Excellent lecture notes on understanding circles 1 1. Talking about teaching materials
1, teaching content:
The teaching content of this lesson is "Understanding of Circle" in Unit 4, Volume 11 of Mathematics published by People's Education Press. The main contents are: draw a circle with compasses, understand the names of each part of the circle, and master the characteristics of the circle.
2. Teaching content and its position and function.
"Understanding of Circle" is the content of Unit 4 in the first volume of Grade 6 of People's Education Press. It is the initial knowledge of geometry, not only the initial course, but also the basis for subsequent study of "circumference", "area of circle", "cylinder" and "cone".
3. Brief analysis of teaching materials:
Circle is a common plane figure and the simplest curve figure. "The Understanding of Circle" is taught on the basis that students have learned the understanding of straight line and area calculation, and have a preliminary perceptual understanding of circle. Students have changed from learning linear graphics to learning curve graphics, whether it is the content itself or the method of studying problems. Through the study of circle, the textbook enables students to understand the basic methods of learning curve graphics. At the same time, it also permeates the relationship between curve graphics and straight line graphics. This not only expands students' knowledge, but also enters a new field in the concept of space. Therefore, through the understanding of the circle, students can not only deepen their understanding of the surrounding things and improve their ability to solve simple practical problems, but also lay a good foundation for studying the circumference, area, cylinder and cone of the circle in the future.
Second, tell the teaching objectives:
According to the mathematics curriculum standard, this paper puts forward such a specific goal in the field of "space and graphics": by observing, operating and understanding parallelogram, trapezoid and circle, you can draw a circle with compasses; Combined with the characteristics of this class, I have determined the following teaching objectives:
1. Knowledge and skills: by drawing a picture, folding, measuring, etc. Observe and experience the characteristics of a circle, know the names of each part of the circle, and understand the relationship between the inner diameter and radius of the same or equal circle. Understand and master a variety of methods of drawing circles, and learn to draw circles with compasses initially.
2. Process and method: Through imagination and verification, observation and analysis, hands-on operation, cooperation and communication, students can realize the distribution uniformity and extensive symmetry of each point of the circle, and at the same time, their thinking can be further developed and improved.
3. Emotion, attitude and values: Experience the close connection between mathematics and daily life in combination with specific situations, and explain simple phenomena in life with circular knowledge.
Third, the key points and difficulties:
Teaching emphasis: Understand and master the characteristics of circles, and learn how to draw circles with compasses.
Difficulties in teaching: understand the concept of "on the circle" and summarize the characteristics of the circle.
Teaching preparation:
Student: Scissors, a few sheets of white paper, colored pencils, compasses, rulers and a round object.
Teacher: Courseware, compasses, rulers, circular pieces of paper, etc.
Four. Oral English teaching methods and learning methods
I will use a variety of teaching methods in this course. The application of "situational teaching method" to introduce new lessons can stimulate students' interest in learning, guide students to deeply study the close relationship between the circle and our lives, and use "activity inquiry method" to let students actively explore and practice, and guide students to understand the names and specific characteristics of each part of the circle in practice. Use "group cooperation method" to let students cooperate with each other in group activities. Let the students draw a picture, click a little, compare and measure, and inspire them to observe with their eyes, think with their brains, participate in discussions with their mouths, analyze answers with their ears, and learn to draw circles.
Fifth, talk about the teaching process.
The new curriculum standards show our teachers a brand-new concept of education and teaching. Facing real children, my design is based on the teaching idea that we should not only pay attention to the training of students' knowledge and skills, but also pay attention to the formation of students' learning process and methods, emotional attitudes and values. I have carefully designed two main links for the teaching of this course.
(A), create a situation, the introduction of new courses
First of all, what are the plane graphics you have learned before? What lines are these figures surrounded by? Briefly describe the characteristics of these figures.
(B), highlighting the main body and exploring new knowledge
1, initial perception circle
First of all, I will ask students to give examples from life. "Which objects are round in daily life?" Students may say: coins, CDs, road signs, clock faces, wheels, etc. These objects are all round. Let students initially perceive the circle and cultivate their spatial imagination. Then, I'll show you two sets of figures to form a correct representation-a circle is a curved figure on a plane.
2. Know the names and characteristics of each part of the circle.
(1) Find the center of the circle
First, let the students fold the round paper prepared in advance and open it. Draw a crease with a pen and ruler, and repeat the origami activity on the round paper two or three times. After the operation, ask, "What did you find?" After the students did it themselves, they found that all the creases would intersect at one point. The intersection of these creases is right on the center of the circle. We call this point the center of the circle mathematically, and it is represented by the letter "O". (Design intention: Through students' intuitive operation, students' learning process will be "action-oriented", and students' multiple senses will be mobilized to participate in learning, and some cognitive conflicts will be deliberately set up to enable students to actively participate in the formation of knowledge. )
(2) Know the radius and diameter
The line segment connecting the center of the circle and any point on the circle is called radius, and the radius is generally represented by the letter R. Let the students draw a picture by hand, discuss it in groups, and guide the students to draw the conclusion that there can be countless radii in the same circle, and all the radii are equal in length.
The line segment passing through the center of the circle with both ends on the circle is called the diameter, and the diameter is generally represented by the letter D. Because the knowledge of radius here is the foundation, I will try my best to let students discuss the knowledge of diameter in groups and guide them to conclude that countless diameters can be drawn on the same circle, and all diameters are equal in length.
(3) Discuss the relationship between radius and diameter.
What is the relationship between radius and diameter in a circle? Through measurement and comparison, let students understand and master the relationship between radius and diameter in the same circle, and let students use a formula with letters to express the relationship between radius and diameter. The letter formulas of d=2r and r=d/2 are obtained, and the corresponding relationship between radius and diameter in a circle is emphasized by filling in the table in the exercise. Students are also required to find out the radius and diameter of some line segments in the circle. (Design intention: Give full play to students' main role reasonably, and let students explore the formation and development of knowledge independently with their brains, hands, mouths and eyes, so as to consolidate their learning achievements in time. )
3, master the method of drawing a circle
In the process of teaching circle drawing, I will also let students use their brains boldly and explore different methods of circle drawing. Students may think of drawing a circle with a round object, drawing a circle with a winding nail, drawing a circle with a compass and so on. Finally, I will try to make students draw a circle with compasses in the exercise book, and ask the steps to draw a circle while drawing. Through the students' reports, I guided them to sum up the general steps of drawing a circle:
(1) fixed point (that is, the position of the center of the circle)
(2) Fixed length (i.e. length with fixed radius),
(3) Rotate and draw a circle. Then I will demonstrate the method of drawing a circle, emphasizing that the center, radius and diameter should be marked after drawing.
The understanding of circle is an excellent lecture II. I said that the content of the class is the first lesson of "Circle" in Unit 10, Grade Five of Primary School Mathematics (Volume II) of Jiangsu Education Publishing House-"Understanding of Circle".
First, the interpretation of teaching materials
"Understanding of Circle" is taught on the basis of students' knowledge of linear graphics and rich perceptual knowledge of circle. Students have changed from the field of linear graphics to the field of curve graphics, and their learning contents and research methods have changed. Through the understanding of the circle, we will lay a good foundation for studying the circumference and area of the circle, as well as the knowledge of cylinders and cones in the future.
Second, the analysis of learning situation
For the fifth-grade pupils, because of their age and psychological characteristics, thinking in images still occupies the main position, and it is difficult to understand the circle rationally.
Based on the above understanding of teaching materials, combined with students' knowledge and experience, and following the spirit of curriculum standards, I have determined the following three-dimensional goals:
Third, the teaching objectives
Fourthly, the difficulties in teaching.
Combining modern information technology with mathematics classroom teaching, using animation demonstration and scene reproduction, leading students to explore the characteristics of circle, breaking through teaching difficulties, and using the knowledge of circle to explain life phenomena.
V. Teaching methods and learning methods
The learning process of students is a process of active construction. In this class, I used multimedia teaching methods to fully mobilize students' various senses to participate in learning, and used teaching methods such as operation, inquiry, discussion and discovery. Students' learning methods correspond to teaching methods, so that students can actively explore, communicate and ask questions. Realize the organic integration of modern information technology and classroom teaching.
