Lecture Draft of Cartographic Corner 1 I. Talking about Teaching Materials
On the basis of students' intuitive understanding of acute angle, right angle and obtuse angle and mastering the measurement of angle, the professor teaches drawing angle. Learning these contents plays a very important role in further learning the understanding of space and graphics and developing the concept of space. Before learning "drawing corners", students have a certain understanding of corners and can classify them.
According to the requirements of curriculum standards and the analysis of teaching materials, and according to the actual level of fourth-grade students, I have determined the following teaching objectives:
Knowledge goal: Through hands-on operation, independent inquiry, group discussion and other activities, make students clear the characteristics of each angle.
Skill goal: You can draw an angle of a specified degree with a protractor, and you can draw an angle of 30 degrees, 45 degrees, 60 degrees and 90 degrees with a triangular ruler.
Emotional goal: make students actively participate in learning activities, gain successful experience, form representations from different angles, and develop spatial concepts.
Emphasis and difficulty in teaching.
How to draw an angle with a protractor is the focus of teaching, and the difficulty is to draw an angle of a specified degree accurately.
Second, talk about the teaching process.
In order to highlight key points, disperse difficulties and create an independent learning atmosphere, I strive to fully embody "student-oriented" in the design of the whole teaching process.
Teaching concept, designed five links.
(1) Review old knowledge and stimulate interest.
1. Sort the angle names in descending order.
2. Measure the degrees of the following angles with a protractor.
3. Thinking: We have learned how to draw a corner. If you know the degree of an angle, how to draw it?
Stimulate students' interest in knowledge in review and pave the way for learning new lessons. )
(2) Hands-on operation to explore new knowledge.
1, the teacher defined the research task: draw a 40 angle.
Instruct students' activities:
The drawing method of teaching angle.
(1) Try to set an angle of 40 using a movable angle and protractor.
(2) Students use protractor to test each other.
3. Guide students to learn how to draw corners:
Requirements: Draw an angle of 40 with a protractor, and then measure it with a protractor after drawing.
Instruct students' activities:
(1) Try and experience drawing a 40 angle.
(2) Questioning and proposing the problems encountered when drawing corners.
(3) Ask students to introduce their skills of drawing corners.
(Hands-on operation and participation in exploration. Give students enough thinking space and give full play to their autonomy and practicality in learning.
4. The teacher demonstrated the drawing of the corner.
5. Discuss the steps of drawing corners. (overlapping, finding points, connecting lines)
(c) Summarize, ask questions and ask difficult questions.
1, guide students to summarize "angle drawing"
2. Let students ask questions and ask difficult questions. Teacher: Do you have any questions that need to be consulted or reminded?
Solve problems with new knowledge.
1. Draw an angle of 30 degrees with a protractor.
Collective revision. Question: If you don't use a protractor, can you draw an angle of 30 accurately? (Remind students to use the existing tools in their hands-triangles)
2. Ask the students to draw an angle of 60, and the student representatives will demonstrate these two methods.
3. Question: What angles can be drawn with a set of triangles?
We often use a pair of triangles with two angles as follows: Let's draw a picture.
⑴ Hands-on experiment: Draw four corners with a triangle.
⑵ Draw an angle by adding or subtracting two triangles.
(3) Cooperation and communication, what angles can be drawn according to the same painting method?
(Students have completed the learning of knowledge in the process of independent exploration, which is intuitive and interesting. In group activities, students also feel the fun of cooperation. )
4. Let students draw angles of 20, 70, 95,135 and165 with a protractor, and compare them with the drawing method of triangles, and find the problems:
It is not easy to draw an angle with a triangle, but it can be drawn accurately with a protractor. Triangle drawing angle has limitations, so we should choose the appropriate method according to the characteristics of the angle.
5. Question: Do you have any other different painting methods?
The problem is open, the goal is clear, the thinking is divergent, the operation is free, and the conclusion is to be determined. Students are always proactive and deepen their thinking in the process of solving problems. )
(5) Design of exercises
The exercise closely revolves around the learning content of this lesson, and arranges two drawing angles of 70 and140.
Reflections on the teaching of drawing corners
After students learned the measurement and classification of angles, they began to teach drawing angles. Students already know the method of measuring angles, and they are very interested in the drawing method of exploring angles in turn.
