People's education printing plate eighth grade mathematics teaching material analysis Fan
People's Education Edition "Compulsory Education Curriculum Standard Experimental Textbook"? The first volume of eighth grade mathematics includes five chapters: congruent triangles, Axisymmetry, Real Number, Linear Function and Algebraic Expression. The content of study involves three fields: number and algebra, space and graphics, practice and comprehensive application.
Chapter 11 "congruent triangles"
In the chapter of "congruent triangles", first, let students know the graphs with the same shape and size, and give the concept of congruent triangles. Then, let the students explore the conditions of the coincidence of two triangles and prove them with relevant conclusions. Finally, master the nature of the angular bisector.
First, the course learning objectives
1. Understanding the concept and nature of congruent triangles can accurately identify the corresponding elements in congruent triangles;
2. Explore the conditions of triangular congruence, use triangular congruence proof, and master the format of comprehensive proof;
3. Knowing the properties of the angular bisector, we can prove the properties of the angular bisector by the congruence of the triangle, and we will prove it by the properties of the angular bisector.
Second, the content of textbooks.
The main content of this chapter is congruent triangles, which mainly studies the nature of congruent triangles and various judgment methods of triangle congruence, and learns how to use congruent triangles to prove it. This chapter is divided into three sections. The first section introduces congruence, including the concept of triangular congruence and the properties of congruent triangles. The second section introduces the judgment method of general triangle congruence and a special judgment method of right triangle congruence. In the third section, the properties of angular bisector are proved by the judgment method of right triangle, and will be proved by the properties of angular bisector.
Chapter 12 "Axisymmetry" Brief Introduction
12 chapter is "axisymmetric", which mainly includes the related contents of axisymmetric and isosceles triangle. This chapter * * * arranges three sections of optional content, and the teaching time is about 12 class hours.
First, the course learning objectives
1. Through concrete examples, 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. Explore the axial symmetry relationship between simple graphs, and make one or two simple graphs with axial symmetry as required; Understand and appreciate the application of axial symmetry in real life, and can use axial symmetry for simple pattern design;
3. Understand the concept of vertical line in line segment, explore and master its properties; Understand the concepts of isosceles triangle and equilateral triangle, explore and master their properties and judgment methods;
4. Be able to use the knowledge learned in this chapter to explain the phenomena in life and solve simple practical problems, develop the concept of space in the process of observation, operation, imagination, demonstration and communication, and stimulate the interest in learning space and graphics.
Second, the content of textbooks.
The main content of this chapter is to start with the graphics in life, learn the axial symmetry and its basic properties, and appreciate and experience the wide application of axial symmetry in real life. On this basis, using the axisymmetric transformation, we explore the properties of isosceles triangle, learn its judgment method, and further learn equilateral triangle.
Chapter 13 Introduction to "Real Numbers"
First, the main contents of the textbook:
This chapter mainly includes the concepts and operations of arithmetic square root, square root, cube root and real number. This chapter focuses on the concepts and solutions of arithmetic square root and square root. The difficulty in this chapter is the concepts of square root and real number.
Second, the course learning objectives
1. Understand the concepts of arithmetic square root, square root and cube root, and use the root sign to represent the square root and cube root of numbers;
2. Knowing that roots and powers are reciprocal operations, we can find the square roots of some non-negative numbers by square operation, the cubic roots of some numbers by cubic operation, and the square roots and cubic roots by calculator;
3. Understand the concepts of irrational numbers and real numbers, and know that real numbers have one-to-one correspondence with points on the number axis, and ordered real number pairs have one-to-one correspondence with points on the plane; Understand the consistency and development of some concepts and operations after the range of numbers is expanded from rational numbers to real numbers;
4. Rational numbers can be used to estimate the approximate range of irrational numbers.
Chapter 14 Introduction of "Linear Function"
I. Status and role:
Elementary function is studied on the basis of plane rectangular coordinate system. Students have a certain understanding of the combination of numbers and shapes, which paves the way for the study of this chapter, and the study of elementary function paves the way for the study of subsequent functions, so the content of this chapter plays a connecting role. 14. 1 variables and functions are the basic parts of the whole chapter, 14.2 linear functions are the key contents of the whole chapter, 14.3 equations and inequalities are the extensions from the perspective of functions, which play a role in strengthening knowledge connection, and 14.4 the selection scheme is the content of inquiry learning, so as to study on special topics.
Second, the teaching objectives
1. With the background of exploring the quantitative relationship and changing law in practical problems, it has gone through the process of "finding out constants and variables, establishing and expressing function models, discussing function models and solving practical problems", and realized that function is an important mathematical model to describe the changing law in the real world;
2. With examples, understand the concepts of constants, variables and functions, understand the idea of "variable correspondence", understand the three expression methods of functions (list method, analytical method and image method), and analyze the simple function relationship by combining numbers with images;
3. Understand the concepts of proportional function and linear function, draw their images, discuss the basic properties of these functions with images, and use these functions to analyze and solve simple practical problems;
4. By discussing the relationship between linear functions and equations (groups) and inequalities, we can deepen our understanding of the learned equations (groups) and inequalities from the perspective of movement changes, and build and develop an interrelated knowledge system;
5. In the process of project learning, take the choice of scheme as the problem situation, carry out inquiry learning, further understand the method and function of establishing mathematical model, and improve the ability of comprehensively applying functional knowledge to analyze and solve practical problems.
Chapter 15 "Multiplication, division and factorization of algebraic expressions"
This chapter is "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. Algebraic multiplication, division and factorization are basic and important elementary knowledge in algebra, which is the basis for later learning about fractions, radical operations and functions, and is of great significance in subsequent mathematics learning. At the same time, this knowledge is also an indispensable basic knowledge of mathematics for studying physics, chemistry and other disciplines and other science and technology.
Second, the teaching objectives
1. Make students master the multiplication and Divison properties of positive integer powers, correctly express these properties with algebraic expressions and written language, and skillfully use them for operations. Make students master the laws of monomial multiplication (or division), polynomial multiplication (or division) and polynomial multiplication, and use them to perform operations.
2. Make students derive multiplication formulas (square difference formula and complete square formula), understand the geometric meaning of the formulas, and use the formulas in multiplication operation.
3. Enable students to master the simple mixed operations of addition, subtraction, multiplication, division and multiplication of algebraic expressions, and flexibly use arithmetic rules and multiplication formulas to simplify operations.
4. Make students understand the meaning of factorization, feel that factorization and algebraic multiplication are operations in opposite directions, master the two basic methods of factorization, namely, the common factor method and the formula method (using the formula directly for no more than two times), and understand the general steps of factorization; Can skillfully use these methods to decompose polynomials.
People's education printing plate eighth grade mathematics teaching material analysis Fan
This semester, I am a math teacher in Class 3 and Class 6 of Grade 8. Judging from last year's achievements, most of the students have made remarkable progress, have a correct attitude and love learning. They hope to continue to work hard and achieve their goals better. However, some students don't like learning mathematics and are not interested in it. What these students need is a correct attitude, and the most important thing is to stimulate their interest in learning. At the same time, we need to communicate more, understand students' interest trends, and reflect on our teaching methods. Keep learning and improve your teaching ability.
Guiding ideology
Educate students to master basic knowledge and skills, cultivate students' logical thinking ability, calculation ability, spatial concept and ability to solve simple practical problems, so that students can gradually learn to calculate correctly and reasonably, and gradually learn to observe and analyze abstractly. Can use induction and deduction, analogy for simple reasoning.
Second, the analysis of learning situation
The eighth grade is a critical period in the learning process of junior high school, and the quality of students' foundation directly affects whether they can enter higher education in the future. Compared with the two classes, students' thinking is very active, but they are backward. A few students are not motivated and their thinking is not with the teacher. Students' overall grades are unbalanced, most of them have poor foundations and serious problems. In order to achieve ideal results in this period, both teachers and students should try their best to check for missing parts, give full play to the role of students as learning subjects and teachers as teaching subjects, pay attention to methods and cultivate their abilities. In terms of learning ability, students' ability to actively acquire knowledge after class is poor. In order to reduce students' financial burden and academic burden, students are not encouraged to buy supplementary books, and their ability to expand their knowledge and learn from the depths has not been cultivated. It is necessary to supplement extracurricular knowledge in time, expand students' knowledge and improve their quality; In terms of learning attitude, most students can concentrate on listening and actively participate in learning in class. A few students are in a state of giving up mathematics. Most students can finish their homework carefully, and a few students need teacher's supervision. These students have also become the focus of teachers' attention. The quality of students' classroom assignments should be discounted. Students' study habits are not ideal, such as the habit of previewing and summarizing, the habit of studying in self-study classes, and actively correcting wrong habits (after exams and homework). Some students don't, and they need the supervision of teachers. Tao Xingzhi said: education is to cultivate habits, which is the focus of this teaching.
