The eighth grade mathematics linear function teaching plan (teaching goal)
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 plan of the first function of eighth grade mathematics (emphasis and difficulty)
Teaching focus:
The concepts of 1, linear function and proportional function and their relationships.
2. The expression of the function will be written once according to the known information.
Teaching difficulties: the application of linear function knowledge teaching method; the spring for teachers to guide students to prepare teaching AIDS by themselves.
The eighth grade mathematics first function teaching plan (courseware teaching process)
First, create problem situations and introduce new courses.
1, briefly review the concept of function (assuming that there are two variables X and Y in a certain change process, if so, then we call Y a function of X, where X is the independent variable and Y is the dependent variable).
2. Demonstrate the deformation of the spring under the action of force, and ask the question: Which variable is the length of the spring in the process of changing the length of the spring? 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, the new lesson learning
1, do it. Ask students to do more than two topics on page 157 in the book, so that students can develop 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. ) 5,
Ask the students to summarize the content of this lesson:
The concepts of 1, linear function and proportional function and their relationships.
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.