The first volume of Mathematics, a standard experimental textbook for the eighth grade compulsory education curriculum, includes five chapters: linear function, data description, congruent triangles, axial symmetry and algebraic expression. The content of study involves the Mathematics Curriculum Standard for Full-time Compulsory Education (experimental draft) (hereinafter referred to as the curriculum standard): number and algebra, space and graphics, statistics and probability, practice and comprehensive application.

The eighth grade of compulsory education used about 62 class hours in the last semester, and the specific distribution is as follows:

Chapter 1 1 A function is about 15 class hours.

The data description of chapter 12 is about 12 class hours.

Chapter 13 About 10 class hours in congruent triangles.

Chapter 14 Axisymmetric about 12 class hours

Chapter 15 Algebraic Expressions About 13 class hours.

I. Content arrangement

We live in a constantly changing world. Time, population growth and wealth accumulation are all examples of change. Function is a mathematical tool to describe these changes. By analyzing the relationship between variables in practical problems, a new mathematical model of practical problems is obtained, which can be used to solve a wide range of problems. For the content of functions, this set of textbooks is arranged in a decentralized way. This book arranges a chapter on functions, the second volume of the eighth grade arranges inverse proportional functions, and the second volume of the ninth grade arranges quadratic functions and acute trigonometric functions. This arrangement can enable students to deepen their understanding of function ideas. In the chapter of "Linear Function" in this book, first, let students explore the quantitative relationship and changing law in specific problems, understand the meaning of constants and variables, and understand the concept and three representations of functions. On this basis, let's learn the content of the function again. In the chapter "Linear Function", the section "Looking at Equations (Groups) and Inequalities from the Functional Point of View" is specially arranged to discuss the relationship between linear functions and linear equations with one variable, linear functions and linear inequalities with one variable, and linear functions and linear equations with two variables (Groups) respectively. It can be seen that this chapter plays a connecting role in the whole set of teaching materials.

In the first volume of grade seven, students have learned "data collection and arrangement". How to describe the collected data is what students need to continue to learn in this volume. In the chapter of "Description of Data", first, let students know several common statistical charts, including bar chart, fan chart, line chart and histogram, then let them learn to describe data more intuitively and clearly with statistical charts, and finally arrange special study to further let students understand the function of describing data with statistical charts.

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.

The chapter "Axisymmetry" first lets students understand the axisymmetry and explore its properties. Then, students can make a simple figure after axial symmetry as required, so that they can use axial symmetry for pattern design. On this basis, learn the related concepts and properties of isosceles triangle. In this way, students can master the related contents of isosceles triangle from the angle of axial symmetry.

Students already know that letters can be used to represent numbers, and formulas containing letters can be used to represent the quantitative relationship in practical problems. Further discussion of algebraic expressions will enable students to solve more problems related to quantitative relations and deepen their understanding of the process from concrete to abstract. This chapter first lets students understand the concept of algebra, and then lets them learn simple algebra addition, subtraction, multiplication and division operations. On this basis, let students understand the concept of factorization, and use common factor method and formula method to decompose factors. These contents are to prepare for the following contents, especially the next chapter.

Second, the writing characteristics

(A) to strengthen contact with reality

1. Introduce relevant contents from reality.

In the chapter of "linear function", the textbook introduces the concepts of variables, constants and functions through examples such as the mileage of cars driving at a constant speed changes with time, the box office income of cinemas changes with the number of tickets sold, and the length of springs changes with the mass of hanging weights. Combined with China population statistics and electrocardiogram, the functions expressed by table method and image method are explained. Direct proportional function and linear function are introduced by flight and temperature change respectively. The purpose of this arrangement is to let students understand the meaning of variables and constants through simple examples, understand the concept and three representations of functions with examples, and experience the meaning of a function with specific situations.

Bar chart, fan chart, line chart and histogram commonly used in statistics have their own characteristics, which can express data clearly and effectively. In the chapter of "Description of Data", these statistical charts are explained in combination with practical problems: bar charts and fan charts are introduced from air quality problems, line charts are introduced from GDP problems, and histograms are introduced from pulse measurement problems. In this way, students realize that statistics are closely related to real life.

In the chapter "congruent triangles", the textbook introduces the concept of congruence from practical examples and asks students to give some examples. Around us, we can often see graphics with the same shape and size, which can not only make students easily understand related concepts, but also arouse their enthusiasm for learning. Another example is to introduce the drawing method of angular bisector from the principle of analyzing the instrument of angular bisector. For example, by determining Bazaar's position, it is concluded that "the points with equal distance to both sides of the corner are on the bisector of the corner", so that students can see that the theory comes from practical needs.

