East China Normal University Eighth Grade Mathematics (Volume II) Textbook Training

Author: Anonymous article Source: Excerpted from Zhejiang Education Network Click Times: 2954 Update Time: 2005- 1-3 1

The arrangement of class hours in each chapter of Book IV

The content of the book (including the review of each chapter) and the arrangement of class hours.

Chapter 16 "Prescription of Numbers"-10 class hour.

Chapter 17 "Functions and Their Images"-16 class hours.

Chapter 18 "Similarity of Images"-1 1 class hour.

Chapter 19 "Solving Right Triangle"-1 1 class hour

Chapter 20 "Data Processing and Preliminary Processing"-12 class hours

Theme learning -4 class hours.

Teaching suggestion

1. Strive to create vivid and concrete learning situations for students.

2. Attention should be paid to guiding students to think independently and cooperate and communicate in teaching.

3. Let students talk and do, and gradually cultivate students' problem-solving ability and initial application consciousness.

Evaluation suggestion

1. Attach importance to the evaluation of students' learning process.

2. Appropriate evaluation of students' understanding and mastery of basic knowledge and skills.

3. Pay attention to the evaluation of students' ability to find and solve problems.

4. The evaluation results are given by qualitative description.

The Root of Number in Chapter 16

First, the teaching objectives

1. Understand the concepts of square root, arithmetic square root and cube root, and express them with the root sign.

2. Knowing that the sum of squares, cubes and squares are reciprocal operations, we can find the square root and cube root of some numbers through the sum of squares and cubes operation, and a non-negative arithmetic square root and cube root of any number can be found through the calculator.

3. Understand the concepts of quadratic roots and similar quadratic roots, and simply add, subtract, multiply and divide and Divison quadratic roots.

4. Understand the concepts of irrational numbers and real numbers, and know that real numbers correspond to points on the number axis.

5. You can estimate the size of irrational numbers, cultivate the estimation ability, and perform simple real number operations.

Second, the characteristics of teaching materials

1. The reorganization and presentation of traditional content reflects the cultivation of students' ability and deletes complex, difficult, biased and outdated knowledge and operations.

(1) The introduction of basic concepts focuses on making students understand and feel the necessity of expanding the number system;

(2) The arrangement and connection of roots, quadratic roots and irrational numbers;

(3) Explore the basic properties and algorithms of quadratic roots;

(4) Requirements for the operation of quadratic roots and real numbers.

2. Paying attention to the connection and analogy between old and new knowledge will help students to establish a new knowledge system through independent exploration, and at the same time, it can also cultivate students' reasonable reasoning ability to a certain extent.

(1) The definition and summation of two sets of operations which are mutually inverse;

(2) Square roots and quadratic roots; The roots of numbers and real numbers;

(3) Quadratic radical multiplication and quadratic radical simplification; Merge similar terms and quadratic radical addition and subtraction;

(4) Generalization of related concepts and algorithms within the scope of rational numbers.

3. Pay attention to the application of calculator, which greatly reduces the difficulty and complexity of real number and radical operation.

Directly applied to the root of (1) number;

(2) Its role in exploring the law of multiplication and division of quadratic roots;

(3) Weakening the requirements for quadratic root simplification and real number operation;

(4) The functions of estimation and exploration are enhanced, and the understanding of the meaning of irrational numbers is improved.

4. Pay attention to let students actively participate in exploration, leaving students with room for operation and thinking.

(1) The connection between the three sections and the foreshadowing of textbook arrangement;

(2) Introduction of some basic concepts, exploration of basic properties and algorithms;

(3) Arrangement and handling of some basic operations that must be practiced;

(4) Arrangement of reading materials and other columns.

Third, the class schedule

The teaching time of this chapter is 10 class hour, which is to be allocated as follows:

16. 1 square root and cube root ... 3 class hours

16.2 quadratic .............................. 3 class hours

16.3 real number and number axis ...................... 2 class hours.

