Function is an important model to study the changing law of the real world, and linear function is the "introductory chapter" of learning function, which is also the focus and difficulty of junior high school mathematics teaching. It studies a changing process, which is the combination of number and shape. Mathematics that students used to learn is a relatively fixed value, while linear function is a changing process. From "dynamic" to "dynamic", there is bound to be a great turning point in mathematical thinking, which is also a "higher level" for students to understand mathematics. However, in the teaching of a function, most students' thoughts still remain in the "fixed" mathematical view. In order to make students' mathematics view leap from "immobile" to "dynamic", the starting point is the learning of a function. Teachers must grasp the teaching of this knowledge point and prepare for future study.

First, deepen students' understanding of the concept of linear function.

Mechanical memory is the most taboo in mathematics. In teaching, first of all, the function model is established with examples from students' daily life. For example, vegetable farmers have to pay 2 yuan per catty for selling vegetables, but they have to pay 5 yuan for health care. Find the relationship between total income y (yuan) and vegetables sold x (kg) (y=2x-5). Ask the students to discuss with each other and give more examples of this type. The teacher leads the induction, such as y=kx+b(k≠0, b is a constant), which is called a linear function. It is emphasized that the independent variable x is a linear algebraic expression. Through students' independent examples, mutual discussion and teacher's induction, students can firmly grasp the concept of linear function and avoid mechanical memory.

Second, pay special attention to the combination of numbers and shapes, and master the images and properties of linear functions.

In teaching, we should pay attention to guiding students from number to shape, and then from shape to number, so as to achieve the organic combination of number and shape, so as to better grasp the essence of linear function. In order to let students intuitively grasp the nature of a linear function, I regard a linear function as "left" and "right" in calligraphy, that is, when k ~ 0, the straight line tends to the left. At this time, if b﹥0, the straight line intersects the Y axis on the semi-axis, which is called "upper left". If b￠0, it is called "upper left". However, when k￠0, the straight line tends to "press down". At this time, if b﹥0, the straight line and the Y axis intersect at the upper half axis of the Y axis, which is called "upward pressure", and if b﹤0, it is called "downward pressure". For "skimming", y increases with the increase of x, while for "holding", y decreases with the increase of x, with b﹤0 straight line passing through the y axis at the top and B﹤0 at the bottom. In this way, students feel intuitive and easy to understand, and have a better grasp of the nature of linear functions. If you know the analytical formula, you can draw a rough image, and when you see the image, you can know its properties.

Third, use the undetermined coefficient method to find the analytical formula.

Many students can't understand the undetermined coefficient method well. In teaching, we should follow the principle of step by step. First of all, we should review the binary linear equations. Students are familiar with binary linear equations, and then change the topic slightly, for example, we know that y=kx+b, and when x=3, y=5, when x=- 1, y=2. In this way, students feel that it is not as difficult as expected, and their self-confidence in learning is enhanced. Then change the above question to, the straight line y=kx+b passes through two points (3,5) and (-1, 2) to find the analytical formula of the straight line, and then the students can easily complete it. Students feel that the original undetermined coefficient method for solving resolution function is to solve binary linear equations, but the abscissa of a point is regarded as the value of X and the ordinate as the value of Y.

Fourth, strengthen the practical application of linear function.

In the teaching of solving practical application problems with the properties of univariate function, on the basis that students have firmly grasped the images and properties of univariate function, we should guide students how to examine the questions, find out the meaning of the questions, establish the model of univariate function, find out the analytical formula, and then draw the images according to the analytical formula to find out what quantity is needed in the questions. Generally speaking, this is a question of finding X with known X or finding X with known Y ... Pay attention to several points, the intersection of a straight line with the X axis, the intersection with the Y axis, or the intersection of two linear function images. Let the students do several kinds of application problems of linear functions, and then make a summary, so that students can use them flexibly on the basis of mastering these typical problems.

In short, in the teaching of a function, the concept-analytical formula-nature-application is the main line, and the idea of combining numbers and shapes is combined to break through one by one, so as to cultivate students' logical thinking ability and problem-solving ability and form systematic and continuous knowledge.