The quantitative relationship of some problems is relatively simple, and students can directly solve problems according to their own life experience or through abstract thinking processes such as analysis and synthesis.

1. Life. Life-oriented refers to the strategy of solving mathematical problems by establishing contact with students' life experience. It is often used to learn new knowledge. The key is to point out the mathematical knowledge and methods involved in the process of solving problems to students after solving them. If we study the greatest common factor, let's start with the question: the teacher recently bought a garage with a length of 40 decimeters and a width of 32 decimeters, and wanted to lay square floor tiles on the garage floor. If you want to make the side length of the floor tile into decimeter, you don't need to cut it when laying the floor tile. How many kinds of floor tiles do you have? Which one should I buy if I want to buy the least number of blocks? Because students are familiar with this kind of problems, it is generally believed that the side length of floor tiles should be the common factor of 40 and 32, and the number of blocks bought is the least when the common factor is the largest. To solve these two problems, we must first find out the factors of 40 and 32. Then let the students sort out the problem-solving process and point out what is the common factor, what is the greatest common factor, and how to find the common factor and the greatest common factor.

2. Mathematicization. Mathematicization refers to the strategy of solving practical problems by establishing contact with students' existing knowledge. Often used in practical problems, the key is to let students know what knowledge and methods to use to solve problems before solving them. For example, when students learn the "rectangle perimeter", they will show it when they already know the rectangle perimeter = (length+width) ×2: Xiaoming walks around a rectangular swimming pool. How many meters did he walk? Let the students know that "how many meters a * * * has traveled is to find the perimeter of a rectangle", then think about "how to find the perimeter of a rectangle" and "what should be known in finding the perimeter of a rectangle", and finally show the information of "50 meters long and 20 meters wide" to let the students solve the problem independently.

3. Pure mathematics. Pure mathematics refers to the strategy of solving mathematical problems by analyzing and utilizing the relationship between quantity and quantity. Often used to learn new knowledge closely related to old knowledge, the key is to build a bridge between the mathematical problems to be solved and the existing mathematical knowledge. If we study a slightly more complicated application problem of fractional multiplication, let's first show the old problem: the cement factory produced 8400 tons of cement in February, an increase of 25% over February. How many tons of cement were produced in March? Students think that: because the increase of several tons = several tons in February× 25%, so several tons in March = several tons in February× (1+25%) = 8400× (1+25%). Let's raise a new question: the cement factory produced 8,400 tons of cement in February, 25% less than that in February. How many tons of cement were produced in March? Let the students talk about the similarities and differences between these two kinds of problems, because these two kinds of problems are essentially related, so teachers only need to build a bridge between them, and students can solve new problems independently through migration. They think: because the reduction of several tons = several tons in February× 25%, several tons in March = several tons in February× (1-25%) = 8400× (.

Second, special strategies.

The quantitative relationship of some problems is complex, and some special problem-solving strategies are often needed to break through the difficulties, so as to find the key to solving problems and solve them smoothly. There are seven common and acceptable special strategies for primary school students:

1. List policies. This strategy is suitable for solving the problem of "information is complex and difficult to understand, and the relationship between information is vague". It is a strategy of "listing information in a table, observing and rationalizing the conditions of the problem and finding a solution". For example, when studying the mathematical problems of pancakes in Book 7 of People's Education Edition, in order to study the relationship between the number of pancakes and the time of pancakes, the list strategy can be adopted, as shown in the right picture. When using this strategy, we should pay attention to: (1) guiding students to complete the process of filling in the form; (2) Guide students to understand the relationship between quantities; (3) Enlighten students to use tables to sort out problem-solving ideas, talk about their own findings and feel the functional relationship.

2. The strategy of painting. This strategy is suitable for solving the problem of abstraction and visualization. It is a strategy of "displaying the meaning of a problem intuitively with a simple chart, expressing the quantitative relationship in an orderly manner, and finding and determining the solution method from it". For example, when learning collocation questions in Book 5 of People's Education Press, in order to solve problems more intuitively and methodically, drawing strategies can be adopted, as shown on the right. When applying this strategy, we should pay attention to: (1) let students experience and learn methods in painting activities; (2) Before drawing, please check the quantity relationship; (3) The drawing shall conform to the quantitative relationship.

3. Enumerate policies. This strategy is suitable for solving the problem of "difficulty in answering questions". It is "to think about all the possibilities of things in an orderly way, list them one by one, and use some kind of