I. Analysis of key points and difficulties
The teaching focus of this section is to let students learn to use substitution method. What are the teaching difficulties? It lies in the flexible use of substitution method, which should be solved through a certain amount of practice; Another difficulty is that after finding the value of an unknown by substitution method, we don't know which equation to substitute to find the value of another unknown.
The key to solving binary linear equations lies in elimination, that is, changing binary into unitary. We eliminate an unknown by equivalent substitution, so as to get the solution of the original equations.
Second, the knowledge structure
Three. Suggestions on teaching methods
1. On the question of testing the solutions of equations, the textbook points out: "When testing, it is necessary to substitute a pair of unknown values into each equation in the original equation set to see whether the left and right sides of the equation are equal." In teaching, we should emphasize "original equations" and "one for each". The function of the test is to make students further clear that substitution method is a basic method to solve equations.
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This pair of values is the solution of the original equation, and they must make the left and right sides of the two equations equal; Thirdly, because we don't use the same solution principle of equations, we use substitution (the transfer of equations) to solve equations, so we need to check whether the obtained pair of values are the solutions of the original equations; Fourth, in order to prevent distortion and calculation errors, the exam can be calculated orally or on draft paper, which is not written in the textbook.
2. In teaching, it should be pointed out that the key to solving binary linear equations here lies in elimination, that is, transforming "binary" into "unitary". We eliminate an unknown by equivalent substitution, so as to get the solution of the original equations. It is necessary to point out the idea of elimination and the method of transforming "binary" into "single" earlier, so that students have a strong purpose.
3. When explaining examples, teachers should pay attention to changing from simple to complex, from easy to difficult, and gradually deepen. Because the examples are from simple to complex and from easy to difficult, special emphasis should be placed on simplifying the deformation equation and simplifying it after substitution. This will not only solve the problem quickly, but also reduce errors.
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First, the goal of quality education
(A) the main points of knowledge teaching
1. Master the steps of solving binary linear equations with method of substitution.
2. Using method of substitution skillfully to solve simple binary linear equations.
(2) Key points of ability training
1. To cultivate students' analytical ability, they can quickly choose an equation with simple coefficients from a given set of deformed binary linear equations.
2. Train students' operational skills and develop the habit of testing.
(C) moral education penetration point
Eliminate elements and transform the unknown into known mathematical ideas.
(D) the starting point of aesthetic education
Through the study of this lesson, I realized the penetrating mathematical beauty and the peculiar mathematical beauty embodied in equation solving.
Second, the guidance of learning methods
1. Teaching methods: guided discovery, practice, and attempted guidance.
2. Students' learning methods: We have learned how to solve the one-dimensional linear equation, and the key to solving the two-dimensional linear equation is to turn the two-dimensional equation into one-dimensional linear equation, so we should always master the thinking method of elimination in the process of solving.
Three. Key points, difficulties, doubts and solutions
(-) Key points
Let students use method of substitution to solve binary linear equations.
(2) Difficulties
Flexible use of substitution skills.
(3) Doubts
How to "divide elements" and "binary" into "single"
(4) Solutions
On the one hand, review the method of using one unknown to represent another unknown, on the other hand, learn to choose an equation with simple coefficients for deformation:
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. The teacher asked how to express an unknown with another one, and compared which one is simpler, for example.
2. Through the application of bananas and apples in textbooks, guide students to enumerate the linear equation of one yuan or the linear equation of two yuan, and explore the method of solving the equation through comparison and attempt.
3. Through comparison and trial-and-error, it is found that the equation with simple coefficient is simpler, and the method of solving the equation with method of substitution is simpler, and the law of solving is found out.
Seven, teaching steps?
(-) Clear objectives
In this lesson, we will learn to use method of substitution to find the solution of binary linear equations.
(B) the overall perception
By reviewing the method of using one unknown to represent another unknown, this paper introduces the solution process of transforming binary equation into univariate equation by substitution method, that is, solving binary linear equations by substitution elimination method.
(3) Teaching steps?
1. Create a scene and review the introduction.
(1) The known equation is expressed by the contained algebraic expression first, and then by the contained algebraic expression. Compare which form is simpler.
(2) multiple choice questions:
The solution of binary linear equations is
A.B. C. D。
The teaching instruction (1) is entitled "Using method of substitution to Solve Binary Linear Equation to Lay the Foundation"; Question (2) not only reviewed the key points of the last lesson, but also became the material for introducing new lessons.
