"Rotation of Graphics" 1 Handout I. Teaching Materials
(A) the content of teaching materials
"Rotation of graphics" is the first lesson of Unit 5 "Motion of graphics" in the fifth volume of Mathematics, the standard experimental textbook of compulsory education curriculum.
(B) the status and role of teaching materials
This part of the textbook "Rotation of Graphics" is a preliminary understanding of the rotation phenomenon in life in the second volume of Senior Two. It can accurately judge whether the movement phenomenon of an object is "translation" or "rotation", further clarify the meaning of rotation, explore the characteristics and properties of rotation, and let students learn to rotate simple graphics 90 degrees on square paper. It is an important knowledge point in the field of space and graphics, which permeates the development of students' space concept, is the basis for subsequent study of symmetrical graphics and central rotation graphics, and plays a connecting role in teaching materials. At the same time, rotation is widely used in daily life, which can help us solve many practical problems.
(c) the learning objective
According to the above analysis of teaching material analysis and his academic situation, I think it is necessary to further cultivate students' ability of observation, induction and generalization, and cultivate students' thinking order and language expression ability. To this end, I think this class should pay attention to the students' exploration process of rotation characteristics, consciously cultivate students' hands-on, reasoning and inductive abilities, and truly understand the characteristics of rotation.
Therefore, according to the above analysis and curriculum standards, I set the learning objectives of this lesson as follows:
1, further understand the rotation transformation of graphics, and clarify the meaning of rotation and the three elements of rotation.
2. You can rotate the triangle 90 degrees on the square paper to further understand the characteristics of the rotating graphics in the process of rotation.
(4) Talk about the key points and difficulties in learning.
This lesson is related to the specific situation, so that students can observe the process of the pointer turning on the clock face and know how the object turns clockwise and counterclockwise. Therefore, it is the focus of this lesson to clarify the meaning of rotation, and to clarify "which point the pointer rotates around", "which direction it rotates" and "how many degrees it rotates". It is difficult to explore the characteristics of graphic rotation in this lesson. Only by recognizing that "the shape and size of the rotated figure have not changed, but the position has changed", can the research and refining of the rotation method become an independent activity, laying a solid foundation for drawing the rotated figure.
Second, oral teaching methods
According to the content and arrangement characteristics of the teaching materials in this class, according to the students' cognitive rules and following the guiding ideology of efficient classroom teaching, I mainly adopted the methods of self-study interactive discussion and teacher guidance feedback exercise. Enable students to perceive new knowledge, summarize new knowledge, apply new knowledge and consolidate and deepen new knowledge.
In the guidance of learning law, I take the method of letting students explore independently, observe and discover, and cooperate and communicate. Encourage students to actively participate in teaching practice activities, and summarize the characteristics of graphic rotation under the guidance of teachers in the form of independent thinking and mutual communication. When guiding inquiry, give students enough thinking time and space to associate and explore, and complete the real self-construction of knowledge. In addition, in the teaching process, I use multimedia-assisted teaching to present the teaching materials intuitively, so as to better stimulate students' interest in learning, increase teaching capacity and improve teaching efficiency.
Third, talk about the teaching process
(A) the creation of situations, the introduction of new courses
The first link is the process of introducing new knowledge. I first show pictures in the courseware, so that students can find the transformation of graphics-rotation by observing pictures. The teacher's camera revealed the theme.
In this lesson, we will learn "the rotation of graphics".
Blackboard writing: the rotation of graphics
[Design intention: Introduce familiar things in students' life, let students perceive the phenomenon of rotation and establish the representation of rotation. ]
(B) Self-study interaction
This link is the key and difficult point of this lesson. In order to highlight these key points and disperse these difficulties, I carefully designed the teaching process, mainly from these steps to guide students to learn, namely: (1) understand the meaning of rotation and understand the three elements of rotation. ⑵ Understand the rotation of graphics and explore the characteristics of rotation.
1. First, let the students talk about what other examples of rotation they have seen in their lives.
Design intention: Let students know the rotation and transformation of graphics through life examples.
2. Then ask the students to observe the pictures, and then discuss the similarities of the rotation phenomenon in groups. Student reporter camera blackboard writing.
Teacher's blackboard writing: rotation center rotation direction rotation angle clockwise counterclockwise
Design intention: Experience the phenomenon of rotation, get a preliminary understanding of the three elements of rotation, and pave the way for learning the example 1
3. Observe and describe the rotation phenomenon.
Work in groups, carefully observe the rotation process of the pointer, and complete the following three sentences in example 1
(Show animation: the pointer points from 12 to 1)
Describe the rotation process of the pointer in one sentence, and the teacher guides the students to describe it completely: the pointer rotates 30 clockwise around the O point from "12" to "1".
Display: The pointer rotates 30 clockwise around the O point from "12" to "1".
(Show the animation: the pointer points from 1 to 3) Consolidate the rotation process of the narrative pointer: the pointer rotates 60 clockwise around the O point from 1 to 3. .
(Show animation: the pointer points from 3 to 6)
Then, by analogy with knowledge transfer, students are required to describe the rotation process of the pointer independently on the same table.
Further deepen the knowledge, if the pointer continues to rotate clockwise around the O point from "6" 180. What will it point to?
(Play animation: the pointer points from 6 to 12)
Summarize and define the elements of rotation.
Guide students to summarize the meaning of rotation.
Design intention: Make full use of the demonstration of multimedia courseware, strengthen intuitive teaching, make students deepen their understanding of the meaning of rotation and reduce the difficulty of understanding. By directly observing the concrete example "the rotation of the clock hands" and the interaction between teachers and students, students can be guided to draw a conclusion. Highlight the three elements of rotation, so that students can consolidate and understand the meaning of rotation in time, optimize their cognitive structure, improve their knowledge system, and make their mathematical understanding break through the difficulties of thinking again. ]
2. Understand the rotation of graphics and explore the characteristics and essence of rotation.
First, I ask students to observe the theme map of Example 2.
Then the team cooperated with the hands-on operation to fix the right-angle triangular ruler on the square paper around the O point.
Rotate the triangle clockwise for 90 times and observe how the position of the triangle ruler changes after each rotation.
Students report the results.
Finally, the characteristics of rotation are revealed: after the triangle rotates, the position of each triangle changes, but the shape and size of the triangle remain unchanged; The position of point o has not changed.
Students have initially constructed the knowledge about the characteristics of rotation, but it is still immature, so strike while the iron is hot.
I also designed a triangular ruler, turned it counterclockwise on the square paper like above, and said something. Where should the triangle turn?
Design intention: Modern mathematics teaching theory points out that the process of thinking must be displayed in teaching, and students should be allowed to explore and sum up experience independently. Here, I let the students study in groups, and the cooperative exchange activity is an active learning activity. In this activity, students explore independently and communicate with teachers and students. Teachers guide students to think and express in an orderly way, cultivate students' logical thinking ability and guide students to summarize the characteristics of graphic rotation. Further consolidate this teaching difficulty, so that students can fully understand and master it.
(3) Standard evaluation
This link is mainly for students to consolidate new knowledge.
Design intent:
(4) class summary.
What knowledge have you learned through this lesson?
Design intention: Summary should not only be a simple list of knowledge, but also an effective means to optimize the cognitive structure and improve the knowledge system. In order to give full play to the main role of students, we should summarize the knowledge, methods and experience of learning.
Lecture 2 of Rotation of Graphics Dear leaders, judges, teachers and online friends:
Hello everyone!
I'm glad to take part in this speech contest! After taking this course, I feel a little confused. This part of the content can not be found in traditional textbooks, and online search is also a course with little or no information sources. I'm also under a lot of pressure, but I'm lucky. With the help of my friends, I clearly understand how teachers should guide students and teach them in this field of knowledge. This is my real harvest! I sincerely thank all my teachers and friends who have helped me. I think the highlight of today's lecture comes from the spark of their wisdom. ...
I said that the content of the class is the fourth grade textbook of Beijing Normal University Edition, Unit 4, the transformation of graphics, the first class, the rotation of graphics.
First of all, talk about my understanding of teaching materials and my children:
The rotation of graphics belongs to the field of "space and graphics", which is the most primitive foundation in the field of space. Students in this period are sensitive to children's spatial concept, and this mathematical concept will develop well and their creativity will be unlimited.
In fact, the children in our class are very quick-thinking, lively and active, and often give me many surprises! When they are very young, they have the experience of moving objects or people. They often do manual activities, such as origami and spinning windmills, from which they accumulate knowledge of graphic conversion. In the third grade, they initially felt the phenomenon of translation and rotation in their lives. On these bases, based on life experience and perceptual knowledge, this study focuses on developing students' spatial concept and cultivating students' observation ability and hands-on operation ability.
Secondly, talk about the teaching objectives and difficulties I have established:
There are three sources of teaching objectives: First, students' learning needs. The second is from the real life of students. The third is the learning materials from the teaching materials.
1. Knowledge and ability goal: Through the observation of examples, understand the process of making complex graphics from a simple graphic through rotation.
2, process and method goal: can design simple patterns.
3, emotional attitude goal: A: Learn to rotate regularly at a certain angle, get beautiful patterns, and learn to appreciate the beauty of mathematics. B: Cultivate students' observation ability and hands-on operation ability, and develop students' spatial concept.
Teaching emphasis: objective 1, 2 teaching difficulties.
Finally, talk about my teaching process:
At the beginning of the class, I adopted Gao Ming's suggestion, and through the demonstration of paper dragonflies made by students themselves, I revealed the examples of rotation in life, so that children had a preliminary understanding of the rotation process of graphics, so as to learn mathematics in connection with life and fully arouse students' interest in learning mathematics.
(Next, play the courseware): Show a group of patterns, all of which are obtained by rotating simple patterns. In my teaching design, only students are allowed to appreciate beautiful patterns. However, after my trial lecture, I found that it is really difficult for students to master the rotation angle, and some students are very confused. So I think it's better to teach this lesson again, and guide students to appreciate pictures and analyze the rotation angle of graphics. Lay the foundation for breaking through the difficulties in this lesson.
In the teaching of observation and demonstration, I designed four teaching activities:
1. The 53-page windmill figure in the demonstration textbook appears in the form of animation, so that students can clearly see the rotation process on the basis of discussion and communication. Students can easily fill in the blanks on page 53 well.
2. What is demonstrated is the strengthening center and direction on page 54 of 1 title.
3. The demonstration is 54 pages and 2 questions about how to judge the rotation angle.
It is worth noting that when discussing the rotation method, a friend of mine asked whether to emphasize counterclockwise rotation. I was confused at that time. I found the door of an outstanding teacher. Under the guidance of Gao Ming, I reread the textbook, further understood the intention of compiling the textbook, and infiltrated this knowledge into the opening and students' demonstration of dragonflies. Good results have been achieved.
Teaching objectives of the third lecture on "Rotation of Figures"
1. Stimulate learning interest, and understand the meaning of "flipping and rotating graphics" through autonomous learning.
2. Master the corresponding processing methods of actual graphics and feel the advantages of computer processing graphics.
3. Further cultivate students' practical ability and innovative ability.
Teaching focus
Use rotation and rotation operations.
Teaching difficulties
The turnover and rotation of graphics and the application of comprehensive knowledge in practical drawing.
Teaching process:
First, the scene import, stimulate interest
Situation lead-in: Spring has arrived. Xiaoxiao took his beloved windmill to the park to play. The flowers and trees in the park are all dressed in new green clothes, which is refreshing! But a little tree was very sad and asked with a smile, "Little tree, little tree, what's wrong with you?" The little tree replied, "Everyone has new clothes to wear, but my leaves haven't grown yet." Smiled and said, "Don't be sad, I will help you."
Q: "How can I help Xiaoxiao?"
Students put forward a solution: making green leaves to "add clothes" to small trees.
[Design Intention] Situation is an important part of classroom teaching design. A relaxed and active classroom environment is very important to stimulate students' thinking and cultivate their ability.
Second, inquiry learning and problem solving
1. Reproduction of old knowledge:
Teacher: We have learned to draw leaves with curve tools before. (Show the painted leaves and trees) But small trees need many leaves. If it's a waste of time to draw leaves one by one, is there any quick way?
Answer: Copy and paste.
After the teacher gives affirmation, let the students dictate the process of copying and pasting while operating.
Move the leaves to the right position and find the problem. (transparent, opaque)
【 Design Intention 】 Use the old knowledge learned to inspire students to find and solve problems themselves, so that students can gradually develop the habit of acquiring knowledge independently and creatively using knowledge.
2. Learn to flip and rotate graphics.
Teacher: We already know that we can add leaves to small trees by copying and pasting. Next, let's take a look at these two pictures. By contrast, what's the difference between these two pictures? (display)
Answer by roll call.
Teacher: Which one do you like? Think about how to become as beautiful as the small tree on the right.
Turn the leaves upside down, turn around, change direction ...
The teacher affirmed and pointed out that "we call this treatment of leaves' rotation'". This function is available in drawing. Let's find out where it is hidden. (Prompt in menu bar)
Students try to operate and explore independently.
Classroom communication: (Ask two students to demonstrate, students evaluate, teachers evaluate).
The teacher demonstrated the operation process again. (Explain while operating)
Show several different flip effects and discuss their differences on the same table.
(Hint: Please check the available usage records. )
Ask the students to turn out the notebook to demonstrate and point out the mistakes in time.
Relax for a minute in class.
Students practice.
[Design Intention] In view of the problem of violating natural phenomena, I asked students to explore their own solutions first, and then demonstrate the operation method. Using the existing resources of use notebook on the desktop, you can practice flipping and rotating, so as to accurately understand the difference between the two commands.
Third, consolidate new knowledge and complete the task.
1, let the students try various flip operations to finish the work. Teachers patrol, find problems in teaching in time, help students with difficulties, remind students and give affirmation.
2. Students who finish the task ahead of time can beautify the overall situation.
【 Design intent 】 To further consolidate the new knowledge learned; The purpose of hierarchical teaching is to meet the learning needs of students with different knowledge levels.
Fourth, the display and evaluation of works, learn to evaluate.
Show and comment on students' works. (self-evaluation, mutual evaluation, teacher evaluation)
[Design Intention] This link is relatively open, which can fully mobilize students' enthusiasm and initiative and expand their thinking. Through students' self-evaluation, mutual evaluation and teachers' comments, students' abilities of observation, analysis and oral expression are cultivated, and their aesthetic taste is improved.
Fifth, summarize and experience success.
Tell me about the gains of this course.
[Design Intention] Teachers and students * * * summarize, further consolidate what they have learned and build a complete knowledge system.
Blackboard writing:
flip horizontal
turn
flip vertical
90 degree rotation
Rotation 180 degrees.
270 degree rotation
Lecture Notes of "Rotation of Graphics" 4 I. Talking about the teaching content;
Beijing Normal University Edition Primary School Mathematics Volume 7 Unit 4 Section 1 "Rotation of Graphics"
Second, the status and role of teaching materials
On the basis of respecting teaching materials, I let students feel the rotation in full experience and appreciation; At the same time, according to the characteristics of students' active thinking, guide students to compare the changes of graphics before and after rotation, and infiltrate the idea of rigid body transformation.
Knowledge goal: Understand the process of a simple figure forming a complex pattern through rotation, and be able to rotate the simple figure 90 degrees on the grid paper and design the pattern through rotation.
Ability goal: to cultivate students' abstract thinking ability and develop spatial concepts by using thinking methods such as observation, operation, induction and association.
Emotional goal: to realize the beauty of mathematics and cultivate students' interest in learning mathematics and passion for life.
Difficulties in teaching: Understanding the rotation of graphics, understanding the process of a simple graphic forming a complex pattern through rotation, can rotate the simple graphic 90 degrees on grid paper.
The difficulty in teaching is that you can rotate a simple figure 90 degrees on a square paper and use the rotation to design the pattern.
Third, talk about teaching methods and learning methods.
Before learning this unit, students only feel the translation and rotation phenomena in life and are exposed to two graphic transformation methods: symmetry and translation. This lesson is to introduce students' perspective into the third graphic transformation-rotation. It is intended to let students experience the process of changing simple graphics into complex patterns through a series of activities such as appreciation, exploration and creation, and understand that different centers, directions and angles of rotation lead to different patterns, so as to further develop students' spatial concept and lay the foundation for continuing to learn graphic transformation in the future.
Fourth-grade students, thinking in images is still dominant in their cognitive process. Therefore, based on the principle of "feeling while operating", let students experience the three elements of rotation and feel the beauty of transformation brought by graphic rotation.
Fourth, talk about teaching preparation.
Picture, small blackboard, square paper, homemade windmill.
Verb (abbreviation of verb) process design;
(A) exciting games, feel the rotation of graphics
In this session, you can feel the rotation by creating a scene. The introduction of windmills, exquisite graphics and other scenes that students like has greatly stimulated their enthusiasm for learning. It shows the process of changing a single pattern into a complex pattern, which not only makes students feel the beauty of mathematics, but also increases their interest and makes them have the desire to explore: how to rotate to get such a beautiful pattern? Really pay attention to children's psychological needs and change "I want to learn" into "I want to learn", so as to smoothly enter the rotation exploration.
(2) Hands-on operation to explore new knowledge.
Put the difficulty of graphic rotation in the table into the scene to explore how the windmill is made, and then let the students discuss the three elements of graphic rotation independently, that is, the center point, the direction of rotation and the degree of rotation. In teaching, I follow the guiding ideology of "students as the main body, teachers as the leading factor, and mathematics activities as the main line", so that students can explore independently. Break through the difficulties in teaching.
(3) Do it by hand
In this session, I designed a set of exercises. When the 55-page 1 question is finished, I ask the students to draw a beautiful pattern on the square paper through what they have just learned. Let students operate and experience the process of graphic rotation, consolidate new knowledge, establish the concept of space and promote the development of students' thinking.
(D) Enlighten and guide, expand thinking
Expand, students use the knowledge they just learned to make their favorite graphics and design beautiful patterns. Further highlight the difficulties of this class and develop students' imagination and creativity.
(5) Summary of this lesson
What did you learn today? Do you have any questions?