Review 2 class hours.

Fourth, teaching suggestions

16. 1 square root and cube root

1. Pay attention to the connection and transformation with square and cubic operations;

2. Pay attention to the understanding and application of basic concepts and be familiar with the necessary mathematical language;

3. Pay attention to the use of calculators and the teaching of estimation, and prevent students from putting forward complicated digital calculation requirements;

4. Pay attention to the irrational numbers that have appeared.

16.2 quadratic radical

1. Understand concepts, explore and accept basic properties;

2. Explore algorithms, inductive reasoning in multiplication, analogy and reduction in division, addition and subtraction, and pay attention to the cultivation of students' ability to acquire knowledge through independent exploration.

3. Weaken the concepts of quadratic root simplification and similar quadratic root, and master the degree of operation requirements;

4. Continue to attach importance to the application of calculator in approximate calculation and exploring the law of numbers.

16.3 real number and number axis

1. Let students perceive the existence of irrational numbers and the necessity of expanding the number system;

2. Understand and accept the idea that real numbers correspond to points on the number axis one by one;

3. Understand and accept the natural extension of related concepts and algorithms within the scope of rational numbers.

Chapter 17 Functions and Their Images

First, the teaching objectives

1. Learn to describe and study the real world by exploring the interdependence and changing laws of quantities in practical problems. Combined with practical problems, let students know the meaning of constants and variables and understand the corresponding ideas initially.

2. With examples, let students know the three representations of functions, and be familiar with their relationships and transformations; I can draw an image of a simple function by "drawing points", or I can study the quantitative relationship in practical problems by analyzing the image of the function, and determine the definition domain of the function according to the background or analytical formula of the function.

3. By knowing and drawing the plane rectangular coordinate system, we can find out the corresponding relationship between points and coordinates in the given rectangular coordinate system, and then preliminarily understand the corresponding relationship between curves and equations (analytical functions).

4. Learn the basic knowledge of linear function. Understand the meaning of linear function with examples, and understand that the image of linear function is a straight line; Can determine the analytical formula of linear function according to known conditions; Exploring and understanding the properties of linear functions can solve simple practical problems.

5. Learn the basic knowledge of inverse proportional function. Understand the meaning of inverse proportional function according to specific conditions, and determine the analytical formula of inverse proportional function according to conditions; Can draw the image of inverse proportional function, explore and understand the properties of inverse proportional function, and solve simple practical problems.

6. Through practical exploration, let students participate in the process of knowledge discovery and formation, further understand the process of "problem situation-modeling-explanation and application-review and expansion" in mathematics learning, infiltrate and learn mathematical thinking methods, and improve students' thinking quality.

Second, teaching material analysis

1. Textbook content

(1) function and the basic knowledge of its image (including plane rectangular coordinate system);

(2) Two basic functions: linear function and inverse proportional function, their properties and simple applications.

2. The position and function of teaching materials

The thought of (1) function is an important mathematical thought in scientific research and the foundation of modern mathematics. The basic knowledge of function is also the basis and tool for students to continue learning.

(2) Function is another important mathematical model to describe and study the quantitative relationship in the real world after the study of equations and inequalities, and it is the continuation and perfection of the original knowledge and methods;

(3) The ideas and methods involved in the transformation from constant mathematics to variable mathematics are new challenges to students' dialectical thinking and ability to observe, study and solve problems.

3. The characteristics of teaching materials

(1) Pay attention to connecting with practice and enrich students' perceptual knowledge. By enumerating more familiar questions, guide students to observe the changing law of quantitative relations, feel the meaning of constants and variables, and understand and accept the basic concepts of functions.

(2) Pay attention to the function of function images, apply the combination of numbers and shapes in inquiry learning, set up more exercises to analyze the quantitative relationship of actual problems by using function images, and attach importance to the intuitive role of function images in exploring the nature of functions.

