As a faculty member, it is often necessary to prepare lecture notes, which can better improve teachers' theoretical literacy and ability to control teaching materials. So how should the course draft be written properly? The following is my collection of axisymmetric lectures on junior high school mathematics, hoping to help you.

Axisymmetric Lecture Notes on Mathematics in Junior High School 1 1. Textbooks

1. Lecture content:

The teaching content of the first lesson of Unit 2 "Symmetry, Translation and Rotation" in Grade 3 of Beijing Normal University Edition.

2. The position and function of teaching materials:

Symmetry is the most basic graphic transformation, which plays an important role in helping students to establish spatial concepts and cultivate spatial imagination. At the same time, symmetry also plays an important role in nature and daily life. The textbook combines the appreciation of folk art paper-cut patterns, as well as the appreciation of costumes, handicrafts and architectural patterns, so that students can perceive the axisymmetric phenomenon that is common in the real world, let students experience the characteristics of axisymmetric graphics, and prepare for further study of symmetric graphics.

3. Teaching objectives:

(1) Understand the symmetry phenomenon in life, understand the characteristics of axisymmetric graphics, correctly identify axisymmetric graphics, and draw axisymmetric graphics with simple graphics on grid paper.

(2) Through observation, guessing, verification and operation, we can experience the process of understanding axisymmetric graphics and cultivate students' practical ability and innovative ability.

(3) In the process of understanding, making and appreciating axisymmetric graphics, feel the symmetrical beauty of objects or graphics and cultivate students' aesthetic interest.

4. Teaching focus:

Understand the basic characteristics of axisymmetric graphics.

5. Teaching difficulties:

Making axisymmetric graphics.

Second, oral teaching methods

According to the characteristics of the content and arrangement of the teaching materials in this section, in order to highlight the key points and break through the difficulties more effectively, based on the development of students, the teaching methods are mainly based on exploration and discovery, supplemented by intuitive demonstration and question induction. In teaching, we should carefully design inspiring and thinking questions to stimulate students' desire to explore knowledge, draw conclusions step by step and cultivate students' thinking ability.

Third, theoretical study.

In order to implement the concept of the new curriculum standard, the learning methods of hands-on practice, independent exploration and cooperative communication are embodied in the teaching of this course. In order to let students fully experience the characteristics of axisymmetric graphics, a series of interesting practical activities are arranged, such as playing, folding, cutting and drawing, which provide students with sufficient learning materials, create a relaxed learning space and experience the formation of knowledge.

Fourth, talk about the teaching process

(A) play symmetry, stimulate the introduction of interest

At the beginning of class, the teacher said: Give you a piece of paper, how will you play? A word game aroused students' interest, and then the teacher's performance of tearing paper and the appearance of small clothes pushed students' interest to the extreme! Can you play like a teacher? As soon as the voice fell, the children couldn't wait to start origami and tearing. Clever little hands turned a piece of white paper into a beautiful figure, scrambling to paste the work on the blackboard. The introduction of this new class captures the age characteristics of children who are active and playful. Through the operation of tearing paper, students can see and feel the beautiful axisymmetric graphics, intuitively lead to the beauty of symmetry, and classroom teaching goes straight to the learning theme.

(B) understanding symmetry, understanding characteristics

1. Looking for features and understanding axisymmetric graphics (works)

Combining the students' tearing paper works, the teacher said: Do these figures have the same place? Finding the students' cognitive starting point, students quickly discovered the mystery through observation and comparison: the left and right sides of these figures have the same shape, and they will completely overlap after being folded in half. On this basis, I skillfully introduced the concept of axisymmetric graphics, and then guided students to understand the symmetry axis of axisymmetric graphics from the perspective of axis symbols.

2. Check the features, and then identify the axisymmetric figure (picture).

Show me the photos. Are they axisymmetric figures? Is there any way to verify it? Grasping the competitive characteristics of students, students soon thought of using the method of folding in half to verify their own statements; This link deepens students' understanding of axisymmetric graphics.

3. Distinguish the features and find out the true and false axisymmetric graphics (courseware)

Pleasant facial mask exercises enhance the initiative of students' thinking; The level of practice promotes students' internalization of knowledge.

