As an excellent people's teacher, you need to prepare a lecture at ordinary times, which can correct the shortcomings of lectures well. So what problems should we pay attention to when writing a speech? The following is my collection of junior high school mathematics lecture notes-"Factorization", welcome to share.
Draft of junior high school mathematics handout-Factorization 1 What I'm talking about is that the topic of this course is selected from Factorization in the fourth quarter of Chapter 14 in the first volume of Grade 8 of East China Normal University Edition, which is a classic of junior high school mathematics tradition. Under the concept of new curriculum standards, we should re-understand its profound connotation.
To this end, I set the lecture program as follows:
First, re-examine the educational value of factorization.
Second, the idea of teaching materials processing
Third, the overall design of teaching
Fourth, an overview of the teaching process
(A) re-examine the educational value of factorization
The traditional factorization is a mathematical tool, which can make students master some factorization skills skillfully and make the original simple problems very complicated (such as filling in numbers, decomposing terms, adding and adding, cross multiplication).
The new curriculum takes factorization as the carrier to cultivate students' ability of reverse thinking, comprehensive thinking and flexible conflict resolution. To this end, dilute the theory. Simplify the complex and master the most basic teaching methods (extraction of common factors and formula method). This is the most obvious change in the educational value of the new curriculum. To this end, it is important for this course to work hard on students' thinking methods and understanding of world affairs.
Through the reciprocal inverse transformation of algebraic expression multiplication and factorization, students can make it clear that this inverse transformation is the opposite, not the inverse operation, which is the difficulty in teaching (inverse operation is two operations with different forms and the same essence in a formula, and factorization is two expressions of an identity transformation).
In order to realize the educational value of this class, in the determination of teaching objectives, the key consideration is that my students are weak in understanding, good at imitation and content with a little knowledge. I am convinced that:
1, the ability goal of knowledge: understand the significance of factorization, master the method of extracting common factors and formulas, stimulate students' interest in learning, and cultivate students' ability to create factorization problems.
2. Methods and process objectives: adopt the method of self-study and self-training, open the doors of students' thinking one by one, learn to look at problems with dichotomy, and experience the process of knowledge occurrence is the whole process of students' thinking development.
3, emotional attitudes and values: through situational teaching, let students stimulate learning emotions in participation, pay attention to the changes of each student's thinking, encourage the success and comprehensive embodiment of students' values, and let students devote themselves to the study of this class with full enthusiasm and a scientific and positive attitude.
(B) Teaching materials processing ideas
As a developer of teaching resources, I reorganize the teaching content, increase the creation of teaching situations, clarify the purpose and motivation, and let students realize the value of this section with practical problems (see teaching process).
(C) the overall design of teaching
Overall framework of teaching: Teachers design practical problems in life, so that students can think in the problem situation → Learn the meaning of factorization by revealing the concept of factorization → Students explore and find common factors and formulas in practice → Skillfully use this method to solve problems, develop students' rational thinking → Cultivate students' creative thinking by compiling questions.
The subject of teaching is concepts and methods. During the 20-minute training, students will explore topics independently and study cooperatively.
(D) Overview of the teaching process
Teaching link 1: Create a situation: "Have you been to Benxi?" "What is the most famous mineral in Benxi?" The iron ore in Waitoushan, Benxi contains 75% iron per ton, and the miners mined 203 tons of stone on the first day. So, what was the iron content of the ore on the first day? (75%×203) The second day's iron mining 198 tons (75%× 198) and the third day's iron mining16 tons (75 %× 2 16). Now the total iron content of the ore mined in these three days is expressed by an algebraic formula: 75 %× 75%(203+ 198+2 16). If 75% is represented by a, and the number of thunder in three days is represented by x, y and z, it is ax+ay+az=a(x+y+z).
Through this example, the concept of factorization is revealed: transforming a polynomial into the product of several algebraic expressions, which is factorization. Combined with ax+ay+az=a(x+y+z), it is revealed that this method is called "just the opposite" common factor extraction method. Through discussion, it is realized that algebraic multiplication and factorization are not inverse operations, but reciprocal transformations, thus breaking through the teaching difficulties and realizing the first teaching.
