Lecture Notes on "The Rotation of Figures"

As a conscientious people’s teacher, it is necessary to carefully design a lecture script. With the help of the lecture script, teachers can better improve their theoretical literacy and ability to control teaching materials. How should you write a course manuscript? The following is the lecture notes on "The Rotation of Figures" that I compiled. Welcome to read and collect. "The Rotation of Figures" Lesson Manuscript 1

1. Talking about the teaching materials

(1) The content of the teaching materials

"The Rotation of Figures" is the "Compulsory Education Curriculum Standard" The first lesson of the fifth unit "Movement of Figures" in Experimental Textbook Mathematics for Grade 5, Volume 2.

(2) The status and role of teaching materials

This part of the teaching material "Rotation of Figures" is a preliminary understanding of the rotation phenomenon in life in the second volume of the second grade "Translation and Rotation". It can more accurately determine whether the motion phenomenon of an object is "translation or rotation" and further clarify the meaning of rotation, explore the characteristics and properties of rotation, and let students learn to rotate simple graphics by 90° on graph paper. It is an important knowledge point in the field of space and graphics. It is a penetration into the development of students' spatial concepts. It is the basis for subsequent learning of central symmetrical figures and the drawing of rotated figures. It plays a connecting role in the teaching materials. At the same time, rotation is also widely used in daily life, and using rotation can help us solve many practical problems.

(3) Talking about learning objectives

Based on the above analysis of teaching materials and academic situation analysis, I think we should further develop students’ abilities of observation, induction, generalization, etc., and develop students’ ability to learn in an orderly manner. Thinking and language expression skills. To this end, I think this lesson should focus on students' exploration of the characteristics of rotation, consciously cultivate students' practical, reasoning, and induction abilities to truly understand the characteristics of rotation.

Therefore, based on the above analysis and course standard requirements, I set the learning goals 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. Be able to rotate a triangle 90° on graph paper to further understand the characteristics of rotating graphics during the rotation process.

(4) Talking about the key points and difficulties of learning

This lesson is related to specific situations, allowing students to observe the process of the hands of the clock face rotating, and understand how objects rotate clockwise and counterclockwise. The clockwise direction rotates, so clarifying the meaning of rotation and clarifying "which point the pointer rotates around", "in which direction it rotates" and "how many degrees it rotates" become the focus of this lesson. Exploring the characteristics of figure rotation is the difficulty of this lesson. Only by realizing that "the shape and size of figures do not change after the figure is rotated, but the position changes" can the research and refinement of the rotation method become an independent activity, and at the same time provide a basis for painting. Lay a solid foundation for the rotated graphics.

2. Lecture teaching method

According to the content and arrangement characteristics of this lesson's teaching materials, according to the students' cognitive rules, and following the guiding ideology of learning first and teaching later in the efficient classroom, I mainly adopted Teaching methods include self-study interactive discussions and teacher feedback exercises. In this way, students can achieve the purpose of perceiving new knowledge, summarizing new knowledge, applying new knowledge, consolidating and deepening new knowledge.

In terms of guidance on method study, I adopt the method of allowing students to independently explore, observe and discover, and cooperate and communicate. Encourage students to actively participate in teaching practice activities, in the form of independent thinking and mutual communication, and summarize the characteristics of graphic rotation under the guidance of teachers. When guiding exploration, students are given enough thinking time and space to allow students to associate, Exploration, in the true sense, completes the self-construction of knowledge. In addition, during the teaching process, I use multimedia-assisted teaching to visually present teaching materials, thereby better stimulating students' interest in learning, increasing teaching capacity, and improving teaching efficiency.

3. Teaching process

(1) Create situations and introduce new lessons

The first step is the process of introducing new knowledge. I first show pictures in the courseware, Let students discover the transformation-rotation of graphics by observing pictures. The teacher's camera reveals the subject.

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

Blackboard writing topic: Rotation of graphics

[Design intention: Introducing familiar things in students’ lives to enable students to perceive the phenomenon of rotation and establish the representation of rotation. ]

(2) Self-study interaction

This link is the focus and difficulty of this lesson. In order to highlight these key points and disperse these difficulties, I carefully designed the teaching process and mainly guided students to learn through these steps, namely: (1) Understand the meaning of rotation and know the three elements of rotation. ⑵ Understand the rotation of graphics and explore the characteristics of rotation.

1. First, let students talk about what other examples of rotation they have seen in life?

Design intention: Through life examples, students can initially understand the rotation transformation of graphics.

2. Then let students observe the pictures, and then discuss in groups what similarities the rotation phenomena have. Student reporter writes on camera and blackboard.