In class, I completely let students explore painting independently. Judging from the classroom effect, it is still relatively good. But some students still made mistakes. I think the reasons for the mistake are as follows:
1, I'm still not familiar with the scale on the protractor, and I can't find the exact number. Especially when using all ten degrees, there are more mistakes. Many students draw 10 degrees more or less, which shows that they are not very clear about the range of this degree when drawing corners.
2. When students draw corners, the most common mistake is that the internal and external scales are unclear. In the process of painting, students often confuse internal and external scales. This shows that when they draw angles, they don't seriously think about whether to find the internal scale or external scale in their minds. They just clicked when they saw this degree, which led to drawing an acute angle as an obtuse angle and an obtuse angle as an acute angle.
3. Some students have few graduation marks on the protractor, some have many patterns on them, and some have a small hole in the center. When students move to the left or right, there will be an error of 10 degrees, which also interferes with students' learning.
4. Some students draw an angle with an inner circle scale, and the angle is 5 degrees, such as 75 degrees.
Lecture Notes of "Drawing Corners" 21. Talking about Teaching Materials
Drawing corners is the content of line and corner in unit 2 of the first volume of fourth grade mathematics of Beijing Normal University. Regarding the understanding of angle, this textbook is arranged in three stages. In the first stage, the second grade published the first book. Combining life scenes and operation activities, students can have a preliminary understanding of angles and right angles and know the names of various parts of angles. They can draw angles with a ruler and judge right angles with triangles. In the second stage, the second volume is published in the second grade, so that students can know the acute angle and obtuse angle, and can judge whether an angle is a right angle or an acute angle and obtuse angle with the help of the right angle on the triangle. The third stage is the unit of this textbook, which allows students to learn angle measurement further.
Drawing angle is an action skill operation course based on understanding ray, angle, protractor and mastering angle measuring skills. The textbook arranges "drawing corners" in the fourth lesson of this unit, which is intended to let students further experience the definition of corners and the size and area of various angles in the process of drawing corners. The knowledge transfer point is the use of protractor-the similarity between measuring angle and drawing angle, that is, "two-in-one alignment". The examples in the textbook show several steps of drawing corners, so that students can draw according to the prescribed steps, so as to initially cultivate their drawing ability, and let students experience the method of transferring and learning new knowledge, and at the same time lay the foundation for learning polygon knowledge in the future. When arranging teaching materials, pay attention to let students discover mathematical laws in hands-on operation. Draw and spell corners with a triangle to deepen students' understanding of graphics.
Second, talk about teaching objectives
Based on the above understanding, I will set the teaching objectives of this lesson as follows:
1. Knowing and mastering the steps of drawing an angle can correctly draw an angle with a specified degree, form the skills of drawing an angle, and develop students' good and standardized painting habits.
2. Guide students to choose a suitable method to draw an angle with a specified degree, and cultivate students' flexible and divergent thinking ability.
3. Let students experience the joy of learning success in the process of independent attempt and group cooperation, and improve students' inquiry ability and creativity.
Teaching emphasis: Understand and master the steps of drawing an angle, and draw an angle with a given degree correctly. Teaching difficulty: mastering the correct corner drawing skills.
Three. Oral English teaching methods and learning methods
My understanding of efficient classroom is that efficient classroom is a simple and simple classroom where students learn to learn. No students study by themselves seriously, and there is no new teaching; Without students' full independent thinking, there will be no communication; No learning disabilities were found and no explanation was given. Let students explore learning in independent attempts, questioning, discussion and cooperation, self-presentation, problem solving and practical activities, and highlight the cultivation of students' learning interest, learning methods and learning ability. Therefore, combined with the students' strong curiosity, like exploring the unknown world and hands-on activities, I adopt inquiry mode in my class. Combining the trial teaching method and hands-on operation method, students can experience the specific steps of drawing corners in their personal experience of trying to draw corners, and enrich their experience in learning Space and Graphics. The cooperative communication method is also adopted, so that students can inspire each other, communicate in various directions, complement each other, check feedback, give students more time to think, more space for activities, more opportunities to express themselves and more joy in trying to succeed.
Fourth, talk about the teaching process
First, check the import.
Review the degree of each angle of a triangle.
Pave the way for drawing some angles with special degrees with triangles.
Second, take the initiative to explore (designed three activities)
1, activity 1: Draw a 60 angle.