(3) Pay attention to students' participation and intensify inquiry learning. From the main content of the textbook to the setting of exercises, situations are given to encourage students to actively acquire knowledge through observation, guessing and verification. There are still some problems in the content of "practical exploration" that cannot be completely solved.

(4) Reflect the student-centered thinking and pay attention to students' development space. The arrangement of the five sections, the setting of exercises and exercises all take into account the needs of different students.

Third, the class schedule

The total teaching time of this chapter is 16 class hours, and it is suggested to allocate it as follows:

17. 1 variables and functions -2 class hours

17.2 function image -2 class hours.

17.3 main functions -5 class hours

17.4 inverse proportional function -2-3 class hours

17.5 Practice and Exploration -2-3 Class Hours

Review -2 class hours.

Fourth, teaching suggestions

1. Pay attention to the connection with students' existing knowledge and reduce the difficulty of accepting new concepts. (Algebraic expressions, equations, inequalities, etc.). ; Knowledge of number axis and statistical graph; The positive and inverse relationship of numbers)

2. Create rich realistic situations and attach importance to students' intuitive perception. Attach importance to students' understanding and acceptance of basic concepts, prevent the formal listing of concepts, and then illustrate the practice with examples. )

3. Pay attention to students' understanding and correct application of necessary mathematical languages and symbols. Pay attention to students' narration and communication, deepen understanding and use it correctly in application and problem solving.

4. Give students enough time to explore independently. Teachers should fully understand the concept that "students' experiences and experiences in the learning process are also teaching purposes" and devote themselves to creating situations, setting questions and guiding students to exchange and discuss. )

5. Make full use of teaching material space and actively organize and implement diversified teaching for different students and classes.

Verb (abbreviation of verb) evaluation suggestion

1. Pay attention to students' ability to apply existing knowledge to explore new knowledge, as well as their understanding and feelings about variables and functions. (Contact real life and related knowledge to find application examples of functional knowledge. )

2. Pay attention to students' active exploration and cooperation in learning, whether they can have innovative ideas in exploration and communication, and their ability to correct their own views (exploration of functional nature, undetermined coefficient method).

3. Pay attention to the cultivation of students' rational reasoning and reasoning ability, use descriptive language to reflect students' learning situation, and put forward positive opinions and suggestions.

Chapter 18 Graphic Similarity

First, the teaching objectives

1. Understand the similarity between objects and graphics through examples in life. Exploring the properties of similar figures, we know that the corresponding angles of similar polygons are equal and the corresponding edges are proportional.

2. Knowing the ratio of line segment to proportional line segment can determine whether the known line segment is proportional. Understand the golden section.

3. Understand the concept of similar triangles, and explore the similar conditions of two triangles.

4. Explore the essence of similar triangles: the height line, median line, angular bisector and the ratio of perimeter to area corresponding to two similar triangles.

5. Be able to use the nature of similar triangles to solve some simple practical problems.

6. Understand the similarity of graphics, and zoom in and out a graphic by similarity method.

7. A suitable coordinate system can be established to describe the position of the object. Can flexibly use different ways to determine the position of objects.

8. In the same rectangular coordinate system, feel the change of the coordinates of points after graphic transformation.

Second, the characteristics of teaching materials

1. This chapter starts with similar figures in life, and then the contents of similar polygons and similar triangles. This arrangement is more in line with students' cognitive characteristics.

2. Mathematics content is basically introduced from practical problems, and conclusions are drawn through the analysis and solution of practical problems, so that students can fully feel the connection between mathematics and the real world.

3. Most of the conclusions in this chapter are not through strict reasoning, but through observation, measurement, drawing, calculation and other methods for students to explore, with more emphasis on the process of finding conclusions and reasonable reasoning.

4. Not every question in the textbook has a conclusion, so we should pay attention to leaving appropriate space for students and teachers to guide students to explore and discover.

5. Emphasize the application of similar triangles in real life.

6. The content of determining the position by coordinates has been added, and the connection between coordinates and real life has been strengthened.