Teaching link 2: Thinking is carried out in exploration: in teaching, grasping the "reverse direction" allows students to consider from the reverse direction of thinking, and how to decompose factors is completed by students here.
A(x+y+z)=ax+ay+az。
ax+ay+az=a(x+y+z)
a2—b2=(a+b)(a—b)
a2+2ab+b2=(a+b)(a+b)
(making courseware)
Multiplicative factorization of algebraic expressions
Prototype monomial and polynomial, polynomial and polynomial multiply monomial and monomial, monomial and polynomial, polynomial and polynomial add.
Synthetic polynomial order product
Scope that can be completed but not completed: 3ab+5ac+7mn.
Students realize that factorization of polynomials is conditional in practice, and not all polynomials can be factorized. So observation and judgment are very important.
Teaching link 3: fixed thinking teaching: This lesson focuses on mastering 1 and extracting the common factor method. 2. Formula method For this new knowledge point, students are unfamiliar, so first of all, we must remember that this is the first thinking mode.
For example, in the formula method, the square difference formula A2-B2 = (a+b) (a-b).
For example-A2+25b216x2-4/9y2
Function: 1 binomial 2 square 3 different symbols
Teaching link 4: the innovation of problem-making thinking: after students understand the relationship between algebraic multiplication and factorization, it is not difficult to make up many factorization problems (simple and clear, easy to solve).
In short, the focus of teaching is not skilled skills, but the development of thinking, which makes students have profound changes in the values of learning emotions and attitudes.
Draft of Junior Middle School Mathematics Lecture Notes-Factorization 2 i. Textbooks
1, on the position and function of teaching materials.
The content of my speech today is factorization. As far as mathematics is concerned, factorization is a key to open the whole treasure house of algebra. As far as this lesson is concerned, it focuses on two aspects, one is the concept of factorization, and the other is the relationship with algebraic expression multiplication. It discusses the concept of factorization on the basis of students mastering factorization and algebraic expression multiplication. Through the study of this lesson, students can not only master the concept and principle of factorization, but also pave the way for studying fractions, solving equations and algebraic equivalent deformation in the future. So it plays a connecting role.
Second, say the goal.
1, teaching objectives.
"New Curriculum Standard" points out that "the teaching of junior high school mathematics should not only enable students to learn basic knowledge well and develop their abilities, but also pay attention to cultivating students' initial dialectical materialistic views." Therefore, according to the orientation of this section, I set the following teaching objectives:
Knowledge goal: to understand the concept and significance of factorization and master the relationship between factorization and algebraic expression multiplication.
Ability goal:
① Experience the analogy process from factorization to factorization, and cultivate students' ability of observation, discovery, analogy, induction and generalization;
② By understanding the relationship between factorization and algebraic expression multiplication, we can overcome students' mindset and cultivate students' reverse thinking ability;
Emotional goal: cultivate students' habit of being willing to explore and cooperate, experience the success of exploration and feel the joy of success.
2. Teaching emphases and difficulties.
The emphasis is on the concept of factorization. The reason is that understanding the essential attribute of the concept of factorization is the soul of learning the whole chapter of factorization.
The difficulty lies in understanding the relationship between factorization and algebraic multiplication, because students' transformation from algebraic multiplication to factorization is a kind of reverse thinking. Before studying algebraic expression multiplication for a long time, students are prone to "backward-looking inhibition" and hinder the formation of new concepts.
Third, oral teaching methods
1, analysis of teaching methods
In view of the age characteristics and psychological characteristics of junior one students and their knowledge level, I adopt heuristic and discovery teaching methods to cultivate students' ability to analyze and solve problems. At the same time, it follows the teaching principles of teacher-oriented, student-oriented and training-oriented.
