What do you do when you can't find an exit in the crisscross road? Some clever students often do the opposite, go back from the exit to find the entrance, and then come back along their own road. Because when returning from the exit, the road is single, you will soon find the entrance, and then go back the same way, so it is not difficult to get out of the maze. The same is true for solving application problems. Some application problems are difficult to be solved by forward reasoning. If we start from the result of the problem and reason step by step from back to front, the problem will be easily solved. This is the reverse thinking method, that is, first determine the goal you want to achieve, then think backwards from the goal until you are where you are now, and figure out which barriers or obstacles to cross along the way and who is guarding them. Because this way of thinking is different from the routine, it can often win by surprise and achieve unexpected results. There are two main ways to use this thinking method in solving mathematical application problems in primary schools: one is reverse analysis, and the other is reverse deduction. 1, reverse analysis Reverse analysis is to correctly select the two required conditions from the problem solver. If the two conditions (or one of them) required for solving the problem are unknown, we should solve them separately to find out the two conditions (or one condition), and then deduce them in turn, and analyze the conditions required for solving the problem step by step until we know the required conditions. The last step of this analysis chain is the first step to solve the problem, then gradually regress from it, and finally list the correct formula to solve the problem. The reverse thinking method is especially suitable for solving practical problems with complex quantitative relations. The analytical thinking of this question is: How many days are actually less than originally planned? The number of days planned for production, the total number of parts actually produced, and the number of parts actually processed every day. To know how many days are actually less than the original plan, we must subtract the actual production days from the original plan. The original planned production days are known, but the actual production days are unknown. To ask the number of days actually produced, you must know the total number of parts produced and the number of parts actually processed every day, because the total number of parts produced? The number of parts actually processed every day = the actual number of days to complete the production task. The actual number of parts processed every day has been told to us, but the total number of parts produced is unknown. Further derivation, the total number of parts produced = the number of parts originally planned to be produced every day? The original planned production days, these two conditions appear in the title, therefore, finding the total number of production parts is the first step for us to solve the problem. The formula can be listed: 2000x 10=20000 (pieces). In the second step, the actual production days can be calculated. The formula is as follows: 20000? 2500=8 (days). The third step is to find out how many days are actually less than the original plan. The formula is: 10-8=2 (days). The comprehensive formula is: 10-2000x 10? 2500=2 (days). Therefore, this batch of production tasks was actually completed two days ahead of schedule. 2. Inverse Method When the known condition of the application problem is the result of multiple changes in the original number, its solution is different from the previous method. To solve this kind of application problem, we must first find out how the original number has changed several times. We should also know what the result of the change is, and then take the result as a clue and restore it according to the opposite meaning of the original question. What is the antonym here? If the change of the original number is entered. Then, the result of reduction is output. The operation of the original number is addition or multiplication. Then, the operation of reduction is subtraction or division. The solution to finding the original number from the result is the reverse method, or reduction method. Analysis: in this question, the original number of TV sets in shopping malls is the original number. The original number has undergone three changes according to the meaning of the question. The first change is that I sold 30 TV sets in the morning; The second change is that 50 sets were shipped from the manufacturer at noon; The third change was that 15 units were sold in the afternoon. The original number was changed three times before it became 72. From the above picture, we can clearly see the process of reverse calculation: Step 1: There are 72 TV sets in the shopping mall. So, how many TV sets do you need to sell 15? It can be calculated by addition, which is 72+ 15=87 (pieces). Step 2: How many TV sets were there in the mall before 50 sets were shipped? By subtraction, we get 87-50=37 (unit). As you can see, before 50 sets were shipped, there were 37 TV sets in the mall. But the problem was not finally solved, because the mall also sold 30 TV sets in the morning and had to take a step back. Step 3: How many TV sets were there before the mall sold 30 TV sets in the morning? This is the number of original TV sets in the mall. Addition calculation: 37+30=67 (pieces). The comprehensive formula is: 72+ 15-50+30=67 (pieces). For students, learning reverse thinking method can not only add a problem-solving method, but also have positive significance for cultivating the reasoning ability of reverse thinking. It is worth noting that when you first learn to solve application problems with reverse thinking, you must draw ideas. When you are familiar with the problem-solving method of reverse thinking, you can stop drawing ideas and directly analyze and solve application problems.