7. The content of using coordinates to study graphic transformation has been added, so that students can initially understand the relationship between number and shape.

8. The text is friendly and natural, and the content is close to the reality of students' lives, which stimulates students' interest in learning.

Third, the class schedule

The teaching time of this chapter is about 1 1 class hour, and it is suggested to allocate it as follows:

18. 1 similar figure-1 class hour

18.2 Characteristics of similar graphics-1 class hour

18.3 similar triangles -4 class hours.

18.4 Draw similar figures-1 class hour.

18.5 graphics and coordinates -2 class hours

Review -2 class hours.

Fourth, teaching suggestions

18. 1 similar graphics

1. This section is to let students understand similar concepts through some similar examples.

In teaching, students should fully feel the similar characters in life, and let them experience the similarity in life by themselves, so as to understand similar concepts.

2. This chapter mainly studies similar polygons and triangles, so most of the examples in this section are examples of similar plane graphics. For the similar three-dimensional graphics, students can feel it properly in teaching without too much expansion.

3. Try P65 in the textbook, so that students can draw a figure similar to the original quadrangle intuitively, laying the groundwork for exploring the characteristics of similar polygons in the future.

18.2 characteristics of similar graphs

1. At the beginning of the textbook, let students measure the length of line segments corresponding to two similar maps by "doing one thing", and then let students calculate the proportion of line segments. There is no special definition of "line segment ratio" in teaching materials, and the meaning of line segment ratio can be pointed out at the same time in teaching: it refers to the ratio of the lengths of two line segments. Students are not required to memorize concepts, but can gradually understand them in future study.

2. For the basic nature of proportion, there is no special introduction in the textbook, but some exercises will involve related content, and students can master the basic nature of proportion through exercises.

3. For the characteristics of similar polygons, students can first observe similar polygons, guess the relationship between them, and then measure with a scale and a protractor to verify the results.

18.3 similar triangles

For the question of "do one thing" in 1 P72, this textbook adopts the way of rational reasoning, allowing students to draw conclusions through measurement and reasoning.

2. For the identification of similar triangles, the textbook is from corner to edge, that is, from three corners, two corners, one corner to two sides and one corner, and then to three sides. This order is more natural and accords with students' cognitive law.

3. The conclusion of similar triangles's identification method adopts reasonable reasoning instead of logical argumentation in teaching materials, and makes full use of observation, induction, measurement, experiment, reasoning and other means in teaching, so that students can fully experience the process of drawing conclusions and feel the fun of discovery. Only by fully embodying the process of exploration can students truly understand and master the conclusion.

4. For each identification method, textbooks generally use the column of "exploration" or "thinking" to put forward a guess, and then let students verify the guess through "doing" or "trying". Or just ask questions to make students think. For example, for the question "If the corresponding angle is not the included angle of the corresponding two sides, are these two triangles similar?" There is not much development in the textbook, mainly leaving the relevant conclusions to students to discover and give them more space.

5. Using the previous conclusions and simple reasoning, various properties of similar triangles are obtained.

6. For the application of similar triangles nature, two examples are given in the textbook. There are many such problems in ancient China and abroad, which can be appropriately selected according to the actual situation of students in teaching, and some examples that are in line with the local actual situation can also be added.

18.4 draw a similar figure.

1. The main purpose is to let students understand the concept of similarity in practical application. The textbook introduces the concept of similarity by drawing a similar figure of a polygon, mainly to let students master several methods to enlarge and shrink a polygon with similarity, so that students can draw their own pictures according to the steps in the book during teaching.

2. Read the material "The Wonderful Combination of Mathematics and Artistic Fractal". Through the geometric sketchpad, you can easily draw the self-similar figure of the front snowflake and the back equilateral triangle, and show it to students if possible. There are many contents and patterns about fractals on the Internet. Where conditions permit, students can collect some information online after class.

