02. synthesis method: synthesis method is a way of thinking that gradually calculates the problem to be solved from the known conditions in the topic.
Analysis and synthesis: on the one hand, we should seriously consider the known conditions, on the other hand, we should pay attention to what the problems to be solved in the topic, so that our thinking can have a clear direction and purpose.
04, decomposition method: a complex application problem is decomposed into several basic application problems, from which we can find clues to solve the problem.
05. Graphic method: Graphic method is to express the listening conditions and problems of the topic clearly with pictures or line segments, and then try to solve the application problems "according to the pictures".
06. Hypothesis method: Hypothesis method is to make appropriate assumptions about some phenomena or relationships in the topic when solving problems, and then use the contradiction between facts and assumptions to find the correct solution.
Example: The refrigerator factory produces a batch of refrigerators. The original planned daily output is 800, but the actual daily output is 120. As a result, the task was completed three days ahead of schedule. How many days did it actually take? Scheme 1: (800+120) × 3 ÷120-3 = 20 (days) (this is a conventional scheme); Scheme 2: Assuming that the original production plan is 3 days shorter, * * * will produce 800× 3 = 2,400 refrigerators. At this point, the planned production days are equal to the actual production days. The reason for the shortage of 2400 units is that the planned daily output is less than the actual output 120 units, so the actual production days are: 2400÷ 120 = 20 (days), that is, the formula is: 800×3÷ 120 = 20.
07. Transformation method: Transformation method is a method of transforming a mathematical problem into another mathematical problem through mathematical transformation, and then solving it.
Example: It takes 65,438+00 hours for a truck to drive from City A to City B, and 6 hours for a bus to drive from City B to City A. Both cars start at the same time, and the directions are opposite. As we all know, the distance between city A and city B is 600 kilometers. Two cars will meet in a few hours. Scheme 1: 600÷(600÷ 10+600÷6) Scheme 2: Take the distance between the two places as "1", the truck speed as 1/ and the bus speed as/kloc-0.
08. Inverse deduction method (reduction method): Starting from the final state of conditions, using the reciprocal relationship of addition, subtraction, multiplication and division, the method of solving problems step by step from back to front is called inverse deduction method or reduction method.
For example, there are several bags of goods in a warehouse. The first shipment was 1/3, and the remaining half was shipped out, with 2 bags missing. There are 106 packages left in the warehouse. How many bags are there in the warehouse? (106-2) × 2-4 ÷ (1-1/3) = 306 (bag)
09. Find the corresponding method: In some mathematical problems, there are some related corresponding relationships. By analyzing some quantitative corresponding relations between conditions, the unknown can be transformed into the known. This way of thinking can be called "correspondence method".
For example, a book reads 32 pages on the first day, 40 pages on the second day, and the remaining pages account for 1/4 of the book. How many pages are left in this book? (Find the corresponding quantity of each correlation)
10, substitution method: "substitution" means equivalent substitution. Replace one quantity (or part of one quantity) with another quantity (or part of another quantity) equal to it, thus reducing the quantity in the problem and reducing the difficulty of solving the problem, and then try to find out the replaced quantity.
The canteen used up a barrel of oil in three days. On the first day, it used 6 kilograms, the next day, it used the remaining 3/7, and on the third day, it used exactly half of this barrel of oil. How many kilograms of oil did * * * use on the second and third days? (Analysis: 6 kg corresponds to the remaining 1/7, that is, 1-3/7-3/7. Finding this correspondence, the remaining amount is exactly the oil consumption on the second day and the third day: 6÷( 1-3/7-3/7)= 6.
1 1, the method of finding invariants from variables:
(1) There is a constant change-the same as: Example: Two construction teams, A and B, have *** 180 people, and 2/1of their own are transferred from Team A to Team B, and the number of the two teams is equal. How many people are there in each team? Team A:180 ÷ 2 ÷ (1-2/1) =110 (person)
(2) unchanged-the difference is unchanged: Example: A deposit 2000 yuan, and B deposit it in 400 yuan. If, from now on, everyone deposits in 200 yuan every month, after a few months, A will deposit three times as much money as B? (Analysis: A has more 1.600 yuan than B, and this 1.600 is exactly twice the amount of money B has for several months, so the formula is: (2000-400) ÷ (3-1)-400 ÷ 200 =
(3) the process has not changed-the quantity of a certain part remains unchanged. Example: 25 kilograms of salt water with salt content of 16%, how many kilograms of water should be evaporated to get 40% salt water? (analysis: the total amount of this problem is the weight of salt water, which consists of salt and water. After the brine evaporates, the weight of water decreases, the total weight of brine also decreases, and the concentration changes. But if we want to see that there is a constant in the change, and the weight of salt has never changed, we can get the answer by grasping the invariant of salt: 25-25×16% ÷ 40% =15 (kg).
(4) Invariance in change-Invariance in deformation: For example, a cuboid iron block with a length of 9 cm, a width of 7 cm and a height of 3 cm and a cubic iron block with a length of 5 cm are cast into a cylinder. The diameter of the bottom of this cylinder is 20 cm. What is its height? (Analysis: Although the shape has changed, the total volume has not changed: (9× 7× 3+5× 5) ÷ 3.14× (10 ×10) =1cm) This method can also be used in the fifth grade.
12. Construction method: When calculating some graphics problems, the irregular graphics that were originally difficult to handle are reconstructed into a new one that is more convenient to handle after translation, rotation and folding. This way of thinking is called constructivism.
13, enumeration method: the quantitative relationship is complex, and it is difficult to list formulas or equations to solve. We should list the possible answers one by one according to the requirements of the topic, and then gradually eliminate or narrow the scope according to the conditions in the topic, and screen out the answers to the topic.
For example, if you have a nickel, four dimes and eight dimes, how can you get eight cents?
14, elimination method: There are two unknowns in a math problem. When solving a problem, through simple operation, one unknown is eliminated first, and then another unknown is found. This way of thinking to solve problems is called elimination method.
Example: In the department store, two ballpoint pens and three pens of 6 yuan Money are worth 6 cents, and three ballpoint pens and three pens of 7 yuan Money are worth 2 cents. How much is a ballpoint pen?
15, number method: some topics contain uncertainty. It is difficult to find a solution according to the general idea of solving problems. If we set an indefinite quantity in the topic as a concrete number, we can abstract the original problem into concrete and the problem will be simple. This thinking method of solving problems is called number method.
Xiaohua took part in mountain climbing activities. After climbing from the foot of the mountain to the top of the mountain, he went down the mountain in the same way, walking 20 meters per minute when going up the mountain and 30 meters per minute when going down the mountain, in order to find the average speed of Xiaohua going up and down the mountain. (Analysis: According to the question "Total distance ÷ time = average speed", the distance is not given, so it can be set to 600 meters. Then the formula is: 600×2÷(600÷20+600÷30)=24 (m/min).