Teaching material analysis: The content of this section is selected from the second section of the second lesson of binary linear equations in Chapter 8 of Mathematics for Grade Seven published by People's Education Publishing House. This lesson is based on the fact that students have learned to solve binary linear equations by substitution and elimination. It is a further in-depth study of elimination thought and the premise and foundation for students to systematically learn binary linear equations. Through addition and subtraction, the purpose of elimination is achieved, so that students can fully understand the transformation process from unknown to known, understand and master the most commonly used basic methods for solving binary linear equations, and lay the foundation for learning functions and other knowledge in the future; On the other hand, binary linear equations is one of the key contents of junior high school mathematics, which is the continuation and perfection of linear equations knowledge and the basis of learning other mathematical knowledge. In view of this understanding, I think this lesson has played a role in connecting the past with the future. In addition, this lesson will also explain the addition, subtraction and elimination methods from the system of "one thought, two types and five steps", so that students can establish a systematic knowledge system.

Analysis of learning situation

1. knowledge base:

(1) Primary school stage: In primary school stage, students have a preliminary understanding of equations and can solve simple equations.

(2) Junior high school stage: Students further study equations and basically master the process and steps of solving linear equations with one variable.

2. Cognitive level: Students initially have the ability to observe, analyze and summarize knowledge, have certain learning experience and group activities experience, have a certain sense of cooperation and ability, and will conduct certain cooperative explorations under the guidance of teachers.

Teaching objectives

Knowledge and skills:

1. Simple binary linear equations can be solved by addition, subtraction and elimination.

2. Understand the basic idea of the method of addition, subtraction and elimination, and realize the thought method of turning the unknown into the known.

Process and method:

1. By watching the video, experience the process of adding, subtracting, eliminating and solving equations, so that students can experience the application of eliminating ideas.

2. Through guidance, discussion and communication, let students understand the general steps of solving binary linear equations according to the method of addition, subtraction and elimination.

3. Complete the limited-time puzzle by watching the video.

Emotions, attitudes and values:

1. Improve students' abilities of observation, induction and analogy.

2. Cultivate students' ability of unity and cooperation through cooperative inquiry.

3. Cultivate students' awareness and ability of group cooperation.

Teaching emphases and difficulties

Emphasis: We will use addition, subtraction and elimination to solve simple binary linear equations.

Difficulties: Flexible use of the skills of addition, subtraction, multiplication and division to convert "binary" into "single"

teaching method

Cooperative inquiry method, combination of lecture and practice method, and micro-lesson counseling method

Teaching AIDS and media

Onion video, blackboard, multimedia equipment

teaching process

Introduce new courses:

1. Learn new things by reviewing old ones.

Warm up:

Students, last class, let's review the relevant knowledge of solving binary linear equations by substitution and elimination.

1, eliminated:

2, into the elimination method:

(1) An idea: Destroy Yuan?

(2) Basic steps: five steps

(Teacher: Ask questions and bring out knowledge. Student: Recall the knowledge according to the teacher's thinking and build a knowledge framework. )

(Design intent: Help students to build a knowledge system and knowledge framework. At the same time, prepare for the introduction of new courses. )

3 Example Application Review

Teacher-student interaction: Watch the onion video and review the ideas and steps of substitution and elimination. )

(Design intention: further consolidate how to solve binary linear equations by substitution elimination method)

Zhixin:

In fact, method of substitution is not a universal formula for solving binary linear equations. Do you know how to solve the following binary linear equations? Can you solve it quickly by substitution method?

(Teacher-student interaction: think about the questions raised by the teacher and try to substitute)

(Design intention: By asking questions, this paper introduces a new method of solving binary linear equations by adding, subtracting and eliminating elements, and at the same time, lets students try to understand the limitations of solving binary linear equations by substitution. )

Teach new lessons:

Step 2 learn new knowledge

Through just trying, I believe all the students feel the difficulty of solving this binary linear equations with method of substitution. Let's learn a new method to solve binary linear equations-addition, subtraction and elimination with "Little Onion Cute".

(A) addition and subtraction elimination method

Limitations of 1. substitution method

2. Addition, subtraction and elimination method

(Teacher-student interaction: watch the video to understand the limitations of substitution method, and at the same time understand the basic steps of addition and subtraction)

(Design intent: Through video, let students intuitively feel the limitations of method of substitution and vividly understand the process of addition, subtraction, multiplication and division.)

Through the study of the video just now, can you talk about addition, subtraction and elimination? What are the basic steps to solve the binary linear equation by adding, subtracting and eliminating?

(group discussion)

(1) addition and subtraction elimination method

(2) Element addition, subtraction and elimination problem solving steps.

Teacher-student interaction: students discuss in groups, learn the basic concepts of addition, subtraction and elimination independently, summarize the basic steps of solving binary linear equations, be familiar with simple methods, and let teachers patrol and guide. )

(Design intention: Let students understand concepts in the process of thinking and induction, and cultivate students' teamwork ability. )

What are the characteristics of using addition and subtraction to solve binary linear equations in video learning by analogy substitution? That is, when can we solve binary linear equations by adding, subtracting and eliminating?

(Teacher-student interaction: The teacher guides the students to observe the coefficient of the unknown quantity, and the students observe and summarize the final result while listening. )

(Design intention: to cultivate students' summing-up ability and help students break through the key points)

(B) the application of addition, subtraction and elimination.

I The coefficient of the same unknown is the same or opposite.

(Teacher-student interaction: Students and teachers watch videos together to test the conclusion. )

How to destroy Yuan:

The coefficients are the same: subtraction and elimination.

The coefficients are opposite: addition and cancellation.

Teacher-student interaction: watch the video to understand how to eliminate the same unknown when the coefficients are the same or opposite. At the same time, the steps of solving this kind of binary linear equations are clarified again, so that students can clearly take the first two steps of addition, subtraction and elimination as their own characteristics. After the teacher plays how to destroy Yuan, pause the video to lead the students to recall and summarize again. )

(Design intent: Let students know how to eliminate elements, and at the same time help students strengthen knowledge points through video and teacher's summary again. )

practice

According to the study just now, we know that the characteristic of substitution elimination method in solving binary linear equations is to choose the correct elimination method according to the characteristics of coefficients. Then, we will train this key step through practice.

1. Who and how to eliminate it?

Eliminate unknowns with equal or opposite coefficients,

If the coefficients are the same, you want to subtract them; if the coefficients are opposite, you want to add them.

Teacher-student interaction: students watch videos and learn how to add, subtract and eliminate elements.

(Design intent: Let students intuitively understand the addition, subtraction and elimination methods through the video, and make it clear that the addition, subtraction and elimination methods refer to the addition and subtraction of similar items. )

In mathematics learning and real life, this kind of binary linear equations with the same or opposite coefficients is rare and inevitable, and it is more common for the following. How to solve the popular binary linear equations by addition, subtraction and elimination?

(Teacher-student activities: teachers ask questions and students think)

(Design intent: Introduce the generality and universality of addition, subtraction and elimination method. )

Ⅱ The same unknown coefficient is different, not the opposite number.

Teacher-student activities: Students watch the video carefully and think about how to solve ordinary binary linear equations by addition, subtraction and elimination.

(Design intent: Use video to visually show how to solve binary linear equations with different coefficients by addition and subtraction. The key step is to unify the coefficients. )

By watching the video, can you talk about the key steps of how to solve the general binary linear equations by addition, subtraction and elimination?

Deformation: coefficient unification of unknown to be eliminated

Teacher-student activity: Students think and answer according to the video.

The teacher summed up the methods and key steps again. )

(Design intention: break through the difficulties and help students strengthen their memory)

Exercise:

According to the analysis, please think about how to solve the following equation by elimination method.

Idea: unify the coefficient of x and eliminate x; Unify the coefficients of y and eliminate y

How to unify the coefficients of unknown quantities?

I. add, subtract and eliminate y to solve binary linear equations.

You first know how to eliminate elements by choosing options, and then point out that the essence of this step lies in 6, that is, 6 is the least common multiple of the coefficients 2 and 3 of Y, so that students can clearly understand the method of unifying coefficients-finding the least common multiple.

