Quadratic root belongs to the field of numbers and algebra. It is based on students' learning square roots and cubic roots, and it is an extension and supplement to the contents of "real numbers" and "algebraic expressions" in the first volume of grade seven. The operation of quadratic root is based on algebraic expression, and the algorithm used in quadratic root operation is similar to the operation of algebraic expression and fraction. When adding and subtracting secondary roots, the method adopted is similar to merging similar items; In the multiplication and division of quadratic roots, the rules and formulas used are similar to the multiplication algorithms and formulas of algebraic expressions. All these explain the internal connection of knowledge before and after.

The main content of this chapter is the quadratic root, its properties and its operation (there is no letter in the root sign and no denominator).

First, teaching materials and teaching objectives

Teaching requirements of this chapter.

(1) Understand the concept of quadratic root and the letter range of simple quadratic root;

(2) Understand the nature of quadratic radical;

(3) Understand the addition, subtraction, multiplication and division of quadratic roots;

(4) We will use the properties of quadratic root and operation rules to perform four simple operations on real numbers (the denominator is not required to be rational).

This chapter teaching material analysis.

On the basis of reviewing the arithmetic square root, the textbook introduces the concept of quadratic square root through three questions of "cooperative learning" and explains that the arithmetic square root of previously learned numbers is also called quadratic square root. In the arrangement of examples and exercises, three requirements are emphasized: one is to find the range of letters in the quadratic root; The second is to find the value of quadratic root; The third is to express related problems with quadratic roots.

For the nature of quadratic roots, the textbook uses the figure 1-2 on page 4. This diagram means that if the area of a square is 0, then the side length of the square is 0; On the other hand, if the side length of a square is, then the area of this square is, so there is. Thus, the first property of quadratic radical is obtained. As for the second nature, it can be found by students' calculation, so the textbook arranges a "cooperative learning" for students to discover and summarize themselves. The first lesson of this section focuses on the understanding and application of these two properties, and the design of examples and exercises revolves around these two properties. The second lesson is to learn the other two properties of quadratic radical. The textbook arranges two groups of exercises, which are intended to let students discover these two properties through their own attempts and cooperation with their classmates. Through two examples and a set of exercises, let students know that using the properties of quadratic roots can simplify the operation of real numbers and the formula that the result is quadratic roots. The "inquiry activity" on page 9 of the textbook is not only the application of quadratic root, but also the cultivation of students' inquiry ability, observation, discovery and induction.

1.3, the operation of quadratic root, including four operations of addition, subtraction, multiplication and division of quadratic root and simple application. The textbook is arranged in three classes, step by step and comprehensively used. The first category focuses on the multiplication and division of two (equivalent to two monomials) quadratic roots, and its rules come from the nature of quadratic roots, which is more natural. Example 1 is the direct application of two arithmetic rules, which makes students have a familiar and skilled process with the rules; Example 2 is an application of practical problems, including Pythagorean theorem and area calculation of triangle. The second kind is the mixed operation of addition, subtraction, multiplication and division of quadratic root, which is similar to polynomial single multiplication, polynomial multiplication (including multiplication formula and power) and polynomial single division. The concept of "similar secondary root" does not appear in the textbook, but only mentions "similar to merging similar items" and "items with the same secondary root". This analogy method can be understood by students, and they can also perform operations such as algebraic expressions. The third category is the application of quadratic radical operation. The number in Example 6 looks very complicated, in order to apply the operation of quadratic root. Example 7 comprehensively applies the knowledge of right triangle, division of figure and calculation of area. Its solution process is long, and it is also a comprehensive application of quadratic root knowledge.

Second, the writing characteristics of this chapter

Pay attention to cultivating students' abilities of observation, analysis, induction and inquiry.

