Junior high school mathematics teaching design scheme 1
pythagorean theorem
1. teaching material analysis: Pythagorean theorem is a very important property of right triangle, which students learn on the basis of mastering the related properties of right triangle. It reveals the quantitative relationship among the three sides of a triangle, which can solve the calculation problem in a right triangle and is one of the main bases for solving a right triangle. It is of great use in real life.
When compiling teaching materials, we should pay attention to cultivating students' hands-on operation ability and problem analysis ability, and make students get a more intuitive impression through practical analysis, puzzles and other activities; Understanding Pythagorean Theorem through contact and comparison is beneficial to correct application.
Accordingly, the teaching objectives are as follows: 1. Understand and master Pythagorean theorem and its proof. 2. Be able to use Pythagorean theorem and its calculation flexibly. 3. Cultivate students' abilities of observation, comparison, analysis and reasoning. 4. By introducing the achievements of ancient Pythagoras characters in China, we can inspire students' thoughts and feelings of loving the motherland and its long culture, and cultivate their national pride and research spirit.
Second, teaching emphasis: proof and application of Pythagorean theorem.
Third, teaching difficulties: proof of Pythagorean theorem.
Fourth, teaching methods and learning methods: teaching methods and learning methods are embodied in the whole teaching process, and the teaching methods and learning methods of this course reflect the following characteristics:
Give priority to self-study counseling, give full play to the leading role of teachers, stimulate students' desire and interest in learning by various means, organize student activities, and let students actively participate in the whole learning process.
Effectively reflect students' dominant position, let students understand theorems through observation, analysis, discussion, operation and induction, improve their hands-on operation ability, and their ability to analyze and solve problems.
By demonstrating objects, students are guided to observe, operate, analyze and prove, so that students can gain a sense of success in acquiring new knowledge, thus stimulating their desire to learn new knowledge.
Verb (abbreviation of verb) teaching procedure: The teaching of this section is mainly reflected in students' hands-on and brain. According to students' cognitive rules and learning psychology, the teaching program is designed as follows:
(A) to create a new situation
1, the story is introduced. More than 3,000 years ago, a man named Shang Gao told the Duke of Zhou that if you fold a ruler into a right angle and connect the two ends, you will form a right triangle. If the hook is 3 and the rope is 4, then the rope is equal to 5. This has aroused students' interest in learning and stimulated their thirst for knowledge.
2. Do all right triangles have this property? Teachers should be good at arousing doubts and let students enter a state of being willing to learn.
3. Write it on the blackboard to show the learning objectives. (B) the initial perception and understanding of teaching materials
Teachers guide students to learn new knowledge through self-study, which embodies students' awareness of autonomous learning, exercises students' initiative to explore knowledge, and forms good self-study habits.
(3) Discussion and summary of questioning and problem solving: 1, teachers ask questions or students ask questions. How to prove Pythagorean theorem? Through self-study, students above the intermediate level can basically master it, which can stimulate students' desire to express themselves. 2. Teachers guide students to do puzzles and observe and analyze them as required;
(1) What are the characteristics of these two graphs? (2) Can you write down the areas of these two figures?
(3) How to use Pythagorean theorem? Are there any other forms?
At this time, the teacher organizes students to discuss in groups, arouses the enthusiasm of all students, achieves the effect of everyone's participation, and then communicates with the whole class. First of all, one group of representatives spoke and expounded their understanding of the problem, while the other groups made comments and supplements. Teachers give enlightening guidance in time, and finally teachers and students sum up each other, form a consensus and finally solve the problem.
(4) Consolidate practice and strengthen improvement.
1, show exercises, students answer in groups, and students summarize the law of solving problems. Combine static and dynamic in classroom teaching to avoid causing students fatigue.
2. Give an example of 1. Students try to solve the problem, and teachers and students evaluate it together, so as to deepen the understanding and application of the example. In order to further improve students' ability to use knowledge, we can take the form of mutual evaluation and discussion on the problems in practice, and teachers can take the form of classroom discussion to solve the representative problems in mutual evaluation and discussion, thus highlighting the teaching focus.
(5) Summarize practical feedback.
Guide students to summarize the main points of knowledge and sort out their learning ideas. Distribute self-feedback exercises, and students can complete them independently.
