The focus of this section is to summarize the properties of inverse proportional function with pictures. After learning the first three basic functions, students have a certain ability to read pictures and master the basic research methods. After a drawing process, students can gradually form a comprehensive understanding of inverse proportional function through observation, analysis, mutual discussion and communication with classmates. Students can be trained to use the mathematical thinking method of combining numbers and shapes. It is also a process of finding and solving problems by mathematical methods. Another key point of this section is to find the analytical formula of inverse proportional function by undetermined coefficient method. This method has been used to find four basic resolution functions. This lesson can further improve the understanding of the undetermined coefficient method through consolidation exercises. For example, students can observe that there are several undetermined coefficients, so they need several pairs of corresponding values of independent variables and functions, that is, several equations

The difficulty of this section is sketching and drawing. Due to the limitation of students' knowledge, sketch and painting can't have a comprehensive grasp of graphics. In this way, students will find it difficult to sketch and draw, and they can't estimate what this image looks like. Therefore, we can make a preliminary analysis from the analytical formula and realize that the image of inverse proportional function is divided into two branches, so as to preliminarily understand the general changing trend of its image.

Teaching suggestion

One of the purposes of mathematics education is to help students understand mathematics closely related to the real world, and the development of mathematics is an exploration process full of observation, experiment, induction, analogy and speculation. Therefore, while acquiring knowledge, students should also cultivate the attitude of respecting objective facts, the spirit of being brave in exploration and the habit of thinking independently and cooperating with others. The specific arrangements are as follows:

(1) Abstracts a mathematical model from an example.

Primary school students have learned the knowledge of inverse proportion, and now there are many examples of inverse proportion in physics, chemistry and other disciplines. Students can abstract the characteristics of this kind of function from simple examples and form the concept of inverse proportional function.

(2) Draw an image and study the properties of inverse proportional function.

Mathematical situations can be created to guide students to find out the relationship between numbers and shapes. For example, k>0, X and Y have the same symbol, and the images are in the first and third quadrants, K.

(3) Grasp the undetermined coefficient method firmly.

I am familiar with the general steps of solving problems by undetermined coefficient method. Through continuous application, I gradually find that there are several undetermined coefficients, so I need to list several corresponding equations, so that the inverse proportional function can determine its analytical formula only by a pair of independent variables and the corresponding values of the function.

Teaching objectives

1, which enables students to abstract the inverse proportion decomposition function from simple practical problems;

2. I will draw the image of inverse proportional function, summarize the properties of inverse proportional function with the image, and infiltrate the mathematical thought of combining numbers with shapes; .

3. The analytical expression of inverse proportional function is obtained by undetermined coefficient method;

4. By revealing the connection and transformation between the proportional function and the inverse proportional function, the idea of dialectical materialism is infiltrated;

5. By observing, summarizing and summarizing the nature of inverse proportional function, cultivate students' scientific spirit of being brave in exploration;

6. Cultivate students' ability to find problems in mathematics and solve problems with mathematical knowledge.

Teaching focus:

The concept, image and properties of inverse proportion and the analytical formula of inverse proportion function determined by undetermined coefficient method, because the above problems of inverse proportion function must be clarified before we can study inverse proportion function.

Teaching difficulties:

Draw the image of inverse proportional function, because the image of inverse proportional function has two branches, and the changing trends of these two branches are different, so it will be difficult for students to contact for the first time.

Teaching process:

First, the introduction of new courses:

Please look at the following example: (showing slides)

1. The distance from Xiaohong's home to school is 5 kilometers. Write the functional relationship between the time t she needs to go to school and the speed v;

2. There is a rectangle with an area of 3 square meters, and write the functional relationship between its length A and width B;

During the seven-day holiday, the teacher assigned 36 words by heart. Let the number of days completed by Xiao Ming be n and the number of words per day be m, and write the functional relationship between m and n?

A: From the point of view of function, in the process of movement change, these two variables can be regarded as independent variables and functions respectively, which are recorded as: (), (), ().

Second, the new lesson explanation:

1, let students observe the characteristics of these functions, and then get the concept of inverse proportional function: (blackboard writing)

Generally speaking, a function (k is a constant) is called an inverse proportional function.

Note: the exponent of the independent variable is-1, not 1.

Example 1. Determine which of the following formulas x and y represents the inverse proportional function relationship?

⑴ ⑵ ⑶

Example 2. Write the analytical expressions of the following functions to determine whether they are inverse proportional functions. If so, find their domain names.

The volume of cylindrical steel is 800cm3. Write the functional relationship between its bottom area and its height. ⑵ The pressure is determined by the pressure per unit area. Then, when the vertical pressure on the object is 100 N, write the functional relationship between the pressure and the stress area.

2. According to the previous experience of learning special functions, what will you learn next after learning the concept of functions?

A: Images and attributes.

Through this question, students can have a clear understanding of the occurrence and development of the knowledge given in the textbook. Later,

Students can learn other functions in this way.

Next, let's look at an example: (showing slides)

Example 3. Draw the inverse proportional function and the image in the plane rectangular coordinate system.

Question: (1) What are the key problems in drawing function images?

A: Choose the list of values reasonably and correctly.

⑵ What problems do you think should be paid attention to when choosing values?

Answer: I. Because the characteristics of the function image are not clear, it is better to choose more points;

Ⅱ. You can't choose because the time function is meaningless;

Three. Choosing an integer is better for calculation and drawing.