Method 1: Draw with a triangle: (4 steps)
(Draw a ray, two coincide, draw another ray, angle symbol and degree)
Method 2: Draw with a protractor: (5 steps)
Draw a ray, overlap, find a point, and then draw a ray, angle symbol and degree.
Pay attention to emphasize in the process: the zero scale line on the right corresponds to the degree of inner circle.
2. Activity 2: Can you draw the corner of 150?
Method 1: Review the method of drawing angles with protractor.
Method 2: Use two triangles to introduce an angle 150 (two angles are added).
3. Activity 3: Think about it. What other angles can you spell with a set of triangles?
90 +60 = 150 30 +45 =75
45 +60 = 105 30 +90 = 120
45 +90 = 135
45-30 = 15 (addition or subtraction of two angles)
Third, consolidate the cognitive classroom practice
Try the second question on page 29 of the textbook.
Fourth, class summary.
What did we learn today?
1, the method of drawing an angle with a protractor.
2. Draw corners with triangles.
3. What angles can be drawn directly with triangles?
4. You can spell it with a triangle (addition or subtraction of two angles): 75, 105, 120, 135, 150, 15.
Lecture Notes of "Drawing Corners" 3 I. Talking about Teaching Materials
1. teaching content: the first lesson of unit 2, section 1, book 7 of the standard experimental textbook for nine-year compulsory education, that is, the contents of pages 22 to 23 of the textbook.
2. The position and function of teaching materials.
The classification and drawing of angles are based on students' intuitive understanding of acute angles, right angles and obtuse angles and the measurement of angles. Learning these contents plays a very important role in further learning the understanding of space and graphics and developing the concept of space.
3. The compiling characteristics of teaching materials.
(1) Pay attention to learning new content in connection with real life.
(2) On the basis of original knowledge, guide students to construct new knowledge in learning activities.
(3) Pay attention to let students know and master new content through hands-on operation.
4. Teaching objectives.
According to the requirements of curriculum standards and the analysis of teaching materials, and according to the actual level of fourth-grade students, I have determined the following teaching objectives:
Knowledge goal: Through hands-on operation, independent inquiry, group discussion and other activities, make students clear the characteristics of each angle.
Skill goal: You can draw an angle of a specified degree with a protractor, and you can draw an angle of 30 degrees, 45 degrees, 60 degrees and 90 degrees with a triangular ruler.
Emotional goal: make students actively participate in learning activities, gain successful experience, form representations from different angles, and develop spatial concepts.
5. Emphasis and difficulty of teaching.
Clarifying the characteristics of various angles is the focus of teaching, and how to draw angles with protractor is the difficulty of teaching.
6, teaching AIDS, learning tools
Second, talk about learning.
Before learning the Classification and Drawing of Corners, students have a certain understanding of corners, and some school buildings have been able to classify corners. Therefore, in teaching, students can further master the steps of drawing angles with protractor through their own practical experience, which is much easier for all students to learn.
Third, teaching methods. (omitted)
Fourth, speaking and learning. (omitted)
Fifth, talk about the teaching process.
In order to highlight key points, disperse difficulties and create an autonomous learning atmosphere, I try to fully embody the "student-oriented" teaching concept in the whole teaching process design and design five links.
(1) Introduction of stories and creation of situations.
I introduced it with the story of "rabbits making colorful flags".
(2) Hands-on operation to explore new knowledge.
1, teaching angle classification.
(1) Students intuitively operate and perceive.
Observe and compare the colorful flags made by students, and find that there are different angles and the same size on the flags. (This design is the cornerstone of learning angle classification. )
(2) Ask students to measure the degrees of these angles. Show different angles.
(3) Through observation, find out the characteristics of these angles, and give the names of acute angle, right angle and obtuse angle.
(4) Turn one side of the active angle to guide students to observe and get angles different from these three types of angles: straight angle and rounded angle.
(5) Divergent thinking: Students find out the boxers and rounded corners in life.
(6) Guide students to discover the order of five kinds of angles and the equivalent relationship among right angles, straight angles and rounded corners.
2. The drawing method of teaching angle.
(1) Please draw a 60-degree angle and tell me what tool you used to draw it. Why? Please share your thoughts at the same table.
(2) Ask students to draw an angle of 70 degrees. How to draw? Say the method of painting and correct the mistakes of the local teacher.
(3) The teacher explained that the best way to draw an angle with a specified degree like this is to use a protractor.