Third, teaching material analysis
The first chapter mainly studies fractions and their basic properties, general and approximate fractions of fractions, addition, subtraction, multiplication, division and power operation of fractions, fractional equations and so on. Combined with the operation of fractions, this paper studies the exponential power of integers, extends the exponential power operation of positive integers to the range of integers, and improves the scientific counting method.
Chapter 2 congruent triangles is an important tool to study graphics. Only by mastering congruent triangles's content and using it flexibly can students learn quadrilaterals and circles well. The students learned line segments, angles, intersecting lines, parallel lines and triangles. Some reasoning contents have been arranged in two textbooks for Grade 7, and the concept and nature of congruent triangles have been studied before. This is the first lesson to explore the congruence conditions of triangles, so that students can experience the exploration process of all conditions of triangles and highlight the design ideas of new textbooks. Starting from this section, students should understand the basic process of proof and master the format of comprehensive method proof. This is not only the focus of this chapter, but also the difficulty of teaching. The textbook focuses on the first condition ("edge-edge" condition), and takes the "edge-edge" condition as an example to help students understand what a triangle is and how to judge it. On the basis of mastering the "edge-edge-edge" condition, students can learn how to use the "edge-edge-edge" condition for reasoning and argumentation, and how to correctly express the proof process. Once you master the "edge-edge" condition, it is not difficult to learn other conditions.
Chapter III Adjustment of Real Numbers Compared with the textbooks under the syllabus, this chapter has made some adjustments:
(1) strengthens the sense 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. The basis of these adjustments is similar to rational numbers and their operations, mainly based on thinking about such problems: why do you want to operate, that is, what is the significance and role of operation? What are the requirements for operation in real life? Are they all accurate? Can they be accurate? Can not be accurate, how to estimate and approximate calculation?
3. In the past, the textbooks under the syllabus generally learned the square root first, and then learned the arithmetic square root. The specific method is generally: directly think about "the square of the known original number" from the perspective of operation, so as to get the square root, but in real life, you may only choose a positive one, so learn the arithmetic square root. This approach is based on the consistent thinking of textbooks: get all kinds of operations from mathematics and apply them to real life, that is, prepare knowledge first and then apply it. However, this textbook adjusts the introduction of irrational numbers, hoping to introduce new knowledge into problems, as well as roots, and the roots studied in practical problems are mostly positive, so we should first study the positive square root, that is, the arithmetic square root.
The fourth chapter is one-dimensional linear inequality, which is an effective mathematical model to describe the unequal relationship between quantities in the world. One-dimensional linear inequality is the most basic tool to express inequality relations, and it is also the basis for learning other related mathematical knowledge. Through the study of this chapter, we can understand the solution and set of inequality and the concept of inequality, explore the basic properties of inequality, and master the solutions of linear inequality and linear inequality.
The fifth chapter is the quadratic root. This chapter mainly studies the concept and properties of quadratic root, multiplication, addition and subtraction of quadratic root. Master the algorithm of square root and its application in life. Attach importance to using what you have learned to solve practical problems in life.
Four, the main measures to improve the quality of subject education:
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, make papers carefully, and let students learn to study hard.
Einstein said that interest is the best teacher. Stimulate students' interest, introduce mathematicians and history of mathematics to students, introduce corresponding interesting mathematical problems, and give out extracurricular thinking questions of mathematics to stimulate students' interest.
3. Guide students to actively participate in the construction of knowledge, and create an efficient learning classroom that is democratic, harmonious, equal, independent, exploring, cooperating, communicating, sharing and discovering happiness, so that students can experience the joy of learning and enjoy the fun of learning. Instruct students to write small papers and review outlines, so that knowledge can come from students' structure.
4. It is one of the fundamental ways to improve students' quality, cultivate students' divergent thinking and maintain their state of mind 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 draw inferences from others.
5. Instruct teaching with the concept of new curriculum standards, and actively update the inherent educational concept in your mind. Different educational ideas will bring different educational effects.
6. Cultivate students' good study habits. Tao Xingzhi said: Education is to cultivate habits, and habits help students to steadily improve their academic performance, develop students' non-intellectual factors, and make up for their intellectual deficiencies.
7, guide the establishment of "extracurricular interest groups" of non-governmental organizations, to carry out various extracurricular activities, extracurricular surveys, operational practices, to drive class students to learn mathematics, and at the same time develop their specialties.
8. Implement hierarchical teaching and assign homework. A, B and C are suitable for poor, medium and good students respectively. The problems in the classroom take care of the good, medium and poor students and let them wait for development.
9, individual counseling, gifted students improve their ability, lay a solid foundation knowledge, for poor students, some key knowledge, counseling poor students to pass, paving the way for the future development of poor students.
People's education printing plate eighth grade mathematics teaching material analysis Fan Wensan
This book includes five chapters: congruent triangles, Axisymmetry, Real Numbers, Multiplication, Division and Factorization of Linear Functions and Algebraic Expressions. The following chapters are analyzed as follows.
Chapter 11 "congruent triangles", the main content of this chapter is congruent triangles, which mainly studies the nature of congruent triangles and the judgment methods of triangle congruence, and at the same time learns how to prove it by congruent triangles.
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.
Chapter XII Axisymmetry, the main content of this chapter is to learn the axisymmetry and its properties from the graphics in life, and to 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.
Chapter XIII Real Numbers. This chapter mainly includes the concepts and operations of arithmetic square root, square root, cube root and real number.
The teaching objectives of this chapter are:
1, understand the concepts of arithmetic square root, square root and cube root, and express the square root and cube root of a number with a root sign.
2. Knowing that roots and powers are reciprocal operations, we will find the square roots and cubic roots of some numbers.
3. Understand the concepts of irrational numbers and real numbers, and know that there is a one-to-one correspondence between real numbers and points on the number axis. Rational numbers can be used to estimate the approximate range of irrational numbers.
Students have not been exposed to square roots, cubic roots and irrational numbers in their previous studies, so they should pay attention to strengthening the connection with reality when learning these knowledge. In the process of solving practical problems, let students understand the related concepts and operations of real numbers, and experience the consistency of concepts and operations in the process of expanding numbers. Leave space for students to explore and communicate, and let students experience a cognitive process from special to general through inquiry activities.
The fourteenth chapter is linear function. The main contents of this chapter include: the concepts of variables and functions, three representations of functions, the concepts, images, properties and application examples of proportional functions and linear functions, re-understanding linear equations, linear inequalities and binary linear equations from the perspective of functions, and studying "selection schemes".
1, combined with examples, understand the concepts of constants, variables and functions, understand the idea of "variable correspondence", understand the three representations of functions, and analyze the simple function relationship through the combination of numbers and shapes.
2. Understand the concepts of proportional function and linear function, draw their images, discuss the basic properties of these functions with images, and use these functions to analyze and solve simple practical problems.
3. By discussing the relationship between linear function and equation (group) and inequality, we can deepen our understanding of the equation (group) and inequality from the perspective of motion change.
4. By discussing the problem of choosing the best scheme in project learning, we can improve our ability to analyze and solve practical problems by comprehensively applying the learned functional knowledge.
The chapter of function is the most difficult content in this book for students. It is especially difficult for students to learn and understand. Therefore, in teaching, we should understand the function from concrete to abstract with the help of practical problem situations, and embody the idea of mathematical modeling through examples of function application. Attach importance to the research method of the combination of numbers and shapes. Pay attention to mastering basic knowledge and skills and improve basic ability. Combined with subject study, we can improve our practical consciousness and comprehensive ability to apply mathematics knowledge.
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 knowledge is the basis for learning the knowledge of fractions, radical operations and functions in the future, and it is also an indispensable mathematical tool for learning science and technology such as physics and chemistry.
The teaching objectives of this chapter are:
1, so that students can master the multiplication and Divison properties of positive integer powers, correctly express these properties with algebraic expressions and written language, and skillfully use them for operations.
2. Make students deduce the multiplication formula, understand the geometric meaning of the formula, and use the formula for multiplication.
3. Enable students to master the simple mixed operations of addition, subtraction, multiplication, division and multiplication of algebraic expressions, and flexibly use arithmetic rules and multiplication formulas to simplify operations.
4. Make students understand the meaning of factorization, feel that factorization and algebraic multiplication are deformations in opposite directions, and master two basic methods of factorization, namely, putting forward common factorization and using formulas to understand the general steps of factorization; Can skillfully use these methods to decompose polynomials.
The content of this chapter is similar to that of Divison in addition, subtraction, multiplication and division of rational numbers, which is easy for students to learn and master quickly. However, we should pay attention to the nature of operation and the process of formula generation and induction, infiltrate into thinking methods and pay attention to the memory connection between mathematical knowledge in time, and give full play to students' subjective initiative.
Teaching material analysis's related articles on eighth grade mathematics published by People's Education Press;
1. People's Education Edition, Grade 8, Volume I Mathematics Teaching Plan
2. The first volume of the eighth grade mathematics syllabus
3. People's Education Edition Grade 8 Teachers' Mathematics Plan
4.20 16 the first volume of the eighth grade mathematics teaching plan
5. The math teaching plan for the eighth grade last semester is free.