Teacher writes on the blackboard: Rotation center Rotation direction Rotation angle Clockwise Counterclockwise

Design intention: Experience the phenomenon of rotation and initially understand the three elements of rotation to pave the way for learning Example 1.

3. Observe and describe the rotation phenomenon

Work in groups, carefully observe the rotation process of the pointer and complete the three sentences below Example 1.

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

Use one sentence to completely describe the rotation process of the pointer. The teacher guides the students to describe the complete description: the pointer goes from "12" to "1" Rotate 30 degrees clockwise around point O.

Show: the pointer rotates 30 degrees clockwise around point O from "12" to "1".

(Show animation: the pointer points from 1 to 3) Consolidate the description of the pointer's rotation process: the pointer rotates 60 degrees clockwise around point O from "1" to "3". .

(Show animation: the pointer points from 3 to 6)

Then, through the knowledge transfer analogy, students at the same table are asked to independently describe the rotation process of the pointer

Then deepen the knowledge , if the pointer continues to rotate 180 clockwise around point O from "6". Where will it point?

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

Summary, clarify the elements of rotation

Guide students to summarize the meaning of rotation.

[Design intention: Make full use of multimedia courseware demonstrations to strengthen intuitive teaching, allowing students to deepen their understanding of the meaning of rotation and reduce the difficulty of understanding. Guide students to conduct inductive reasoning and draw conclusions through direct observation of a specific example "the rotation of clock hands", interactive communication between teachers and students. Highlighting the three elements of rotation allows students to consolidate and understand the meaning of rotation in a timely manner, optimize students' cognitive structure, improve their knowledge system, and enable students' mathematical understanding to once again break through the difficulties of thinking. ]

2. Understand the rotation of graphics and explore the characteristics and properties of rotation

First, I let students observe the theme map of Example 2.

Then work together in groups to fix the right-angled triangle ruler on the graph paper and rotate the triangle 90° clockwise around point O every time

Observe the triangle ruler after each rotation How did the 'position change?

Students report the results.

Finally, the characteristics of rotation are revealed: after the triangle is rotated, the position of each triangle has changed, but the shape and size of the triangle have not changed; the position of point O has not changed.

Students have initially constructed knowledge about the characteristics of rotation, but they are not yet mature, so they are working on it while it is still hot

I designed another triangle ruler and pressed it on the graph paper. Turn counterclockwise like above and say something. Where should the triangle turn?

Design intention: Modern mathematics teaching theory points out that the process of thinking must be shown in teaching, and students should be allowed to explore independently and summarize experience. Here, I let students work in groups to learn, and the cooperative and exchange activities are An active learning activity. In the process of this activity, students conduct independent research and exploration, and teachers and students communicate with each other. At the same time, the teacher guides students to think and express in an orderly manner, cultivates students' logical thinking ability, and guides students to summarize the principles of graphic rotation. feature. Further consolidate this teaching difficulty so that students can fully understand and master it.

(3) Compliance assessment

This link mainly allows students to consolidate new knowledge

Design intention:

(4) Full Lesson summary.

What knowledge have you learned through studying this class?

Design intention: Summary summary should not be just a simple list of knowledge, but 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, from the learned knowledge , methods and experiences are summarized. "The Rotation of Graphics" Lecture Note 2

Dear leaders, judges, teachers and all online friends:

Hello everyone!

I am very happy to participate in this lecture contest! After choosing this course, I felt a little bit confused. This part of the content is not included in traditional textbooks, and it is also a course for which there are few or almost no sources of information found online. I am also very stressed, but I am lucky. , with the help of my friends, I have a clear understanding of how teachers should guide students and teach in this field of knowledge. This is my real gain! I sincerely thank all the teachers and friends who helped me. I think the highlight of today’s lecture comes from the sparkle of their wisdom...

The content of my lecture is the fourth grade textbook of Beijing Normal University. The first lesson of the fourth unit "Transformation of Figures" in the first volume "The Rotation of Figures"

First, let me talk about my understanding of the teaching material and my children:

"The Rotation of Figures" It belongs to the field of "space and graphics" and is the most primitive foundation in the field of space. This period is the sensitive period for children's spatial concept. If this mathematical concept is well developed, the creative ability 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 were very young, they had experience with the movement of objects or graphics. They often did handcrafts such as origami and windmill spinning, from which they accumulated knowledge of graphic transformation. In the third grade, they initially experienced the phenomena of translation and rotation in life. Based on these foundations, this study will focus on developing students' spatial concepts and cultivating students' observation and hands-on abilities based on life experience and perceptual knowledge.

Secondly, let’s talk about the teaching goals and key points that I established:

Teaching goals have three major sources: First, they come from students’ learning needs. The second is from the real life of students. The third is learning materials from textbooks.

1. Knowledge and ability objectives: Understand the process of rotating a simple figure to create a complex figure through example observation.