(4) Summarize and demonstrate the method of drawing corners.
(5) Students try to draw the angles of rays in different directions, name them and exchange a quantity at the same table.
(3) Apply knowledge to solve problems.
"Apply what you have learned", once new knowledge is formed, it must be applied to solving problems, so as to further form skills and skills. Psychological research shows that the combination of learning and application is an important link to improve and deepen students' knowledge, so the following exercises are designed.
(4) class summary:
What did we learn in this class? How many angles can it be divided into? How to draw an angle of a specified degree with a protractor?
Extracurricular expansion: students collect different angles and compare who finds the most in the next class.
(5) Students evaluate each other and self-evaluate.
Sixth, talk about blackboard design.
The content of blackboard writing is the essence of a class, which can reflect the teaching content and teaching focus, and reflect the teaching thinking process.
Seven, talk about teaching evaluation.
In the teaching of this class, I boldly organized the teaching materials, with distinct levels, prominent points and scattered difficulties, and always carried out teaching around the teaching objectives. Introduce novelty, create scenarios, let students enter orderly thinking, echo interests from beginning to end, pay attention to students' participation in the whole teaching process, fully reflect students' main role, this class is generous, clear at a glance, and the links are reasonable.
"Drawing Corners" Lecture Notes 4 I. teaching material analysis
After students learned the measurement and classification of angles, they began to teach drawing angles. "Drawing corners" can not only consolidate "measuring angles", but also need to draw corners in real life, so it is still an application. The new curriculum standard points out: "Mathematics curriculum should emphasize the foundation, popularization and development." Let students learn to draw corners and focus on their future development.
Second, the teaching objectives
Teaching goal is the starting point and destination of classroom teaching. To determine a reasonable and accurate teaching goal, we must consider it from three dimensions: knowledge and skills, process and method, emotional attitude and values. Therefore, I am convinced that:
Teaching goal-explore different methods to draw angles with specified degrees.
Target decomposition: in this goal, "the method of drawing corners" is the knowledge goal; "Being able to draw an angle with a specified degree correctly" is the ability goal; What I value more is "exploring the process of different angle drawing", because it can cultivate students' mathematical thinking ability and help them develop the habit of thinking and the spirit of bold innovation. These are the abilities, emotions and attitudes that students can benefit from for life.
Third, single task, thick line
Textbooks are the carrier of knowledge and the basis of classroom teaching. Teaching is not only to complete the content of textbooks, but more importantly, to educate a person with personality and life. There are differences between students. In the process of using teaching materials, teaching should be designed according to the actual level of students in the class, rather than taking this as the key link. After learning the measurement of angles, students have been able to use protractor to measure angles correctly, and it is not difficult to draw angles with protractor. Therefore, I think this class should not only focus on the knowledge goal of protractor drawing angles, but also boldly break through the teaching materials, creatively use the teaching materials and pay attention to cultivating students' inquiry ability. So I decided the single task of this class: drawing corners in different ways as a carrier to cultivate students' inquiry ability.
In order to accomplish this important task, the teaching process will be organized with the main line of "exploring the use of various methods to draw corners with specified sizes".
Fourth, the learning part.
Drawing board 1: explore the method of drawing angles with triangle board
In "cooperative inquiry", teachers pay attention to the guidance of mathematical methods, and activities such as speaking, spelling, drawing, "drawing directly", "adding one" and "subtracting one" clearly reflect the guidance of thinking process and methods. "Comparison" is a method in itself, and it is also permeated with the idea of choosing the best scheme.
In this process, "swinging the angle" paves the way for "drawing the angle", just like building a bridge between "measuring the angle" and "drawing the angle", so that students can smoothly enter the drawing angle. Piaget, a famous psychologist, once said: "All truths should be obtained by students themselves, or rediscovered by them, at least reconstructed." The new curriculum standard also emphasizes that students should go through the process of knowledge formation. Therefore, in the links of "cooperative inquiry" and "drawing a conclusion", I give full play to the advantages of group cooperative learning, let children explore independently, speak fully and show fully, give students the initiative in class, let them experience the formation process of knowledge and draw their own methods. Let's participate and develop actively.
Panel 2: Explore the method of drawing angles with protractor.
