Teaching is actually how you teach and why you teach like this. Speaking lessons is also a necessary part of the teacher qualification examination and the teacher recruitment examination. The following is a model essay on the lecture of "Inequality Solution Set" in junior high school mathematics. Welcome to learn!

Lecture notes on inequality solution sets

Hello, judges and teachers! I said that the topic of the class is "Solution Set of Inequalities" in the second quarter of Chapter 8 of the seventh grade junior high school mathematics. I will elaborate the design of this course from teaching material analysis and other aspects.

I. teaching material analysis

This lesson studies the solution set of inequality and its representation on the number axis. Prior to this, students have preliminarily learned inequality and inequality solution. This part not only plays a connecting role in this chapter, but also lays a foundation for the application of learning functions in the future, so it is in a very important position in the teaching materials. The solution set of a linear inequality is a generalization of the solution of the previous linear equation, and there are both differences and connections between them. Representing the solution set of inequality on the number axis is another time for students to come into contact with the corresponding relationship between graphics and quantities after learning the number axis, and also provides methods and basis for future function learning.

Second, the target analysis

According to the students' existing cognitive foundation and the current situation of undergraduate textbooks, mathematics teaching is not only the imparting of knowledge and the training of skills, but also the cultivation of ability and emotional education, so the teaching goal is determined as 1, 2,3.

Namely:

1. Knowledge goal: to understand the meaning of inequality solution set and its representation on the number axis.

2. Ability goal: establish the corresponding relationship between number and quantity, express the solution set of inequality on the number axis, and infiltrate the mathematical idea of combining number and shape.

3. Emotional goal: guide students to participate in the discussion of problems on the basis of independent thinking, stimulate students' interest in actively acquiring knowledge, and enhance their learning confidence.

Teaching emphasis: solution set and representation of one-dimensional linear inequality.

Teaching difficulties: the meaning of one-dimensional linear inequality solution set and the representation of inequality solution set on the number axis.

Breakthrough method of teaching difficulties: through observation, analysis and induction, students can have a preliminary understanding of the solution set of inequality, and then express the solution set of inequality intuitively through the number axis, thus deepening students' understanding of the solution set of inequality.

Third, the analysis of teaching methods

In order to create a relaxed and democratic learning atmosphere, stimulate students' initiative in thinking, and successfully complete the teaching objectives, guided discovery method and computer-aided teaching are adopted according to students' characteristics and actual situation. Connect students' self-feedback, cooperation and exchange among groups and information between teachers and students in time to form multi-level and multi-faceted cooperation and exchange, and jointly discover and acquire knowledge. The process of students mastering knowledge is inseparable from their own intellectual activities. Therefore, in teaching, we should guide students to observe, analyze, explore the old and explore the new, guess and demonstrate, and reveal mathematical problems, and take various forms such as personal thinking, group discussion, and result report, so that every student can participate in learning, and let students feel the truth and draw conclusions in the process of acquiring knowledge, thus enhancing their self-confidence in learning mathematics.

Fourthly, the analysis of learning methods.

1. Students should think deeply, turn practical problems into mathematical models, and form a good habit of thinking seriously.

2. Cooperative analogy: In the learning process, students discuss with each other and draw inferences from others.

Teaching process of verbs (abbreviation of verb)

1. Create scenarios and ask questions.

Through the practical application of the problem, let the students find several solutions that meet the meaning of the problem first, and then find the problem. In this way, they not only reviewed inequalities, but also paved the way for new courses. It can be found that there are many solutions to inequality, which form a set called inequality solution set. This not only conforms to the cognitive law, but also finds the best starting point, which makes students have the desire to explore, thus leading to the solution set of inequality.

Explore new knowledge

Through discussion, communication and induction, it is concluded that every number greater than 3 is an inequality x+2 >; 5, and every number less than 3 is not the inequality x+2 >; 5, so the inequality x+2 >; 5 there are infinitely many solutions, which form a set, which is called the unary inequality x+2 >; 5 sets of solutions. That is, it is represented as x>3.

The solution set of inequality and the concept of solution inequality are summarized by examples: all solutions of an inequality constitute the solution set of this inequality, which is called the solution set of this inequality for short; The process of finding the solution set of inequality is called solving inequality.

As we know, the solution of inequality should not only seek individual solutions, but also its solution set. Generally speaking, the solution set of inequality is not composed of one number or several numbers, but an infinite number, such as x>3. So how to express inequality x+2 > intuitively on the number axis? Solution set x > 5；; What about 3? The inequality solution set x>3 can be expressed intuitively on the number axis. As shown in figure 8.2. 1.

If an inequality x? -2, can also be intuitively expressed on the number axis, as shown in figure 8.2.2.

Note: 8.2. 1 Draw a hollow circle at the point indicating the performance of the fan, but this point is not in the table, which means turning right when it is big; In Figure 8.2.2, a black dot is drawn on the point indicating -2, indicating that this point is included, indicating that it turns left in hours.

3. Explain supplementary examples,

Example 1: Judgment:

①x=2 is the inequality 4x.

② x=2 is the inequality 4x.

Example 2. Represent the solution set of the following inequality on the number axis:

( 1)x & lt； 2

(2)x？ -2

(Design intent: Example 1 is to let students understand the solution of inequality and the solution set of inequality. Connection and difference, Example 2 reveals a corresponding relationship between the solution set of inequality and the range of numbers on the number axis, which further deepens students' understanding of the solution set of inequality and makes them further understand that the method of combining numbers and shapes has the advantages of being vivid, intuitive and easy to explain)

4. Consolidation exercises: Exercise 2 and Exercise 3 on page 44 of the textbook.

5. To sum up,

Combined with blackboard writing, guide students to sum up by themselves, focus on explaining knowledge and learning methods, and achieve the purpose of grasping the key points and being logical.

6. Homework: Exercise on page 49 of the textbook 1, 2.

Design intention: to promote students to review the text in time, consolidate and strengthen what they have learned and improve their ability to solve problems.

Attached book design: (omitted)

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