Teaching process and design concept of intransitive verbs
In order to highlight the key points, break through the difficulties and achieve the established teaching objectives, I mainly arranged the following teaching links.
First, walk into life and appreciate the beauty of the circle.
Pre-class lead-in is divided into two levels: awakening-display. First, let students recall the circles they have seen in their lives and awaken relevant life experiences. Then show pictures of circles that can be seen everywhere in nature, and feel the beauty of circles while looking for them.
Beautiful pictures with soft music make students feel the beauty of life and discover the components of mathematics-geometric figures. In this way, the design builds a bridge for students from knowing the objects in life to knowing the geometric figures in mathematics, which not only highlights the process of geometric modeling, but also enables students to gradually learn to look at life from a mathematical perspective, discover mathematics from life, and effectively stimulate students' intrinsic learning motivation.
Second, the actual operation, master the painting method.
When students create a circle for the first time, using multimedia courseware can let students intuitively feel the basic characteristics of circle-curve graphics. At this time, compasses, a tool for drawing circles, were introduced, and students' works were displayed on multimedia booths, which greatly stimulated their creative enthusiasm. At the same time, the nonstandard circle caused them to think: how can we draw a successful circle? Make students rise from simple hands-on operation to method induction. After students fully communicate, play multimedia courseware, and students can quickly master the method of drawing a circle with compasses and draw a circle for the second time by using basic methods. On this basis, three concepts are naturally introduced: center, radius and diameter. The application of concepts is a process from abstraction to concreteness. Supplement "practice" to consolidate new knowledge in time, and show the third attempt to draw a circle, and the deeper you draw. While mastering the method of drawing a circle, I also perceive the concept of circle, which leads to the role of center and radius-the center determines the position of the circle and the radius determines the size of the circle. With the introduction of modern information technology, this problem can be easily solved by clicking the mouse.
Third, group cooperation, exploring characteristics.
This link boldly allows students to explore for themselves. Arrange students' cooperative learning purposefully and consciously. This open teaching method enables students to discover the essential characteristics of radius and diameter and their relationship in the concrete and intuitive operation process. After that, arrange outward bound exercises to realize the transfer of knowledge and ability.
Fourth, expand the application and show the charm of the circle.
By introducing Mozi's description of the circle, the cultural connotation of the circle is further highlighted, and at the same time, students can feel the long-standing national pride of China's mathematical culture. Then I asked the students to explore: In real life, why do wheels have to be round? Where should the axle be installed? We should not only consolidate basic knowledge, but also cultivate students' application ability in combination with practice. I give full play to the advantages of modern information technology: the reproduction of animated scenes greatly stimulates students' imagination, helps students to establish the connection between mathematics knowledge and real life, and lays a solid foundation for breaking through teaching difficulties. Appreciating the circle again gives students room for imagination. Through this extension, we can echo from beginning to end, let students deeply feel that mathematics knowledge comes from and serves real life, further understand the relationship between mathematics and life, and enhance their confidence in learning and applying mathematics.
Five, after-school reflection:
In my whole teaching design, I used modern information technology to creatively design teaching activities according to the subject characteristics of mathematics teaching, making the teaching form more vivid, diversified and visualized, fully revealing the formation and development of mathematical concepts, the process and essence of mathematical thinking, showing the formation of mathematical thinking, and making mathematics classroom teaching more effective.
Finally, I would like to thank the expert judges and urge them to criticize and correct me.
Round understanding excellent lecture 3 Hello everyone! As I said today, the content of the class is "understanding the circle". I will lecture from the following aspects:
First of all, talk about textbooks.
The understanding of the circle is the teaching content of 93 -94 pages in the second volume of the fifth grade of Jiangsu Education Press.
