As an excellent people’s teacher, it is necessary to prepare detailed lecture notes, which will help to carry out teaching activities smoothly and effectively. So how should the course manuscript be written appropriately? The following is a sample course script of "Understanding of Cylinders" that I compiled for you. It is for reference only. You are welcome to read it. "Understanding of Cylinders" Lecture Notes 1

1. Teaching Materials

"Understanding of Cylinders" is the learning content of the third unit of the second volume of the sixth grade primary school published by the People's Education Press, which belongs to space and In the graphics field, students have a preliminary perceptual understanding of cylinders in the lower grades and can identify cylindrical objects. Based on the study of plane figures such as circles and three-dimensional figures such as cuboids and cubes, this class further explores geometric shapes with curved surfaces - cylinders. This part of teaching is conducive to further developing students' spatial concepts and laying the foundation for further learning about the lateral area, surface area, and volume of cylinders and solving practical problems. Senior students already have strong abilities in independent thinking and hands-on operation. Based on the analysis of the teaching materials and the students’ understanding, I determined the following teaching goals:

2. Teaching goals

1. Understand the cylinder, understand the names of its parts, and master the characteristics of the cylinder.

2. Understand the shape of the expanded view of the side of the cylinder, and understand the relationship between the expanded view and the cylinder.

3. Through activities such as looking at, touching, and cutting, develop students’ image thinking and cultivate students’ spatial concepts and hands-on abilities;

Teaching focus: understanding Cylinder, understand the names of each part of the cylinder, and master the characteristics of the cylinder.

Teaching difficulties: Understand the shape of the expanded view of the side of the cylinder, and understand the relationship between the length and width of the expanded view and the cylinder.

3. Teaching method, learning method

This lesson will use the observation method, starting from intuitive objects, so that students can understand the shape of the cylinder: using practical operation methods, so that students can understand The expanded view of the side of a cylinder is a rectangle, and the relationship between its length and width and the circumference and height of the base of the cylinder. If the above teaching methods are implemented, students will explore independently during learning and use group cooperation and communication methods to truly understand the cylinder

4. Talking about the teaching process

For effective implementation In order to achieve teaching goals and break through the important and difficult aspects of teaching, I designed the following six teaching links:

1. Create situations and introduce topics

Students: Before class, I asked everyone to Looking for the cylinder, have you found it? Who wants to talk about it. The classmates all talked about the cylinders they saw in life (tea cups, medicine bottles, pencils, pillars). There are so many cylinders in life! Today we will study cylinders together.

Blackboard writing topic: understanding of cylinders. My design intention is to let students connect with life and talk about the cylindrical objects they see, so that students can realize that mathematics is everywhere in life.

2. Independent learning and preliminary understanding. I adopt the method of student self-study and let students combine the content on page 18 of the self-study textbook that comes with them. Let students think about it while reading:

(1) What are the characteristics of the upper and lower surfaces of the cylinder? What's it called?

(2) What is the height of a cylinder? What are its characteristics?

(3) What are the sides of a cylinder? Then let the students communicate in the group, and finally the whole class communicates, reports, organizes and writes on the blackboard:

Two equal circular surfaces are the bottom surfaces of the cylinder;

Surrounded by a curved surface called a cylinder Side;

The distance between the two bases is the height of the cylinder. The cylinder has an infinite number of heights.

Students read the textbook based on the physical objects in their hands, initially understand the names of the various parts of the cylinder, and establish the concepts of base, height and side. Based on students' full thinking, they then communicate and further deepen their understanding of the cylinder. understanding.

3. Guide participation and in-depth exploration

(1) Explore whether the two bases of a cylinder are equal: After students pass the operation, they may make the following statements: Cut out the two circles and compare them ;Measure their diameters or radii for comparison; use the circumference of the upper and lower bottom surfaces of the coil to compare, etc. Combined with the first-grade understanding of cylinders and intuitive operations, we can more accurately draw the conclusion that the areas of the two bases of the cylinder are equal.

(2) Explore that the cylinder has countless heights: first let the students talk about how they prove that the heights of the cylinders are equal. (Students may prove it by measuring or using the equal distance between two parallel bases.) Then show that there are countless heights by showing the demonstration of the course material.