Symmetry and deepen the experience

1. Guess: (showing half of the axisymmetric figure) What is this? The students all guessed confidently and got the last one right. After opening it, it is not a vase that the students guess in unison. ) In the students' surprise, the teacher took the opportunity to inspire the students: Think about it, what shape and size will the other half of the vase be? Can you try to cut this complete vase?

2. Cut it: the group cooperates to complete the vase painting, and the whole class focuses on guiding the students to talk about the production method and giving them an encouraging evaluation.

3. Draw a picture: Do you want to make an axisymmetric figure yourself? When the class communicates, encourage students to tell their painting skills.

The design of this link aims to let students walk into practice with knowledge, get the method of making axisymmetric graphics without trace, and advocate students to learn to use knowledge and develop their thinking through practice.

(4) Appreciate symmetry and enhance understanding.

From axisymmetric graphics to axisymmetric phenomena in real life. Guide students to feel the beauty and magic of nature through appreciation, further broaden their horizons, be influenced by beauty, and feel the close connection between mathematics and life.

Axisymmetric lecture notes on junior high school mathematics 2 i. Textbooks

Textbook analysis

Axisymmetric graphics are selected from the second volume of Mathematics, the standard experimental textbook of compulsory education curriculum. The arrangement of teaching materials is from concrete to abstract, from perceptual to rational, from practice to theory, guiding students to perceive the axisymmetric phenomenon of graphics, with distinct levels and step by step.

Symmetry is a basic graphic transformation, including axial symmetry, central symmetry, translational symmetry, rotational symmetry and mirror symmetry. There are many symmetrical things in nature and daily life, and students are no strangers to symmetry. For example, many works of art and architectural design embody symmetrical style. Symmetrical objects give people a symmetrical and balanced aesthetic feeling.

The textbook starts with things that students are familiar with, and through various activities, students can initially perceive the symmetry phenomenon in life, and then know the simple axisymmetric figures and axes of symmetry, so as to lay a good foundation for students to further explore the axisymmetric characteristics of simple figures, master the axisymmetric relationship between simple figures, and use axisymmetric methods to transform or design patterns. Textbooks are gradually developed in the order of knowledge introduction-concept teaching-knowledge application, which embodies the formation process of knowledge. The textbook first asks students to observe and analyze their similarities and differences through Tiananmen Square, airplanes, trophies and other physical pictures, and leads to the concept of "symmetry". Next, the textbook abstracts these objects into plane graphics, guides students to find the basic characteristics of axisymmetric graphics by folding them in half, and initially describes the concept of axisymmetric graphics. In the textbook, the term "symmetry axis" also appears in the picture, but it is not defined or described, just for students to understand.

The second example is to let students use the preliminary knowledge of axisymmetric graphics they have just mastered to "make" axisymmetric graphics. Through these activities, students can further accumulate perceptual knowledge, enrich the experience of axisymmetric graphics and exercise their hands-on ability.

In "Want to Do", through a series of exercises, deepen students' understanding of axisymmetric graphics. Among them, the third question provides half of an axisymmetric figure on a grid paper and requires drawing the other half, so that students have the opportunity to experience the characteristics of axisymmetric figures again in operation. After "think about it and do it", I also arranged "Do you know" to introduce some symmetrical phenomena in nature and some famous symmetrical buildings in the world, so as to further expand students' knowledge horizons and help them appreciate the scientific and aesthetic values of symmetry.

Analysis of learning situation

Axisymmetric phenomenon is a new knowledge point for students, which is widely contained in nature. Learning this part of knowledge requires students to have the ability to observe and operate.

On teaching objectives

1. Knowledge objective: Let students feel the universal axisymmetric phenomenon in the real world. Through observation, operation and other activities, we can explore the characteristics of axisymmetric graphics, understand the meaning of symmetry axis and feel the beauty of mathematics.

2. Ability goal: to cultivate students' thinking methods from concrete to abstract, and then from abstract to concrete. Cultivate the ability of observation, operation, expression, thinking and exploration, give play to students' imagination and creativity, stimulate students' aesthetic appreciation and cultivate students' ability to create beauty.

3. Emotional goal: let students experience the fun of learning mathematics in practical operation activities, encourage them to feel, appreciate and create beauty, appreciate the charm of mathematical knowledge, and stimulate students' desire to learn mathematics well.