2. Process and method goals: be able to design simple patterns.

3. Emotional attitude goals: A: Learn to rotate regularly at a certain angle, get beautiful patterns, and learn to appreciate the beauty of mathematics. B: Cultivate observation ability and hands-on operation ability, and develop students' spatial concept.

Teaching focus: Objectives 1 and 2 are difficult to teach.

Finally, let me talk about my teaching process:

At the beginning of the class, I adopted teacher Huihuang’s suggestion and demonstrated the paper dragonflies made by the students to reveal the rotation in life. The examples allow children to have a preliminary understanding of the rotation process of graphics. This way of learning mathematics in connection with life fully mobilizes students' interest in learning mathematics.

(Next play the courseware): Show a set of patterns, which are all obtained by rotating simple graphics. In my teaching design, I just let students appreciate the beautiful patterns, but through my trial lecture Later, I found that it was indeed difficult for students to grasp the angle of rotation, and some students were confused. Therefore, I thought I would teach this lesson again and guide students to analyze the angle of rotation of graphics while appreciating the pictures. Lay the foundation for overcoming the difficulties of this lesson.

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

1. The graphic of the windmill on page 53 of the demonstration textbook appears as an animation, allowing students to discuss, On the basis of communication, the rotation process can be clearly seen. Students easily filled in the blanks on page 53 and did a good job.

2. The demonstration is about question 1 on page 54, which focuses on strengthening the center and direction.

3. The demonstration is about how to judge the angle of rotation in question 2 on page 54.

It is worth noting that when exploring the rotation method, a friend of mine raised the question of whether to emphasize counterclockwise rotation. I was very confused at that time, so I sought the guidance of Teacher Huihuang. Under the guidance of Teacher Huihuang, I read the textbook carefully again, further understood the intention of writing the textbook, and infiltrated this knowledge into the opening chapter when I demonstrated the dragonfly with the students. Achieved very good results. "The Rotation of Figures" Lecture Note 3

Teaching Objectives

1. Stimulate interest in learning and understand the connotation of "flipping and rotating figures" through independent learning.

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

3. To further develop students’ practical and innovative abilities.

Teaching focus

The operation of flipping and rotating.

Teaching difficulties

Flip and rotate graphics and the application of comprehensive knowledge in actual drawing.

Teaching process:

1. Scenario introduction to stimulate interest

Situation introduction: Spring is here, Xiaoxiao takes his beloved windmill to the park to play, the park The flowers, plants and trees here are all wearing new green clothes, so they are full of energy! But there was a little tree with a sad face. It smiled and stepped forward and asked: "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." Smiling Said: "Don't be sad, I'm here to help you."

Question: "How should Xiaoxiao help it?"

The student proposed a solution: make green leaves into a small tree "Add clothes".

[Design Intention] Situation is an important part of classroom teaching design. A relaxed, active and active classroom environment is very important for stimulating students' thinking and cultivating students' abilities.

2. Exploring learning and solving problems

1. Reappearance of old knowledge:

Teacher: We have already learned to use curve tools to draw leaves. (Show the painted leaves and trees) But a small tree needs a lot of leaves. If painting leaves one by one is a waste of time, is there any quick method?

Student answer: Copy and paste.

After the teacher gives the affirmation, he asks the students to dictate the copying and pasting process while operating.

Move the leaves to the appropriate position and find the problem. (Transparent, opaque)

[Design Intention] Use the old knowledge learned to inspire students to discover and solve problems by themselves, so that students can gradually develop the habit of independently acquiring knowledge and using knowledge creatively.

2. Learn to flip and rotate graphics.

Teacher: We already know that we can use copy and paste methods to add leaves to small trees. Next, let’s take a look at these two pictures. Compare, what is the difference between these two pictures? (Show)

Answer by name.

Teacher: Which one do you like better? Think about it, how can you make it look as beautiful as the little tree on the right?

(Turn the leaves over, turn them around, change directions...)

The teacher affirmed and pointed out, "We call this kind of processing of leaves 'Flip and spin'". There is this function in Paint, where is it hidden? (Tip can be found in the menu bar)

Students try the operation and explore independently.

Whole class communication: (ask two students to come up to demonstrate, classmates evaluate, teacher evaluates).

The teacher demonstrated the operation process again. (Explain while operating)

Show several different flip effects, and discuss the differences between them among deskmates.

(Tip: Please flip through the notebook when using it)

Ask students to demonstrate using the notebook and point out any mistakes in a timely manner.

Relax in class for a minute.

Student practice.

[Design Intention] For problems that violate natural phenomena, I let students first actively explore ways to solve the problems themselves, and then demonstrate the operation methods. Use the existing resource of the notebook on the table to practice flipping and rotating, so as to accurately understand the difference between the two commands "flip" and "rotate".

