Su Ke Edition Junior High School Mathematics Textbook "Axisymmetric and Axisymmetric Figures"
Introduction: Experience the process of exploring the properties of axial symmetry, accumulate experience in mathematical activities, and further develop the concept of space and the ability to think and express logically. Let’s take a look at the contents of the Su Ke version of the junior high school mathematics textbook "Axisymmetric and Axisymmetric Figures" that I have compiled for you.
1. Textbook Analysis
The content of this section is Chapter 1, Section 1, Lesson 1, Volume 1, Volume 8, Su Ke Edition of Mathematics. This section is based on Students have existing life experience and preliminary experience in mathematical activities, starting from observing the axial symmetry phenomenon in life, and understanding the characteristics of axial symmetry from an overall perspective; at the same time, one of the three movements of graphics (translation, folding, rotation) There is an inseparable connection with "turning". By studying this lesson, students can not only feel the role of "turning" in geometric knowledge among the three basic movements of graphics, but also prepare students for subsequent learning of symmetric transformations. Be fully prepared for relevant knowledge of central symmetry, central symmetry figures and parallelograms; at the same time, this section is also a bridge between mathematics and life.
2. Teaching objectives:
Based on the above analysis of teaching materials and taking into account students’ existing cognitive structures and psychological characteristics, the following teaching objectives are formulated:
1 . Understand the concepts of axial symmetry and axially symmetrical figures through specific examples; be able to recognize axially symmetrical and axially symmetrical figures, and be able to find the axis of symmetry; know the differences and connections between axially symmetrical and axially symmetrical figures.
2. Experience the process of observing axially symmetrical phenomena and axially symmetrical figures in life, exploring their unique characteristics, and developing students' spatial concepts and abstract generalization abilities.
3. While appreciating the beauty of axially symmetrical figures in real life, realize the widespread application of axial symmetry in real life and its rich cultural value; stimulate students' desire to learn and actively participate in mathematics learning activities.
3. Teaching focus and difficulty:
Based on the teaching objectives, I think the focus of this lesson is: the difference and simple application of the concepts of axial symmetry and axisymmetric graphics. The difficulty is: the connection and difference between axial symmetry and axially symmetric figures.
IV. Teaching and learning methods
In order to highlight the key points and break through the difficulties, so that students can achieve this section According to the set teaching goals, in this lesson I will guide students through the process of observation, operation and other activities. During the activities, students will be given sufficient space for independent exploration and communication, so that students can fully discuss, communicate, cooperate and express boldly, so that students can fully discuss, communicate, cooperate and express boldly. Students truly become the masters of learning.
5. Teaching process:
Based on the above analysis, let me talk about the teaching process of this lesson in detail. Exploration activities (1): Axisymmetric graphics
1. Introduction of excitement and feeling of life (use multimedia to demonstrate relevant pictures in life) Picture appreciation (courseware): Test your observation skills, this eye-catching The title arouses students' competitive spirit and allows students to observe and think: What are the unique 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 graphics are symmetrical. Then, the teacher asks the question in due course: How are these figures symmetrical? How can we make the symmetrical parts coincide? Let students observe, guess, explore, and discuss. Teachers can guide them appropriately so that students can discover that folding a certain part of a figure 180 degrees along a straight line can completely coincide with another part of the figure. Let students feel that mathematics is everywhere in life and mathematics is around us, and stimulate students' interest in learning mathematics.
2. Activity exploration to form concepts: Experimental exploration: Fold a piece of paper in half and cut out a pattern (do not cut it completely at the crease), then open the folded paper and cut out a beautiful pattern. Ask your classmates to imitate the teacher's method and give it a try. On the basis of appreciating and perceiving axial symmetry, students must be eager to understand the beauty of these graphics.
Therefore, I set up paper-cutting activities to allow students to create beauty through hands-on practice and perceive the concept of axially symmetrical figures during operation. Then compare some of the patterns in the previous activity and communicate with each other to find that their most common features are "the existence of straight lines - fold them - overlap each other". Thus, the concepts are summarized through cooperation and the teacher writes the concepts on the blackboard.
3. Give several examples of axially symmetric figures based on actual practice, and name the axes of symmetry (courseware attached)
Students can name the figures that meet the conditions based on their own life experience. Let students realize the widespread existence of axially symmetrical figures in life. Many axially symmetrical figures in life not only embody a kind of symmetrical beauty, but also contain certain scientific principles. Do you know? ① The symmetry of the dial ensures the uniformity of travel time ② The symmetry of the aircraft enables the aircraft to maintain balance in the air; ③ The symmetry of the human eye enables people to view objects more accurately and comprehensively; ④ The symmetry of the binaural ears enables a stronger sense of sound. Three-dimensional sense...
4. Comprehensive exercises, divergent thinking: This set of exercises is designed with graphics, mathematics... It explores various patterns in life, strengthens the penetration and integration between disciplines, Let students find answers to knowledge through mutual debate, supplementation, and communication, and experience the joy of learning.