In the way of presenting knowledge in this chapter, the textbook highlights the narrative mode of "problem situation-mathematical activities-generalization-consolidation, application and expansion", which is mostly completed through "cooperative learning". "Cooperative learning" creates opportunities for students to engage in mathematical activities such as observation, guessing, verification and communication. For example, on page 5, let students calculate the specific values of three groups of sums, discuss the relationship between sums again, and then get the property of quadratic root "=". Several other properties of quadratic roots are also used in textbooks in a similar way. After learning the related properties of secondary roots, the textbook designed an "inquiry activity". By simplifying the related quadratic roots, students can discover, express, verify and communicate with their peers. All these are the guidelines for compiling textbooks to cause some changes in teaching methods and learning methods.

Pay attention to the connection between mathematical knowledge and real life.

The textbook strives to overcome the complexity of learning quadratic roots in traditional concepts, avoid the simplification or calculation of a large number of pure formulas, properly insert practical applications or give formulas some practical significance. Whether learning the concept of quadratic root or the nature and operation of quadratic root, we should try our best to link the knowledge we have learned with real life and attach importance to the cultivation of the ability to solve practical problems by using the knowledge we have learned. For example, in the study of quadratic radical concept, three practical problems are introduced into the textbook, with the aim of paying attention to the actual background and formation process of the concept and overcoming the learning mode of mechanical memory concept. For another example, on page 3 of the textbook, the distance traveled by ships is represented by the square root, the area of road signs is calculated at 1 1 page, and the planting area of flowers and plants is calculated at 2 1 page. Especially in the quadratic root operation, a special section is arranged to learn the application of quadratic root operation. The background of Example 6 is the slides that students are familiar with, and the background of Example 7 is the paper-cut strips that students are interested in, as well as the problems of dams and speedboats in their homework.

Make full use of graphics to organically combine algebra and geometry.

For the content of number and algebra, the textbook pays attention to the geometric background of the content and uses geometric intuition to help students understand and solve algebraic problems, which is a writing feature of the textbook and a guide to teaching. In this chapter, if the quadratic root is closely related to the calculation of the relevant sides of right triangle, the textbook selects a certain amount of problems in this respect, which not only enriches the application of Pythagorean theorem, but also learns the calculation of quadratic root. Another example is the introduction of secondary roots. The textbook is based on graphics, so that students can give the concept of quadratic root through calculation. When learning the properties of quadratic roots, the textbook requires students to read the graph 1-2, understand its meaning from both positive and negative aspects, and get the properties of quadratic roots. Examples are combined with graphic symbols to help students understand and solve problems; Design some figures in homework or textbook exercises and calculate the length of line segments; Draw a triangle by square and rectangular coordinate system, determine the position of the point and so on. When arranging the application of quadratic radical operation in daily life and production practice, the selected problems also lie in reflecting the connection between students' learned knowledge, feeling the integrity of the learned knowledge, constantly enriching students' problem-solving strategies and improving their problem-solving ability.

Third, teaching suggestions

Pay attention to the use of pre-holiday words.

There are not many words before this chapter, but they are all closely combined with the content of this section and put forward a specific question. They can be used to create problem situations and introduce topics in teaching. For example, paragraph 1. 1, "The height of volleyball net is 2.43 meters, and CB is meters. Can you express the length of AC by algebraic expression? " A few short sentences are not only familiar problem situations for students, but also seemingly familiar but challenging problems, which are related to mathematics learning. The teacher can ask a question related to this lesson. This role should not be ignored in teaching.

Pay attention to the difficulty of teaching.

Compared with the previous textbooks, the quadratic root formula reduces the requirements. If we use the properties of quadratic root to simplify quadratic root, we only need simple formula, not too complicated formula, and make it clear that there are no letters in the root sign. The four operations of quadratic radical are simple, and there are no letters in the radical sign, so there is no need to add questions other than the requirements of textbook topics in teaching. Of course, students at different levels should be flexible. The homework questions 7 and 8 on page 15 of the textbook can also be worked out with a calculator.

Make full use of analogy.

