First, the goal of quality education

(-) Knowledge teaching schools

1. Understand the concepts of binary linear equations, binary linear equations and their solutions.

2. A binary linear equation will be written as an algebraic expression, and one unknown will be used to represent another unknown.

3. It will be tested whether a pair of values is the solution of binary linear equations.

(2) Key points of ability training

Cultivate students' ability to analyze, solve and calculate problems.

(C) moral education penetration point

Cultivate students' rigorous and serious learning attitude.

(D) the starting point of aesthetic education

Through the study in this section, the solution of seepage equation must satisfy the mathematical beauty of each equation, and stimulate students' interest and passion in exploring mathematical mysteries.

Second, the guidance of learning methods

1. Teaching methods: discussion, practice and guidance.

2. Students study law: understand the concepts of binary linear equations and binary linear equations and their solutions, compare the concepts of equations and their solutions, and strengthen the discrimination of concepts; At the same time, the writing process of the experimental equation solution is standardized, which lays a good mathematical foundation for future study.

Third, the key point? Difficult point? Doubts and solutions

(-) Key points

Make students understand the meaning of binary linear equations, binary linear equations and the solution of binary linear equations, and check whether a pair of values is a solution of binary linear equations.

(2) Difficulties

Understand the meaning of the solution of binary linear equations.

(3) Questions and solutions

To test whether a pair of unknown values are solutions of binary linear equations, it is necessary to satisfy both equations of the equations at the same time, which is a doubtful point in this lesson. This problem can be solved by giving a series of counterexamples in teaching.

Fourth, the class schedule

One class hour.

Verb (abbreviation for verb) Prepare teaching AIDS and learning tools.

Computer or projector, homemade film.

Sixth, the design of teacher-student interaction activities.

1. Teachers create situations and introduce topics by reviewing equations and their solutions and solutions, and introduce the concepts of binary linear equations and binary linear equations.

2. Through repeated practice, let students learn to correctly judge binary linear equation and binary linear equation.

3. Through the teaching of the concept of binary linear equations and the demonstration role of teachers, students can learn to correctly test the solutions of binary linear equations.

Seven, teaching steps

(-) Clear objectives

The teaching goal of this course is to understand the concepts of binary linear equations and binary linear equations, and to judge whether a pair of unknown values are the solutions of binary linear equations.

(B) the overall perception

By reviewing the equations and their solutions, the concepts of binary linear equations and binary linear equations are introduced and judged. At the same time, learn to use one unknown to represent another unknown, laying the groundwork for solving the equation in the future; Finally, learn to test the solution of binary linear equations.

(3) Teaching process

1. Create a situation, review and import it.

(1) What is an equation? What is the solution of the equation and the solution of the equation? Can you give an example of a linear equation?

Answer the teacher's questions and give free examples.

The teaching method shows that raising this question can make students reproduce the knowledge about the linear equation in their minds and pave the way for learning the linear equation in binary.

(2) Solve a linear equation with one variable.

Banana price 5 yuan/kg, apple price 3 yuan/kg. Xiaohua * * * bought 9 kilograms of bananas and apples, and paid 33 yuan how many kilograms of bananas and apples each?

Student activities: think, set unknowns and answer.

Suppose you buy one kilogram of bananas, then one kilogram of apples.

According to the meaning of the question, you must

To solve this equation, you must

Xiaohua bought 3 kilograms of bananas and 6 kilograms of apples.

In the above question, two numbers are needed. Can you set two unknowns at the same time?

Suppose you buy one kilogram of bananas and one kilogram of apples. According to the meaning of the question, two equations can be obtained

Observe whether the above two equations are linear equations. If not, what are the characteristics of these two equations?

Observe, discuss, raise your hand and speak, and summarize the similarities and differences between the two equations.

There are two unknowns in the equation, and the degree of the unknowns is 1. Equations like this are called binary linear equations.

In this lesson, we began to learn the knowledge closely related to binary linear equations-binary linear equations.

The teaching method is that students give the concept of binary linear equation after summing up the characteristics of the equation itself, which is more impressive than the direct definition and helps to understand the concept.

2. Explore new knowledge and teach new courses.

The teaching of (1) binary linear equation.

