Application problem is an important part of mathematics teaching, and it is also a difficult point in mathematics teaching. In order to make students not afraid of application problems and master the methods of analyzing application problems, I think they can be trained from the following aspects:

First, pay attention to cultivate students' ability to analyze the equal relationship.

Correctly analyzing the equivalence relation is the key to solve practical problems in teaching practical problems. The process of solving application problems is the process of analyzing the relationship between quantity and quantity, reasoning and finding the unknown from the known. When students solve application problems, only by clarifying the relationship between the numbers in the problems can they solve the problems correctly. On the other hand, if students are not clear about some quantitative relationship in the topic, it is impossible to solve the topic correctly. To analyze equivalence relations, we must first understand and remember some commonly used equivalence relations. For example, work efficiency × working time = total workload, number of copies × total quantity, unit price × quantity = total price, speed × time = distance, and related formulas for geometric figure calculation. Here are some examples of how to analyze equivalence relations:

(A) to cultivate students' ability to analyze equivalence relations when solving general application problems.

For example, a company wants to produce 540,000 mobile phones. In the first 654.38+00 days, it will produce 6.5438+0.5 million mobile phones every day, and the rest will be completed in 20 days. Tens of thousands of mobile phones are produced on average every day. When the students understood the meaning of the question, the teacher asked how many tens of thousands of units would be produced on average every day? What two conditions must be known? (How much is left and how long will it take) What kind of equivalence relation is used? (Remaining amount to be produced ÷ remaining time = daily average amount to be produced), don't tell us how to ask for the remaining amount? What kind of equivalence relation is used? (What was produced the day before 10 * * = the remaining quantity to be produced), what was produced the day before 10 * * didn't tell us how to get it? What kind of equivalence relation is used? (Daily production 15000 pieces × 10 days = before 10 days * *). Analyzing a problem requires several equivalence relations. Only by analyzing the equivalence relationship step by step can students find a solution to the application problem and solve it continuously.

(B) to cultivate students' ability to analyze equivalence relations when solving fractional application problems.

The analysis of the equivalence relation of fractional application problems should find the key sentence in the problem, that is, fractional sentence. When analyzing the application problems of fractions, I ask students to find out the unit "1" from the fractions, and then write the equivalent relationship of three words, namely "1"× = quantity. For example, China has a vast territory, with a distance of 5,500 kilometers from north to south and a distance of 52/55 from east to west. How many kilometers is the distance between east and west? Find the unit "1" from the ratio statement that the kilometer distance from east to west is 52/55 of the kilometer distance from north to south. The distance between north and south kilometers multiplied by 52/55 equals the distance between east and west kilometers, that is, the distance between north and south kilometers × 52/55 = the distance between east and west kilometers. Both fractional multiplication and fractional division can use the same equivalence relation. As long as the equivalence relation is found, multiplication is performed according to the known quantity of the unit "1", and division is performed according to the unknown quantity of the unit "1".

(c) Cultivate students' ability to analyze equivalence relations when solving application problems with equations.

Using column equation to solve application problems needs to find equivalence relation. Using column equation to solve the equivalence relation of application problems can be found along the meaning of the problems. After finding the equivalence relation, let the unknown quantity be x, and the known quantity * * * participates in the formula. For example, there used to be some jiaozi powder in the store, each bag was 5 kg. After selling 7 bags, there are still 40 Jin left. How many kilograms of jiaozi powder are there in this shop? Its equivalence relation follows the meaning of the question. The original weight minus the sold weight equals the remaining weight, that is, the original weight-sold weight = remaining weight. According to the equivalence relation, the equation (x-5× 7 = 40) can be listed.

Second, focus on cultivating students' ability to list or draw line segments.

Drawing and analyzing application problems is a kind of ability, which needs to be cultivated step by step in the whole teaching process of application problems. Application problems are abstract, and analysis by list or line drawing can help students understand the relationship between the quantities in the problem.

(a) General application problems related to actual quantity and planned quantity can be analyzed with the help of lists.

For example, the canteen bought 280 kilograms of rice and planned to eat it for 7 days. In fact, I eat 5 kilograms less than planned every day. How many days did this batch of rice actually eat? The following table can be listed for analysis.

The number of kilograms eaten every day, the total number of kilograms per day.