The operation of quadratic roots is based on algebraic expressions, and its rules and formulas are similar to algebraic expressions, especially the addition and subtraction of quadratic roots. The textbook does not put forward the concept of similar quadratic root, and completely refers to the method of merging similar items; The multiplication, division and multiplication of quadratic roots are similar to algebraic expressions. Therefore, in the teaching of four operations of quadratic root, we should make full use of analogy to let students understand its theory and algorithm and improve their computing ability.

Chapter II Quadratic Equation in One Variable

First, the content of teaching materials and course learning objectives

(A) the contents of textbooks

This chapter includes three parts:

2. 1 unary quadratic equation;

2.2 solution of quadratic equation in one variable;

2.3 the application of quadratic equation.

Section 2. 1 is the basic part of the whole chapter, section 2.2 is the key content of the whole chapter, and section 2.3 is the content of knowledge application and extension. In addition, the reading material introduces the development of quadratic equation in one variable, so that students can understand the development history of mathematics.

(B) the knowledge structure of this chapter

(C) curriculum objectives

(1) Understand the concept of unary quadratic equation and solve the equation in the form of (b≥0) by direct Kaiping method;

(2) Understand the collocation method, and use it to solve the unary quadratic equation of digital coefficient; Master the derivation of the root formula of quadratic equation in one variable, and use the root formula to solve quadratic equation in one variable; Factorization can be used to solve the quadratic equation of one variable, so that students can flexibly use various solutions of the quadratic equation of one variable to find the root of the equation according to the characteristics of the equation.

(3) Experience the process of estimating the solution of the equation by observation, drawing or calculator.

(4) According to the quantitative relationship in specific problems, we can enumerate the quadratic equations of one yuan to solve practical problems, find and put forward practical problems that can be solved by using the quadratic equations of one yuan in daily life, production or other disciplines, and correctly express the problems and the solving process in language. Empirical equation is an effective mathematical model to describe the real world.

(5) Combining with the teaching content, further cultivate students' logical thinking ability and educate students on dialectical materialism. Through the teaching of quadratic equation with one variable, students can further gain the understanding that things can be transformed.

(4) Class arrangement

2. 1 quadratic equation with one variable 2 class hours.

In which: the concept of quadratic equation in one variable 1 class hour.

................. 1 class hour of factorization method for solving quadratic equation of one variable.

2.2 the solution of quadratic equation in one variable

Among them: opening method and matching method.

Formula method

2.3 the application of quadratic equation in one variable

Summary, goal and evaluation 2 class hours.

Second, the guiding ideology and characteristics of writing

Equation teaching occupies a large proportion in middle school mathematics teaching, and quadratic equation with one variable plays an important role in junior middle school algebra. On the one hand, the quadratic equation of one yuan can be regarded as the comprehensive application of the relevant knowledge learned before, such as the concepts of rational number and real number, the operation of algebraic formula, fraction and square root, the knowledge of the quadratic equation of one yuan and the solution of the quadratic equation of one yuan, which are all applied in this chapter. From a mathematical point of view, the study of this chapter is difficult. If a link in the front is weak or there is a problem with knowledge points, it will bring difficulties to the study of this chapter. Therefore, the teaching of this chapter is a test of the relevant knowledge learned before, and it is also a review and consolidation. Of course, the knowledge of unary quadratic equation is also the continuation and development of the previous knowledge, especially the deepening and development of equation knowledge.

The main content of this chapter is the solution and application of quadratic equation in one variable. Firstly, the concept of quadratic equation with one variable is introduced into the textbook. Starting with the properties of real numbers, two quadratic equations with zero linear factors are transformed into two quadratic equations with one variable. This paper introduces the method of solving a quadratic equation with one variable by factorization, which embodies the transformation idea of mathematics. Then the textbook starts with the square root knowledge of numbers, and directly talks about Kaiping method, and then introduces collocation method and formula method in turn. While talking about the formula method, the textbook gives an example of solving a quadratic equation with a calculator to reveal the influence of technological development on mathematics learning, which is also a new attempt. At the same time, the application of quadratic equation in one variable is mainly introduced with the establishment of mathematical model, and the problem background in charts, three-dimensional graphics, object movement and economic activities is fully considered in the setting of examples, so that students can learn mathematics in real environment.

