1、 Talking about textbooks

（1） Teaching content

The main content of this lesson is the concept of proposition, which can rewrite the form of "if p, then q", and permeate the transformation mathematical thought from special to general.

（2） The position and role of textbooks

The concept of proposition, if p then q form proposition is the important content of this chapter and the basis of sufficient and necessary conditions for subsequent learning. In this chapter, we learn common logic terms on the basis of junior high school, understand the role of logic terms in expressing and demonstrating, which will become the theoretical basis for the method of disproof, and lay the foundation for further learning, especially for cultivating students' thinking ability and reasoning ability

（3） Teaching objectives

1. Knowledge and skills:

(1) Understand the concept and composition of proposition, judge whether a given statement is a proposition, and judge whether a proposition is true or false;

(2) Can rewrite the proposition into the form of "if p, then q";

2. Process and method:

(1) Let students give more examples of propositions to develop their ability of discrimination;

(2) Can rewrite the proposition into the form of "if p, then q"; Cultivate students' ability to find, raise, analyze and solve problems creatively; Cultivate students' abstract generalization ability and thinking ability

3. Emotions, attitudes and values:

Through the participation of students, stimulate students' interest in learning mathematics.

（4） Teaching focus:

The concept and composition of proposition

（5） Teaching difficulties:

Distinguish the condition and conclusion of proposition and judge the truth and falseness of proposition

Second Way of Teaching

The teaching process is a process of joint participation of teachers and students, and a process of multi-directional cooperation between teachers and students. Students are encouraged to learn independently and fully mobilize their enthusiasm and initiative. Based on student development, I effectively infiltrate mathematical thinking methods to improve students' quality. According to such principles and teaching objectives to be achieved, and in order to stimulate students' interest in learning, I adopt the following teaching methods:

(1) Guided discovery method

(2) Practice consolidation method

3、 Didactic method

Teaching students learning methods is more important than teaching them knowledge. In this lesson, we should pay attention to mobilizing students to think actively, explore actively, and let students participate in teaching activities as much as possible. I give the following guidance on learning methods:

(1) The classification method from special to general: under the guidance of teachers, students can observe, discuss, explore, analyze, discover, summarize and summarize through specific cases

(2) Practice consolidation method

4、 Teaching process

Student inquiry process:

1. Thinking and analysis

What are the characteristics of the following statements? Can you judge whether they are true or false?

(1) The sum of the three internal angles of a triangle is 1800

(2) If a and b are any two positive real numbers, then a+b ≥ 2 (ab) 1/2;

(3) If the real number a satisfies a2=9, then a=3;

(4) The current academic burden of middle school students is too heavy;

(5) China will reach the level of moderately developed countries by the middle of this century

2. Discussion and judgment

Through discussion, students can conclude that all sentences are in the form of declarative sentences, and each sentence judges what is going on. Where (1) (2) is true, (3) is false, and (4) (5) needs to be determined according to the actual situation, and it can always be determined

Teacher's guidance and analysis: the so-called judgment is to affirm what a thing is or is not, and cannot be ambiguous.

3. Abstraction and induction

Definition: Generally, we call statements that can be judged true or false expressed in language, symbol or formula as propositions. The statements that are judged true are called true propositions, and the statements that are judged false are called false propositions

The main point of the definition of propositions: declarative sentences that can judge truth and falsehood

In mathematics class, only mathematical propositions are studied. Students are asked to give some examples of mathematical propositions. Teachers and students will judge whether the examples given by students are propositions from the definition of propositions, and deepen their understanding of the concept of propositions from the perspective of "judgment"

Example 1: Which of the following statements is a proposition? Is it true or false?

(1) An empty set is a subset of any set; True proposition

(2) If integer a is prime, then a is odd; (false proposition)

(3) Is exponential function an increasing function? (Not)

(4) If two lines in space do not intersect, they are parallel; (false proposition)

(5) X>15. (Not)

Let the students think, analyze, discuss and solve, and guide them to conclude through practice: the key to judge whether a sentence is a proposition is two points: first, "declarative sentence", second, "can judge whether it is true or false". These two conditions are indispensable. Questions, imperative sentences, exclamatory sentences are not propositions

practice

Determine which of the following statements is a proposition? Is it true or false?

(4) To prove that π is an irrational number

(5) If X is a real number, X2+4X+5 ≥ 0

4. Composition of propositions - conditions and conclusions

In example 1 above, (2) and (4) have the form of "if p, then q". In mathematics, propositions of this form are common

"If p, then q" can also be written as "if p, then q", "as long as p, there is q" and other forms

Where p is the condition of the proposition and q is the conclusion of the proposition

Example 2 points out the condition p and conclusion q in the following propositions;

(1) If integer a can be divided by 2, then a is even;

(2) If a quadrilateral is a diamond, its diagonals are perpendicular to each other and bisected

Solution: (1) Condition p: integer a can be divided by 2. Conclusion q: integer a is even;

(2) Condition p: A quadrilateral is a diamond. Conclusion q: The diagonals of the quadrilateral are perpendicular to each other and bisected

Some propositions are not in the form of "if p, then q" on the surface, but can be rewritten into the form of "if p, then q", for example:

Two planes perpendicular to the same line are parallel

If two planes are perpendicular to the same line, they are parallel

Example 3 reword the following proposition into the form of "if p, then q", and judge whether it is true or false;

(1) Two lines perpendicular to the same line are parallel;

(2) The cube of a negative number is a negative number;

(3) Equal to the vertex angle;

Solution: (1) If two straight lines are perpendicular to the same straight line, the two straight lines are parallel, which is a false proposition.

(2) If a number is negative, its cube is negative. It is a true proposition.

(3) If two angles are opposite to each other, they are equal. It is a true proposition.

5. Exercise: P4:1.2.3

6. Class summary

(1) Concept of proposition

(2) Be able to point out the conditions and conclusions of the proposition

7. Thinking questions

1、 In the following four propositions, what are the conditions and conclusions of proposition (1) and proposition (2) (3) (4) respectively?

(1) If f (x) is a sine function, then f (x) is a periodic function;

(2) If f (x) is a periodic function, then f (x) is a sine function;

(3) If f (x) is not a sine function, then f (x) is not a periodic function;

(4) If f (x) is not a periodic function, then f (x) is not a sine function;

2、 Is there any relationship between any two of the four propositions? What is the relationship? Is there any relationship between their authenticity? What is the relationship?

8. Homework P8: Exercise 1.1 Group A, Question 1