Examples of axial symmetry can be found from natural landscapes to miniature models, from architecture to works of art, and even daily necessities. In the chapter "Axisymmetric", the textbook introduces axisymmetric and axisymmetric transformation from reality, so that students can feel it concretely. Another example is the conclusion that "equilateral" is introduced from the problem of life-saving at sea. Another example is to find the quantitative relationship between the right-angled side and the hypotenuse of a right-angled triangle with the help of two triangular rulers with an included angle of 30.

The quantitative relations of some simple problems can be expressed by algebraic expressions, so in the chapter of "algebraic expressions", the concepts of monomial and polynomial are introduced with examples. Algebraic expressions are handled similarly. For example, computer processing introduces multiplication with the same base, chain store sales revenue calculation introduces multiplication with monomial and polynomial, computer storage problem introduces division with the same base, and comparison between Jupiter's mass and Earth's mass introduces division with monomial.

In short, all chapters of this textbook focus on abstracting mathematical problems from specific problem situations, thus helping students understand relevant mathematical contents.

2. Use relevant content to solve practical problems

In the chapter of "Linear Function", let students describe the relationship between variables in some practical problems with appropriate function representation, for example, analyze the relationship between oil consumption and mileage, the change of water level with time, freight and internet access fees with functions. This chapter also pays attention to the analysis of relevant information from images, such as the observation on page 1 1, and the example 2 on page 12.

In the chapter of "Description of Data", statistical charts are used to describe practical problems, such as fan charts to show the percentage of all kinds of educated population in the total population, and charts and tables related to histograms to solve the problem of selecting contestants according to their height. This chapter also set up a special topic to study, saving water from data, and providing students with practical opportunities to describe data with charts.

In the chapter "congruent triangles", the triangle congruence is used to explain the truth of practical measurement methods, such as measuring the distance between two ends of the pond, measuring the distance between two opposite points on both sides of the river, and measuring the width of the inner groove of the workpiece with calipers. A mathematical activity of measuring the height of flagpole with triangle congruence is also arranged.

In the chapter "Axisymmetry", after learning the relevant knowledge of axisymmetry, let students design patterns by using axisymmetry. This chapter also uses the properties of special triangles to solve practical problems, such as using isosceles triangles to solve the rope length problem and using equilateral triangles to solve the measurement problem.

In the chapter of "algebraic expression", students are required to use algebraic expression operation to solve practical problems such as carton materials.

In a word, all chapters focus on letting students use what they have learned to solve practical problems and deepen their understanding of what they have learned.

(2) Leave space for students to think and explore.

Compared with the two volumes of Grade Seven, the content of this volume is deeper, and all chapters focus on letting students experience the process of exploring knowledge.

In the chapter of "linear function", let students think about some problems that reflect the changing process of different things, and then give the concepts of variables and constants. Let the students know the relationship between variables not only through formulas, but also through observing China's demography and electrocardiogram, and then give the concept of function. The textbook does not directly compare the three representations of functions, but puts forward a question for students to think for themselves with examples. By enumerating some analytic expressions of functions and drawing some images of linear functions, the concept and properties of linear functions are summarized.

In the chapter of "Data Description", the relevant contents are all around statistical issues, such as air quality, gross domestic product, pulse measurement, etc., so that students can understand bar charts and fan charts, line charts, histograms, and the percentage of educated population in the total population, and let students explore the drawing methods of fan charts and so on. In this way, in the process of putting forward and solving problems, teachers and students think together, experience and master the method of describing data with statistical charts.

When writing the chapter "congruent triangles", eight explorations were designed in the section "Conditions of triangle congruence", so that students can 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) Three sides are equal;

(2) Two sides and their included angles are equal;

(3) The angles subtended by two sides and one of them are equal;

(4) Two angles are equal to their clamping edges;

(5) The opposite sides of two angles and one angle are equal;

(6) The three angles are equal.

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.

In the chapter "Axisymmetry", students obtained the properties related to axisymmetry through observation and exploration. For the relationship between the coordinates of axisymmetrical 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.

In the chapter "Algebraic Formula", the multiplication with the same base number is found through some concrete calculations. The textbook allows students to apply the multiplication rules of polynomials to some special forms of polynomial multiplication and discover the rules themselves. On the contrary, let students decompose some special forms of polynomials by multiplication formula, and then they can get the formula method of factorization.