(3) Explore the expanded view of the side of the cylinder:

A. Guess: If you expand the side of the cylinder, what shape will you get? This link allows students to first guess what shape the side of a cylinder will be when unfolded, cultivating students' reasonable guessing and spatial imagination abilities.

B. Cut and cut: Students cut the side of the cylinder and unfold it to see what shape they can get. In this link, I did not emphasize asking students to cut along the height. Instead, I let students cut according to their own ideas. Most students got a rectangle after unfolding, and some students said it was a parallelogram or a square. I promptly affirmed and Let him tell you how to cut it. And guide students to discover that no matter how the side is cut, the resulting figure can be transformed into a rectangle through the method of cutting and patching. A square is a special rectangle. In this way, students gradually establish the connection between three-dimensional figures and plane figures by personally experiencing the transformation between three-dimensional figures and their unfolded figures, and further develop the concept of space.

C. Discussion: Then let students observe and discuss in pairs what is the relationship between the expanded graphics and the cylinder? During the inspection, we found that some students used the rolling method, and some used the measurement and calculation method. During the exchange, the students mastered that the length of the rectangle obtained by unfolding the side of the cylinder is equal to the circumference of the base of the cylinder, and the width is equal to the height of the cylinder. If the sides are expanded into a square, then the height of the cylinder is equal to the circumference of the base. In this link, students gained a deep understanding of cylinders through hands-on operations, group cooperation, and other independent exploration activities, which not only highlighted the teaching focus but also broke through the difficulties. It also improves students' interest in learning and awareness of cooperation and communication, allowing students to develop their spatial concepts, emotional values, etc.

4. Consolidate practice and strengthen new knowledge

Practice is an important part of mastering knowledge, forming skills, and developing intelligence. According to the age characteristics and cognitive rules of students, in the spirit of thinking and The principle of comprehensiveness, from easy to difficult, from shallow to deep, strives to reflect the vertical and horizontal connections of knowledge. I designed the following exercises:

　(1) Determine which of the following are cylinders, and point out the base, sides and height of the cylinder. This exercise is to consolidate the names of the various parts of the cylinder so that students can point out the base, sides and height of the cylinder in different placements.

(2). Here are some round surfaces and rectangles that can be used to make cylinders. Which ones can be used to make cylinders? How many different shapes of cylinders can be made? This exercise is to consolidate the knowledge that the length of the unfolded side view of a cylinder is equal to the circumference of the base, and to realize that cylinders of different shapes can be formed by curling the sides in different ways, and the corresponding size of the base will also change accordingly.

5. Classroom Test

Judgment: mark “√” if correct, “×” if wrong

6. Summary of the whole lesson

The classroom leaves more space for students to have independent thinking, hands-on operations, cooperation and communication, which improves the effectiveness of independent inquiry. Let students conduct self-study based on physical reading teaching materials, make good use of the teaching materials, and use several methods such as "take a look," "touch," "discuss," and "cut to cut" throughout the student learning process. Activities are connected together to make the entire teaching process form a dynamic teaching whole. The teaching of "height of a cylinder" is also a focus of this lesson, and this link should be treated in more depth. During class, students should be allowed to personally measure the height of the cylinder in their hands. This not only allows students to experience that there are countless heights, but also knows that it is more convenient to measure the outer height. It also lays the foundation for the practical homework assigned later. "Understanding of Cylinders" Lecture Notes 2

1. Teaching materials

(1) Analysis of teaching materials:

The understanding of cylinders in this lesson is a section of geometry Knowledge lesson, it is a relatively common three-dimensional figure, including the characteristics of the cylinder, the names of the various parts of the cylinder and the expanded view of the side of the cylinder. This part of teaching is conducive to further developing students' spatial concepts and laying the foundation for further learning about the lateral area, surface area, and volume of cylinders and solving practical problems.

(2) Teaching objectives

1. Knowledge objectives enable students to understand the cylinder, master its characteristics, and understand the names and side expansion diagrams of each part of the cylinder.

2. Ability goals:

(1) Through observation of common cans, logs and other physical objects, students can understand the shape of cylinders and abstract cylinders from real objects. geometric figures.

(2) Through observation and touch, we know that the side of the cylinder is a curved surface. Develop the side of the cylinder into a rectangle, square, or parallelogram, and test the relationship between each side of the expanded shape and the perimeter and height of the base of the cylinder.

