In junior high school, plane geometry is the main way to learn geometry knowledge. In the rich graphic world, starting from the observation of three-dimensional space objects, making full use of students' rich background experience, in the mutual representation and transformation of physical objects, geometric objects, direct vision and plane graphics, the perception level of geometric graphics is improved and the concept of space is developed. Through observation, operation, thinking and communication, we can accumulate mathematical experience, feel the necessity of learning plane graphics and the foundation of simple graphics, realize that basic graphics are an important tool to describe the real world, and learn to observe the world with mathematical eyes, which can bring endless intuitive sources to real life. In "Plane Figure and Its Position Relationship", the role of understanding the basic concepts of geometry and rational reasoning is highlighted.
Through the discussion of practical problems, Data in Life enables students to understand the important role of data, the process of data processing and the information it expresses, and develop their sense of numbers and statistical concepts. In the chapter of "Possibility", the characteristics of uncertain phenomena are preliminarily understood, and the hidden regularity in random phenomena is understood through experiments, and the random concept is initially formed.
The first chapter is a rich graphic world.
In the teaching of the first chapter, it seems that students cut, fold, cut and cut in class, unlike math class, it is simply a skill class. I think the content of the first chapter has not really touched on mathematical knowledge; Do other teachers feel that high school solid geometry is decentralized? How do you feel like a "dragonfly water", not deep and impenetrable, not as systematic and perfect as the old textbooks. There is no multimedia demonstration in class, but some teachers use it, let the students watch it themselves, and the teacher will briefly summarize it. Junior high school students are only the primary stage of the development of space concept, and they are cognitive processes that conform to the nature of three-dimensional graphics in life. Students are required to start from observing objects in life, and gradually form their own understanding of space and graphics through observation, operation, imagination, reasoning, communication and many other mathematical activities according to their existing life background and preliminary experience in mathematical activities. Therefore, the learning content of this chapter mostly adopts the learning method of "hands-on operation, cooperation and communication". As far as teachers are concerned, teaching should not only stay on the surface of vivid operation, but also help students to think rationally while carrying out activities such as operation and communication, guide students to discover and discover some mathematical relationships hidden in activities, and really help students accumulate learning experience and develop spatial concepts.
On the surface, the chapter "Rich Graphic World" seems to have few specific knowledge points. In fact, a space figure can be unfolded and folded through its surface. Using plane cutting and three views to realize the conversion between three-dimensional graphics and two-dimensional graphics. Cultivate students' concept of space by doing, thinking and doing. Through hands-on operation, abstract objects can be simplified and visualized, and rational thinking can be inspired and prompted at the same time. If you cut a cube with a plane, can the section be heptagon? Doing "thinking" includes rational analysis and reasoning-why it can or cannot be done. Developing students' spatial concept and improving their visual thinking ability and level are the main learning objectives of this chapter.
In the rich graphic world, learning geometric objects does not start from the logical starting point of geometry, but conforms to the process of mathematical history, and has gone through the process from concrete to abstract, and then from abstract to concrete. Starting from the investigation of real-world objects, we abandon secondary factors, decompose simple geometry or basic graphics, and develop geometric intuition and spatial concepts in the process of decomposition and integration. We don't study solid geometry in advance, but learn "mathematicization" through activities. In chapter 4, the concept of geometry is naturally introduced one after another, and the positional relationship and basic properties of simple plane graphics are found through operation and expressed in symbolic language. Textbooks provide a lot of hands-on opportunities, reproduce the process from intuitive action thinking to intuitive image thinking, and make necessary preparations for further development to abstract (logical) thinking stage.
It is the teaching goal of the chapter "Rich Graphic World" to accumulate the experience of mathematical activities and develop the concept of space. The content is close to students' life experience, which is easy to arouse their interest in learning, feel that mathematics is around, and improve their bad impression of mathematics. In teaching, we should fully explore the connotation of mathematics in activities and lead our interest to mathematics. In the activity, students should be guided to think about a series of math problems. For example, in the process of unfolding the surface of a cube into a plane figure, students may encounter many mathematical problems.
Usually, mathematical problems or mathematical thinking can be triggered by vivid and interesting situations, which can provide empirical support for mathematical understanding, but we should cut into the subject in time to avoid "playing peripheral wars" for a long time. First of all, we must grasp the basic orientation of all classes. For example, from different directions, the main purpose is to learn three kinds of views, and to learn the mutual expression of spatial graphics and plane projection. On this basis, students should think about avoiding one-sidedness of problems.
