Excellent Lecture Notes on the Characteristics of Triangle 1 I. Textbooks
1. Teaching content: The triangle is characterized by the teaching content of the compulsory education curriculum standard experimental textbook 80-8 1 page published by People's Education Press.
2. The location and arrangement intention of teaching materials.
This part includes the definition of triangle, the names of various parts of triangle, the height and bottom of triangle, the stability of triangle and so on. Students have an intuitive understanding of triangles by studying the space and graphic content in Book One, and can distinguish triangles from plan views. Example 1: It is about the teaching of triangle definition, and the key point is to let students further perceive the attributes of triangles in the operation of "drawing triangles". Abstract concept. Example 2: The important feature of the key triangle is "stability", which is widely used in life. Students can have a more comprehensive and in-depth understanding of triangles. At the same time, it is beneficial to cultivate students' practical spirit and practical ability.
3. My choice.
In order to let students discover the mystery that triangles are stable and parallelograms are easy to deform, I not only let students "pull", but also add the link of "swing", that is, let every student understand that the lengths of three sides of a triangle are certain, and the shape and size of this triangle are unique, so it is stable; However, although the four sides of the parallelogram are determined, it can pose different shapes and sizes of graphics, so the parallelogram is not stable, but easy to deform.
This link will take a lot of time. After careful consideration, I decided to put the base and height of the triangle in the last link as an extension of the next lesson.
4. Teaching objectives
(1) Let students know more about triangles and understand their concepts through hands-on operation and observation and comparison.
(2) Through the experiment of pulling and swinging, let students know the stability of triangle and its application in life.
(3) Cultivate students' ability of observation and operation, and the ability of applying mathematical knowledge to solve practical problems. Experience the close relationship between mathematics and life and cultivate students' interest in learning mathematics.
5. Teaching emphases and difficulties
Teaching emphasis: summarize the concept of triangle and understand the stability of triangle.
Teaching difficulties: same as above.
Second, talk about teaching methods and learning methods.
teaching method
1, operation discovery method.
The concept and characteristics of triangle are abstract for primary school students. Therefore, I ask students to connect abstract mathematical concepts with concrete figures through hands-on practice, so as to enrich students' representations and help students abstract the definition of triangles and master their characteristics on the basis of their original perceptual knowledge.
2. Discussion method.
In the hands-on operation, discussion and communication, students express their opinions, which not only inspires students' thinking, but also enhances students' sense of cooperation. Students use their hands and brains to solve problems in the process of exploring and discovering problems, which truly embodies the teaching concept of taking students as the main body. Teachers play the role of organizer, guide and collaborator in class.
(2) study law
The new curriculum standard points out that teaching should pay more attention to students' learning process rather than learning results, and our teaching should teach students learning methods. The learning methods that students in this course should master are: learn to summarize the concept of triangle through observation and operation, understand the stability of triangle and cultivate the ability of exploration.
Third, talk about teaching procedures.
A triangle appears on the blackboard before class.
(A) cut to the chase and introduce the topic.
1, Teacher: You know what? Today, in this class, we will continue to learn triangles.
2. Teacher: Why do you think it is called a triangle?
3. Teacher: Can you name the parts of the triangle accurately?
(B) operational perception, understanding concepts
1, draw a picture.
Teacher: Please empty a triangle with your finger. What should I pay attention to when drawing?
2, put a pendulum.
Teacher: Each stick is equivalent to a line segment. What should I pay attention to when putting a triangle with three sticks?
The whole class put a triangle on the desktop independently and let a student put it in front of the projector. Tell me how it was put.
3. Tell me about it.
(1) Teacher: The students all drew triangles correctly. Can you summarize what kind of figure is called triangle in a short sentence?
Teachers and students discuss with each other, and the teacher gradually improves the blackboard writing.
(2) The courseware presents a complete concept: a figure surrounded by three line segments (the endpoints of every two adjacent line segments are connected) is called a triangle.
(3) Teacher: Which words do you think are the most important in the definition of triangle?
Organize students to understand "three lines" and "encirclement" in the discussion.
4. Sentence.
Please tick √ if the picture below is a triangle, please tick × if it is not a triangle and give your reasons. (Students gesture together)
5. Teacher: For the convenience of expression, the letters A, B and C are used to represent the three vertices of a triangle, which can be written as △ABC.
6. look for it.
(1) Teacher: Where have you seen triangles in your life?
(2) Courseware shows pictures: telephone poles, lifting frames, bicycles and basketball stands.
