herself has repeatedly expressed her gratitude for this method. Now my nephew is in the fourth grade of primary school, and he starts asking me math questions in this field. I began to teach my nephew in this way. The following two questions were asked by him tonight. I will take these two topics as examples to talk about my method. Question 1: There are 60 more female employees than male employees in a shopping mall, and the female employees are three times as many as male employees. How many men and women employees are there in this shopping center? Question 2: The father is 27 years older than his son. Four years later, the father is four times older than his son. How old is father now? I told my nephew that you treat "Bi" and "Yes" as =, "More" and "Big" as+,"Less" and "Small" as-and "Several Times" as "Several Times". Then list the relationships step by step in words according to the meaning of the question. For example, in the first question, "there are 60 more female employees than male employees" can be written as "female employees = male employees +60" and abbreviated as "female = male+60"; "The number of female employees is three times that of male employees" can be written as "the number of female employees = the number of male employees ×3 times" and abbreviated as "female = male× 3". In this way, we easily listed two relationships in the first question: female = male +60 (1) and female = male× 3 (2), and then taught him to substitute (2) into (1) to get: male× 3 = male +60 (3), and then taught him. Available: 2 male =60 (4) solution: male =30 (5) and then substitute (5) into (1) or (2), available: female =90 (6), so that the topic can be easily explained to him. The second question is only slightly changed, and the explanation is similar. There are two main points in my method: First, take "Bi" and "Yes" as "=", "Duo" and "Da" as "+","Shao" and "Xiao" as "-"and "times" as "X". Second, list the mathematical relations in words. In fact, the difficulty in the application of mathematics in primary schools lies in these two points. First, the meaning of the question is not easy to understand. Sometimes they don't know whether "many" and "big" should be "+"or "-"; Whether "less" and "small" should be "-"or "+"; "Several times" should be "X" or "∫"; The unknowns before and after "Bi" and "Yes" are reversed. Second, they have never studied algebra, or only learned to solve an unknown number-the equation of "X", and can't enumerate relationships. If we teach them to set the unknown quantities as "x", "y" and "z", they will be very incomprehensible and unacceptable. But if we directly use the words in the title to list the mathematical relations (that is, directly use the words "father", "son", "female worker" and "male worker" in the title as unknowns to list the mathematical relations), they will naturally understand. Then teach them simple equation solving skills, and the equation solving of elementary school math application problems is generally very simple. The second point of my method-"listing mathematical relations in words" can be said to be the intermediate transition stage of mathematical application problems from arithmetic solution to algebraic solution, but this link is missing in the teaching of mathematical application problems in our primary school. It is precisely because of the lack of this link that it is difficult for our teachers to explain clearly the reasons and solving process of arithmetic solutions to such mathematical application problems, which makes it difficult for our students to understand some arithmetic solutions, not only for students, but also for parents who are "adults". However, when our parents are faced with such questions raised by their children, it is easy to solve them with the algebra method of senior one, but it is difficult to explain the arithmetic method clearly. The arithmetic methods listed are usually evolved from algebraic methods, that is, in the process of solving "x" and "y" by algebraic methods, only derivation is carried out without calculus operation, and the final derivation is used as the arithmetic solution. And using my above method to explain to children can let children have an adaptive process from arithmetic solution to algebraic solution. In fact, the biggest failure in the teaching of mathematical application problems in our primary school is the lack of the link of "enumerating mathematical relations in words" It is difficult for students to use arithmetic, but it is easy to use algebra to solve it. This is a teaching method that completely tortures students, but it is euphemistically called training children's logical thinking ability. Children's logical thinking ability is not this kind of practice method, but a progressive process from arithmetic method to word method to algebra method. This method of mine is a method that I realized under the torment of the algorithmic solution of mathematical application problems in primary schools and the method of learning algebra in senior one. I appeal to parents and teachers to teach your children in this way to make up for a big defect in our primary school mathematics education. I also hope that the Ministry of Education can accept this way and let it enter the classroom to reduce the torture to our children and parents. 1 Application Teaching Plan of Equation and Inequality

First, [knowledge] column equation (group) to solve the general steps of application problems, column inequality (group) to solve application problems, the main types of application problems.

2. [Outline Requirements] Can use equations (groups) and inequalities (groups) to solve application problems.

Third, the content analysis enumerates the general steps of solving application problems by equations (groups): (1) Find out the meaning of the problem and the known numbers and unknowns in the problem, and use letters to represent one (or several) unknowns in the problem; (2) Find out one (or several) equivalent relationships that can express all the meanings of the application questions; (iii) According to the found equation relation, the required algebraic expression is listed, thus the equation (or equation) is listed; (iv) solving the equation (or system of equations) and finding the value of the unknown quantity; (five) write the answer (including the name of the unit). Teaching Design of "Fractional Application Problem" in the Fifth Grade of Primary Mathematics.