Teaching emphasis: understanding the characteristics of axisymmetric graphics

Teaching difficulty: mastering the discrimination method of axisymmetric graphics

Two. Speaking and teaching methods

Mr. Tao Xingzhi once said: "We want to live books, not dead books; Real books, not fake books; Books that need to be moved are not static books; Use books, don't read them. Generally speaking, we should be guided by life-centered teaching, not text-centered textbooks. " In mathematics teaching, starting from the objects that students are interested in in in life, students are strongly attracted to realize the close relationship between mathematics and life; Create a situation of inquiry learning for students; At the same time, according to the arrangement of teaching materials and the psychological and thinking characteristics of children, this class plans to adopt the methods of observation and discovery, group discussion and cooperative learning discovery to cultivate students' inquiry ability and cooperation ability.

Three. Methods of speaking and learning

The new curriculum standard points out that students are the main body of learning. To make students become real masters, we must learn mathematics in mathematics activities, that is, learn mathematics in creating mathematics. This lesson allows students to find problems, ask questions and experience the happiness of successful exploration from the specific objects that students are interested in; Solve your own problems through hands-on operation and group discussion; By practicing in different levels, students' problem-solving ability is improved and their knowledge is consolidated.

Fourth, talk about the teaching process

I started with the games that children are interested in, and narrowed the distance between me and my classmates in the process of playing with them, thus achieving the purpose of entertaining. At the beginning of this class, I cut out a picture of "love" to attract students' attention, stimulate their interest and naturally reveal the topic of this class.

Next, show the pictures in the example, and let the students discover that these objects are symmetrical through careful observation and self-folding, revealing the concept of "complete coincidence", so that the students can initially perceive the symmetry of plane graphics, and then let the students continue to origami, further revealing the concept of "axisymmetric graphics" and let the students initially understand the symmetry axis.

Then give some geometric figures and other figures that students know, that is, "try it" in the textbook, or use the learning method of group discussion to solve the problem. This design can fully mobilize students' various senses to participate in learning, which not only gives play to students' initiative in solving problems, but also cultivates students' divergent thinking. At the same time, it is difficult to judge graphics, so that students can pick the fruits they want under the premise of jumping, and stimulate students to use their brains and dare to explore.

After learning "Try it", students now know a lot about axisymmetric graphics. At this time, they need some exercises and games to consolidate their previous knowledge. I arranged three links: "find out", "make it" and "guess it". Finding out the first, fifth and sixth questions in the textbook means thinking about it. "Do it" is an example 2 in the textbook. Let students make axisymmetric graphics by themselves, giving students space for self-expression and self-creation, which is conducive to cultivating students' positive learning attitude and intimacy in learning mathematics, and also conducive to cultivating students' ability to feel beauty. "Guess" is to let students guess the shape of an axisymmetric figure on the basis of giving half. On this issue, it is from shallow to deep, step by step. This can not only arouse students' enthusiasm, but also enable them to further deepen their understanding of axisymmetric figures and axes of symmetry.

Finally, I arranged a session of "Appreciating Pictures and Experiencing Emotions", and showed a series of beautiful axisymmetric graphics with courseware, so that students can fully enjoy the visual impact brought by these beautiful axisymmetric graphics and feel and appreciate the beauty. At the end of this class, I used an axisymmetric Chinese character-"Mei" to summarize and supplement the topic with complete and beautiful axisymmetric graphics.

The design of the whole class is to meet the students' cognitive characteristics, try to create a lively teaching situation, so that students are always in a curious learning mood, so that every student can learn something and feel the joy of success.

Axisymmetric lecture notes on junior high school mathematics 3 i. teaching material analysis

The content of this section is lesson 1 in the first section of the first volume of the eighth grade mathematics of Su Ke Edition. This section is based on students' existing life experience and preliminary experience in mathematical activities, and starts with observing the phenomenon of axial symmetry in life, so as to understand the characteristics of axial symmetry from a holistic perspective. At the same time, it is closely related to the "folding" of one of the three major movements of graphics (translation, folding and rotation). Through the study of this lesson, students can not only feel the role of "folding" in the three basic movements of graphics in geometry knowledge, but also make full preparations for students to learn symmetric transformation, central symmetry and central symmetry graphics and parallelogram related knowledge. At the same time, this plate is also a bridge between mathematics and life.