In short, each chapter of the textbook tries to explain the ins and outs of knowledge and present the formation and application process of knowledge to students.

(C) to strengthen the links between knowledge

In the chapter "Linear Function", the section "Looking at Equations (Groups) and Inequalities from the Functional Point of View" is specially arranged to discuss the relationship between linear functions and linear equations with one variable, linear functions and linear inequalities with one variable, and linear functions and linear equations with two variables (Groups) respectively. In this way, students can find the relationship among linear functions, linear equations and linear inequalities, and unify the interrelated equations (groups), inequalities and functions from the perspective of functions.

In the chapter of "data description", statistical chart is also an example of the relationship between numbers and shapes. In this way, the collected data can be sorted out and represented by statistical charts, so that we can intuitively understand the distribution characteristics and laws of the data and help us obtain information from the data and draw conclusions.

In the chapter of "congruent triangles", the drawing method of triangles is combined with the exploration of triangle congruence conditions, that is to say, instead of giving triangle congruence conditions directly, students are asked to draw triangles corresponding to some elements of known triangles, and then cut them after drawing, on this basis, students are inspired to think about what conditions are needed to determine the congruence of two triangles. In this way, students will be impressed by the relevant conclusions by drawing experiments themselves. Combining the triangle drawing with the exploration of triangle congruence conditions is also better than the simple triangle drawing, which is easy to be monotonous and boring.

In the chapter of "Axisymmetry", the transformation of graphics is combined with the understanding of graphics, and the content of axisymmetry is arranged first, and then the content of isosceles triangle is arranged. In this way, we can understand the isosceles triangle from the perspective of transformation, thus strengthening the relationship between them. In addition, this chapter also arranges the content of "axis symmetry expressed by coordinates", aiming at combining numbers and shapes and strengthening the connection between knowledge.

In the chapter of "Algebra", the multiplication and factorization of algebra are arranged in the same chapter, which is also to strengthen the connection between them. In addition, let students explain the multiplication formula by area, and let students grasp the relevant content from the perspective of number and shape, for example, from the perspective of graphics, students can easily avoid mistakes.

(D) Developing reasoning ability

In the chapter of "congruent triangles", the proof and its format formally appeared. Some reasoning contents are arranged in the two textbooks of grade seven, which is to prepare for the formal practice and proof now. It is difficult to ask students to reason and prove that the process of expressive reasoning is concise and accurate. In order to solve this difficulty, the textbook has made some efforts.

1. Pay attention to gentle slope, step by step. At the beginning, it proved that the direction was clear, the process was simple and the writing was easy to standardize. At this stage, students are required to experience the proof ideas and formats of examples, and then gradually increase the complexity of the questions and make small steps forward. Every step is to prepare for the next step, and the next step is to review the contents of the previous step. Especially in the thirteenth chapter, by carefully selecting congruent triangles's proof problems, the slope of students' learning geometric proof is slowed down.

2. At different stages, arrange different exercises, highlight a key point, and put forward clear requirements at each stage for teachers to master. For example, in the chapter "congruent triangles", let students prove that two triangles are congruent, and prove that two line segments or two angles are equal by proving that triangles are congruent, and be familiar with the steps and methods of proof. Chapter 14 focuses on cultivating students' analytical thinking and choosing relevant conclusions to prove it according to their needs.

3. Pay attention to the analysis of thinking, let students learn to think, pay attention to the writing format, and let students learn to express their thinking process clearly.

4. Arrange the content of the proof in the relevant chapter of "Number and Algebra". For example, in the chapter "Algebra", let students find some laws and prove them (exercise 15.5, question 10 and two math activities), or directly let students prove some conclusions (review question 15, question 13).

Third, several issues worthy of attention

(A) Pay attention to students' emotional attitude

In the teaching of this book, we should pay attention to cultivating students' interest in learning and good personality. There is a lot of content in this book that combines numbers with shapes, such as functions and their images, data and statistical charts, symmetrical points and their coordinates. We should use the characteristics of these contents to stimulate students' interest in learning. Through step-by-step teaching, students can master basic knowledge, basic skills and development ability, and at the same time have tenacious learning perseverance, full learning confidence, scientific attitude of seeking truth from facts, and the spirit of independent thinking and exploration and creation.