Plan 2 8 0 ÷7 7 days 2 8 0 kg

Eat 5 kilos less than planned? 8 0 kg the next day

It is easy to see from the table that if you want to know how many days you have actually eaten, you must first know what you plan to eat every day. What you plan to eat every day can be calculated by subtracting 5 kilograms from what you plan to eat every day, and then the formula of what you actually eat every day can be obtained: 280÷(280÷7-5). Using this method to analyze this kind of application problems, even poor students can solve them, especially middle and low grade students.

(2) The application of scores and percentages can be analyzed by drawing a line graph.

The application problems of fractions and percentages can help students understand the relationship between related quantities and standard quantities with the help of line graphs, and find ways to solve problems. In teaching, students are often guided to do line drawing training, so that students can master the basic methods of drawing: first, draw a line segment representing the unit "1", pay attention to the standardization of line segments and the flexibility of drawing, and use drawing skills such as supplement, truncation, shift and overlap to pay attention to the scientificity of drawing. At the same time, guide students to look at pictures carefully, analyze and think, understand the quantitative relationship, and synchronize students' thinking and drawing. Only in this way can we give full play to the intuitive enlightenment of line segment diagram.

Third, pay attention to cultivating students' comparative analysis ability.

For confusing and error-prone questions, consciously design some specious variant problem groups, so that students can practice comparison and master the law of solving problems. For example, (1) Children's Palace Dance Team has 23 people. The chorus is three times more than the dance team, 15. How many people are there in the choir? (2) There are 84 chorus members in the Children's Palace, with three times more chorus members than the dance team, 15. How many people are there in the dance team? By comparison, students can understand and master how to solve the multiple of (1) by arithmetic and how to solve the unknown multiple of (2) by equation. For example, in the application of fractions, there are two questions that students are very confused about: (1) Cut from an 8-meter rope 1/4, how many meters are left? (2) Cut1/4m from the 8m rope. How many metres are left? By comparison, students can understand that 1/4 in (1) means a fraction, while 1/4m in (2) means a quantity that cannot be confused.

Fourth, pay attention to cultivating students' divergent thinking ability.

Divergent thinking is to explore and think in various directions and in different ways when solving problems. Let students carry out multi-angle and multi-level association training and multi-solution training, and cultivate students' multidirectional and flexible thinking. For example, there are 18 white rabbits and black rabbits in the feeding group, and the number of black rabbits is 1/5 of that of white rabbits. How many white rabbits and black rabbits are there? We can solve the equation (1) in four different ways: solution: if there are x rabbits, there are 1/5x rabbits, and the equation X+ 1/5x = 18. (2) Normalization method: According to the fractional sentence, there are 5 white rabbits, 1 black rabbits and 6 * *, and the black rabbits press 18 ÷ 6× 1 = 3 (only), and press18 ÷ 6×. (3) Proportional distribution method: According to proportional sentences, there are 5 white rabbits, 65,438+0 black rabbits, 6 * *, 65,438+0/6 black rabbits, 5/6 white rabbits, 65,438+08× 65,438+0/0 black rabbits. (4) Using fractional method: From the fractional sentence, we know that the unit of white rabbits is "1", while the number of black rabbits is 1/5,18 ÷ (1+1/5) =/kloc. In normal teaching, students should be trained to solve more than one problem, so as to expand their thinking of solving problems, and compare various solutions to find the best one. Let students understand that when solving practical problems, they should choose the simplest method as much as possible.

Fifth, pay attention to cultivating students' inspection ability.

Checking calculation is an important link in mathematics teaching and an important step to cultivate students' good learning quality and self-evaluation ability. The methods of checking calculation include estimation method, substitution method and other solutions. The following is an example of estimation.

For example, the oil yield of rapeseed is 42%. How many kilograms of rapeseed does it take to refine 2 100 kilograms of oil? When students do this problem, they often have the wrong solution of 2 100× 42% = 882 (kg). In teaching, students should be guided to think: Is it realistic to squeeze 2 100 kg of oil with only 882 kg of rapeseed? So as to judge that the answer is wrong. Then guide students to re-examine the questions and understand the meaning of "42%%", that is, how much oil is rapeseed, and get that kilogram of rapeseed × 42% = that kilogram of oil, and find the correct solution, 2 100 ÷ 12% = 5000 (kg), and that's it.