Teaching objectives of function teaching plan in junior middle school
1. Develop students' abstract thinking ability in the process of exploring general laws. 2. Understand the concepts of linear function and proportional function, write a simple expression of linear function according to the given conditions, and cultivate students' mathematical application ability.
Teaching emphasis: the concepts of 1, linear function and proportional function and their relationship. 2. The expression of the function will be written once according to the known information. Teaching difficulties: the application of linear function knowledge; Teaching methods; Teachers guide students to prepare a teaching aid by themselves in the spring;
Courseware teaching process
First create a problem situation, introduce a new lesson 1, and simply review the concept of function (if there are two variables X and Y in a certain change process, then we call Y a function of X, where X is the independent variable and Y is the dependent variable). Second, demonstrate the deformation phenomenon of the spring under the action of force, and ask the question: which variable is the length of the spring in the process of change? Why? 3. What is the relationship between the remaining oil in the fuel tank and the constant speed of the car? Does this work?
Second, learn a new lesson 1 and do it. Ask students to do more than two topics on page 157 in the book, so that students can develop their abstract thinking ability in the process of exploring general laws. 2. Discussion on the concept learning of linear function and proportional function: What are the similarities between the two relationships y=3+0.5x and y= 100-0. 18x just written?
Let the students analyze their similarities: ① algebraic expressions with dependent variables on the left and independent variables on the right; ② The degree of independent variable X and dependent variable Y is1; (3) formally, the form is y=kx+b, and k and b are constants.
Q: As far as the number of independent variables is concerned, what do you think such a function can be named? Guide students to summarize the concept of linear function: if the relationship between two variables X and Y can be expressed as y=kx+b(k, B is constant, K? 0), say y is a linear function of x (x is the independent variable and y is the dependent variable).
Q: in the linear function y=kx+b, can k be 0? Can b be 0? Guide students to acquire the concept of proportional function.
Then guide students to compare the relationship between linear function and proportional function (through set comparison): linear function includes proportional function, and proportional function is a special case of linear function.
3. Example learning
Example 1 is to examine students' understanding of the concepts of linear function and proportional function, and students can answer directly.
Example 2 is to cultivate students' ability to enumerate simple linear function relationships according to the meaning of the questions and solve practical problems by using linear functions. Strictly speaking, the third question must first judge that the salary range is 800.
Third, classroom exercises.
1, find the following linear function, and point out the values of k and b. If it is not a linear function, please explain the reason.
a、y= +x B、y=-0.8x C、y=0.3+2x2 D、y=6-
2. The function y=(m+ 1)x+(m2- 1) is known, when m and y are linear functions of x; When m and y are directly proportional functions of x.
Fourth, expand applications.
The school organized some students to experience the revolutionary history in Jinggangshan. As for tourism, I'm going to choose one of the two travel agencies, A and B. It is known that the two travel agencies offer the same price, each in 200 yuan. However, the group discount offered by Travel Agency A (more than 15 people) is to return cash to 500 yuan as the entrance fee, while the group discount offered by Travel Agency B is 10% discount on all personnel fees. Assuming that the number of students is X and the fees charged by two travel agencies are Y A and Y B respectively, answer the following questions: (1) Write the functional relationship between the fees charged by two travel agencies and the number of students X (people); What is the function of this relationship? (Y A =200x-500, Y B = 180x)(2) If there are 20 students, calculate the expenses of the two travel agencies respectively. Which is cost-effective? (y a =200？ 20-500=3500 (yuan); Y b = 180？ 20=3600 (yuan); Y a < Y B, so it's cost-effective to go to a travel agency. (3) Under what circumstances do you choose B Travel Agency? (According to the meaning of the question, Y A-y B > 0, that is, (200 x-500)-180 x >; 0, solving inequality, x & gt25, so in the case of more than 25 people, it is more cost-effective to go to B travel agency. ) V. Class Summary
Ask students to summarize the contents of this lesson: 1, linear function, proportional function and their relationship. 2. Write the relationship of the function once according to the known information.
Reading assignment: China ancient seal cutting must be done: 16 1 Page Exercise 6.2 1, 2, 3 questions: 16 1 Page Try it.