The content of this book contains the viewpoint that mathematics comes from practice and acts on it in turn, including the viewpoint of movement change, mutual connection and mutual transformation. For example, functions are produced due to practical needs, and the theories of functions are enriched and developed, and these theories are also used to solve practical problems. Function, axis symmetry and other contents vividly reflect the viewpoint of motion change, mutual connection and mutual transformation. In teaching, we should use these contents to educate students in dialectical materialism, so that they can form a scientific world outlook.

(B) to strengthen the application of information technology

With the development of knowledge content, the role of information technology in dealing with related content is becoming more and more obvious. In this book, we can pay attention to the application of information technology from the following three aspects.

1. Drawing function image with computer

Drawing the image of the function can directly reflect the relationship between variables, and it is also convenient to study the properties of the function (monotonicity, extremum, parity and zero point of the function) from the image. Compared with manual calculation and drawing of function images, function images can be easily obtained by using some computer software: as long as the analytical expression of the function is input, the computer will automatically generate function images. In this way, students can learn more about functions through function images.

2. Make statistics by computer.

Computer software can be used to draw bar charts, fan charts, line charts and histograms. Drawing statistical charts by computer is not only quick and convenient, but also standardized and beautiful. This can stimulate students' interest in learning, make them willing to try, and improve their design and practical ability.

3. Explore the nature of axial symmetry

Using computer software, we can draw an axisymmetric figure of a graph conveniently, from which we can observe the relationship between the connecting segment of the symmetrical point and the axis of symmetry, change the position of the axisymmetric figure or axis of symmetry, and observe whether the conclusion is still valid. Similarly, we can discuss the characteristics of symmetrical point coordinates and the properties of the vertical line in the line segment. On the other hand, the pattern can be designed by computer.

In short, the use of information technology can enrich students' learning content, and if conditions permit, research in this area can be carried out to improve teaching efficiency.

Ⅱ. Volume II of Grade Eight

The second volume of Mathematics, the standard experimental textbook for compulsory education, consists of five chapters, which takes about 6 1 class hour for the eighth grade in the next semester. Details are as follows:

The score of chapter 16 is about 13 class hours.

17 chapter inverse proportional function is about 8 class hours.

Chapter 65438 +08 Pythagorean Theorem takes about 8 class hours.

Chapter 19 quadrilateral 17 class hours

Chapter 20 Data analysis is about 15 class hours.

The five chapters of the book cover four areas of mathematics curriculum standards: number and algebra, space and graphics, statistics and probability, practice and comprehensive application. For the content in the field of "Practice and Comprehensive Application", the textbook arranges a special study in chapter 19 and chapter 20 respectively, and arranges 2 ~ 3 math activities at the end of each chapter, through which the requirements of "Practice and Comprehensive Application" are implemented. Generally speaking, these five chapters are arranged in a concentrated way. The first two chapters basically belong to the field of number and algebra, the last two chapters basically belong to the field of space and graphics, and the last chapter is the field of statistics and probability. This arrangement helps to strengthen the vertical connection between knowledge. In the preparation of the specific content of each chapter, special attention is paid to strengthening the horizontal connection between various fields.

I. Content analysis

Chapter 16 score

This chapter mainly studies fractions and their basic properties, addition, subtraction, multiplication and division, Divison, fractional equations and so on. These contents are divided into three parts.

16. 1 Section gives the concept of fraction by analogy, discusses the basic properties of fraction, and introduces the general points and simplification points of the analogy method of fraction, which lays a theoretical foundation for the following two sections. Section 16.2 discusses four algorithms of fractions. Starting from practical problems, the textbook first studies the multiplication and division of fractions and discusses the multiplication and division algorithm of fractions by analogy. Next, the textbook also learns the addition and subtraction of fractions by analogy, obtains the operation rules, and learns the elementary arithmetic of fractions. Finally, the textbook combines the operation of fractions to study the exponential power of integers, and extends the operation properties of exponential power of positive integers to the range of integers, perfecting the scientific notation. The content of this section is the focus of the whole chapter, and the mixed operation of fractions is also the difficulty of the whole chapter. 16.3 discusses the concept and solution of fractional order equations, mainly involving fractional order equations that can be transformed into linear equations with one variable. Starting from practical problems, the textbook analyzes the quantitative relationship in the problem and lists the fractional equation, thus leading to the concept of fractional equation. Then, the solution of fractional equation is studied. Combining with the students' experience, the textbook discusses how to transform fractional equation into integral equation, so as to get the solution of fractional equation. If the basic properties of fraction are to be applied to solving fractional equations, it is necessary to test the roots, which is a problem that has not been encountered in previous equations. The textbook explains why the fractional equation needs root test with concrete examples. Fractional equation provides a mathematical model for solving practical problems, and it has a special function that the whole equation can't be replaced. Listing fractional equations according to practical problems is another difficulty in teaching this chapter.