This lesson is taught on the basis that students have learned the understanding of straight lines, the calculation of area and the initial perceptual knowledge of circles. Students have changed from learning linear graphics to learning curve graphics, whether it is the content itself or the method of studying problems. Through the study of circle, the textbook enables students to understand the basic methods of learning curve graphics. At the same time, it also permeates the relationship between curve graphics and straight line graphics. This not only expands students' knowledge, but also enters a new field in the concept of space. Therefore, through the understanding of the circle, students can not only deepen their understanding of the surrounding things and improve their ability to solve simple practical problems, but also lay a good foundation for studying the circumference, area, cylinder and cone of the circle in the future. Through the relationship between the diameter and radius of circles and their lengths, textbooks enable students to understand the characteristics of circles. On this basis, make students understand the steps and methods of drawing a circle and further deepen their understanding of the circle. According to the characteristics of textbook arrangement and students' reality, I have formulated the teaching objectives of this course:
1. knowledge and skills: let students know the names of the circle and its parts; Master the characteristics of circles, understand the relationship between diameter and radius, and learn to draw circles with compasses.
2. Process and method: Through intuitive teaching and hands-on operation, students can understand and form the concept of circle on the basis of full perception, cultivate students' observation ability, spatial imagination ability and abstract generalization ability, and use the learned mathematical knowledge to solve simple practical problems in life.
3. Emotion and values: Through learning, improve students' curiosity and thirst for knowledge about mathematics, initially understand the close relationship between mathematics and human life, and experience the significance and role of mathematics activities.
Teaching emphasis: know the names and characteristics of each part of the circle, so that students can learn to draw a circle with compasses.
Difficulties in teaching: understand the concept of "on the circle" and summarize the characteristics of the circle.
Second, oral teaching methods
"Mathematics Curriculum Standard" emphasizes that students should be provided with sufficient opportunities to engage in mathematics activities and exchanges based on their life experience and existing knowledge background, so that they can truly understand and master basic mathematics knowledge, mathematical ideas and mathematical methods in the process of independent exploration, and at the same time gain rich experience in mathematics activities. In this class, I use multimedia teaching methods, mainly using independent inquiry, hands-on operation, cooperative discussion, observation and discovery. Create scenes in teaching, provide students with rich, vivid and intuitive courseware, stimulate students' enthusiasm and initiative in learning, and let students discover and master the characteristics of circles.
Third, theoretical study.
Starting from students' familiar life experience, this course provides students with enough time and opportunities to actively participate in the learning process of knowledge and cultivate their hands-on operation ability, independent learning consciousness and innovation consciousness through hands-on operation, active exploration, cooperation and exchange and observation.
Fourth, talk about teaching preparation.
1. Circular objects, rulers, compasses, circular pieces of paper, etc.
2. Multimedia courseware.
Verb (abbreviation for verb) talks about teaching procedure.
In this lesson, we have arranged four parts. The first part is to discover and appreciate the circle. The second part, perception circle, understanding circle. The third part, learn to draw a circle and explore it. The fourth part is to consolidate and expand the circle.
(1) Find and appreciate the circle.
As the saying goes, "everything is difficult at the beginning", and a good beginning is half the battle. In this class, our fifth-grade math group decided that we don't need anything fancy to guide the class, but let the students see the circle through the blackboard, courseware or learning tools on the desktop and go straight to the theme-circle. Then, with the help of a mathematician in ancient Greece, the teacher once said that "the circle is the most beautiful in all plane figures", which brought the students into the round world (classroom). This kind of guidance is direct, simple and effective.
(2) Perceive the circle and know the circle.
Mathematics Curriculum Standard points out that teachers should make full use of students' existing knowledge and experience to design vivid, interesting and intuitive mathematics teaching activities, so that students can understand and know mathematics knowledge in vivid and concrete activities. According to this idea, we designed a game to touch the circle. By touching, seeing, dividing and speaking, we can not only help students recall the plane figures we have learned, but also help them experience the difference between the circle and other plane figures from the senses. The feeling of circle is curved, and students have a preliminary understanding of circle. Next, the teacher asked the students to divide these plane figures into two categories. For students, it is easy to classify rectangles, squares, triangles, parallelograms and trapezoid into one category, while it is easy to classify circles separately. Then, ask the students why they divide it like this. In fact, it is to let students compare the circle with other plane figures. By comparison, students can clearly see that the first type of figure is surrounded by line segments end to end, while the circle is surrounded by curves, forming a correct representation.
(3) Learn to draw a circle and explore it.