Exploration activities (2): Axial symmetry
1. Hands-on operation to introduce new knowledge
After folding a piece of paper in half, use the tip of a needle to pierce the paper Observe the resulting pattern as shown in the figure. What does the part on either side of the crease matter? Look at Figure 14.1-3 on page 119 of the textbook and see what unique characteristics each pair of figures have? How many shapes does each pattern consist of? Because students have already understood the concept of axially symmetrical figures, they may mistakenly believe that there is no difference between two figures that form axially symmetrical and axially symmetrical figures. Therefore, we first use hands-on practice to cut paper, and use various human senses to highlight the axial symmetry of two figures, which means "the two figures overlap". Following the main line of "there is a straight line - fold it - the two figures coincide", under the guidance of the teacher, the students came to the concept that the two figures form axial symmetry and symmetrical points. Teacher writing concept on blackboard.
2. Consolidate the exercises and apply and improve (courseware) to understand and consolidate the knowledge learned
3. List examples to show your talent and give examples of axial symmetry in life , to deepen the understanding of axial symmetry.
Activity (3): Summary Observe the following two graphics and talk about your findings. Compare axisymmetric and axisymmetric graphics: (List the table to deepen your impression) Axis symmetry Axis symmetry Axis symmetry Axis symmetry The relationship between two graphics is a characteristic of the shape itself. After folding in half, the two shapes are completely The difference between overlapping and folding and completely overlapping with the other half of the figure: axial symmetry refers to the symmetrical relationship between "two" figures, while axially symmetric figures refer to the symmetrical properties of "one" figure.
Contact: ① Both are defined by the overlap of folded and folded 180° figures;
②The two can be transformed into each other. If two axially symmetrical figures are regarded as Integrated, then this "one" figure is an axially symmetrical figure. Conversely, if the two symmetrical parts of an axially symmetrical figure are regarded as two figures, then these "two" figures are axially symmetrical. Here, the dialectical relationship between the whole and the part is penetrated to further develop students' abstract thinking ability.
Activity (4): Identify graphics and feel the beauty of symmetry
(1) Appreciate pictures and appreciate the beauty of symmetry created by axial symmetry.
(2) Among the numbers 0 to 9 displayed on the calculator, which ones are axially symmetrical? Many Chinese characters are axially symmetrical figures, such as: Tian, ??Ri, Yue, Zhong, Shen, Wang, etc.
There are many axisymmetric examples and axisymmetric graphics in the trademarks of various companies and enterprises, such as Lenovo, United Securities, Xiangcai Securities, Industrial and Commercial Bank of China, and Bank of China; many of the logos of various brands of cars are axisymmetric graphics, such as Audi, Hyundai, Honda, Fukang, Opel, BMW; rectangle, rhombus, square, equilateral triangle, etc. are all axially symmetrical figures; line segments are also axially symmetrical figures, and the vertical bisector of the line segment is its axis of symmetry.
Emphasis: The axis of symmetry of a graph is a straight line, not a line segment or ray, but the straight line where the line segment or ray is located. For example, students tend to think that the angle bisector is the axis of symmetry of an angle, and the height of the base of an isosceles triangle is its axis of symmetry, which can be a good way to correct errors. Secondly, grasp that angles and isosceles triangles each have one axis of symmetry, rectangles have two, equilateral triangles have three, squares have four axes of symmetry, and circles are the most special axisymmetric figures with countless axes of symmetry, so its Symmetry is the most widely used. This allows students to use the symmetry of graphics to solve some related problems in the future.
Activity (5): Hands-on operation, active practice, and creation of graphics
(1) On the basis of giving one half of the axially symmetrical figure, let students create the other half of the symmetry axis. Draw the other half on one side to form a complete axially symmetrical figure. From easy to difficult, proceed step by step.
(2) Let students use their imagination and creativity to create a beautiful axially symmetrical figure with their own hands.
(The design of this part is open, which can give full play to students’ imagination, creativity and hands-on ability, making students the real masters of learning, and giving students space for self-expression and self-creation. It is conducive to cultivating students' positive learning attitude and affinity for learning mathematics, and is also conducive to cultivating students' ability to feel beauty)
(6): Class summary
(1), What knowledge did you learn in this lesson?
(The definition of axial symmetry and axially symmetrical figures; the properties of axially symmetrical figures; which of the polygons we have learned are axially symmetrical figures; the applications of axially symmetrical figures.)
(2) Talk about your experience and confusion about this lesson.
(7): Homework Design
Use your imagination and use the knowledge learned in this section to design a class emblem for our class. The pattern required to be designed is an axially symmetrical figure or It is axially symmetrical and has a certain meaning. This is an open, interesting and challenging homework question that provides students with a platform to use their imagination and creativity, allowing students to move from class to life.
The above is my opinion on this lesson. Please forgive me for any shortcomings! Thanks! ;