This course aims to create a pleasant and harmonious learning atmosphere, optimize teaching methods, improve classroom teaching efficiency with the help of multimedia, and establish an equal, democratic and harmonious relationship between teachers and students. Strengthen the cooperation between teachers and students, create a classroom atmosphere in which students dare to think, feel and ask questions, make all students lively in teaching activities, and cultivate their innovative spirit and practical ability in learning.
Junior high school mathematics teaching design scheme II
parallelogram
Let's talk about the textbook first: This lesson is mainly about understanding the parallelogram through measuring operation activities, understanding that the opposite sides of the parallelogram are parallel and equal, and the diagonal lines are equal, mastering the concepts of the base and height of the parallelogram, and initially drawing the height on the base of the parallelogram.
Teaching method: The introduction method of new textbooks is different from before. It uses a quadrilateral generated by overlapping two equal-width belts to introduce a parallelogram. First highlight the image of the parallelogram "face", and then go to the "edge" (the edge of the face). Teaching is divided into two parts. The first step is to know the parallelogram. Ask the students to observe the quadrangles where two parallel transparent ribbons overlap, and then observe the characteristics of these quadrangles. After calculation, comparison and thinking, students find that the two opposite sides of these quadrangles are parallel respectively, and then guide students to summarize the definition of parallelogram and give mathematical symbols. Let students look for examples of parallelograms in their lives, which can enrich the expressions of parallelograms on the one hand, and deepen their understanding of "two groups of sides are parallel respectively" on the other hand.
The second step is to know the base and height of the parallelogram. The base and height of a parallelogram are relative, not absolute. Any side of the parallelogram can be the bottom, so the vertical line of the bottom starts from a point on the opposite side of the bottom, and the line segment between this point and the vertical foot is the height of the bottom. However, the concept of "height" is not easy for students to establish, thinking that the height of students in life experience is often height, tree height, tower height and so on. , refers to the height of an object standing upright on the ground, implying the definition of vertical. So in the textbook, I introduce the concept of vertical line, and then establish the concept of height through vertical line segments, and observe the position and relationship of these heights at the same time. It is concluded that countless heights can be drawn on the same base, and the lengths of these heights are all equal, but in general, we only need to make one height. On this basis, expand, such as the calculation of external height, or how to calculate height when the bottom is not horizontal, so as to broaden students' understanding of "height" in plane graphics.
19. 1 parallelogram
[Knowledge and ability goal]: 1. Understanding parallelogram through operating activities. 2. Master the concept of parallelogram base and height, and draw the corresponding height on the parallelogram base.
[Process and method]
[Emotional goal]: Let students enjoy the joy of learning and share the joy of success. Teaching emphasis: the corresponding height on the base of parallelogram will be drawn. Teaching difficulty: the corresponding teaching process at the bottom of parallelogram will be drawn.
First, create scenarios to stimulate interest.
1, class, what geometric figures do you know? These geometric figures can be seen everywhere in our lives. It makes our life more colorful.
2. What did you find? -A new quadrilateral appears.
What's so special about this quadrilateral? Today we will study it.
Blackboard writing: parallelogram
Second, the new curriculum exploration
1, Teacher: According to your understanding of parallelogram, please choose a stick to make a parallelogram. Roll call students to show with real input and organize students' evaluation.
2. Teacher: Open the schoolbag and find out the parallelogram.
3. Q: Please put the parallelograms discovered by the study group together, observe them and see what you can find.
Requirements: In groups of four, make full use of learning tools, use your brains, find ways and discuss with each other. Group report, collective communication. Summarize the characteristics of parallelogram.
Q: Through observation and hands-on operation, we discovered the characteristics of parallelogram in our own way. What is a parallelogram? Can you use your own words?
Summary:
Two groups of parallelograms with parallel opposite sides are called parallelograms.
4. Show the objects in the picture that we often see, pushing and pulling iron gates, railings, signs and flower windows. There is a parallelogram hidden in these objects. Can you find it?
Judge: Is the figure below a parallelogram?
What do you think is the key to judge whether a figure is a parallelogram?
Third, the base and height of parallelogram
The base and height of a row quadrangle
1. The students try to draw the height of the parallelogram on the homework paper.
2. The teacher guides the method of writing and painting on the blackboard.
Q: What's new about painting height?
(1) A parallelogram has four bases, and each side can be used as the base.
(2) There are countless heights on the same base, and each height is equal.
3. Identify and improve.
(1) Projection presentation: Draw the height outside the parallelogram for students to identify.
Summary: The height of a parallelogram can be drawn inside or outside the parallelogram. No matter where you draw, you should pay attention to the corresponding relationship between the bottom and the height.
4, painting high practice
Junior high school mathematics teaching design scheme 3
Understanding parallelogram lecture notes
textbook
1. Lecture content: Pages 43-45, Volume II of Grade Four Mathematics, Jiangsu Education Press.
Second, the position, function and significance of teaching content:
This part of the content is to further understand the parallelogram and master its characteristics on the basis that students have initially mastered the characteristics of rectangle, square and triangle, as well as the preliminary understanding of parallelism and intersection. Through in-depth study of this lesson, students will lay a foundation for further study of parallelogram area calculation. The first example in the textbook first asks students to find out some parallelograms on common objects in connection with real life, and then asks students to fully perceive parallelograms according to their personal life experience. Then let the students make a parallelogram and communicate with each other, and feel the basic characteristics of the parallelogram initially. On this basis, the figure of parallelogram is abstracted to let students know and guide them to explore and discover the basic characteristics of parallelogram. The second example identifies the base and height of a parallelogram and reveals the meaning of the base and height. "Try it" allows students to measure the height and the corresponding bottom surface on the designated bottom surfaces of several parallelograms, and further feel the significance of the height and the bottom surface.
Third, say the goal.
1, knowledge and skills target
(1) Understand the concept and characteristics of parallelogram.
(2) Knowing the base and height of the parallelogram, we can draw the height.
(3) Cultivate students' practical ability, observation ability and analysis ability.
2, process and method objectives
Let the students further accumulate the learning experience of understanding graphics through hands-on operation, eye movement observation, speech expression and brain thinking, learn to make parallelograms in different ways, draw parallelograms on grid paper, correctly judge whether the plane graphics are parallelograms, and measure or draw the height of parallelograms.
3. Emotional attitudes and values goals
Let students feel the close connection between graphics and life, feel the learning value of plane graphics, further develop their interest in "space and graphics" and feel the pleasure of successful exploration.
Four, the teaching emphasis and difficulty:
Teaching emphasis: understanding parallelogram; Make a parallelogram with materials and find its characteristics; You can measure or draw the height of the parallelogram.
Teaching difficulty: students' understanding of the characteristics of parallelogram in the process of making it.
V. Preparation of teaching AIDS and learning tools
Teaching AIDS: triangular, parallelogram paper, rectangular movable frame, small blackboard, etc.
Learning tools: triangle, parallelogram paper, protractor.
Talk about learning.
The fourth-grade students are active in thinking, eager for knowledge and like to use their hands and brains. Have a strong curiosity and desire to explore. Therefore, in teaching, I grasp these characteristics and make them understand what they have learned through eye movement observation, hands-on operation and brain analysis and induction.
Oral English teaching methods and learning methods
In this class, teachers should pay attention to teachers' guidance and students' learning, and ask questions, demonstrate and guide them through teachers. Students use hands-on operation, observation, analysis, discussion, induction and other methods to complete the teaching, so that students can gain new knowledge in a relaxed and happy way. We believe that the teaching of this course should reflect the following points.
First, combine teaching with practice.
"Making mathematics live, and letting students learn realistic mathematics" is one of the new curriculum ideas. In teaching, students should first find the parallelogram from the life scene diagram, and then find the parallelogram in life. Finally, an example is given to illustrate the application of parallelogram deformation in life. Let students feel that "mathematics comes from life and moves towards life". Let the mathematics classroom return to the life world.
Second, let students explore in the activities
Psychologist Piaget said: "Activity is the basis of cognition, and wisdom begins with action." In teaching, students can feel the characteristics of parallelograms by making them and communicating with each other. Let students feel the connection between different plane graphics through activities such as spelling, moving and cutting.
Third, independent thinking and cooperation.
There are two cooperative exchanges in this course. Before the cooperation and exchange, I gave students enough time to think independently, so that they could have nothing to say and their thoughts could collide.
On the Teaching Process
First, create situations to introduce new lessons.
1, introducing jigsaw puzzle
Teacher: Have you ever played Tangram? Do you know what different shapes of jigsaw puzzles are made of?
More than 1000 years ago, people in China invented jigsaw puzzles. Tangram consists of seven figures, which can spell out rich patterns. Foreigners call it "China's Magic Disc". In their view, no intellectual toy is more magical than it.
2. Import: Let's meet one of the characters today? Parallelogram. (Show the topic)
Design intention: Take the "Tangram" that students like as the starting point to arouse students' learning enthusiasm.
Second, try to explore the establishment of the model
(a) Recognition of an acknowledgement that constitutes an expression
Teacher: The figure here is a parallelogram. After changing the direction, I asked: Is it still a parallelogram?
A parallelogram is a parallelogram no matter how its direction changes. (The picture is posted on the blackboard)
(2) Looking for perceptual features.
1, find the parallelogram in the diagram.
Teacher: Here are some pictures. Can you find a parallelogram on them?
2. Find the parallelogram in life
Teacher: Actually, there are parallelograms around us. Where have you seen parallelogram? (Can be displayed through the camera: removable clothes rack)
(3) Do some distinctive explorations.
1. We just found some parallelograms in our life. Now can you make a parallelogram with the materials at hand?
2. Talk about what you did in the group and choose the representative to report in class.
3. Just now, the students made a parallelogram successfully. Did you find anything or gain in the process? How did you find out? (Group communication)
4, the whole class exchanges, the teacher summarizes the characteristics of parallelogram. (Two groups of opposite sides are parallel and equal respectively; Diagonally equal; The sum of internal angles is 360 degrees. )
Design intention: The new curriculum emphasizes experiential learning. Students should not only think with their brains, but also see with their eyes, listen with their ears, speak with their mouths and do with their hands, that is, experience with their own bodies and feel with their own hearts. Here, students can go through the process from representation to abstraction by knowing parallelogram, finding parallelogram and making parallelogram. Let students feel the characteristics of parallelogram in a series of activities.
(4) practice to consolidate appearances.
Do the questions after thinking 1 and 2.
(5) draw pictures to understand the level.
1. For example. Can you tell the distance between the two red lines of a parallelogram? (Students draw on homemade pictures) Tell me how you measured it.
2. Teacher: The vertical line you just drew is the height of the parallelogram. This opposite side is the base of the parallelogram.
3. What did the parallelogram book say? (Students read books)
4. How many such high-energy paintings are there? Why? Can you draw the height of another group on the opposite side and measure it? (mobile phone)
5. Try teaching. Students measure each other and emphasize the corresponding relationship between bottom and height when communicating.
6. Draw high (think about doing the fifth question) (remind students to draw rectangular marks)
Third, hands-on operation has been consolidated and deepened.
1, think about doing questions 3 and 4 after you finish.
Question 3: Spell it out and move it. Tell me how to move it.
Question 4: Master Zhang, a carpenter, wants to saw a parallelogram board in half to make a rectangular desktop. If you were Master Zhang, what would you think? Want to try it? Try to find a parallelogram paper.
2. Do the sixth question after thinking (do well before class and do activities in class. )
(1) The teacher took out his rectangle, took it sideways and pulled it in the opposite direction. Look what you found. Teachers observe students and communicate with each other.
(2) Judgment: Is a rectangle a parallelogram? Discuss in groups and then explain the reasons. At this time, the teacher can ask the students what kind of parallelogram the rectangle is. What is (special) special?
(3) Obtaining the features of parallelogram.
Then the teacher holds the diagonal of the parallelogram and pushes it inward. Look what you found.
Teacher: Triangle has stability. What do you think of the characteristics of parallelogram through the hands-on operation just now? (unstable, easily deformed)
(4) Application of characteristics
Teacher: parallelogram is easy to deform and has a wide range of applications in life. Can you give some examples? (Students read textbook P45 after giving examples. "Do you know?" )
Design intent:
Fourth, talk about the expansion and extension of harvest.
1, Teacher: Did you get anything from this class today?
2. Use the puzzle in your hand to spell out the figures we have learned.
3. Find the application of parallelogram deformation in life.
Design intention: expand the limited space of classroom teaching and combine closely inside and outside the class. After class, students are given practical homework, which requires them to find the application of parallelogram's easy-to-deform characteristics in life, so that students' classroom learning can be linked with after-school life, and students can feel the application of classroom knowledge in life, which can not be separated from mathematics all the time, thus enhancing the intimacy and practicality of mathematics learning.
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