Using information technology to make courseware can produce good results in teaching, but attention should be paid to avoid teaching activities becoming technical demonstration classes.
The Relationship among Points, Lines and Surfaces
Show more three-dimensional figures in life, let students see, fully describe the relationship between points, lines and surfaces in their own language, summarize more accurate mathematical language through operation, and better imagine figures. In teaching, we should pay attention to the process from describing the characteristics and nature in students' own language to forming a more standardized language through full communication. )
The relationship between wanting and doing.
At the beginning, you should do and think first (hands-on operation is an important part in the learning process-at the beginning of learning, it can help students understand graphics and develop spatial concepts, and later it can be used to verify students' spatial imagination of graphics. Therefore, at the beginning of learning, students should be encouraged to do it first and then think. In the future, students should be encouraged to imagine before doing it.
For example, the surface development diagram of a cube can be explained clearly by the teacher, so that students can do it, and then the students can show the communication and see which diagrams can be folded into a cube and which ones can't. Let students think, do and see if their thinking is correct (some teachers also guide students to classify the obtained plane figures, which is required in the teaching reference, but I think the real test is not whether they can be folded into squares. )
What does the positioning of plane graphics do on page 25?
Chapter II Rational Numbers and Their Operations
I. Understanding Logarithm and Algebra Content
Orientation in compulsory education mathematics curriculum-algebra is a very important tool when we describe the mathematical characteristics of an object (group) from the perspective of quantity; When we try to obtain some mathematical characteristics of an object (group) through mathematical operation, algebra can give us great help; When we need to obtain the mathematical characteristics of an object, we can't do without algebra.
In the way of dealing with numbers, the background of numbers-the characteristics of numbers-the representation and operation of numbers: highlighting the induction and analogy of actual background and operation rules.
Second, the content analysis:
1, main position and its function:
2. The biggest difference from previous textbooks is that:
(1) reduces the requirements for the difficulty and length of calculation questions;
(2) In the mixed operation of numbers, the number of numbers does not exceed 4;
(3) Find the absolute value of a number without discussing the letter A;
(4) Desalinate the teaching of related concepts and attach importance to their application;
(5) Add some interesting knowledge, such as: 24-point game to train students' basic computing ability.
(6) The use of calculators has increased. Calculators can be used to calculate rational numbers, that is to say, students don't need to do complicated written calculations, but have more time to use rational numbers to solve problems. The basic requirements of rational number operation cannot be lowered. Therefore, the content of rational number operation with calculator should be introduced after students master the corresponding operation. Let calculators serve students to master rational numbers. You can have a calculator check after writing. No, students should be allowed to find mistakes and correct them in the process of writing. Using the moderator of calculator to explore the operation law. For example, if we examine whether the multiplicative commutative law, multiplicative associative law and distributive law are used within the scope of rational numbers, students can choose more complex numbers to try, and a calculator can get the results. )
3. Key points, difficulties and key points
This chapter focuses on the operation of rational numbers. The difficulty is the understanding of rational number operation rules, especially the understanding of rational number multiplication rules. The key of rational number operation is the determination of symbols in rational number addition and multiplication.
What changes have been made in rational numbers and their operations compared with the past?
Pay attention to the connection with daily life, pay attention to the cultivation of number sense (feeling and estimation of large numbers), pay attention to the diversification of calculation methods, pay attention to solving problems and exploring laws, and downplay complex operations.
With the help of examples in life, this paper introduces the operation of rational numbers. Through induction, students sum up the algorithm and operation law. In order to avoid diluting the focus of learning because of the complexity of decimal and fractional operations, we have mastered (rules and arithmetic can pass) from the beginning of learning integer operations, especially the addition of rational numbers, and we have mastered addition and subtraction (algebra and processing, focusing on essence and diluting form), and then transitioned to operations involving decimals and fractions. Using rational number operation to solve practical problems.
Regarding the operation of rational numbers, the understanding of the operation significance is emphasized. The understanding of the operation law is obtained in the process of independent exploration. Because we can use computing tools to perform complex digital operations, the cultivation of computing skills mainly focuses on the understanding and flexible application of computing rules. Encourage the diversity of algorithms, because different algorithms may come from different understandings or thinking habits, and they can share resources through communication.
Diversification of calculation methods for 67 pages
Chapter III Letter Representation of Numbers
The content of this chapter: 1, which is used to reflect the quantitative relationship or change law.
2, using the operation method
3. Use formulas to express the changing laws of common and basic quantitative relations.
What can the first letter mean? What is the purpose of "setting matchsticks"?