This chapter is a key content of the whole book and even the whole junior high school algebra. Because this part of the content is not only a summary, consolidation and improvement of what we have learned before, but also a knowledge foundation for future study. So this chapter can talk about the role of connecting the preceding with the following. The exponential equation, logarithmic equation and trigonometric equation in senior high school are nothing more than a comprehensive knowledge of exponential, logarithmic and trigonometric functions, a linear equation and a quadratic equation. Many main skills, problem-solving methods and some commonly used mathematical thinking methods in junior high school algebra are reflected in this chapter. For example, substitution method, factorization method, collocation method, etc. In addition, the generalization ability and logical reasoning ability from concrete to abstract are also reflected in this chapter. It can be said that this chapter plays an important role in basic knowledge and skills. This chapter focuses on the solution of quadratic equation in one variable, especially the formula method.

Third, the mathematical thinking method embodied in textbooks.

This chapter is the focus of junior high school algebra in content, and it is also a more comprehensive chapter in junior high school mathematics in mathematical thinking methods.

The concept of 1. equation

The equation itself provides an important mathematical thinking method, which is more fully reflected in the unary quadratic equation. Learning equation not only lays a foundation for further learning other knowledge, but also can be used to solve some practical problems. In a broader sense, equations can communicate the relationship between the known and the unknown, so that problems can be solved by solving equations, which is commonly called equation thinking. As a mathematical thought, equation thought occupies an important position in the history of mathematical development and is also of great significance to solving mathematical problems.

2. Formula solution

The formula solution of quadratic equation with one variable is of great significance in mathematical thinking method. First of all, formula method is the first formula (root) solution of known polynomial equation, which opens the way for future research on formula solution, is one of the problems that cause the origin of approximate algebra, and is also of great significance in mathematics learning; Secondly, the formula solution embodies the idea of operators in mathematics and is an important way to abstract, symbolize and program mathematical problems.

3. Mathematical thought of classified discussion

In the formula for finding the root of a quadratic equation, the problem of square root is involved, that is, the square root is to be implemented, but the negative number has no square root. Therefore, the state of determines the state of the roots of quadratic equations. Symbols that must be discussed. The mathematical thought of classified discussion is an extremely important mathematical thinking method. The discussion of three classifications of δ = in textbooks is implicit in classroom teaching. Through "thinking", it is a reasonable way to let students draw conclusions naturally and reduce the learning difficulty brought by the requirements of mathematical thinking. In fact, the discussion of discriminant is an important index for qualitative study of equation roots without understanding the equation. It is of great significance to study the images and properties of quadratic functions and to study the problems of quadratic curves. Discriminant is essentially to study the properties of the equation by using the coefficients of the equation, and it is a method to explore the specific properties through local research. Finding a key quantitative relationship to study a class qualitatively is also a common mathematical thinking method.

4. Transformation (transformation) of mathematical thinking

In this chapter, the thinking method of "transformation" is more prominently expressed. For example, using factorization to solve a quadratic equation is to transform a quadratic equation into two quadratic equations. Strictly speaking, the thought of transformation is an important way to know and master new knowledge of mathematics. Mastering this method can improve students' mathematical ability and expand their mathematical knowledge. For example, substitution method is a very important reform idea, which is also reflected in this chapter.

Fourth, the teaching material processing.

Regarding the treatment of teaching materials, according to the arrangement of teaching materials and the requirements of curriculum standards, it is analyzed in three parts:

1. One-variable quadratic equation

This section includes the concept of univariate quadratic equation and the factorization solution of univariate quadratic equation. This unit is the basis of this chapter. The concept of quadratic equation with one variable is introduced into the textbook. One is the area of square and rectangle that students are familiar with, and the other is the statistical data published in the newspaper. The focus of teaching is to understand the general form of equation and the solution of equation. On this basis, the method of solving a quadratic equation with one variable by factorization is introduced.