2. Guidance on learning methods
Teachers inspire students to become the main body of behavior. As the new curriculum standard requires, let students "practice, explore independently, cooperate and communicate".
3. Teaching methods
Multimedia-assisted teaching is adopted to increase classroom capacity and improve teaching effect.
Fourth, talk about the teaching process
The teaching process of this lesson is divided into the following six links:
Create scenarios and introduce new knowledge; Observe and analyze, explore new knowledge;
Teacher-student interaction and application of new knowledge; Strengthen training and master new knowledge;
Organize knowledge and form a structure; Assign homework, consolidate and improve.
The specific process design is as follows:
The first link: create a scene and lead to new knowledge.
1. I'll show you some algebraic multiplication exercises for students to do. Teachers patrol.
After the students finished speaking, the teacher led: Does the above equation hold?
△ Design intention: Arrange the above exercises: 1. Review algebraic multiplication to activate students' original cognitive structure of algebraic multiplication, which is in line with the teaching principle of "reviewing the past and learning the new". The second is to pave the way for achieving the objectives of this section. On this basis, the topic decomposition is introduced.
The second link: observation and analysis, exploring new knowledge.
2. Ask the students to practice again: When A = 10 1 and B = 99, find the value of A2-B2. The teacher made a tour and gave two solutions represented by two students.
△ Design intention: The purpose of arranging this process is to make students realize that changing A2-B2 into the form of algebraic expression product will bring convenience to calculation and conform to the derivation of the concept of factorization.
3. Question is the heart of mathematics. Putting forward a good question will arouse students' curiosity and trigger the climax of teaching, which is an effective driving force for the development of students' knowledge and ability. Therefore, when teaching the concept of factorization, I designed the following two questions:
(1) Can you try to convert A2-B2 into the product of several algebraic expressions? And compared with the factorization of primary school.
(2) What is the relationship between factorization and algebraic expression multiplication?
Let the students discuss in groups of four. Definition of inductive factorization.
A polynomial → algebraic expression+product → factorization.
4. The teacher wrote on the blackboard:
Problems that teachers and students should pay attention to in induction;
(1) Factorization is a variant of polynomial.
(2) The result of factorization is still an algebraic expression;
(3) The result of factorization must be a product;
(4) Factorization is just the opposite of algebraic expression multiplication.
△ Design intention: Through analogy, let students further understand that factorization is the inverse operation of algebraic expression multiplication, and cultivate students' reverse thinking.
The third link: teacher-student interaction, using new knowledge in order to let students further understand that factorization is the inverse operation of algebraic expression multiplication and cultivate students' reverse thinking.
I have specially set up three examples for students to complete independently, fully exposing students' thinking process and making them really become the main body of learning.
△ Design intention: Through the examples of 1 and 2, some specious and error-prone objects are listed for students to discriminate and make them understand the reciprocal relationship between algebraic multiplication and factorization. Promote them to understand the essence of the concept and determine the extension of the concept, thus forming a good cognitive structure. Through example 3, we can understand the simplicity of solving related problems by factorization.
The fourth link: strengthen training and master new knowledge.
Mr. Hua, a mathematician, once said, "Learning mathematics without practicing is like entering Baoshan and returning empty." Proper consolidation and application exercises are very important for learning and mastering new knowledge. In order to promote students' understanding and mastery of new knowledge, I arranged for students to complete two exercises in time.
△ Design intention: Through these two exercises, let students learn to discriminate and factorize this deformation. Make students further understand and master factorization, and lay the foundation for extracting the common factor method of factorization in the next section; At the same time, train, cultivate and develop students' basic skills and abilities.
The fifth link: organizing knowledge and forming structure.
Finally, I designed a table to summarize. It makes students master knowledge as a kind of ability, which is incorporated into the existing cognitive structure, and also cultivates students' generalization and refining ability.
The sixth link: consolidation and improvement of assignment.
In my homework, I arranged reading, exercise books and thinking questions. This not only helps students to consolidate their knowledge, but also enables students at different levels to develop accordingly.
;