Main Chapters of Mathematics in Grade One and Grade Eight (Part One)

Chapter 65438 +0 1 congruent triangles Chapter 65438 +02 Axisymmetric Chapter 65438 +03 Real number.

Chapter 14 Linear Function Chapter 15 Multiplication, division and factorization of algebraic expressions.

Chapters 1 1 and 12 are geometric contents, which mainly allow students to explore congruence and symmetry through hands-on operation. In chapter 14, linear function is difficult, so we should pay attention to modeling ideas in abstraction. Chapter 15 Multiplication, division and factorization of algebraic expressions are very important, especially flexible factorization. According to last year's experience, there are practical activities in the middle of this semester, and the course is more tense, so the first two chapters are relatively simple, and the preview progress should be more compact. Focus on 15, focus on 14.

Chapter 1 1 congruent triangles

Are you online? What are the conditions of triangle congruence? In the first section, eight explorations are designed to let students experience the exploration process of triangle congruence conditions and highlight the design ideas of new textbooks. First of all, let students explore whether one or both of the six conditions that two triangles satisfy the equality of three sides and three angles are necessarily congruent. Then ask students to explore whether two triangles meet three of the above six conditions, and expand them in the following order:

1)SSS； (2)SAS； 3)SSA； (4)ASA； (5) atomic absorption spectrometry; (6)AAA

The overall development is three sides, with one corner on both sides (including (2) and (3)) and two corners on one side (including (4) and (5)) and three corners, which makes it easy for students to master the process of exploration. This kind of processing is also different from the case of judging congruence first, and then giving the case of not necessarily judging congruence. It is more natural to exclude the factors arranged by people as much as possible. Finally, let the students apply the condition of triangle congruence to right triangle, and discuss the condition of right triangle congruence. Among them, the hypotenuse is equal to a right-angled side, so the condition of triangle congruence cannot be applied, and students need to do further experimental exploration.

Chapter 12 Axisymmetry

Are you online? Axisymmetric? In the first chapter, students obtained the properties related to axial symmetry through observation and inquiry. Regarding the relationship between the coordinates of axisymmetric points, the textbook is obtained by asking students to draw some known points and their symmetrical points, determine the coordinates of symmetrical points, and compare the coordinates of each pair of symmetrical points. According to the nature of isosceles triangle, let the students fold the isosceles triangle in half, find out the overlapping line segments and angles, and find out the relevant conclusions by themselves.

Chapter 13 Real Numbers

Compared with the textbooks under the syllabus, this chapter has made some adjustments: (1) strengthened the feeling of the necessity of learning real numbers; (2) Pay attention to the understanding of the meaning of operation and the application of operation in the realistic background; (3) The requirement for accurate operation is reduced, and the denominator is not required to be rational; (4) Strengthen evaluation; (5) Encourage the use of calculators for complex and approximate calculations.

Chapter 14 Functions

? A linear function? Compared with traditional textbooks, the current textbooks pay attention to the process of knowledge exploration and highlight mathematics. Modeling? Thought; Pay attention to the cultivation of students' imaginative thinking ability and improve students' utilization rate? Combination of numbers and shapes? Ability to solve problems; Attention? A linear function? The application of this method strengthens the connection between mathematics and real life.

Chapter 15 multiplication, division and factorization of algebraic expressions

The main contents of this chapter are multiplication and division operations, multiplication formulas and factorization of algebraic expressions. This chapter is based on rational number operation, simple algebraic expressions, linear equations and inequalities, addition and subtraction of algebraic expressions and other knowledge. Multiplication, division and factorization of algebraic expressions are basic and important elementary knowledge in algebra, which is the basis for learning knowledge such as fractions, radical operations and functions in the future, and is of great significance in subsequent mathematics learning.

Pay attention to the interesting learning of formulas and supplementary multiplication, and take shortcuts to solve the application problems of quadratic equations in one variable.

The efforts of the third and eighth grade math group this semester.

1, do a good job in teaching. Taking teaching Grade Six seriously as the main method to improve grades, we should study the new curriculum standards, study new textbooks, expand the content of textbooks according to the new curriculum standards, listen to lectures carefully, correct homework, give guidance carefully, and do test papers carefully, so that students can learn to study hard.

2. Guide students to actively participate in the construction of knowledge, and create an efficient learning classroom that is democratic, harmonious, equal, independent, exploratory, cooperative, communicative, sharing and seeking happiness, so that students can experience the happiness of learning and enjoy learning. Instruct students to write small papers and review outlines, so that knowledge can come from students' structure.

3. It is one of the fundamental ways to improve students' quality and cultivate students' divergent thinking to guide students to actively summarize the law of solving problems, guide students to solve multiple problems and unify multiple solutions, and cultivate students' ability to see the essence through phenomena and improve their ability to draw inferences.

Finally, I wish you all a happy new semester! thank you

People's Education Edition Grade 8 Volume I Mathematics teaching material analysis Fan

? Congruent triangles? The main content of this chapter is congruent triangles, which mainly studies the properties of congruent triangles and the judgment methods of triangle congruence, and at the same time learns how to use congruent triangles to prove it.

The teaching objectives of this chapter are:

1. Understand the concept and properties of congruent triangles, and you can accurately identify the corresponding elements in congruent triangles.

2. Explore the judgment method of triangle congruence, use triangle congruence proof, and master the format of comprehensive proof.

3. I can make an angular bisector, understand the nature of the angular bisector, prove the nature of the angular bisector with triangular congruence, and prove it with the nature of the angular bisector.

Because students are not familiar with the writing and reasoning of the proof process, it should be difficult for students to learn this chapter. Therefore, the key and difficult point of determining this chapter is to let students understand the basic process of proof and master the format of proof with a comprehensive method.

This chapter focuses on exploring conclusions, cultivating reasoning ability and connecting with practice in teaching.

People's Education Edition Grade 8 Volume I Mathematics teaching material analysis Fan Wensan

Axisymmetry, the main content of this chapter is to start with the graphics in life, learn the axisymmetry and its properties, and appreciate and experience the extensive application of axisymmetry in real life. On this basis, explore the properties of isosceles triangle, learn the judgment method of isosceles triangle, and further learn equilateral triangle by using axis symmetry.

The teaching objectives of this chapter are:

1. Through concrete examples, we can understand axisymmetric and axisymmetric figures, explore the basic properties of axisymmetric, and understand the property that the connecting lines of corresponding points are vertically bisected by the symmetric axis.

2. Introduce the concept of median vertical line, explore and master its properties; Understand the concepts, properties and judgment methods of isosceles triangle and equilateral triangle.

3. Be able to apply the knowledge learned in this chapter to explain the phenomena in life and solve simple practical problems. In the process of observation, operation, demonstration and communication, develop the concept of space and stimulate the interest in learning graphics and geometry.

Axisymmetric properties are the focus of this chapter, and the proof of some graphic properties is the difficulty of this chapter. To overcome this difficulty, the key is to strengthen the teaching of problem analysis and help students analyze the ideas of problems.

Because symmetry is a common phenomenon in real life, we should pay attention to the combination with practice, let students experience the process of observation, experiment, induction and demonstration, and pay attention to the application of multimedia.

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