3. Consolidate new knowledge and complete the task

1. Let students try various flipping operations to complete the work. Teachers patrol, discover problems in teaching in a timely manner, help students with difficulties, remind students, and give affirmation.

2. Students who complete the task in advance can beautify the entire picture.

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

4. Work exhibition and review, learn to evaluate

Show students’ works and give them a review. (Self-evaluation, mutual evaluation, teacher evaluation)

[Design Intention] This link is relatively open, which can fully mobilize students' enthusiasm and initiative and expand students' thinking. Through students' self-evaluation, mutual evaluation and teacher comments, students' observation, analysis and oral expression skills can be cultivated, and students' aesthetic taste can be improved.

5. Summarize and experience success

Talk about the gains from this class.

[Design Intention] Teachers and students summarize together to further consolidate the knowledge learned and build a complete knowledge system.

Writing on the blackboard:

Flip horizontally

Flip

Flip vertically

Rotate 90 degrees

Rotation 270 degrees "Rotation of Figures" lecture notes 4

1. Teaching content:

Beijing Normal University version of primary school mathematics Volume 7, Unit 4, Section 1 "The Rotation of Figures"

2. The status and role of teaching materials

On the basis of respecting the teaching materials, I allow students to fully experience and Understand the rotation while appreciating it; at the same time, according to the characteristics of students' active thinking, guide students to compare the changes of figures before and after rotation to penetrate the idea of ??rigid body transformation.

Knowledge goal: Understand the process of rotating a simple figure to form a complex pattern, and be able to rotate a simple figure 90 degrees on graph paper and use rotation to design patterns.

Ability goal: Use observation, operation, induction, association and other thinking methods to cultivate students' abstract thinking ability and develop spatial concepts.

Emotional goals: to appreciate the beauty of mathematics, to cultivate students’ interest in learning mathematics and their love for life.

Teaching difficulties: Understand the rotation of graphics, understand the process of rotating a simple graphic to form a complex pattern, and be able to rotate a simple graphic 90 degrees on graph paper.

The teaching difficulty is: being able to rotate simple graphics 90 degrees on graph paper and use rotation to design patterns.

3. Teaching and Learning Methods

Before studying this unit, students only had a preliminary experience of the translation and rotation phenomena in life, and were exposed to two ways of graphic transformation: symmetry, Pan. This course introduces students' perspective to the third type of graphic transformation - rotation. It is intended to enable students to experience the process of turning simple graphics into complex patterns through a series of activities such as appreciation, exploration, and creation, and understand the center point of rotation, Different directions and angles result in different patterns, which further develops students' spatial concepts and lays the foundation for continuing to learn graphic transformations in the future.

For fourth grade students, image thinking still dominates their cognitive process. Therefore, it is necessary to adhere to the principle of "perceiving while operating", allowing students to experience the three elements of rotation through experience and feel the beauty of transformation brought about by the rotation of graphics.

4. Preparation for teaching

Pictures, small blackboard, graph paper, homemade windmill

5. Process design:

（ 1) The game is exciting and you can feel the rotation of graphics

In this link, you can initially experience the rotation by creating scenarios. The introduction of students' favorite scenes, such as windmills and beautiful graphics, greatly stimulates students' enthusiasm for learning.

It shows the process of turning a single figure into a complex pattern, which not only makes students feel the beauty of mathematics, but also arouses interest and makes students have a desire to explore: How to rotate to get such a beautiful pattern? Really pay attention to the psychological needs of children, change "I want to learn" to "I want to learn", and thus smoothly enter the exploration of rotation.

(2) Hands-on operation and exploration of new knowledge.

Integrate the difficulty of the rotation of graphics in tables into the scenario of exploring how windmills are made, and then let students independently discuss the three elements of graphics rotation studied in this activity, namely the center point and the direction of rotation. , the degree of rotation. In teaching, I follow the guiding ideology of "taking students as the main body, teachers as the leader, and mathematical activities as the main line" and let students explore by themselves. Breaking through the heavy and difficult aspects of teaching.

(3) Do it by hand

In this link, I designed a set of exercises. After completing question 1 on page 55, I asked the students to practice the knowledge they just learned. On the graph paper, place a beautiful pattern. Allow students to operate and experience the process of graphic rotation, consolidate new knowledge, establish spatial concepts, and promote the development of students' thinking.

(4) Inspiration and guidance, expansion of thinking

Expansion and extension, students use the knowledge they have just learned to make their favorite graphics and design beautiful patterns. Further highlight the difficulties of this lesson and develop students' imagination and creative abilities.

(5) Summary of this lesson

What did you learn today? Do you have any questions