Practice is the source of cognition, and children's wisdom is concentrated at the fingertips. The hand is the cultivator of consciousness and the creator of wisdom. Therefore, we have designed the following links:
1. Hands-on operation (drawing a circle) and self-learning (knowing the center, radius and diameter).
(1) Let the students talk about the method of drawing a circle first, and then introduce the compass, so that the students can try to draw a circle with the compass for the first time. Students will certainly encounter such problems when drawing circles. The teacher will start with the problem and explain clearly every step of drawing a circle, from fixed point (fixing the needle tip) to fixed distance (separating the feet) to making a circle (forming a circle).
(2) The teacher intuitively demonstrates drawing a circle, and after the students master the use of compasses, they arrange to draw a circle freely for the second time.
(3) Name of each part of the self-study circle
This part of the content is to let students construct their own understanding of the concepts of center, radius and diameter through self-study, communication and operation, and then check the effect of self-study in time through communication feedback. Finally, the teacher guides the students to mark the center of the circle and draw the radius and diameter, which are represented by the letters O, R and D respectively.
(4) Practice makes true knowledge. After students know the center, radius and diameter, arrange some exercises to test their mastery of new knowledge. Judge the radius and know the diameter.
The two ends of the line segment in the first picture are not connected with the center and circle, and one end of the second picture is in the center and the other end is in the circle. In the third picture, one end is at the center of the circle and the other end is outside the circle. The fourth graph is the radius. In the process of judging these four pictures, students know the points inside, outside and on the circle, and further clarify the meaning of radius. The line segment connecting the center of the circle and any point on the circle is the radius. There are countless points on the circle, and there are countless radii of the circle.
2. Group cooperation, discussion and communication.
In order to explore the relationship between the inner diameter and radius of a circle, in the form of four-person team cooperation, through the methods of folding, measuring, comparing and drawing:
(1) How many radii and diameters can a circle draw?
(2) Are the radii in the same circle all equal in length? What about the diameter?
(3) What is the relationship between the diameter and radius of the same circle?
(4) Is the circle an axisymmetric figure? How many axes of symmetry does it have?
Design intention: When drawing a circle in kind, let students tell how to draw a circle, which fully reflects students' autonomy in learning, gives students time and space to think and reflects the diversity of methods. The process from drawing a circle in kind to drawing a circle with compasses makes students feel the universality of drawing a circle with compasses and optimizes the method. When learning the names of various parts of a circle, the fifth-grade students already have a strong reading comprehension ability, and can construct their own understanding of the concepts of center, radius and diameter through self-study, communication and operation. When students learn the characteristics of the circle, they master new knowledge in group cooperation, highlight their dominant position and cultivate their awareness of active participation.
(4) Consolidate and expand the circle.
We have arranged three links. First, practice. Second, summarize. Third, expand.
Timely feedback exercises can consolidate new knowledge and improve comprehensive problem-solving ability. We design exercises, pay attention to the organic combination of knowledge, interest and development, and design three groups of exercises.
After the exercise, the teacher asked the students to tell their own gains and ask questions.
After reviewing and summarizing, the students showed the beautiful circles in life for students to enjoy.
The intention of this design is: echo before and after, sort out knowledge through review and summary, and help students gradually form mathematics learning methods and experiences; At the same time, the "circle" will return to life again, and mathematics will be closely combined with life, so that students can appreciate the value of mathematics learning.
Six, say practice design
Timely feedback exercises can consolidate new knowledge and improve comprehensive problem-solving ability. We design exercises, pay attention to the organic combination of knowledge, interest and development, and design three groups of exercises.
Autonomous learning, cooperative learning and inquiry learning advocated by the new curriculum standard are all based on students' active participation. Without the active participation of students, it is impossible to have cooperative learning with independent inquiry. Practice has proved that the depth of students' participation in classroom directly affects the effect of classroom teaching. "Without the active participation of students, there would be no successful classroom teaching. "The purpose of designing this course is to fully reflect the initiative and enthusiasm of students to participate in the learning process.
The teaching philosophy of our class is to give children some rights and let them choose for themselves; Give children some opportunities to experience themselves; Give children some tasks and let them do it themselves; Give children some difficulties and let them solve them themselves; Give children a space of their own creation.
This is the end of my lecture. Thank you for listening.