Second, the teaching objectives:

According to the above teaching material analysis, considering the existing cognitive structure and psychological characteristics of students, the following teaching objectives are formulated:

1. Understand the concepts of axisymmetric and axisymmetric graphics through concrete examples; Be able to identify axisymmetric and axisymmetric figures and find out the axis of symmetry; Know the difference and connection between axisymmetric graphics and axisymmetric graphics.

2. Experiencing and observing axisymmetric phenomena and axisymmetric figures in life, exploring their activity processes with the same characteristics, and developing students' spatial concept and abstract generalization ability.

3. When appreciating the beauty of axisymmetrical graphics in real life, we can appreciate the wide application of axisymmetrical graphics in real life and its rich cultural value; Stimulate students' desire to learn and actively participate in mathematics learning activities.

Third, the teaching emphasis and difficulty:

According to the teaching objectives, I think the focus of this lesson is: the difference and simple application of the concepts of axisymmetric and axisymmetric graphics. The difficulty is: the connection and difference between axisymmetric graphics and axisymmetric graphics.

Fourth, teaching methods and learning methods.

In order to highlight key points, break through difficulties, and enable students to achieve the teaching objectives set in this section, I will guide students to experience observation, operation and other activities in this class, and give students sufficient space for independent inquiry and communication in the activities, so that students can fully discuss, communicate, cooperate and express boldly, so that students can truly become the masters of learning.

Verb (abbreviation of verb) teaching process;

According to the above analysis, I will talk about the teaching process of this class in detail.

Inquiry activity (1): Axisymmetric graph

1. Stimulate interest and experience life (demonstrate related pictures in life with multimedia) Picture appreciation (courseware): Test your observation. This eye-catching title arouses students' competitiveness and makes them think while observing: What are the same characteristics of these pictures? This design follows the principle that teaching should be close to the reality of life. After careful observation, students can find that these figures are symmetrical. Then, the teacher asked in time: How are these figures symmetrical? How can we make symmetrical parts overlap? Let students observe, guess, explore and discuss, and the teacher will guide them appropriately, so that students can find that one part of a graph can completely overlap with another part of the graph after it is folded 180 degrees along a straight line. Let students feel that mathematics is everywhere around us in life and stimulate students' interest in learning mathematics.

2, activity inquiry to form the concept: experimental inquiry: cut a pattern by folding a piece of paper in half (don't cut the crease completely), then open this folded paper and cut out a beautiful pattern. Please try imitating the teacher's method. On the basis of appreciating and perceiving the axis symmetry, students must be eager to know where the beauty of these figures lies. So I set up a paper-cutting activity to let students create beauty through hands-on practice and perceive the concept of axisymmetric graphics in operation. Then, by comparing some patterns in the last activity, we found that they have the same characteristics: "There is a straight line-fold it-overlap each other." Thus, this concept, the concept of teacher writing on the blackboard, came to a conclusion through cooperation.

3. Give some examples of axisymmetric figures in practice and tell the axis of symmetry (with courseware attached).

According to the students' own life experience, let the students say qualified figures, and let the students know the widespread existence of axisymmetric figures in their lives. Many axisymmetric figures in life not only embody a kind of symmetrical beauty, but also contain certain scientific truth, do you understand?

① The symmetry of the dial ensures the uniformity of travel time.

(2) The symmetry of the plane keeps the plane balanced in the air;

③ The symmetry of human eyes makes people look at objects more accurately and comprehensively;

(4) The symmetry of the ear can make the sound have a strong three-dimensional effect. ...

4. Comprehensive exercises, divergent thinking: This group of exercises is designed with graphics and mathematics ... It excavates various patterns of life, strengthens the infiltration and integration between disciplines, and enables students to find answers to knowledge in mutual arguments, supplements and exchanges, and experience the fun of learning.