Chapter 17 inverse proportional function

This chapter mainly includes the concept, image and properties of inverse proportional function, and the analysis and solution of practical problems by inverse proportional function. This chapter is the content of another chapter's function after Chapter 8 (1) "Linear Function in Chapter 1 1". The whole chapter is divided into two sections: 17. 1 inverse proportional function, and 17.2 practical problems and inverse proportional function. The whole chapter revolves around practical problems, which is a main line running through the whole chapter.

17. 1 section mainly studies the concept, image and properties of inverse proportional function. Starting with several practical problems that students are familiar with, this section analyzes the corresponding relationship between variables in practical problems, lists the analytical formula of inverse proportional function, and introduces the concept of inverse proportional function, so that students' understanding of inverse proportional function has gone through a process from perceptual to rational; Next, the textbook draws the image of function sum by tracing points. By discussing the common characteristics of two kinds of function images, the fact that the inverse proportional function image belongs to hyperbola is given, and then the conclusion that the image of function sum is symmetrical about X axis and Y axis is drawn. Next, the textbook allows students to draw the images of the sum of functions by using this conclusion, and further get the properties of the inverse proportional function by analyzing the images drawn by these four functions. The content of section 17.2 is to use inverse proportional function analysis to solve practical problems. In this part, the textbook gives four practical problems by way of examples. These four problems are basically arranged in the order from simple to complex (cylinder bottom area and height, working time and speed, power arm, output power and resistance), which shows that inverse proportional function is an effective mathematical model to solve practical problems from different aspects.

Chapter 18 Pythagorean Theorem

This chapter mainly studies Pythagorean theorem and the inverse theorem of Pythagorean theorem, including their discovery, proof and application. The whole chapter is divided into two sections, section 18. 1 is Pythagorean theorem, and section 18.2 is the inverse theorem of Pythagorean theorem.

In the section 18. 1, the textbook starts with Pythagoras' observation of the legend of Pythagorean theorem on the ground, and asks students to observe and calculate the relationship between the area of some small squares with two right-angled sides and the area of a square with a hypotenuse side, and finds that the sum of the areas of two small squares with right-angled sides is equal to the area of a square with a hypotenuse side, thus seeking Pythagorean theorem. At this time, the textbook took the 65438 proposition. There are many ways to prove Pythagorean theorem. The text of the textbook introduces the proof method of Zhao Shuang, an ancient man in China. After proving the correctness of the proposition 1 through reasoning, the textbook points out what a theorem is and makes it clear that the proposition 1 is Pythagorean theorem. Then, through three inquiry columns, the application of Pythagorean theorem in solving practical problems and mathematical problems (drawing unreasonable line segments, etc.) is discussed. ), so that students have a certain understanding of Pythagorean theorem. 18.2 is the inverse theorem of Pythagorean theorem. Starting with the method of drawing right angles by ancient Egyptians, the textbook gives the conclusion that a triangle is a right triangle when three sides of the triangle meet the requirements. Then, students draw some triangles with the sum of squares of sides equal to the square of the third side. By exploring the shapes of these triangles, we can find that all the drawn triangles are right-angled triangles, and guess that if the three sides of a triangle satisfy this relationship, then this triangle is a right-angled triangle. At this point, this inverse theorem is given in the form of proposition 2. By comparing the topics and conclusions of 1 proposition and 2 proposition, the textbook gives the concepts of original proposition and inverse proposition. Whether proposition 2 is correct needs to be proved. The textbook uses congruent triangles to prove Proposition 2, and obtains the inverse theorem of Pythagorean theorem. The inverse theorem of Pythagorean theorem gives a method to judge whether a triangle is a right triangle, which is widely used in mathematics and practice. Students can learn to solve problems in this way through two examples in the textbook.

Chapter 19 quadrilateral

This chapter mainly studies the concepts, properties and judgment methods of some special quadrangles. For special quadrangles, the teaching materials are divided into two categories according to the parallel relationship of opposite sides: two groups of quadrangles with parallel opposite sides-parallelogram, one group of quadrangles with parallel opposite sides, and the other group of quadrangles with non-parallel opposite sides-trapezoid. For parallelogram, besides the general parallelogram, several special parallelograms such as rectangle, diamond and square are also studied.