Reflections on function teaching? Function and image? This chapter focuses on the concept, images and properties of linear functions. On the one hand, when students are new to the related content of a function, they must learn with specific functions. Therefore, the main content of the whole chapter focuses on the description of specific functions. On the other hand, among several specific functions specified in the syllabus, linear function is the most basic, and the discussion of linear function in the textbook is also comprehensive. Through the study of a function, students have a preliminary understanding of the research methods of the function, so as to better master the learning methods of learning quadratic functions and inverse proportional functions. After teaching, I have a deeper understanding of the new textbook.
Prepare lessons carefully
The process of preparing lessons is a hard and complicated mental labor process. With the development of knowledge, the change of educational objects and the improvement of teaching efficiency, preparing lessons as an artistic creation and re-creation is endless, and the design and selection of an optimal teaching scheme is often difficult to satisfy people completely.
One: The textbook schedule is too tight. There is not enough teaching time for textbooks in senior two. There are two classes in the first section, the second section and the third section of the function, and the class hours are too few. This section should be supplemented with a review class.
Second, the teaching content is not easy to handle.
? What are the properties of linear functions? B has no effect on the image of the function, but there is one problem that needs to be supplemented.
Link 2: Summarize the properties of linear function images.
The linear function y=kx+b has the following properties:
(1) When k >: 0 and y _ _ _ _ increases with X, then the image of the function goes from left to right _ _ _ _ _;
(2) When k < 0 and y _ _ _ _ _ increases with X, then the image of the function goes from left to right _ _ _.
(3) when b>0, when the intersection of the function image and the y axis is:
(4) When b>0, when the intersection of the function image and the y axis is:
Introduction and application of undetermined coefficient method? The length of the spring y (cm)? It's too difficult to tell. Do you want to talk about it in the book first? Do: The image passing point (-1, 1) and point (1, -5) of the linear function y=kx+b are known.
Third, the difficulty is not easy to deal with:
For example, when we are talking about the definition of function (the first category), we add an example: When the function y= is known, when the value of m is taken, is y a linear function of X? When m takes what value, y is a proportional function of x?
It is difficult for students to understand. Personally, I think it is too difficult, which is beyond the students' understanding ability. On the contrary, in a specific linear function y=-2x+3, there is not much emphasis on the number of k and b.
The pen of satisfaction
The linear function satisfies the following conditions:
First, combined with life examples, fully mobilize students' enthusiasm for learning, make appropriate transition, and ignite the desire for knowledge.
In the introduction part of this class, use the real person in the class (using the concrete example of the school sports meeting)? How much money is involved in this operation? Assuming that every player is moving in a straight line at a uniform speed, what is the relationship between speed, time and distance? Transitional questions such as distance is a function of time not only review the knowledge of last class, but also pave the way for the concept of function image.
2. Boldly adjust and modify the teaching materials.
Complete the integrity of knowledge content.
(Image knowledge point of linear function: geometric shape of linear function: a straight line; Drawing method of linear function image; The coordinates of the intersection between the linear function image and the coordinate axis. ) The textbook is correct? Drawing function images? The explanation is incomplete and not detailed. Learning the image of function needs to cultivate students' idea of combining numbers with shapes. The image of primary function is the simplest of all function images, and it is also the basis for learning other complex functions in the future. Therefore, studying the image of elementary function in an all-round way can provide students with a sample of ideas and save their later study time. Although in the exercises and exercise books after class, how to draw the image of the function when the independent variables of the function are limited in a certain range is involved, it seems that such problems are not involved in the teaching materials. For the students in Class B, this kind of problem needs the teacher to demonstrate and solve. (1) Find the functional relationship of y 1 about the range of x and the independent variable x; (2) Draw the image of the above function. Is the image still straight? This topic is called expanding knowledge points: when the independent variables of a linear function are limited in a certain range, the image of a linear function is specially designed as a ray or a line segment. As for how to draw a ray or line segment quickly, let the students discuss and summarize: for a ray, draw a ray at any point different from the starting point and another point; For a line segment, take two endpoints of the line segment and connect them.
disadvantage?
First, the time is not accurate. Because I have broadened the scope and depth of knowledge points on the basis of the original textbook, individual links need group activities or individual students to operate on stage. I want to finish all this in one class, which seems to overestimate my ability and that of students. So I think so much content can be taught in two classes.
Second, there are some mistakes in the content processing: when I first explored the drawing method of function y=x, I directly forced to take five points first: (-2, -2), (-1,-1), (0,0), (1, 65438+.