In this process, "swinging the angle" paves the way for "drawing the angle", just like building a bridge between "measuring the angle" and "drawing the angle", so that students can smoothly enter the drawing angle. Piaget, a famous psychologist, once said: "All truths should be obtained by students themselves, or rediscovered by them, at least reconstructed." The new curriculum standard also emphasizes that students should go through the process of knowledge formation. Therefore, in the links of "cooperative inquiry" and "drawing a conclusion", I give full play to the advantages of group cooperative learning, let children explore independently, speak fully and show fully, give students the initiative in class, let them experience the formation process of knowledge and draw their own methods. Let's participate and develop actively.
Plate 3: expand and extend, cultivate innovation
I designed: "I am a little designer" activity-folding more special angles through origami. Students play and learn. Such learning activities can not only stimulate their interest in learning, but also cultivate their practical ability and innovative consciousness.
Blackboard design:
Draw corners
1. Draw angles with triangles: draw 30, 45, 60 and 90 degrees directly. Add 75, 105, 120, 135, 150 degrees. Minus one minus 15 degrees, etc.
2. Draw angles with triangles: Draw angles with protractors: overlap, find points and connect lines. Reasonable choice of angle drawing.
This blackboard writing is simple, clear and focused, which helps students to sort out their knowledge and guide their learning methods.
"Drawing Corner" Lecture Note 5 says teaching materials:
Drawing corners is the last content of the second unit of mathematics in People's Education Press. The cognitive basis is that students have measured the degree of an angle with a protractor and mastered the basic classification of angles. The learning task of this lesson is to let the students draw the angle of the specified degree correctly according to the steps of drawing the angle, initially cultivate the students' drawing ability, at the same time develop the habit of careful inspection after painting, and strengthen the communication and contact between angle measurement and angle drawing.
In the textbook, there are three basic steps to draw an angle directly: first, draw a ray, so that the center of the protractor coincides with the endpoint of the ray, and the zero scale line coincides with the ray; Then point a point on the scale line corresponding to the protractor; Finally, take the endpoint of the drawn ray as the endpoint and draw a ray through the point just drawn. Considering the development of students in teaching, I feel that if students are taught to draw directly according to these steps, they don't understand why they draw like this and it is not easy to master it. After careful consideration, I think students should try to draw corners and gradually experience the steps of drawing corners in the process of painting. But how to ensure that students can draw the angle correctly in the process of trying? Through repeated study of textbooks, I realized that drawing an angle is actually drawing two rays from a vertex, which is the definition of an angle. The problem is how to ensure that the degrees formed by the two rays meet the requirements, so tools such as protractor or trigonometry are needed to determine the position of the second ray. Thought of here, I immediately had an idea, that is, first use school tools or gestures to pose an angle of a specified degree, then pose an angle of a corresponding degree on the protractor, and finally try to draw an angle of a corresponding degree according to the angle. This teaching method not only organically combines angle drawing and angle measurement, but also sets a gradient for students to explore the method of angle drawing independently, and also cultivates students' good habit of drawing with tools.
Speaking of teaching:
1, oral arithmetic is an essential skill in mathematics learning, and the improvement of oral arithmetic ability can not be realized overnight, it is a long-term training process. Therefore, before each class, we should carry out warm-up training of oral arithmetic to achieve the degree that practice makes perfect. Using courseware to demonstrate oral arithmetic can not only improve classroom efficiency, but also quickly focus students' attention on learning.
2. In order to stimulate students' interest and arouse their enthusiasm for participation, draw a standard five-pointed star, which is a very interesting topic for students to introduce new lessons. According to the two mathematical characteristics of the five-pointed star, each side is equal in length and each vertex angle is 36 degrees. I instruct students to draw an angle of 36 degrees, and further explore how to draw an angle with a specified degree.
3. The premise of drawing an accurate angle is what an angle looks like in your mind. Therefore, before discussing the drawing method of an angle, let the students do it through a series of activities, such as setting the angle, estimating the angle and distinguishing the angle, so as to achieve the effect of accurately drawing the specified degree angle. The use of advanced teaching equipment, such as physical projection, fully demonstrates the students' thinking method and operation process, which is intuitive, vivid, accurate and convenient, and greatly improves the efficiency of classroom teaching.
4. After class, let the students draw a standard five-pointed star, which can be described as echoing from beginning to end and applying what they have learned.
Hello, now Chen Lin will answer the above questions. The general method of finding the inverse matrix, the formula