By comparing with other methods, the reasons for finding the least common multiple by unifying coefficients are summarized.

Teacher-student activities: Watch the video, make clear the specific method of eliminating the uniform coefficient, and understand the reason why the uniform coefficient is the least common multiple. )

(Design intent: Let students know the key steps of addition, subtraction, multiplication and division and master them)

According to what you have just learned, can students talk about how to unify the unknowns and eliminate them?

Find the least common multiple of the coefficient of the unknown quantity to be eliminated, and delete the formula after deformation.

(Teacher-student activity: The teacher introduces the students to summarize how to unify the unknown coefficients again, which is suddenly difficult)

(Design intent: Help students to strengthen knowledge points)

Two. Add, subtract and eliminate x to solve binary linear equations

So according to the video study just now, can you talk about how to eliminate X? (discuss at the same table)

(Teacher-student activities: Teachers ask questions, students discuss with their deskmates according to their learning situation, and use knowledge points)

(Design Intention: Let students draw inferences from others and exercise the ability of knowledge transfer)

Then let's check whether our idea of eliminating X is correct through video.

(Teacher-student activity: Watch the video to test your mastery)

(Design intent: Let students break through the difficulty of unifying coefficients again through video. )

So according to the study just now, can you sum up the steps to solve the binary linear equations?

A) deformation (find the least common multiple of the unknown coefficient to be eliminated)

B) adding, subtracting and eliminating elements (from binary to binary)

C) solving equations

D) the next generation

E) writing solutions

Teacher-student activities: teachers ask questions, and students summarize the steps of solving binary linear equations by adding, subtracting and eliminating according to the learning process.

(Design intention: Through combing, students can understand the steps of solving problems, strengthen the cognitive process and enhance their application ability.)

(3) The application principle of addition, subtraction and elimination.

Then do you know why the two equations can be added and subtracted? Please watch the video to understand the mathematical principle of addition, subtraction, multiplication and division.

Application principle:

The property of the equation is 1,

Properties of Equation 2

(Teacher-student activity: Watch the video to understand the principles of addition, subtraction and elimination)

(Design intention: let students know the application principle of relevant knowledge)

Consolidation exercise:

Two. Consolidation and promotion

Please complete the exercise 1( 1)(2) on page 96 of the textbook according to what you have learned.

(Classroom workbook)

Teacher-student activities: Students apply addition, subtraction and elimination methods according to what they have learned. The teacher makes a patrol, reviewing in class while guiding)

(Design intention: let students use and be familiar with what they have learned, and consolidate and apply it)

Knowledge summary

Watch the video, please recall the whole solution process and its thinking again, and summarize and sort out the knowledge learned in this section.

Video memory:

Knowledge combing;

Solving binary linear equations by addition, subtraction and elimination method

1. Solution: Elimination

Step 2: Solve the problem

(1) deformation (different coefficient): unified coefficient: find the least common multiple of the coefficient of the unknown quantity to be eliminated.

(2) Adding, reducing and eliminating elements (from binary to binary)

(3) Solving equations

(4) the next generation

(5) Write a solution

note:

1. Find the unified coefficient of the least common multiple.

2. The deformation multiplication coefficient of the formula should be multiplied by the whole equation, and no item can be missed.

3. Pay attention to the test after solving the equation

(Teaching activities: Students are required to recall and summarize what they have learned by filling out forms)

(Design intention: summarize the key points and difficulties in this section and make a breakthrough)

Task:

Complete the onion video matching exercise (6 questions)

Blackboard design:

Teaching reflection:

Learning by playing onion videos greatly improves students' interest and attention in learning. At the same time, the onion video shows the ideas and steps of adding, subtracting and eliminating elements, which makes students understand more intuitively and clearly. At the same time, it also saves the time for teachers to write on the blackboard and greatly improves the effectiveness of classroom teaching.

It fully embodies the advantages of modern teaching. In the teaching process, the familiarity with video nodes needs to be strengthened, and the use of onion videos can be increased in future teaching.