Through the study of last class, we will check whether a pair of values is the solution of a binary linear equation system. Then, when a binary linear equation system is known, how to find its solution? We will study in this class.
This introduction can stimulate students' thirst for knowledge.
2. Explore new knowledge and teach new courses.
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: List one-dimensional linear equations and two-dimensional linear equations respectively, and perform by two students.
Suppose you buy one kilogram of bananas, then you buy one kilogram of apples.
Suppose we buy a kilo of bananas and a kilo of apples.
We can solve the linear equation of one variable above with one variable. Can you convert a binary linear equation into a univariate linear equation? We can get ③ from Equation ①, and we can get it by converting it into Equation ②, that is, substituting Equation ③ into Equation ②. In this way, the binary linear equation can be transformed into a unitary linear equation, from which we can get.
Solution: Get from ①: ③
Substitute ③ into ② to get:
∴
Substitute in ③ and you get:
∴
This teaching method shows students the process of knowledge generation by solving a binary linear equation group, which is very important for the formation of students' knowledge.
The above method for solving binary linear equations is substitution elimination method. Can you briefly talk about the basic idea of solving binary linear equations with method of substitution?
Student activities: group discussion, elected representatives to speak, teacher guidance. Modified induction: try to eliminate an unknown number and transform the binary linear equations into the univariate linear equations.
Example 1? solve an equation
(1) Observing the above equation, how should we eliminate it? (Replace ① with ②)
(2) After substituting ① into ②, it can be eliminated, and a linear equation about is obtained.
(3) Which equation is easier to find offspring? (①)
Student activity: After answering the questions in turn, the teacher writes on the blackboard.
Solution: Substitute ① into ②.
∴
Substitute (1) to get
∴
How to check whether the result is correct?
Student activities: oral test.
Teacher: Substitute the obtained results into the equations of the original equations.
Explaining the teaching method, the three questions raised after giving the example of 1 are exactly the students' thinking process, which clarifies the thinking of solving problems; The teacher gave an example of 1 to standardize the solution format of binary linear equations; Through inspection, students can develop rigorous and serious study habits.
Example 2? solve an equation
An equation must be transformed into the form of equation ① in the example 1, and then it can be eliminated by substituting it into another equation. The coefficient in Equation ② is 1, which is relatively simple. Therefore, Equation ② can be deformed first, expressed by an inclusive algebraic expression, and then substituted into Equation ① for solution.
Student activity: Try to finish Example 2.
Teachers patrol guidance, find and correct students' problems, and standardize the writing process.
Solution: from 2, get? ③
Substitute ③ into ① to get.
∴?
∴
Substitute (3) into (3) to obtain.
∴
∴
After the inspection, the teacher and students discuss:
(1) After getting ③ from ②, is it ok to substitute ②? (No) Why not? (Identity obtained, unable to solve)
(2) Can you find it by substituting ① or ②? What are the advantages of substituting (can) into ③? (Simple operation)
Student activities: According to the problem-solving process of Example 1 and Example 2, try to summarize the general steps of solving binary linear equations with method of substitution, and then select representatives to discuss and speak. Then look at the textbook 12 page and summarize each step in a few words.
Teacher's blackboard writing:
Deformation ()
(2) Substitution elimination ()
(3) It is () that solves the linear equation of one variable.
(4) Substitution for solution
Exercise: P 13? 1.( 1)(2); P 14？ 2.( 1)(2).
3. Variant training, training ability
(1) can be expressed as.
(2) in，when，； When, then; .
③ Selection: If it is the solution of the equation, then ()
A.B. C. D。
(4) Summary and expansion
1. the idea of solving binary linear equations:?
2. Steps to solve binary linear equations with method of substitution.
3. method of substitution's skills in solving binary linear equations: ① Deformation skills ② method of substitution skills.
Through the study of this lesson, we should skillfully use method of substitution to solve binary linear equations and check whether the results are correct.
Eight, homework?
(1) required questions: P 15 1. (2) (4), 2.( 1) (2) (3) (4).
(2) Select the topic: P 15 B group 1.
Reference answer
( 1) 1.(2) (4)
2.( 1) (2) (3) (4)
(2),