"Triangle" Lecture Notes 1 In this class, I take the problem as the starting point of teaching. When designing the teaching plan, I don't directly take the perception of the teaching material as the starting point, but adapt the knowledge of the outer corner of the teaching material into a question that students need to explore. The main activities are to let students operate paper-cutting to find problems, summarize laws, stimulate students' interest in inquiry, let students experience and innovate in their attempts, and turn the traditional teaching process into students' exploration and innovation of mathematical problems.
First, teaching material analysis and teaching objectives
The main content of this chapter is the related concepts of triangle and the properties of its angles. The focus of this lesson is to explore and master the nature and summation of the external angles of triangles. In the presentation mode, the presentation mode of "conclusion-example-exercise" has been changed, but the research mode of "question-inquiry-discovery" has been adopted, and a variety of inquiry methods have been adopted: the methods of jigsaw puzzle, measurement and mathematical reasoning have been adopted for "the nature and sum of triangle external angles", so that students can sum up and find problems themselves.
Second, the teaching preparation work
Let the students prepare scissors, cardboard, protractor, triangle and other tools before class.
Third, teaching methods.
Adopt the method of combining theory with practice. In form, autonomous learning and cooperative research are the main methods, and teachers supplement them with timely guidance and tips.
Fourth, teaching hours.
1 class hour
Verb (abbreviation of verb) teaching aid
In order to increase classroom teaching capacity and improve classroom teaching efficiency, multimedia-assisted teaching is adopted.
Sixth, the teaching process.
(1) Passionate devotion
Find the outer and inner angles (adjacent and non-adjacent) of the triangle in a picture. Observe the relationship between the outer angle and the adjacent inner angle (the sum is equal to 180 degrees. Then ask the question: What is the relationship between the outer corner and the other two non-adjacent inner corners? Let's discuss this problem with * * *. Are you confident to learn it well?
Blackboard writing: the sum of the external angles of a triangle
(2) new teaching:
1, and explore two properties of the external angle of triangle.
For this part of the teaching, I mainly ask students to sum up the law in the hands-on puzzle, and then complete it through group discussion, or guide students to think and discover this law. Is there any other way? (such as measuring with a protractor, etc. ). Then let a student show it on the booth. This is more intuitive.
After discussing the two properties of the triangle exterior angle, we should emphasize the properties, especially the individual keywords. Education daquan
2. Explore the triangle exterior angle sum theorem.
In this part, I will let students discover the rules by hand (or use a protractor) and then show them with animation, which will be more intuitive. Finally, I will rise to theoretical reasoning, and gradually guide students to draw the external angle sum theorem through the triangle internal angle sum theorem.
This lesson focuses on these two parts, and then practice. When I design exercises, I consider the principle of going from shallow to deep: the first exercise is about the simplicity of the sum theorem of inner and outer angles; The second exercise is a comprehensive application problem. When I do this problem, I think about training students and cultivating their ability. I asked a student to do it on the blackboard, and then told my classmates his own ideas.
(3) Summary
Think back to what we learned in this class. It can be learning content, learning attitude, etc. Let's talk to some students.
In a word, my course has changed the tendency of paying too much attention to knowledge transmission in the past, emphasizing the formation of a proactive learning attitude, so that the process of acquiring basic knowledge and skills can also become the process of learning to learn and forming correct values. Change the current situation that the course content is too complicated and old-fashioned, strengthen the connection between the course content and students' life, modern society and scientific and technological development, pay attention to students' learning interest and experience, and select the basic knowledge and skills necessary for lifelong learning. We should change the current situation that the curriculum implementation puts too much emphasis on learning, rote memorization and mechanical training, advocate students' active participation, willingness to explore and diligence in practice, and cultivate students' ability to collect and process information, acquire new knowledge, analyze and solve problems, and communicate and cooperate with each other.
Strive to be a successful "three-type" experimental teacher in junior high school mathematics curriculum reform in order to strive for high efficiency under the new curriculum standard.
"Triangle" Lecture Notes 2 I. Talking about Teaching Materials
(1) Contents:
The triangle is characterized by the contents of 80-8 1 page in the compulsory education curriculum standard experimental textbook published by People's Education Press, including the definition of triangle, the names of various parts 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.
(2) 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. Through experiments, students can understand 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.