2. Solution of quadratic equation in one variable

This section is the core content of this chapter, mainly the various solutions of quadratic equation in one variable. Among them, the collocation method and application of quadratic equation of one variable are the key points, which are the difficulties in the teaching process. The solution of quadratic equation in one variable, especially the formula method, is the key to learn this chapter well. So this section is the focus of the whole chapter, and it is also the basis of learning this chapter well.

There are four methods to solve the quadratic equation of one variable, namely, direct Kaiping method, collocation method, formula method and factorization method.

The direct Kaiping method is suitable for the equation of (b≥0) module. In fact, as long as a given general equation has real roots, it can be transformed into. For example, the equation in the textbook is transformed into, so the matching method is an extension of the direct opening method, and the direct opening method is the basis of the matching method.

On the basis of solving the unary quadratic equation by matching method, the formula for finding the root of the unary quadratic equation is naturally derived, which is actually the result of implementing the matching method for the unary quadratic equation in general form (a≠0).

For the three solutions, the formula method can be a "universal" method. As long as △=≥0, the coefficients A, B and C can be substituted into the formula. Pay attention to the condition of a≠0 in the quadratic equation of one variable in teaching. It should be emphasized that adding "half-square of the first coefficient" on both sides of the equation or adding "half-square of the first coefficient" on the left and subtracting "half-square of the first coefficient" is essentially a homotopy deformation of the equation, which requires repeated training to achieve the goal of students mastering the formula skillfully, and is also the basis for deducing the formula for finding roots.

The discussion of △ = must first run through the idea of classified discussion. In addition, in the case of △==0, it must be emphasized that there are two equal real roots: this is consistent with the theory of equation roots, and students will only know one at first, so they should emphasize it repeatedly to correct this incorrect or imprecise conclusion. Right △ =

As for the relationship between roots and coefficients of a quadratic equation, in fact, the formula for finding roots embodies the relationship between roots and coefficients. Because it is not involved in the curriculum standard, this part is very important for future study, and it can be used as the content of inquiry learning in teaching, so that students can explore and draw their own conclusions.

3. The application of quadratic equation in one variable

The application of solving equations by series has been studied, but it is still difficult to solve the application problems by solving quadratic equations by series, because the quantitative relationship is complicated and hidden. The practical background reflected by the application questions is complex and unfamiliar to students; The listed equations become more and more complicated. Subjectively, students were influenced by the fixed thinking of arithmetic solutions at first, lacking extensive knowledge of social, economic, production and life and related disciplines, and their understanding of written and mathematical languages was poor.

For solving application problems, from the perspective of thinking method, solving application problems with equations belongs to mathematical model method, in which solving application problems with equations generally involves six steps: ① Examining the problems, understanding the meaning of the problems, and making clear how many quantities are involved in the problems, some of which are known and some are unknown, and what is the relationship between them. (2) Setting elements, selecting appropriate unknowns according to the requirements of the topic, which can be divided into direct setting element method and indirect setting element method. At the same time, consider setting a few unknowns; (3) Formulating, analyzing the relationship between quantity and quantity in the topic, the key is to find out the arithmetic relationship in the topic. At this time, we should pay attention to mining the hidden equality relationship in the topic, and sometimes use some intuitive means such as graphic method and list method; (4) solving; ⑤ test, that is, whether the obtained solution conforms to the original equation or the original equations, and whether the obtained solution is meaningful to practical problems; 6 Answer and write the correct and reasonable answer. In teaching, students can participate actively, construct independently and learn cooperatively by combining problem-solving strategies, and experience the basic ideas and methods of mathematical modeling.

(Jin Keqin)

Chapter III Frequency and its Distribution

Statistics is the science of collecting data, analyzing data and obtaining overall information according to the data. The first volume of this textbook arranged "data and charts" in the seventh grade, focusing on the preliminary methods of data collection and collation. The first volume of the eighth grade arranged "preliminary analysis of samples and data" By calculating the scattered statistics in the data set, we have a preliminary understanding of how to analyze the basic state of the data. In order to further analyze and process the data for decision-making, sometimes we need to know the distribution of the data. Find out the new function number. The chapter "Frequency and its Distribution" solves this problem. The content of "frequency and its distribution" is also in the original compulsory textbook of Zhejiang edition, but it is only a section in "Preliminary Probability and Statistics". Considering the close relationship between frequency, frequency histogram and frequency line graph and daily life, nature, society, science and technology, the Mathematics Curriculum Standard adds weight to this content. The purpose of this textbook is to set this content as an independent chapter. On the one hand, it can be explained more clearly and in detail with enough space, and it is also a careful arrangement for each book to learn probability statistics step by step.

The teaching time of this chapter is about 7 hours, and the specific arrangements are as follows:

3. 1 frequency and 1 frequency class hours

3.2 Frequency distribution 1 class hour

3.3 Application frequency 3 class hours

Review and evaluation 1 class hour, maneuver 1 class hour, totaling 7 class hours.

First, the content of teaching materials and teaching objectives

(1) The block diagram of knowledge structure in this chapter is as follows:

(2) The teaching objectives of this chapter are as follows:

Target category

Target hierarchy

Knowledge points and related skills, knowledge and skill objectives, process objectives

Understand, understand and master the flexible application of experience (feeling) experience (experience) exploration.

Frequently

count

and

that

minute

Fabric range √√.

The concept of frequency √√

Frequency distribution table √√

The concept of frequency √√

Significance and function of frequency distribution √√

Frequency distribution histogram √√

Frequency distribution line graph √√

Estimate the average value according to the histogram of frequency distribution.

(3) the teaching requirements of this chapter

Through examples, understand the concepts of frequency and frequency, and understand the significance and function of frequency distribution.

(2) Calculate the range, reasonably group the data, find out the frequency and frequency of each group, and list the frequency distribution table.

③ Can draw frequency distribution histogram and frequency distribution line graph, estimate average value according to frequency distribution histogram, make reasonable judgment and prediction according to data processing results, and experience the role of statistics in decision-making.

④ By drawing histograms and line graphs, we can cultivate students' patient and meticulous work style, realistic work attitude and the ability to observe and analyze problems.

Second, the writing characteristics of this chapter

According to the Mathematics Curriculum Standard, simplify the complex and highlight the important content.

Drawing the histogram of frequency distribution without the traditional step-by-step introduction method will affect students' interest in learning at this age. In fact, if we do it according to section 3. 1, "The following is given with a group interval of 0.4 kg, taking 2.75 ~ 3. 15, 3.15 ~ 3.55 ..." There are many reasons for different processing of continuous data and discrete data, and so on. It is the real purpose of teaching to highlight important concepts, let students experience the true meaning of frequency and frequency, and understand the significance and function of frequency and frequency distribution, which is also one of the characteristics of compiling the textbook in this chapter.

Carefully choose cases, close to students' lives, and arouse students' interest.

Frequency itself deals with practical problems. Starting from reality, concepts are introduced in the process of solving practical problems. Carefully select teaching materials and introduce a large number of familiar examples to create familiar situations for students and stimulate their interest. Let students have the desire to solve. To some extent, lengthy narrative cases have aroused students' disgust. For example, blood type distribution, choice of sports shoes and shoe sizes, academic performance, waiting time for lunch, quality of mineral water, etc. It's all about students, who are familiar and kind. At the same time, students are trained to think about the problems related to data information from the statistical point of view, and make reasonable decisions through the process of collecting and analyzing data, so as to improve the ability of processing and decision-making.