This example shows the process of summarizing general laws with special cases and expressing them in letters. In this process, students have to go through the process of operation, thinking, expression, communication and clarity. Let students solve problems in their own way, express their thoughts in their own language, exchange ideas with their peers, and express the laws found in their own language to form a symbolic representation process.
Explore the law
Algebraic method is used to reduce the changing law of numbers to algebraic evaluation.
The changing law of geometric figures represents the law, and algebraic operation verifies the same law.
Through abundant examples, let students experience the two-way process from language narration to algebraic expression, from algebraic expression to language narration (giving algebraic, practical and geometric meanings, etc. ). For example, give 3a a reasonable explanation in the senior high school entrance examination.
Algebraic evaluation is represented by "numerical machine". Algebraic evaluation can be understood as a program or an algorithm. (The first chapter of compulsory mathematics in senior high school 3, the algorithm is preliminary, this is a new chapter. In fact, all our teaching materials are infiltrated here. Fill in the blanks in question 9 of this year's senior high school entrance examination. The following figure is a simple operating procedure. If the input value of x is -2, the output value is-. Input x x2 +2 output. It may also be a proposition trend. ) and initially infiltrated the idea of function.
Through the study of letters representing numbers, students can feel that replacing specific numbers with letters can solve the problem as a whole. Further understanding facilitates formal operations (such as merging similar terms) and the exploration and discovery of laws, which has a direct impact on the understanding of equations.
Chapter IV Plane Figures and Their Positional Relations
Key points: We should pay attention to introducing concepts through examples, starting from our own life background (teachers should fully explore and make use of the realistic background closely related to the learning content, and try their best to teach in appropriate problem situations from topics of interest to students), and carry out the mastered mathematical knowledge, skills and activity experience in activities such as observation, operation, thinking and communication.
(1) This chapter takes a large number of realistic backgrounds and puzzles as raw materials, takes simple plane figures such as lines and corners and the relationship between parallel and vertical positions as the main research objects, and presents relevant contents in a lively form.
(2) This design focuses on mathematical activities, aiming at enabling students not only to master the basic knowledge and skills related to line segments, angles, parallel and vertical positions (especially to understand geometric concepts and geometric facts), but also to enrich and develop their experiences and understandings in mathematical activities. Teachers' demonstration should not replace students' hands-on operation, and students should be encouraged to cultivate good feelings, attitudes and awareness of active participation and cooperation in their studies.
Evaluation 1. Pay attention to the evaluation of students' activities such as observation, operation and exploration of graphic properties.
2. The evaluation of knowledge and skills focuses on related concepts such as line segment, ray, straight line, angle, parallelism and verticality, and pays attention to the understanding of graphic properties, as well as the basic understanding and practical operation of related skills such as simple drawing and origami.
3. Pay attention to students' emotions and attitudes in various mathematical activities, especially in group activities.
4. Pay attention to the cultivation and training of geometric language. Geometric figure is the research object of space and figure, and its general description and representation is carried out according to the program of "geometric model-figure-text-symbol". Among them, graphics is the first abstract product of geometric model, and it is also an intuitive language; Writing language is the description, explanation and discussion of graphics; Symbolic language is a simplification and re-abstraction of written language. Obviously, the graphic language is established first, followed by the written language, and then the symbolic language. Finally, it should be a comprehensive description of the object in three mathematical languages. With this overall understanding, the three languages can be integrated and the objects can be basically grasped.
This chapter pays special attention to the abstract process of "geometric model-figure-text-symbol". The textbook first emphasizes the role of physical prototype, introduces a large number of physical models, and allows students to abstract geometric figures from them. Secondly, the textbook attaches importance to the role of graphic language, and the description of words and symbols of objects is closely related to graphics, combining abstraction with intuition, and developing other mathematical languages on the basis of graphics. For example, the comparison of line segments, the sum and difference of line segments, the comparison between the midpoint of line segments and angles, the bisector of angles, etc. , are given intuitively with graphics first, then with quantity, given the description of words, and finally given the representation of symbols. This is the complementary advantages of several geometric languages to get better results.
In addition to paying attention to the transformation process of "geometric language-graphics-characters-symbols", we should also pay attention to the transformation of "symbols-characters-graphics", that is, we should understand the graphic relationship expressed by symbols or characters and express it intuitively with graphics, so as to change "intangible" into "tangible". This chapter focuses on the design arrangement of the transformation of graphics, characters and symbols in different directions, and arranges some links and exercises. In teaching, we should pay attention to these aspects of training. (Personally, I think it should be bigger than the training in textbooks, especially the symbolic language, writing format and scholars' work are not necessarily strict and logical, but there must be a junior high school format, otherwise the later proof will be more difficult to learn.) Let students adapt quickly and learn geometric figures.