(3) Experiment to dispel doubts and explore characteristics.
1, ask questions.
The teacher pointed to the picture and asked: Why do you want to make these parts into triangles in production and life?
2. Experiment to solve doubts.
(1) pull.
Teacher: Please take out the triangle and quadrilateral learning tools made in advance and experiment in groups: pull out the learning tools one by one. What did you find?
It is concluded that triangles are stable and parallelograms are easy to deform.
(2) pendulum.
A, the teacher asked: Why is the triangle stable? And the parallelogram is unstable?
Health: ...
B. Teacher (showing the triangle posed by classmates before): This is a triangle posed by classmates. Now if the teacher provides the same three sticks, can you make different triangles?
The whole class tried again and put the triangle on the table.
C, collective evaluation, can not put out different, it is concluded that as long as the length of the three sides of the triangle is determined, the shape and size of the triangle are completely determined.
D, Teacher: Just now, the students discovered the mystery of triangle stability through pendulum. Can we continue to analyze why the parallelogram is unstable? You can think in your head, imagine it out of thin air, or actually wave it with four sticks
A. Students should either think independently or cooperate at the same table and put different parallelograms with four sticks.
B. Show some students' works with physical projectors.
It is concluded that although the four sides of a parallelogram are certain, it can pose figures of different shapes and sizes, so the parallelogram is not stable, but easy to deform.
(3) say it.
Teacher: Who can explain clearly why triangles are stable in words? And the parallelogram is unstable?
Excellent lecture notes on "the characteristics of triangles" 2 i. Teaching materials
(1) teaching material analysis
"The characteristics of triangle" is the content of Unit 5, Volume 8, the curriculum standard of PEP. Triangle is the simplest and most basic polygon in plane graphics. All polygons can be divided into several triangles, and the related properties are deduced with the help of triangles. Therefore, the understanding of triangles is the starting point of plane graphics knowledge and the basis of plane geometry and solid geometry.
This lesson is taught on the basis that students have learned line segments, angles and intuitive understanding of triangles, so this lesson is the second stage of triangle understanding.
(B) Teaching objectives
According to the position and function of this course in the textbook, the basic concept of the new curriculum standard and the students' cognitive level, I have drawn up the following teaching objectives:
1, knowledge goal: Understand the definition of triangle, master the characteristics and characteristics of triangle, and draw the height of triangle.
2. Ability goal: learn the learning methods obtained through observation, operation, analysis and generalization, experience the connection between mathematics and life, cultivate students' ability of observation, analysis and operation, and further develop the concept of space.
3. Emotional goal: in the process of group cooperation, exploration and communication, enhance students' innovative consciousness and the spirit of unity and mutual assistance.
(3) Teaching emphases and difficulties
Teaching emphasis: understand the definition of triangle and master the characteristics and characteristics of triangle.
Teaching difficulties: determine the height and draw the height of the triangle.
(4) Preparation of teaching AIDS:
Triangle board, courseware, math toolbox, slide show.
(5) Preparation of learning tools:
Triangular ruler, math toolbox, drawing.
Three. Oral English teaching methods and learning methods
1, theory and teaching method
In this class, based on the idea that teachers are organizers, guides and collaborators, I created a new teaching structure with students participating in activities as the main line. First, create a situation to stimulate students' interest in learning, then let students learn the teaching materials by themselves, explore independently, and then let students operate and practice, so as to achieve the independent construction of concepts; In the whole teaching process, the teaching concept of taking students as the main body and teachers as the leading factor is fully embodied, so that students can feel the beauty of mathematics in activities.
2. Speaking and learning methods
According to the teaching objectives and methods of this class, I mainly adopt the learning methods of independent exploration, cooperative communication and practical operation, so that students can truly understand and master the basic knowledge and skills of mathematics through thinking, talking and hands-on experience in doing mathematics, gain rich experience in mathematics activities, establish a sense of accomplishment and confidence in learning, and make students become masters of mathematics learning.
Fourth, talk about the teaching process
In the teaching process of this class, I adhere to the spirit of the new curriculum standards and strive to fully embody the student-centered and student-oriented educational concept in the whole teaching process design. The author puts forward the teaching ideas of creating situations, inducing interest cooperation and exchange, exploring new knowledge, deepening training, expanding and extending questioning and reflection, and summarizing and evaluating, and strives to build a harmonious classroom teaching model.
Five, say blackboard writing design
The blackboard writing in this lesson is concise and clear, highlighting the key points, reflecting the internal relations of this lesson, and further deepening students' understanding of the characteristics and characteristics of triangles.
The excellent lecture of "The Characteristics of Triangle" 3. I said that the content of the class is: the standard experimental textbook of compulsory education curriculum published by People's Education Press; The teaching content of the first lesson of Unit 5 in the fourth grade of primary school mathematics: "the characteristics of triangles".
I will teach from the aspects of teaching material analysis's treatment, teaching methodology, teaching process and blackboard writing design.
First, the analysis and processing of teaching materials.
(A) the status and role of teaching materials
Triangle is the simplest and most basic polygon in plane graphics. All polygons can be divided into several triangles, and related properties are deduced with the help of triangles. Therefore, the content of triangle is an important basis for studying solid geometry and plane geometry in the future. This lesson is the second stage of triangle understanding.
This year's students already know the knowledge of angles and line segments, and can clearly distinguish triangles from plane figures. They have also accumulated some spatial knowledge in their life, and with some abstract thinking ability, they can understand graphics more abstractly and make some explorations. According to the requirements of the new curriculum standards and the actual situation of students, I set the following teaching objectives:
According to the requirements of mathematics curriculum standards for grades 4-6, namely "understanding the basic characteristics of simple geometric figures, developing students' spatial concepts, learning to cooperate with others to solve problems, understanding the close relationship between mathematics and human life, and experiencing mathematics full of exploration and creation" and the contents of this textbook, the following teaching objectives are formulated:
(B) Teaching objectives
1, through hands-on operation and observation and comparison, make students know the triangle, know the characteristics of the triangle and the significance of the height and bottom of the triangle, and draw the height in the triangle.
2. Let students go through the process of inquiry, cultivate students' observation ability, calculation ability, generalization ability and the ability to solve practical problems by applying mathematical knowledge, and further develop students' spatial concept.
3. In learning activities, let students experience the connection between mathematics and life, and cultivate students' interest in learning mathematics.
(3) Key points and difficulties
I have determined that the focus of teaching is to understand the definition of triangle and master the characteristics and characteristics of triangle. The difficulty in teaching is: draw the height in the triangle.
When presenting teaching information and perceptual materials, I use the method of multimedia demonstration, which can be more intuitive and easier to understand. I also prepared triangular and polygonal frame molds, answer sheets and other teaching AIDS and learning tools to fully prepare for the development of teaching.
Second, talk about teaching methods and learning methods.
The new curriculum standard of mathematics emphasizes: "Mathematics teaching activities must be based on students' cognitive development level and existing knowledge and experience. Teaching should stimulate students' enthusiasm for learning, provide students with opportunities to fully engage in mathematical activities, and help students truly understand and master basic mathematical knowledge and skills, mathematical ideas and methods in the process of independent exploration and cooperative communication, so as to gain rich experience in mathematical activities. Enable students to learn mathematics through observation, operation, thinking and experience. "
According to the basic concept of the new curriculum standard, I organize students to carry out inquiry learning activities in this class by means of intuitive demonstration, guided inquiry, explanation demonstration and operation discovery.
Effective mathematics learning activities can not simply rely on imitation and memory, but a purposeful and active process of constructing knowledge. To this end, in the guidance of learning methods in this class, I will guide students to explore and discover mathematics knowledge independently in hands-on operation. The methods of observation and discovery, operation comparison, independent inquiry and cooperative communication run through the whole learning process of students, so that students can experience the process of "doing mathematics" with their brains, mouths and hands, and realize the effective construction of knowledge.
Third, talk about the teaching process.
According to the new curriculum concept and the characteristics of learning situation, I designed the following four teaching links.
(A) life situation, direct introduction
First, let the students observe the life situation map, intuitively feel that triangles are used in many places in life, and directly introduce a new lesson: "The characteristics of triangles."
In this way, the introduction of life phenomenon into the study of mathematics knowledge not only stimulates students' interest in learning, but also makes them realize the connection between mathematics and life, paving the way for the development of teaching activities (further exploring new knowledge).
(B) self-construction, exploring characteristics
This link is the key content of this lesson. In order to better highlight the teaching focus and break through the teaching difficulties, I divide teaching into three levels.
The first level: try to study and explore the characteristics.
First of all, please take out the math kit and open the nail board to form a fastest triangle on it; Then let the students draw a triangle on the map. Finally, please take out the triangle, count it, feel how many angles and sides it has and talk about your understanding of the triangle. Teachers and students summarize the definition of triangle. Make clear the characteristics of a triangle: a triangle has three sides, three vertices and three angles. Teachers should use this situation to help students understand the meaning of encirclement. Then let the students try to summarize the definition of triangle, mark the names of each part of triangle, and finally teach how to represent triangle with letters.
Design intention: When exploring the concept of triangle, enclosure is the key and difficult point. In order to effectively break through the difficulties, I asked students to circle triangles on the nail board. In effective operation activities, students intuitively understand the meaning of enclosure. Moreover, through a series of mathematical activities such as drawing, counting, touching and saying, students can fully understand the meaning and characteristics of triangles.
The second level: try to operate and experience the painting height.
The understanding and drawing of triangle height is the difficulty of this lesson. In order to break through the difficulties, I put the knowledge of triangle height into the situation of practical problems and designed the following teaching levels:
First, show two herringbone roof truss diagrams with courseware, and let students observe and say which roof truss is higher. Where did you see it? Guide students to measure the height of roof truss. Teachers use the courseware again to abstract the physical drawings of the two roof trusses into two triangles, and draw a dotted line at the part where the height of the roof truss has just been measured, so that the "height of the triangle" is vividly presented to the students and the students can understand it more thoroughly. Then, let the students learn the definition of triangle height and bottom by themselves. On this basis, mobilize the existing knowledge and experience and explore and draw a height by themselves.
Finally, it is required to change the shape and placement of the triangle, and ask students to continue to identify the height of the triangle and enrich their understanding of the height. This link is more difficult for students to think. Many students will encounter difficulties when drawing the other two heights of a triangle. Therefore, I will make full use of the advantages of information technology, demonstrate two high-level painting methods with courseware, guide students to think, broaden students' thinking breadth and solve difficulties in teaching.
Design intention: This link makes full use of the advantages of information technology and multimedia-assisted teaching, so that students can intuitively understand the high image and experience the process of exploring high painting, which not only breaks through the teaching difficulties, but also makes students feel the value of learning and the joy of success.
The third level: experiment to solve doubts and explore the characteristics of stability.
The stability of triangle is not easy for students to understand. Through the introduction of the game, I asked the students to pull the triangular and polygonal frame molds. It is found that the triangular frame die is immobile and the polygonal frame die is deformed. Why is this? To arouse students' thinking, students may think that the quadrangle learned in the fourth grade last semester is easy to deform, so the skeleton in the middle of the school electric door should be designed as a quadrangle, which will produce the idea that the triangle is not easy to deform. So, why are triangles not easy to deform? Ask questions and then lead the students' thinking to the depths. This is the stability of a triangle: as long as the lengths of the three sides of the triangle are determined, the shape and size of the triangle are completely determined. This is why there are so many places in life where triangles are used. Finally, let the students recall the examples of applying triangle stability in their lives. Let students understand that mathematics comes from life and serves life.
Design intention: This link is mainly to conform to students' thinking, and complete a process of doubt-doubt-explanation through students' hands-on operation, communication and inquiry, and teachers' auxiliary explanation, so that students can experience the stability of the triangle.
(C) comprehensive practice, apply what you have learned
Practice is an important means for students to use knowledge, form skills and develop intelligence. I have arranged three gradient exercises here.
One is to identify which triangles are in the diagram and which are not.
The second is drawing, that is, drawing a height on a given triangle to consolidate the drawing method of height.
The third is to use one thing to solve the practical problems of chair repair and fencing by using the stability of the triangle. Let students apply mathematics knowledge to solve problems in life and experience the practical value of mathematics.
Design intention: Through these orderly and diverse exercises, not only the knowledge that students have learned is consolidated, but also the ability of understanding, analysis and reasoning is further cultivated, which embodies the concept of "Mathematics is everywhere in life" and achieves the purpose of "applying what they have learned".
(D) class summary, talk about the harvest.
Design intention: Ask students to talk about the harvest of this class, summarize and sort out the new knowledge, promote the development of students' thinking while forming the knowledge structure, and embody the concept of "everyone learns valuable mathematics".
Fourth, talk about blackboard design.
The blackboard writing in this lesson is based on the students' inquiry process. It is concise, intuitive, vivid and focused, which is beneficial to the cultivation of students' mathematical thinking.
In short, in this class, I try my best to use observation, independent thinking, cooperative inquiry and other learning methods from students' life experience and existing knowledge background to help students understand concepts in practical activities, build knowledge models, apply what they have learned, and truly let students experience the joy of learning.