Inquiry Activity (2): Axisymmetric

1, hands-on operation, introducing new knowledge

After folding a piece of paper in half, use the needle tip to pierce the pattern as shown in the figure on the paper, and observe the resulting pattern. What is the relationship between the parts on both sides of the crease? Then look at the textbook page 1 19, figure 14. 1-3, and see what * * * has in common with each pair of figures. How many figures does each pattern consist of? Because students have understood the concept of axisymmetric figure, they may mistakenly think that the axisymmetric figure formed by two figures is symmetrical and there is no difference. Therefore, first of all, with hands-on practice, paper-cutting, and with the help of people's various sensory understanding, it is emphasized that the symmetry of two graphics is "the coincidence of two graphics." According to the main line of "there is a straight line-fold it-two figures overlap", under the guidance of the teacher, students draw two figures to form the concept of an axis symmetry and a symmetrical point. Teacher's concept of writing on the blackboard.

2, consolidate exercises, improve the application (courseware) to understand and consolidate the knowledge.

3. List examples, show talents, cite examples of axial symmetry in life, and deepen the understanding of axial symmetry.

Activity (3): Summarize and observe the following two figures and talk about your findings. Compare axisymmetric and axisymmetric figures: (The list deepens the impression) Axisymmetric and axisymmetric figures are the relationship between two figures and the characteristics of a figure shape itself. After being folded in half, the two figures completely overlap with the other half. The difference is that axial symmetry refers to the symmetrical relationship between "two" graphs, while axial symmetry refers to the symmetrical nature of "one" graph.

Contact person:

(1) 180 graphic overlap defined by folding and folding;

② The two can be transformed into each other. If two axisymmetric figures are regarded as a whole, then this "one" figure is an axisymmetric figure. On the other hand, if two symmetrical parts of an axisymmetric figure are regarded as two figures, then the "two" figures are axisymmetric. Infiltrate the dialectical relationship between the whole and the part here to further develop students' abstract thinking ability.

Activity (4): Know the figure and feel the beauty of symmetry.

(1). Enjoy the pictures and experience the beauty of symmetry created by axial symmetry.

(2) Which of the numbers 0 to 9 displayed by the calculator are axisymmetric? Many Chinese characters are axisymmetric figures, such as heaven, sun, moon, clock, Shen, Wang and so on. There are many axisymmetric examples and figures in the trademarks of Lenovo, United Securities, Cai Xiang Securities, Industrial and Commercial Bank of China, Bank of China and other companies and enterprises. Many logos of various brands of cars are axisymmetric graphics, such as Audi, Hyundai, Honda, Fukang, Opel and BMW. Rectangular, diamond, square, equilateral triangle, etc. Are all axisymmetric figures; The line segment is also an axisymmetric figure, and the vertical line of the line segment is its axis of symmetry.

Key point: the symmetry axis of a figure is a straight line, not a line segment or ray, but a straight line where the line segment or ray is located. For example, students tend to think that the bisector of the angle is the symmetry axis of the angle, and the height on the bottom of the isosceles triangle is its symmetry axis, which can achieve the effect of error correction well. Secondly, we know that an angle triangle and an isosceles triangle each have an axis of symmetry, a rectangle has two, an equilateral triangle has three and a square has four axes of symmetry, and a circle is the most special figure with numerous axes of symmetry, so its symmetry is widely used. This will enable students to use the symmetry of graphics to solve some related problems in the future.

Activity (5): Hands-on operation, active practice and graphic creation.

(1), on the basis of giving half of the axisymmetric figure, let the students draw the other half on the other side of the axis of symmetry to become a complete axisymmetric figure. From simple to difficult, step by step.

(2) Let students use their imagination and creativity to create beautiful axisymmetric figures with their own hands.

This part of the design is open, which can give full play to students' imagination, creativity and practical ability, make students become the real masters of learning, give students space for self-expression and self-creation, and help cultivate students' positive learning attitude and intimacy in learning mathematics, as well as their ability to feel beauty. )

(6): class summary

(1). What did you learn in this lesson?

(the definition of axisymmetric and axisymmetric graphics; The properties of axisymmetric figures: which of the polygons we have learned are axisymmetric figures; Application of axisymmetric graphics. )

(2) Talk about your experience and confusion about this class.

(VII): Operation design

Give full play to your imagination and use the knowledge learned in this section to design a class emblem for our class. Whether the required design pattern is axisymmetric or axisymmetric has certain meaning. This is an open, interesting and challenging homework problem, which provides a platform for students to exert their imagination and creativity, and makes students' activities move from classroom to life.

These are my views on this course. Please forgive my shortcomings! thank you

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