18.5 graphics and coordinates

1. In the course of "Coordinate Positioning", students should first realize that rectangular coordinate system can be used to locate positions in real life. In teaching, students can find a place in the city map (some maps use letters A, B, C … and numbers 1, 2, 3 … to locate a place, which is convenient for people to find) and let students experience it. Then students are required to establish a suitable coordinate system to describe the position of the object according to the actual problem and background.

2. In P87, Xiaoming uses angle and distance to represent the position of an object. This is actually a polar coordinate method, which is not clearly stated in the textbook, but it can be told to students in teaching that this is also a method of expressing the position of an object with coordinates, which is often used in military and geography and also needs students to master.

Up to this chapter, we have learned translation, rotation, symmetry, similarity and other transformations. In this section, students can experience the changes of coordinates after these transformations, so as to have a deeper understanding of the transformation of graphics and initially penetrate the idea of combining numbers with shapes.

Chapter 19 Solution of Right Triangle

I. Contents of this chapter

The main content of this chapter is the angular relationship of right triangle and its practical application. The textbook starts with measurement, creates learning situations for students, then studies the angular relationship of right triangle-Pythagorean theorem and acute trigonometric function, and finally uses Pythagorean theorem and acute trigonometric function to solve some simple practical problems.

Second, the teaching objectives

1. Experience the exploration process of Pythagorean theorem

2. Understand the history of Pythagorean theorem

3. Know the trigonometric function values of angles of 30, 45 and 60; Will use a calculator to find its trigonometric function value from the known acute angle and its corresponding acute angle from the known trigonometric function value.

4. Understand and master the relationship between the angles of a right triangle.

5. Can comprehensively use the angle relation of right triangle to solve simple practical problems.

Third, the characteristics of teaching materials

1. In presentation, research is emphasized. For example, the meaning of Pythagorean theorem and trigonometric function is deduced by asking questions.

2. The application of Pythagorean theorem and trigonometric function should be connected with practical problems as far as possible to reduce the problem of simply solving right triangle.

3. The choice of practical problems should be linked to students' real life.

4. Pay attention to expanding students' knowledge. Three readings are arranged in this chapter.

5. Pay attention to the scientific nature of the training system, reduce operational exercises and increase the proportion of exploratory questions.

Fourth, the class schedule

The teaching time of this chapter is about 13 class hours, and it is suggested to allocate it as follows:

19. 1 measurement-1 class hour.

19.2 Pythagorean Theorem -2 class hours

19.3 acute trigonometric function -2 class hours

19.4 Solving Right Triangle -4 class hours

Review -2 class hours.

Theme learning -2 class hours.

Suggestions on teaching verbs (abbreviation of verb)

19. 1 measured value

This part plays a connecting role. Through a practical problem-measuring the height of flagpole, on the one hand, it helps students review similar triangles's knowledge, on the other hand, it leads to Pythagorean theorem and acute trigonometric function. In teaching, we should pay attention to inspiring students to solve this problem in two different ways, and at the same time, guide students to find a simpler way to solve this problem, thus deriving new knowledge, so as to arouse students' enthusiasm for learning the follow-up content.

19.2 Pythagorean Theorem

1. The teaching in this section is divided into five steps: exploration conclusion-verification conclusion-preliminary application conclusion-proof conclusion-application conclusion for solving practical problems.

2. In the stage of exploring the conclusion, we should arouse students' enthusiasm and let them fully participate.

3. The key point of the preliminary application conclusion stage is to make students clear: in a right triangle, if you know two sides, you can find the third side.

4. The conclusion stage of proof is mainly to sort out ideas, not just to introduce some proof methods.

5. Applying conclusions to solve practical problems can be divided into two categories: exploratory problems and applied problems.

19.3 sharp trigonometric function

1. The acute trigonometric function is introduced according to the solution of the problem in section 19. 1. Students should be inspired to draw directly from the meaning of trigonometric function: