The rotation of shapes

(a) the content of the material

"Rotation of shapes" is the "Compulsory Education Curriculum Standards Experimental Textbook Mathematics Fifth Grade Lower" Unit 5, "Motion of shapes" of the "Compulsory Education Curriculum Standards Experimental Textbook Mathematics Fifth Grade Lower". "The movement of shapes" of the first lesson.

(B) the status and role of the material

"Rotation of shapes" this part of the textbook is in the second year of the second book "translation and rotation" preliminary understanding of the phenomenon of rotation in life, can be more accurate to determine the movement of an object The phenomenon is "translation or rotation" on the basis of further clarification of the meaning of rotation, to explore the characteristics and properties of rotation, and let the students learn to rotate a simple figure 90 ° on the grid paper. It is an important knowledge point in the field of space and graphics, which is a penetration to the development of students' spatial concepts, and is the basis for the subsequent study of centrosymmetric shapes and their drawing of rotated shapes, which plays a role in the teaching materials. At the same time, the rotation in daily life is also very widely used, the use of rotation can help us solve many practical problems.

(C) that the learning objectives

According to the above analysis of the materials and the analysis of the learning situation, I feel that we should further develop the students' ability to observe, generalize, generalize, etc., and develop the students' ability to think and express their ideas in a structured way. For this reason, I feel that this lesson should focus on students' exploration process of the characteristics of rotation, consciously cultivate students' practice, reasoning, generalization ability, and truly understand the characteristics of rotation.

Thus, according to the above analysis and the requirements of the curriculum standards, I will set the learning objectives of this lesson as follows:

1, to further understand the rotation of the graphic transformation, clear the meaning of rotation, and the three elements of rotation.

2, to be able to rotate the triangle 90 ° on the grid paper to further recognize the characteristics of the rotating figure in the process of rotation.

(D) said the key learning points, difficulties

This lesson is linked to the specific situation, let the students observe the clock face of the hands of the process of rotation, to recognize how the object is rotating according to the clockwise and counterclockwise direction, so clear the meaning of rotation, to say that "the hands are rotating around which point" Therefore, clarifying the meaning of rotation and stating "around which point does the pointer rotate", "in what direction does it rotate" and "how many degrees does it rotate" become the focus of this lesson. For the exploration of the characteristics of the rotation of the figure is the difficulty of this lesson, only to realize that "the shape of the figure after the rotation of the size did not change, but only the location of the change", then the method of rotation of the study and refinement can become a kind of independent activity, but also for the drawing of the rotation of the figure to lay a solid foundation.

Two, said the teaching method

According to the content of this lesson and the arrangement of the characteristics of the material, according to the law of student cognition, follow the guiding ideology of the efficient classroom first learn and then teach, I mainly used the self-study interactive discussion, teacher pointing feedback practice methods for teaching. So that students can achieve the purpose of perceiving new knowledge, generalizing new knowledge, applying new knowledge, consolidating and deepening new knowledge.

In the guidance of learning method, I take the method of letting students explore independently, observation and discovery, cooperation and communication. Advocating students to take the initiative to participate in teaching and learning activities, in the form of independent thinking and mutual communication, under the guidance of the teacher to summarize the characteristics of the rotation of the figure, in the guidance of the exploration, to give the students out of enough time and space to think, let the students to associate, explore, and from the real meaning of the completion of the knowledge of the self-construction. In addition, in the teaching process, I use multimedia teaching to visualize the presentation of teaching materials, so as to better stimulate students' interest in learning, increase teaching capacity, improve teaching efficiency.

Third, the teaching process

(a) create a situation, the introduction of a new lesson

The first part of the process of the introduction of new knowledge, I first classroom pictures, so that the students through the observation of the picture, so as to find the graphic transformation - rotation. Teacher camera reveals the subject.

In this lesson, we will study the "rotation of shapes".

The subject of the board: the rotation of shapes

[Design intention: the introduction of familiar things in the life of the students, so that the students perceive the phenomenon of rotation, the establishment of rotation of the surface].

(b) Self-study interaction

This link is the focus of this lesson, but also difficult. In order to highlight these key points and decentralized to resolve these difficulties, I carefully designed the teaching process, mainly from these steps to guide students to learn, namely: (1) understand the meaning of rotation, know the three elements of rotation. (2) Recognize the rotation of shapes and explore the characteristics of rotation.

1. First of all, let the students say what other examples of rotation have been seen in life?

Design intention: through life examples, make students initially understand the rotation transformation of shapes.

2, then let the students observe the picture, and then group discussion of rotation phenomena have what **** the same point. Students report teacher camera board.

Teacher's board: center of rotation direction of rotation angle clockwise counterclockwise

Design intention: experience the phenomenon of rotation, the initial understanding of the three elements of rotation for the study of Example 1 to make preparations.

3. Observe and describe the phenomenon of rotation

The group cooperation operation, carefully observe the rotation of the pointer and complete the three sentences under Example 1.

(show the 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 complete the narrative: the pointer rotates from "12" to "1" around the point O in a clockwise rotation of 30.

(show the animation: the pointer points from 12 to 1)

The teacher guides the students to describe the rotation process of the pointer in one sentence. p>

Produce: the pointer rotates from "12" to "1" around the point O in a clockwise rotation of 30.

(Show animation: the pointer points from 1 to 3) Consolidate the description of the rotation of the pointer: the pointer rotates from "1 " to "3" in a clockwise rotation.

(show animation: pointer from 3 to 6)

Then through the transfer of knowledge analogies require students to describe the rotation of the pointer independently of each other at the table

And then deepen the knowledge, if the pointer from the "6" continues to rotate 180 clockwise around the point O. How many will it point to?

(Show animation: the pointer points from 6 to 12)

Summarize and clarify the elements of rotation

Lead students to generalize the meaning of rotation.

[Design intent: to make full use of multimedia courseware to strengthen visual teaching, so that students deepen their understanding of the meaning of rotation, reduce the difficulty of understanding. Guide students through the specific examples of "clock hands of the rotation" of direct observation, teacher-student interactive communication, inductive reasoning, to draw conclusions. Highlighting the three elements of rotation allows students to consolidate and understand the meaning of rotation in a timely manner, so that the cognitive structure of students is optimized, the knowledge system has been perfected, so that the students' mathematical understanding of another breakthrough in the thinking of the difficulty].

2. Recognize the rotation of shapes and explore the characteristics and properties of rotation

First I asked students to observe the theme map of Example 2.

Then group work hands-on fixed right-angle triangular ruler on the grid paper around the point O every

time in a clockwise direction to rotate the triangle 90 °, observe each rotation after the ruler of the triangle 's position is how to change?

Students report their results.

Finally, reveal the characteristics of the rotations: after the triangle is rotated, the position of each triangle changes, while the shape and size of the triangle do not change; the position of the point O does not change.

For the characteristics of the rotation of the students have been initially constructed knowledge, but not yet mature, so while it is hot

Iron I designed to change the other tape measure, in the direction of counterclockwise on the grid paper like the above to turn around and say a. What position should the triangle turn to? Where should the triangle turn?

Design intent: modern mathematical teaching theory points out that teaching must show the process of thinking, should allow students to explore independently and generalize their experiences, here, I learn by letting students work in small groups, the cooperative exchange of activities is a kind of active learning activities, in the process of this activity, the students independently research-based exploration, teacher-student and student-student exchanges, at the same time the teacher guides the students to think and express themselves in a structured way , cultivate students' logical thinking ability, and guide students to generalize the characteristics of graphic rotation. Further consolidation of this difficult teaching point, so that students fully understand and master.

(C) Assessment

This link is mainly for students to consolidate new knowledge

Design intention:

(D) Summary of the lesson.

What have you learned through this lesson?

Design intent: summary induction should not just be a simple list of knowledge, but should be optimized cognitive structure, improve the knowledge system of an effective means, in order to give full play to the main role of the students, from the learning of knowledge, methods, experience of induction.

"Rotation of Figures" Lecture Notes 2

Dear leaders, judges, teachers and all friends online:

Hello!

It is a pleasure to participate in this lecture competition! After choosing this lesson, it was a bit difficult, this part of the content of the traditional textbooks do not have a part, but also the Internet to check the information in the very few, almost no source of information in the lesson, I heart pressure is also very big, but I am lucky, in the friends of the help, so that I have a very clear understanding of this field of knowledge, the teacher should be how to guide the students, how they should be taught, and that's what I really gained! Sincerely thank you for helping me all teachers and friends, I think the wonderful thing about today's speech comes from the spark of their wisdom shine ......

I said the content of the lesson is the North Shida version of the textbook of the fourth grade book of the fourth unit of "transformation of shapes," the first lesson of "rotation of shapes"

First of all, my understanding of the material and my children.

In fact, our classroom children are very quick thinking, lively and active, often give me a lot of surprises! They are very young, they have the experience of object or figure movement, they often do origami, turn the windmill and other handmade activities, from which the knowledge of graphic transformation has been accumulated, the third grade and the initial feeling of life in the phenomenon of translation and rotation. On the basis of these foundations for the current study, in the life experience and perceptual understanding of the basis, focus on the development of students' spatial concepts, cultivate students' observation skills and the ability to operate.

Secondly, let's talk about the teaching objectives and key points that I have established:

There are three major sources of teaching objectives: one is from the students' learning needs. The second is from the students' real life. The third is the learning material from the textbook.

1, knowledge and ability objectives: through the example of observation to understand the process of a simple figure after rotation to make complex shapes.

2, process and method objectives: to be able to design simple patterns.

3, emotional and attitudinal goals: A: learn to rotate regularly according to a certain angle, get a beautiful pattern, learn to appreciate the beauty of mathematics. B: the development of the observation ability and the ability to operate, the development of students' spatial concept.

Teaching focus: objectives 1, 2 teaching difficulties.

Finally, my teaching process:

At the beginning of the lesson, I used the suggestion of Mr. Brilliant, through the students' demonstration of the paper dragonflies made by their own hands, revealing examples of rotation in life, so that the children have a preliminary epistemological understanding of the process of rotation of shapes, so that the connection between life and learning mathematics, and fully mobilized the students' interest in learning mathematics.

(next to play the courseware): show a set of patterns, are obtained from simple shapes by rotation. In my teaching design just let the students appreciate the beautiful patterns, but through my trial, found that the students for the rotation angle of mastery does have some difficulty, part of the students appeared to be confused, so I feel that the teaching of this lesson again, in the appreciation of the picture at the same time to guide the students to analyze the angle of rotation of the figure. To break through the difficult points of this lesson to lay the foundation.

In the observation and demonstration of this teaching link, I designed four teaching activities:

1, the demonstration of the textbook 53 pages of the windmill graphics, as animation appeared, so that the students in the discussion, exchange of information on the basis of the process of rotation can be clearly seen. Students are very easy to fill in the blanks on page 53 to do a good job.

2. Demonstration of the 54 page 1 question to strengthen the center and direction of the problem.

3. Demonstrated is the activity on page 54, question 2 on how to determine the angle of rotation.

It is worth noting that: when exploring the method of rotation, one of my friends came up with the question of whether to emphasize counterclockwise rotation, at that time, I was confused, I sought to the door of the brilliant teacher, in the brilliant teacher's guidance, I once again read the textbook carefully, to further understand the intention of the textbook preparation, and to infiltrate this part of the knowledge of the opening and the student demonstration of the dragonfly. Achieved a very good effect.

Rotation of Figures

1. To stimulate interest in learning, through independent study to recognize the meaning of "flip and rotate figures".

2. Master the corresponding processing of the actual graphics, feel the advantages of computer graphics.

3. To further develop students' practical and creative abilities.

Teaching Focus

The use of flip and rotate operations.

Instructional Difficulties

Flipping and rotating graphs and the application of the combined knowledge in practical drawing.

Teaching process:

I. Scenario introduction to stimulate interest

Scenario introduction: spring is here, Xiaoxiao took his beloved windmill to the park to play, and all the flowers, plants, and trees in the park put on a new green coat, can be a spirit! But there is a small tree is crying, Xiaoxiao went up and asked: "small tree, small tree, what's wrong with you?" The tree replied, "Everyone has new clothes to wear, but my leaves haven't grown yet." Xiaoxiao said, "Don't be sad, let me help you."

Question: "How can Smiley help it?"

Students suggest a solution: make green leaves to "dress" the tree.

[Design Intent] Context is an important part of the classroom teaching design, a relaxed, **, active classroom environment, to stimulate students' thinking, cultivate students' ability is quite important.

Second, explore the learning, problem solving

1. old knowledge reproduction:

Teacher: Earlier we have learned to use the curve tool to draw leaves. (show the leaves and trees have been drawn) but the small tree needs a lot of leaves, if one by one to draw the leaves is a waste of time, do we have any fast way ah?

Students answer: copy and paste.

After the teacher gave the affirmation, while the operation of the students to oral copy and paste process.

Move the leaves to the right place and discover the problem. (Transparent, opaque)

[Design intent] Using the old knowledge learned, inspire students to find their own problems, solve their own problems, so that students gradually develop the habit of independently acquiring knowledge and creative use of knowledge.

2. Learning to flip and rotate shapes.

Teacher: We already know that we can use the copy and paste method to add leaves to the small tree, then we look at these two pictures together. What is the difference between these two pictures? (Show)

Name the answer.

Teacher: Which one do you like better? Think about how you can look as good as the little tree on the right.

(Turn the leaf upside down, turn it around, change the direction. ......)

The teacher is sure that the leaf will look good. /p>

The teacher confirmed and pointed out that "we call this kind of treatment of leaves 'flip and rotate'". This feature is available in Paint, so find out where it's hidden. (Hint: look in the menu bar.)

Students try it out and explore independently.

Class exchange: (ask two students to come up to demonstrate, classmate evaluation, teacher evaluation).

Teacher again demonstrated the operation process.

(Tip: available to use the record book to turn over)

Please demonstrate the use of the record book to turn over, point out the wrong place in time.

Classroom relaxation minute.

Students practice.

[Design intent] In response to the problem of contrary to natural phenomena, I allow students to explore the solution to the problem on their own initiative first, and then demonstrate the method of operation. Using the existing resources on the desktop, we practiced flipping and rotating, so that we could accurately understand the difference between "flip" and "rotate" commands.

Third, consolidate new knowledge, complete the task

1, let the students try a variety of flip operation, complete the work. Teacher patrol, timely detection of problems in teaching, help students with difficulties, prompt students, and give affirmation.

2. Students who finish the task in advance can beautify the whole picture.

[Design intent] Further consolidate the new knowledge learned; the purpose of hierarchical teaching is to meet the learning needs of students with different levels of knowledge.

Four, the works of the exhibition, learn to evaluate

Show students work, evaluation. (Self-assessment, mutual assessment, teacher assessment)

[Design intent] This link is more open, can fully mobilize students' enthusiasm and initiative, expanding students' thinking. Through the students' self-assessment, mutual evaluation and teacher review, you can cultivate students' observation, analytical ability and oral expression ability, and improve students' aesthetic appeal.

Fifth, summarize, experience success

Say the harvest of this class.

[Design intent] Teachers and students **** with the summary, further consolidate the knowledge learned, build a complete knowledge system.

Board:

Horizontal Flip

Flip

Vertical Flip

90-degree rotation

Rotation 180-degree rotation

270-degree rotation

A. Speaking of the content of teaching:

Bei Shi Da version of elementary school mathematics, book 7, unit 4, section 1, "rotation of shapes"

Second, the status and role of the teaching materials

I respect the teaching materials on the basis of letting the students in the full experience and appreciation of the rotation of the sense; at the same time for the students to think actively, guiding the students to compare the changes before and after the rotation of shapes, in order to penetrate the The idea of rigid body transformation.

Knowledge Objectives: To understand the process of forming a complex pattern by rotating a simple figure, and to be able to rotate a simple figure by 90 degrees on a grid paper, and to design a pattern using rotation.

Ability Goal: Using observation, manipulation, induction, association and other thinking methods to develop students' abstract thinking ability, the development of spatial concepts.

Emotional objectives: to understand the beauty of mathematics, to cultivate students' interest in learning mathematics and love of life.

Teaching Difficulties: Recognize the rotation of shapes, solve the process of rotating a simple shape to form a complex pattern, and be able to rotate a simple shape by 90 degrees on a grid paper.

Teaching difficulties are: to be able to rotate a simple figure by 90 degrees on a grid paper, and to use rotation to design a pattern.

Third, the teaching method and learning method

Before studying this unit, students only initially feel the life of the phenomenon of translation and rotation, exposure to two kinds of graphic transformation: symmetry, translation. This lesson is to introduce the students' perspective to the third graphic transformation - rotation, intended to appreciate, explore, create a series of activities, so that students experience the process of simple shapes into complex patterns, to understand the rotation of the center point, direction, angle of the formation of different patterns, to further develop the students' spatial concepts, for future

These are the first steps in a series of activities to make students experience the process of turning simple shapes into complex patterns.

Fourth-grade students, image thinking is still dominant in their cognitive process. Therefore, in line with the principle of "operating while feeling", let the students in the experience of the three elements of rotation, feel the graphic rotation brought about by the beauty of the transformation.

Fourth, the teaching preparation

Pictures, small blackboard, grid paper, homemade windmill

Fifth, the process of design:

(a) the game of stimulation, the feeling of the rotation of the figure

This link through the creation of a scenario, the initial feeling of rotation. The use of students preferred scenarios, that is, the windmill, the introduction of beautiful shapes, etc., greatly stimulate the enthusiasm of students to learn. It shows the process of turning a single figure into a complex pattern, which not only makes students feel the beauty of math, but also increases their interest in exploring: how to rotate to get such a beautiful pattern? The real attention to the children's psychological needs, change "to learn" for "I want to learn", so that the smooth into the rotation of the exploration.

(2) hands-on, explore new knowledge.

The graphics in the form of rotation of this difficult point into the exploration of how the windmill is made in the scenario, and then let the students independently discuss this activity to study the graphics of the rotation of the three elements, that is, the center point, the direction of rotation, the number of degrees of rotation. In teaching, I follow the guiding principle of "student-oriented, teacher-led, mathematical activities as the main line" and let students explore on their own. Break through the teaching of important and difficult points.

(C) hands do a do

This link I designed a set of exercises, when the 55 page 1 questions completed, I let the students through the knowledge they just learned, hands on the grid paper, set a beautiful pattern. Let the students hands-on, experience the process of graphic rotation, consolidate new knowledge, the establishment of spatial concepts, promote the development of student thinking.

(D) inspire and guide, expand thinking

Extension, students use the knowledge they have just learned, make their own favorite graphics as well as design a beautiful pattern. Further highlight the difficulties of this lesson, the development of students' imagination, creative ability this.

(E) Summary of the lesson

What did you learn today? Do you have any questions