Chapter 5 One-variable linear equation
This chapter introduces the concept of linear equation of one variable from some practical problems. Through the balance experiment, the basic properties of the equation are intuitively summarized and introduced, and students are allowed to try to solve a linear equation with the basic properties of the equation.
Through concrete examples, this paper summarizes a common deformation of solving equations-the law of shifting terms, and then sets up some realistic and interesting problem situations to make students realize that equations are important mathematical models to describe the real world. Finally, through the presentation of practical problems, students can understand how to list a linear equation to solve practical problems, from which the idea that "unknown" can be transformed into "known" can be infiltrated. Algebraic method is superior to arithmetic method in dealing with some problems. In the content presentation, the textbook changes the model directly given in the traditional textbook, but starts with the practical problems that students are familiar with and begins to learn equations. By exploring problems in situations, students can realize that the emergence of equations stems from the need of solving problems, the significance and function of learning equations, and that equations are effective mathematical models to describe the real world and appreciate the application value of mathematics in the process of establishing equation models to solve practical problems.
Solving equations is one of the main contents of algebra. Solving linear equations with one variable is the basis of learning other equations and equations. Equations are widely used in life, such as solving problems in calendar games, counting relevant data in population census, and solving many problems in discount sales and educational savings ... The focus of this chapter is to enable students to list linear equations of one variable according to the quantitative relationship in specific problems, master the basic methods of solving linear equations of one variable, and use linear equations of one variable to solve practical problems. The latter is the difficulty of this chapter.
Second, teaching suggestions
1. In practical teaching, we should introduce some practical problems and familiar things around us as much as possible, so that students can feel that learning mathematics is really the need of real life, and at the same time, they can find more similar problems around them for analysis and consolidation, and feel the universality and superiority of equation application.
2. In the teaching process, teachers should try their best to understand the concept of new textbooks, set relevant enlightening questions from reality, and let students form new knowledge through independent exploration and cooperation.
3. The steps of solving equations should not be unified, but should guide students to choose reasonable steps. But to sum up the general steps to solve the equation.
4. When solving practical problems with one-dimensional linear equations, some students are not easy to get rid of the arithmetic calculation in primary schools and are unwilling to solve problems with equations. This phenomenon occurs because students do not fully understand the usefulness and superiority of the equation. At this time, teachers need to set relevant questions so that students can know the superiority of solving practical problems with equations in comparison.
5. Using equations to solve application problems is actually a "mathematical" process. Through the analysis and research of some practical problems, the key to help students understand that the key to solving practical problems by using equations is to establish an equal relationship. To solve the problem, we must grasp three important links. First, we should study the meaning of the problem as a whole and systematically. The second is to grasp the "reciprocal relationship" in the problem; The third is to correctly solve the equation and determine the rationality of the solution. The application of the equation is mainly to master the equivalence relation, test and explain the solution. Manual classification (engineering problems, distances, etc. )
Adhere to the principle of "four noes";
(1) Teachers don't teach students what they can learn;
(2) Teachers do not guide students to explore what they can;
(3) Teachers don't do anything that students can do by themselves;
(4) Teachers don't quote what students can say.
Chapter VI Data in Life
The ultimate goal of statistical learning is to develop students' statistical concepts. The formation of statistical concepts is not spontaneous, nor can it be solved by preaching. Students need to personally participate in such activities, and feel that solving problems requires collecting data, characterizing data, analyzing data, and making appropriate judgments by using the results of data analysis. Therefore, the design of statistics-related content in the whole textbook should try to let students experience the whole process of statistical activities from practical problems. For example, the textbook 1 puts forward "What competitions will you organize to watch in order to attract students to participate as much as possible" and "Are you confident to learn math well?" Driven by these problems, guide students to engage in statistical activities, acquire corresponding knowledge and methods in activities, and develop their own abilities.
The content of this chapter focuses on letting students learn statistical charts in primary school, then let them know the characteristics of fan-shaped statistical charts and master the drawing method of fan-shaped statistical charts. Finally, by choosing three suitable statistical charts, let students learn to display and describe more complex data, let them understand the role of statistics in decision-making, and then lay a solid foundation for further learning statistical knowledge. To sum up, this chapter plays a connecting role in the study of statistical knowledge.
The main points of this chapter include:
(1) Through practical activities, use the familiar things around students to feel and estimate large numbers from all angles. Learn an important method to represent large numbers: scientific notation;
(2) Understand the meaning and characteristics of departmental statistical charts;
(3) Through the process of data statistics, make a fan-shaped statistical chart, get as much information as possible from it, understand the relationship between the whole and the part reflected by the fan-shaped statistical chart, and learn to make a fan-shaped statistical chart;
(4) By analyzing the data in the newspaper, students can understand the different characteristics of the three statistical charts, and can choose the appropriate statistical chart to describe the data according to specific problems.
Among them, determine the estimation method, feel the large number from multiple angles and develop the sense of number; According to the different characteristics and specific problems of the three statistical charts, it is difficult to choose a suitable statistical chart to describe the data in this chapter. According to the different characteristics and specific problems of the three statistical charts, it is difficult to choose a suitable statistical chart to describe the data in this chapter.
Teaching suggestion
1. The first section pays attention to the practical meaning and feelings of large numbers, and encourages students to determine the actual estimation method through group communication activities on the basis of their own thinking, so as to feel, estimate and express large numbers from multiple angles and develop students' sense of numbers.
2. Teachers should change the previous practice of summing up knowledge, strengthen students' group cooperation activities, and encourage students to explore new knowledge, enrich their views, seek reasonable answers and gain experience through their own thinking and discussion with others.
In the section of "Scientific notation", teachers should design the topic of exploring laws step by step, and then students can discuss in groups to explore the expression of scientific notation and who will decide the power exponent of 10 in notation.
3. The textbook presents the survey data of a class in a middle school with a pie chart (Section III), so that students can learn to get information from the pie chart and feel the characteristics of the pie chart. Through the problems in the chart, students can be guided to understand the characteristics of fan-shaped statistical charts, and teachers need not be limited by these problems.
5. Selection of statistical charts: fully tap the materials in students' life in teaching, and let students go through the process of data processing: collecting, sorting, describing and analyzing data, making decisions or making predictions, and putting the study of statistical charts in the situation of solving problems.
The teacher assigned practical homework in this class, for example, if you are a class librarian, what should you do to make the students in the class take a fancy to their favorite books in organizing a class reading activity? What method do you use to show the basis of your decision on this activity?
Chapter VII Possibility
The ultimate goal of probability learning is to develop students' random concepts, which have multiple levels. Therefore, it is impossible to cultivate students' random concept overnight, and it takes a long process. For this reason, this book aims to make students feel the universality of random phenomena in the real world and the possibility of random phenomena through specific practical activities. As for how to describe them, study them in the second book. In addition, for randomness, we only pay attention to the feelings in practical activities and don't want to analyze it theoretically. I don't want students to say, "There are three possibilities in this situation and only two possibilities in that situation, so this situation is more likely to happen." This description is actually based on "every possibility is exactly the same", which is already a theoretical calculation. Maybe your analysis in this case is not bad, but if students feel this way when learning probability, it may be easy to put this (equal possibility).
The main content of this chapter is related to some preliminary knowledge of probability theory. This chapter provides students with opportunities to fully engage in mathematical activities and exchanges, thus helping students truly understand and master basic mathematical knowledge and skills in the process of independent operation, and comprehend more profound mathematical ideas and methods.
Based on students' favorite ball-touching games, students can experience that some events are uncertain through experiments, and enrich their understanding of uncertain events through practical examples.
By touching the ball in groups, students can have a qualitative understanding of the probability of uncertain events according to the results of touching the ball, know the possibility of events, and get a preliminary understanding that people usually do experiments to estimate the possibility of events.
Through roulette games, students can further understand the probability of events, and review the meaning and operation of some basic statistics (such as average), as well as the addition and subtraction of rational numbers.
This paper discusses "who turns out the four digits is big", so that students can accumulate the experience of random experiments, further understand the characteristics of uncertain phenomena, and investigate students' random concepts and their understanding of the connotation of random concepts.
Project learning
Content involved: cuboid expansion, algebraic expression, algebraic evaluation law, statistical table.
The activities include: making a cuboid without a cover, representing the cuboid's volume, changing the cuboid's volume rules, and finding the largest possible volume.
Through the study of this theme activity, students can further enrich the concept of space, experience the application of function thought and symbolic representation in practical problems, and then experience the process of abstracting mathematical problems from practical problems, establishing mathematical models, and comprehensively applying existing knowledge to solve problems, deepen their understanding of relevant knowledge and develop their thinking ability.