Emphasize practical operation, design a certain amount of mathematical activities, and enhance the awareness of mathematical application in communication.

This chapter arranges a certain amount of practical activities, such as "the distribution of the height of boys and girls in grade eight, the distribution of wearing sports shoes", "the frequency distribution of skipping rope for students in grade eight", "the weight data distribution of boys and girls in grade eight" and "the sales of color TV sets at different prices in shopping malls". These activities require students to cooperate in groups, carefully design and plan in advance, and extensively investigate unfamiliar people and things. It is hoped that through these activities, students can learn a lot of mathematical information contained in the real world. Mathematics is closely related to the real world, which can enhance students' awareness of mathematics application and cultivate their practical working ability, so as to gain the joy of overcoming difficulties or achieving success.

Third, teaching suggestions

(1) The general steps for drawing the histogram of frequency distribution are: ① calculating the extreme range; (2) Determine the number of groups and the distance between groups. Generally, when the data is within 100, it is often divided into 5~ 12 groups according to the number of data; Group distance refers to the "distance" between two endpoints of each group, = group distance; (3) Determine the dividing point. In order to avoid some data falling on the split point, the split point often takes one decimal place; (4) list and scribing; ⑤ Draw the histogram of frequency distribution. Teachers should be flexible in explaining according to the actual situation, but don't completely repeat the above steps on the blackboard, which violates the original intention of compiling teaching materials.

(2) Using frequency distribution table, frequency histogram and frequency line chart to analyze some characteristics of data is one of the key points in teaching. In teaching, we should give full play to students' enthusiasm and let them observe carefully, speculate boldly and verify reasonably. "What problems should we pay attention to when ordering sportswear and sports shoes in a unified way?" "How long should the school arrange for students to have lunch?" "Estimating the number of fish in the fish pond" and "analyzing the difference of swimming performance between boys and girls" are not the only standard answers to the original math problems. Students should be encouraged to express their opinions and finally form a more consistent opinion on the basis of full discussion. This is an important way to communicate with people, dare to explore and express their views clearly, and it is also an important aspect of mathematics teaching in the new curriculum. Teachers should try their best to reflect it in this chapter according to the specific situation.

(3) The main feature of this chapter is its complicated calculation and close connection with practice. In addition to the examples provided in the textbook, teachers can also make appropriate supplements according to the actual situation. At the same time, teachers should make full use of multimedia, make some teaching AIDS in advance, and don't waste precious time in class on copying and drawing.

Fourth, the problems that should be paid attention to in the teaching of this chapter

(1) There are two kinds of data: continuous data and discrete data. It is generally easy to group discrete data, such as the blood type of textbook 5 1 page, but it is not unique to group discrete data. Only according to experience, different groups generally draw different conclusions, but as long as they are reasonable, they are all considered correct.

(2) When carrying out practical activities, we should pay attention to some problems that may involve students' personal privacy. For example, a chubby female classmate doesn't want to talk about her weight. She thinks it is an invasion of personal privacy to disclose her weight. Students who jump rope several times a minute may also feel embarrassed and have some unpleasant things. In view of these situations, teachers should make full preparations and take measures such as avoiding or choosing some suitable students or choosing other suitable data as the survey object. Our purpose is to cultivate the spirit of mutual cooperation through some practical activities, to have a pleasant experience in cooperation with others, to solve practical problems with mathematical knowledge, and to enhance our self-confidence in applying mathematics. Don't interfere with the whole teaching plan for individual special reasons.

(3) Generally speaking, the ordinate and abscissa of the histogram have different units, and the specific length of each unit should be selected in comparison. The ultimate requirement is to draw more beautiful graphics, which can clearly reflect the distribution and changing trend. The way to draw broken lines in textbooks is to avoid drawing figures in extreme positions. Frequency histogram or frequency line graph can be more beautiful without affecting the basic characteristics reflected by the whole graph. You can also compare and show the charts drawn by students.