(3) Teaching emphasis: understanding the characteristics of triangles.
(4) Teaching difficulty: Draw the height in the triangle.
Second, oral teaching methods
(1) Situational teaching method.
Learning in a specific situation can stimulate students' interest and activate their thinking. In order to solve problems, students will actively explore new methods, thus integrating problem solving and methods. This arrangement is conducive to the close connection between mathematics and life.
(2) Operation discussion method.
Students express their opinions in hands-on operation and discussion, 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.
Third, speaking and learning.
(1) Independent Inquiry The Mathematics Curriculum Standard points out that effective mathematics activities cannot be simply imitated and memorized, and hands-on practice, independent inquiry and cooperative communication are important methods for students to learn mathematics. So in teaching, I let students experience it through hands-on practice. For example, drawing a picture, discussing, talking and other activities discover and construct new knowledge, so as to master new knowledge, cultivate cooperation consciousness and inquiry quality, and develop thinking ability and problem-solving ability.
(2) apply what you have learned. After learning new knowledge, I timely guide students to use what they have learned to solve some practical problems in life. This not only increases the wisdom of students, but also makes students feel the inseparable relationship between mathematics and life, and enhances students' interest and confidence in learning mathematics.
Fourth, talk about teaching procedures.
(A), contact life, situational import
1, show 80 pages of situation map, students observe and find the description triangle.
2. Say: What other objects in life have triangles?
3. The courseware shows triangles on common objects in life.
4. Introduce the theme of blackboard writing.
(B), operational perception, understanding the concept
1, find the characteristics of triangle.
2. Summarize the definition of triangle.
(1), guide the students to sum up what a triangle is in their own words.
(2) Discussion: Is the figure below a triangle?
(3) Discussion: Which statement is more accurate?
④ Guide reading the definition of "triangle" on page 80.
3. Know the base and height of the triangle.
(1), a house with a triangular roof. Q: Can you measure the height of the triangular roof? Students do it by hand)
(2) How did you measure it? (Student exchange report).
(3) Explain the measurement process? (Get the concept of triangle height and bottom).
(4) Show me the triangle on page 8/kloc-0 (Q: Is this the set of the base and height of this triangle? Can you draw other bottoms and heights? Students do it and then discuss it.
4. Development
In triangle ABC, the height with AB as the base is (); The height based on AC is (); The height with BC as the base is ().
(C), the experiment to solve doubts, explore the characteristics
1. Ask a question: Show the illustration on page 8 1 and ask where there is a triangle in the picture. Why should this part be made into a triangle in production and life? What are its characteristics?
2. Experiment to solve doubts
(1), the students take out the triangle and quadrilateral learning tools prepared and experiment in groups. What do you find when you pull the learning tool?
(2) Draw the conclusion that the triangle is stable.
(3) Illustrate the application of triangle stability in life with examples.
(4) Consolidate application and raise awareness.
Courseware demonstration exercises 14: 1, 2 and 3
(5) Summarize the evaluation and question the difficulties.
1. What did you learn in this class?
2. What do you know about triangles?
"Triangle" Lecture Note 3 Hello, judges and teachers:
I said that the topic of the class is the sum of the internal angles of the triangle, and the content is selected from the first lesson of the seventh section of the seventh grade of nine-year compulsory education published by People's Education Publishing House.
First, the design concept:
Mathematics is the spiritual communication between people. The communication in classroom teaching is mainly between teachers and students and between students. It needs to use the "dialogue" learning method and adopt a variety of teaching strategies to enable students to develop their own abilities in cooperation, exploration and communication. In the new curriculum, students' feelings, experiences, values and ways to acquire knowledge are contrary to the traditional teaching mode, which is the focus of teachers' search for new teaching methods in the new curriculum.
It should be said that with the gradual perspective of teachers on the new curriculum, new teaching methods will form a new path. It is necessary to break the original framework of teaching activities and establish a teaching activity system that adapts to the interaction between teachers and students; Meet students' psychological needs and realize emotional harmony between teachers and students; Give students a chance to experience success and change "I want to learn" into "I want to learn".
I think the change of teachers' role will definitely promote the development of students and education. In the future teaching process, what teachers should do is: help students decide appropriate learning goals, and confirm and coordinate the best way to achieve these goals; Guide students to form good study habits and master learning strategies; Create rich teaching situations, cultivate students' interest in learning and fully mobilize students' enthusiasm for learning; Provide all kinds of conveniences for students and serve their study; Establish an acceptable, supportive and tolerant classroom atmosphere; As a participant in learning, share your feelings and ideas with students; Seek truth with students and be able to admit your mistakes and mistakes. The creation of teaching situation is a challenge for teachers after entering the new curriculum. The teaching situation that adapts to the new round of basic education curriculum reform is not agreed in the article, nor can it be used immediately. We need to explore, study, discover and form in the whole process of teaching activities.
Second, teaching material analysis and handling:
The theorem of the sum of internal angles of a triangle reveals the quantitative relationship of the three angles that make up a triangle. In addition, the auxiliary line is introduced in the proof, which lays the foundation for the subsequent study. The theorem of triangle interior angle sum is also the embodiment of algebra of geometric problems.
Third, student analysis:
Students of this age group have the ability to collect, sort out and reform mathematical modeling problems that are suitable for their own use and close to the reality of life. They are willing to try, explore, think, communicate and cooperate, have the ability of analysis, induction and summary, and they are eager to experience success and pride. Therefore, teachers should give students full freedom and space, and at the same time pay attention to the openness and development of the problem.
Fourth, the teaching objectives:
1. Knowledge goal: In situational teaching, through exploration and communication, the "triangle interior angle sum theorem" is gradually discovered, so that students can experience the process of knowledge and simply apply it. Be able to explore the quantitative relationship and changing law in specific problems and understand the idea of equations. Try to find solutions to problems from different angles through open-ended propositions. In teaching, through effective measures, students can gain experience in the process of solving problems and learn individually in the process of reflection on solving problems.
2. Ability goal: To cultivate students' ability of logical reasoning, bold guessing and hands-on practice through jigsaw puzzles, problem thinking, cooperative exploration and inter-group communication.
3. Moral education goal: Infiltrate the education of aesthetic thought and method by increasing auxiliary line teaching.
4. Emotion, attitude and values: Under the good teacher-student relationship, establish a relaxed learning atmosphere, so that students are willing to learn mathematics, avoid difficulties, gain a successful experience in mathematics activities, enhance their self-confidence and enhance their sense of collective responsibility in cooperative learning.
The establishment of the key points and difficulties of verbs (abbreviation of verb);
1. Emphasis: Exploration and proof of triangle interior angle theorem.
2. Difficulty: Discussion on the proof method of triangle interior angle and theorem (with auxiliary lines).
Six, teaching methods, learning methods and teaching methods:
The teaching mode of "problem situation-modeling-explanation, application and expansion" is adopted.
Use dialogue, try teaching, problem teaching, hierarchical teaching and other teaching methods to achieve the teaching purpose.
Seven, teaching process design:
(A), the creation of situations, the introduction of suspense
The introduction of new courses is the beginning of communication between teachers and students, the psychological preparation for students to learn new knowledge, and the key to narrowing the distance between teachers and students and getting rid of the psychology of being difficult to learn and boring. Successful lead-in is to make students feel familiar with their own life, so that students can quickly enter the classroom in the shortest time, resulting in great interest and curiosity. Then teaching activities will become a pleasure for them.
Specific practice: throw a question: "What is the angle of the top when the folding ladder (computer display graphics) in the school logistics office is opened?" A student gave the answer immediately after measuring the angle between two ladder legs and the ground. Do you know why? "The student thought for a moment, and I pointed out that you can answer this question after learning this lesson. So as to introduce new courses.
(2) Explore new knowledge
1, hands-on practice, trying to find that students are required to cut the triangle cardboard prepared in advance according to lines, and then use the cut ∠A and ∠B to make the vertices of the three pieces coincide with the ∠C puzzle in the complete triangle cardboard. What kind of phenomenon can they find? Some students will find that the three are at right angles. At this time, let the students observe each other's puzzles and verify the results. Through observation and communication, we can learn from each other's methods and realize the interaction between life and life. When the communication is sufficient, paste the spelled graphics in groups, and the teacher comments and summarizes the classification. Divide the spelled figure into two situations: ∠A and ∠B are on the same side and both sides of ∠C respectively. Give praise to the team with cooperative spirit.
(Show the puzzle on the blackboard)
2. Try to guess: the teacher asks questions. What did you find from the activity? Adopt the way of intra-group communication to produce thinking collision. At this time, I will go to the students and give appropriate guidance to the disadvantaged groups. After that, the students report their findings in groups. That is, the sum of the three internal angles of a triangle is equal to 180 degrees.
3. Proof conjecture: First, help students recall the basic steps of proposition proof, and then let students finish drawing independently, write out the known and verified steps, and other students supplement and improve. Ask the students to explore the proof method in groups according to the hands-on exercises just now. This link should give students enough time to think, discuss, discover and experience, so that students can learn from each other's strong points, explore together, find the breakthrough point of proof and experience success. Pay more attention to and guide students with learning difficulties, don't give up any students, improve the teacher-student relationship of students with learning difficulties, and lay the foundation for continuing learning. After cooperative exploration, report the proof method and pay attention to standardizing the proof format. The concept of auxiliary line is naturally introduced here. However, it should be noted that adding auxiliary lines is not blind, but in order to prove a conclusion, it is necessary to quote a definition, axiom and theorem, and the original drawing does not have the conditions to use them directly, so it is necessary to add auxiliary lines to create conditions and achieve the purpose of proof.
4, apply what you have learned, feedback exercises
(1) In △ABC, it is known that ∠ A = 80. Can you know the degree of ∠B+∠C?
Solution: ∫∠A+∠b+∠C = 180 (triangle interior angle sum theorem)
∴∠ b+∠ c = 100 in △ABC
(2) If ∠ A = 80 and ∠ B = 52, then ∠C=?
Solution: ∫∠A+∠b+∠C = 180 (triangle interior angle sum theorem)
∠∠A = 80∠B = 52 (known)
∴∠C=48
(3) In △ABC, ∠ A = 80, ∠ B-∠C= 40, then ∠C=?
(4) Given ∠A+∠B = 100∠C = 2∠A, can we find the number of times ∠A, ∠B and ∠C?
(5) In △ABC, ∠A: ∠B: ∠C = 1: 3: 5 is known. Can you find the degree of ∠ A, ∠ B and ∠ C?
Solution: Let ∠ A = X, then ∠ B = 3x, ∠ C = 5x.
X+3x+5x= 180, which is derived from the theorem of sum of interior angles of triangles.
Solution, x=20
∴∠A=20 ∠B=60 ∠C= 100
(6) It is known that in △ABC, ∠C=∠ABC=2∠A, how to find the number of (1)∠B? (2) If BD is the height of AC side, what is the degree of ∠DBC?
Question (6) is adapted from the examples in the book. This question is typed by an auxiliary courseware with auxiliary lines, giving students an intuitive graphical demonstration from simple to complex.
Through this group of exercises, we can infiltrate the idea of simplifying graphics, continue to infiltrate the idea of unity, and solve geometric problems with algebraic methods.
5, consolidate and improve, student-oriented.
(1) As shown in the figure: B, C and D are on a straight line, ∠ ACD = 105, and ∠A=∠ACB, then ∠B =- degrees.
(2) As shown in the figure, AD is the bisector of △ABC, and ∠ B = 70 and ∠ C = 25, then ∠ADB =- degree, ∠ADC =- degree.
This group of exercises is a comprehensive application of triangle interior angle sum theorem, angle definition and angle bisector, which can cultivate students' ability to analyze and solve problems and help them gain some experience.
6, thinking expansion, open divergence
As shown in the figure, it is known that at △PAD, ∠ APD = 120, b and c are points on AD, and △PBC is an equilateral triangle. Try to find out the relationship between geometric quantities.
This topic aims to stimulate students' independent thinking and innovative consciousness, cultivate innovative spirit and practical ability, and develop individual thinking.
(C), induction, assimilation and adaptation
1, students talk about their experiences.
2. The teacher summarized and showed the main points of this part.
3. The teacher's comments give affirmation and hope to the students' active cooperation in class.
(4), homework:
1, required questions: Exercise 3, 1, 18+0, 12.
2. Choose to do the problem: Question 3, 1, 13, 14.
(5) Blackboard design
Sum of internal angles of triangle
Student jigsaw puzzle display
Known:
Verification:
Prove:
Open questions: