First, be good at helping students generalize.
The actual problems are actually those kinds of problems, and the laws for solving them are summarized. Students can answer accurately as long as they look at the questions carefully. For example, in the sixth grade, the application problems in the chapters such as fractional multiplication, fractional division, percentage, etc., I do this in teaching: the application problems in these chapters are roughly divided into these categories: a score of a number, then give a number × a score; If A has one more score than B, give B+B × a score; If a is a score less than b, give B-B × a score; If a is greater than or less than b, then use greater than or less than the latter, and if you don't know which one, set it as unknown. Only a few percent of the application problems need to be changed to a few percent. In this way, after students get the question, they only need to read it carefully, analyze what kind of question it is, and then substitute it into the relational expression to answer it accurately.
Second, cultivate students' habit of carefully examining questions.
Examination of questions is the foundation, and the teaching of applied questions must work hard on examination of questions. Look at the problem in order to understand its meaning. In teaching, I ask students to read the problem carefully at least three times before solving the application problem, and then start with the key words and sentences in the problem to understand the meaning of each sentence and find out the known conditions and problems in the problem. For example, 60 trees were planted in the sixth grade, and the trees planted in the fifth grade were 80% of those planted in the sixth grade. How many trees were planted in the fifth grade? What does 80% mean? Whose 80%? 80 yuan of a pair of trousers is 160% of that of a coat. How much is a suit? Whose 160%? A wooden strip of1.8m for a round picture frame. What is the diameter and area of this picture? What does "1.8m" mean for this frame? ..... Using this way of asking questions to help students understand the meaning of questions not only promotes the development of students' thinking, but also helps students solve problems quickly and accurately. You must read the question carefully. Understand the meaning of the question through reading, and master what is said in the question, how it went through and what the result is. Read the questions to find out what conditions are given and what questions are required. Practice has proved that students can't do it because they don't understand the meaning of the question. Once you understand the meaning of the question, its quantitative relationship will be clear. So from this perspective, understanding the meaning of the topic is equivalent to doing half of the topic. Of course, students should learn to think while reading.
Third, strengthen the analysis of quantitative relations.
Another key to solving application problems is to analyze the quantitative relationship in the problem. Quantitative relationship refers to the relationship between known quantity and unknown quantity in application problems. Only when the quantitative relationship is clear, can the solution be properly selected according to the meaning of the four operations, and the mathematical problem can be transformed into a mathematical formula and solved by calculation. For example, "Sixth grade boys 16, 20% less than girls. How many girls are there? " Analyze the relationship in the problem: the number of boys = the number of girls-the number of missing people, and combine the summarized relationship of several types of application problems: A is a few points less than B, and then give B-B × several points, so that the problem can be solved smoothly. In addition, students should also pay attention to oral analysis when revising exercises.
Fourth, the starting point of solving problems should be combined with real life.
Mathematics comes from life and serves life. The new curriculum standard of mathematics emphasizes the connection between mathematics and real life, and requires teachers to make use of various opportunities to make students feel the connection between mathematics and real life, so as to obtain necessary mathematical knowledge, basic mathematical thinking methods and necessary application skills from them, so as to adapt to future social life and further development. Initially learn to use mathematical thinking to observe and analyze the real society, solve problems in daily life and other disciplines, and enhance the awareness of applied mathematics; Experience the close relationship between mathematics and nature and human society, understand the practical value of mathematics, enhance the understanding of mathematics and the confidence to learn mathematics well, thus stimulating students' interest in learning mathematics.
In order to improve and strengthen the teaching of fractional application problems, so that it can properly reflect the practical application, thus stimulating students' interest in learning, enhancing the purpose and practicality of learning, and really improving the teaching quality. Teaching should be linked with students' real life. For example, we can stimulate students' enthusiasm for participation by extracting mathematics information close to life, such as "class size, people's age, and familiar fruits", so that students can feel that mathematics is around, learn mathematics in life, and live in mathematics middle school.
5. Choose something familiar to students as the theme.
The application problem itself comes from life and serves real life at the same time. Therefore, in teaching, it is not necessary to copy the examples or exercises after class, but to start with what students can usually see and touch, so that students can find mathematical problems in specific examples, concretize mathematical knowledge, make students feel that mathematics is also interesting and easy to understand, and improve their interest in learning mathematics. In the specific operation, when choosing examples and exercises, we should consider choosing things that are close to students' lives and are of interest to students as materials. For example, after learning Percent, I asked my classmates to look at several people who were absent in the class that day, and then asked them to check the absenteeism rate and attendance rate. Finally, I ask you: "If all the students in our class are here today, what should be the attendance rate?" Can the attendance rate be greater than 100%? "Students are interested in these familiar contents and can devote themselves to learning.
Sixth, the design of exercises should be gradual.
In each new lesson, in order to consolidate new knowledge, exercises should be done properly to test whether students can turn knowledge into ability and apply what they have learned to changed situations, so as to cultivate students' flexibility, logic and creativity in thinking. The exercises designed by teachers should have levels, proper gradients and certain flexibility, because students need a gradual internalization process to acquire knowledge, master skills, develop intelligence and improve their abilities. For example, when teaching "Cylinders and Cones", the exercises I designed in turn are: A drum with front wheel width 1.2 m and diameter 1 m rotates 15 times per minute, and how much does it advance per minute? What is the area of the road intersection? This step by step helps students solve problems in different ways.
Seven, pay attention to inspection and training.
Checking calculation is an important link in mathematics teaching and an important step to cultivate students' good learning quality and self-evaluation ability. In teaching, paying attention to the cultivation of students' inspection habits and strengthening the guidance of inspection methods and steps are important ways to improve the teaching effect of application problems. For example, the yield of rice is 70%. How many kilograms of rice does it take to grind 350 kilograms of rice? Some students have a wrong solution of 350× 70% = 245 (kg). When teaching, students should be guided to think: Is it objective to grind 350 Jin of rice and need 245 Jin of rice? So as to judge that the answer is wrong. Then guide students to re-examine the questions and understand the meaning of "70%", which means that rice is a few percent of rice. Get the number of kilograms of rice × 70% = the number of kilograms of rice, and find the correct solution, 350 ÷ 70% = 500 (kilograms), so as to find the mistakes and correct them in time.
In short, in the teaching process of application problems, we should purposefully and systematically create conditions for students to actively think and explore, guide students to understand the meaning of problems, pay attention to the relationship between analysis and quantity, grasp the conditions and problems of application problems, learn to generalize and summarize by analogy, and constantly improve students' ability to analyze and solve application problems.