We already know what a binary linear equation is. Let's finish the exercise.

Exercise 1

Judge whether the following equations are binary linear equations and explain the reasons.

① ② ③

④ ⑤ ⑥

Exercise 2

Group exercise: form a group at the same table, with one person giving an example and one person judging whether it is a binary linear equation.

Student activities: Complete exercise 1 in the form of quick answers, and assign several groups of students to complete exercise 2.

Teaching practice shows that this can not only enliven the atmosphere, but also deepen students' understanding of the concept of binary linear equation.

Exercise 3

Exercise on page 6 of the textbook 1.

Question: Is the solution of binary linear equation unique? After the students answered, the teacher came to the conclusion that the univariate linear equation has only one solution, while the bivariate linear equation has infinitely many solutions, each unknown (or) takes a value, and the other unknown (or) has a unique value corresponding to it.

Exercise 4

Fill in the table so that the values of each pair of up and down satisfy the equation.

-2 0 0.4 2

- 1 0 3

Teachers and students * * * have the same summary method: knowing, seeking, and using algebraic expressions containing, for; What is known, discovered and expressed by the algebraic expression of inclusion is.

The teaching method shows that through this exercise, students can really understand that binary linear equations have infinite solutions; Moreover, the binary linear equations can be expressed as an algebraic expression of one unknown to another, which lays the foundation for solving the binary linear equations by substitution method.

(2) The teaching of binary linear equations.

The above problem contains two conditions that must be met at the same time. One is that banana and apple * * * bought 9 kilograms, and the other is that * * * paid 33 yuan, that is, both equations must be satisfied at the same time. So these two equations are written together.

These two equations together form a binary linear equation system.

In the equation, the same letter must represent the same quantity to be combined.

Exercise 5

Known, all unknown, determine whether the following equations are binary linear equations?

① ②

③ ④

The teaching method shows that Exercise 5 is helpful for students to understand the concept of binary linear equations, so as to avoid students' misunderstanding of binary linear equations.

For the former problem, it is easier to establish binary linear equations than unitary linear equations. According to the result of the last solution, we can know that we bought 3 kilograms of bananas and 6 kilograms of apples, that is, here, we satisfy Equation ① and Equation ② at the same time, we say.

This is a system of binary linear equations.

Solution.

Student activities: Try to summarize the concept of the solution of binary linear equations, and speak freely after thinking.

Teachers correct and guide the writing on the back board;

The values of two unknowns that make the left and right sides of two equations of binary linear equations equal are called the solutions of binary linear equations.

Examples judge whether it is the solution of binary linear equations.

Student activities: examples of oral answers.

This example is the focus of this lesson. Through this example, students clearly realize that the solution of binary linear equations must satisfy two equations at the same time; At the same time, cultivate students' serious calculation habits.

3. Try feedback to consolidate knowledge

Exercise: (1) Title 2 on page 6 of the textbook: Highlight the key points of this lesson.

(2) The title 1 on page 7 of the textbook aims to cultivate the accuracy of students' calculations.

4. Variant training, training ability

Exercise: (1) P84.

The explanation of teaching methods makes students have a deeper understanding of the concept of the solution of binary linear equations, which lays the foundation for solving binary linear equations.

(2)P8 B group 1.

The explanation of teaching methods lays a foundation for finding the equivalence relation of binary linear equations and cultivates students' ability to analyze and solve problems.

(4) Summary and expansion

1. Let the students speak freely and find out what they have gained in this class.

2. The teacher clearly requires that understanding binary linear equations, binary linear equations and the meaning of their solutions will test whether a pair of values is the solution of a binary linear equation.

3. Hot spots in the senior high school entrance examination: there are sometimes problems in the senior high school entrance examination to test whether a coordinate point is on a resolution function.

Eight, homework

(1) Required question: P73.

(2) Multiple choice questions: P8 B group 2.

(3) Preview: Page 9 ~ 13 of the textbook.

Reference answer

leave out

Comments on teaching plans:

The combination of situational teaching, teachers' guidance and guidance, students' active participation and gradual understanding, teachers' summary and students' independent learning evaluation can improve the efficiency of classroom teaching and fully embody the principle of learning-oriented.