19. 1 section mainly studies the concept, properties and judgment of general parallelogram. Starting from the graphics in real life, the textbook abstractly summarizes the concept of parallelogram, and through a series of exploration activities, it obtains the nature and judgment method of parallelogram, and proves the conclusion appropriately through reasoning. As an application of judgment method, the textbook obtains the triangle midline theorem through examples. 19.2 mainly studies the concepts, properties and judgments of rectangle, rhombus and square. This section further studies these special parallelograms on the basis of the previous section. The textbook first studies rectangles and diamonds, both of which are parallelograms with special conditions. A rectangle is a parallelogram with right angles, and a diamond is a special parallelogram with a set of equal adjacent sides. On this basis, the textbook studies a parallelogram with two special conditions at the same time, namely a square, which is a special rhombus with a right angle and a group of special rectangles with equal adjacent sides. 19.3 section studies trapezoid, which is another special quadrangle juxtaposed with parallelogram, with one set of opposite sides parallel and the other set of opposite sides non-parallel. This section mainly introduces a special trapezoid-isosceles trapezoid, and discusses the properties and judgment methods of isosceles trapezoid. The last section of the textbook, namely 19.4, arranged a special study: the center of gravity. Through the activity of finding the center of gravity of geometric figures, it is known that the center of gravity of regular geometric figures is its geometric center, and the relationship between mathematics and physics is understood.

Chapter 20 Data Analysis

This chapter mainly studies the statistical significance of average (mainly weighted average), median, mode, range and variance. The whole chapter is divided into three sections.

20. Section1studies statistics that represent the trend of data sets: average, median and mode. In this section, the textbook first gives a practical problem, solves this practical problem through analysis, and introduces the concept of weighted average. In order to highlight the role and significance of "right", textbooks show the role of "right" from different aspects through two examples. Then the textbook expands the weighted average, including how to unify arithmetic average and weighted average, how to calculate the weighted average of interval grouping data, how to use the statistical function of calculator to calculate the average, how to estimate the overall average by sample average and so on. For median and mode, the textbook studies their statistical significance through several specific examples. At the end of this section, through a concrete example, the textbook studies the examples of comprehensively applying the average, median and mode to solve problems, and summarizes these three statistics, highlighting their respective statistical significance and characteristics. Section 20.2 will study statistics describing the degree of data fluctuation: range and variance. The textbook first uses the example of temperature difference to study the statistical significance of extreme difference. Variance is a statistic commonly used in statistics to describe the degree of data dispersion, and variance is studied in detail in textbooks. Firstly, the research on the fluctuation of two groups of data is put forward through a practical problem, and the scatter diagram is drawn to reflect the fluctuation of data intuitively. On this basis, the textbook introduces the method of describing the dispersion degree of data with variance, introduces the formula of variance, and analyzes how variance describes the fluctuation of data from the structure of variance formula. Then, the method of calculating variance by using the statistical function of calculator is introduced. At the end of this section, the textbook solves the problems raised in the preface of this chapter with what it has learned, and studies the problem of estimating population variance with sample variance. In the last section of the textbook, a comprehensive and practical "subject study" is arranged. This "research project" chooses physical health problems closely related to students' lives. Because this chapter is the last chapter in the statistics section, the comprehensive research on this topic is stronger than the previous two chapters. In order to facilitate the teaching operation, the textbook provides an example according to the Registration Form of Middle School Students' Physical Health.

Second, the writing characteristics

1. Strengthen the connection with practice and reflect the formation and application of knowledge.

Closely connecting with practice, reflecting the ins and outs of knowledge, and reflecting the formation and application process of knowledge are the characteristics of this set of teaching materials and the main characteristics of this book. When writing each chapter of this book, we should pay attention to the introduction of concepts and the formation of knowledge from practical problems, reflecting that mathematics comes from reality, and at the same time, we should pay attention to applying the obtained mathematical conclusions to practice, reflecting that mathematics serves reality by solving practical problems. For example, in the chapter of "fraction", the textbook arranges several practical problems for the introduction of the concept of fraction. By analyzing the quantitative relationship in practical problems, the concept of score is listed, which shows that the concept of score is produced because of objective practical needs. When discussing the fractional order equation, combined with practical problems, it is shown that the fractional order equation is a mathematical model to solve practical problems. In the chapter "Inverse Proportional Function", the concept of inverse proportional function is abstracted from several practical problems, and this chapter also specially arranges the section "Practical Problems and Inverse Proportional Function", highlighting that inverse proportional function is mathematics to study practical problems.