3. Moral education goal: Cultivate students’ ability to help each other and cooperate with each other.

Teaching focus: Characteristics of cylinders

Difficulty: Abstract the geometric shape of a cylinder from the real thing.

2. Teaching method, learning method

This lesson will use a variety of teaching methods, using observation methods, starting from intuitive objects, so that students can understand the shape of the cylinder: use demonstrations Use the introduction method to let students know the names of each part of the cylinder; use the practical operation method to let students understand that the side expansion of the cylinder is a rectangle, and the relationship between its length and width and the circumference and height of the base of the cylinder. If the above teaching methods are implemented, students will independently explore and use group cooperation and communication methods to truly understand the cylinder during learning.

3. Teaching process design

My design should not only focus on the cultivation of students’ knowledge and skills, but also pay attention to students’ learning processes and methods, emotions, attitudes and values. Based on the teaching ideas formed, I have carefully designed the following main links for the teaching of this course.

(1) Introduction of new lessons

I adopted the review method to introduce new lessons

I took out some cuboids and cubes that I prepared before class. Ask students to determine what shape it is and what characteristics it has? After the students answered, I designed a question like this: If the upper and lower faces of the cube were changed into cylindrical shapes, what would you imagine it would look like? Ask the students to close their eyes and imagine. Then, the teacher will demonstrate the graphics on the computer. The students will open their eyes and see. Which of the graphics on the screen matches your imagination? Verify whether the students' imagination is correct. The figure marked with a √ is the geometric shape cylinder we are listening to today. Blackboard writing topic: understanding of cylinders.

(2) Explore new knowledge

1. Perceive the characteristics of the cylinder and recognize the names of each part of the cylinder

Let students take out the cylindrical shape prepared before class Objects, you can understand the characteristics of the cylinder through multiple senses such as looking at it, touching it, and thinking about it. (First observe and think independently, then study and discuss the characteristics of the cylinder in groups, and then communicate in groups) When students explore, the teacher shuttles between groups, either guiding or listening

2. Report the results of the communication ( Each group recommends a lifetime report, and the teacher chooses to write on the blackboard based on the students’ reports)

3. Prove that the students’ discussion results are correct through demonstrations and strengthen students’ intuitive understanding.

4. Understand the side expansion diagram of a cylinder

The teacher set a question: Students, do you know what the side expansion diagram of a cylinder is? Would you like to work in groups and answer the teacher's questions? Ask the students to use the cylindrical object with the trademark paper given to you by the teacher to conduct research. Which group makes more discoveries?

The teacher does not emphasize that students should cut along a high line. Three situations may occur

①Cut along a line segment to obtain a rectangle

②Cut along a line segment Cut it and get a parallelogram

③Tear it apart with your hands and get an irregular figure

You can get a rectangle by cutting and spelling parallelograms and irregular figures. Students observe what parts of the cylinder the length and width of the rectangle obtained by unfolding the side of the cylinder are related to? What does it matter? Does the demonstration prove that the students’ scientific research results are correct?

5. Questioning after reading the book

Students open page 31 of the textbook, read pages 31 and 32, and ask what they don’t understand. Students solve key problems with each other and provide guidance and guidance to the teacher.

6. Feedback exercises to consolidate new knowledge

① Display (point out the base, sides and height of the following cylinders)

② Point out the cylindrical object on your desk The base, sides and height of The length of the cylinder is (), the side of the cylinder is expanded to obtain a () shape, the length of the rectangle is equal to (), the width of the rectangle is equal to the cylinder ()

(3) Summary at the end of the lesson:

The students are great and work well in groups. I used the stimulated discussion method, and the results of the discussion and research were very correct. What did you gain from studying this class? I hope that students will observe more on weekdays and use the knowledge they have learned to solve practical problems around you. "The Understanding of Cylinders" Lesson Note 3

1. Teaching materials

(1) The understanding of cylinders is the content of the twelfth volume of primary school mathematics published by the People's Education Press. Students in the first grade have already Intuitive understanding of objects such as cylinders through real objects. This lesson is based on learning some plane figures such as rectangles, circles, squares, and rectangular, cube, and cube figures, and further explores the basic characteristics of geometric cylinders containing curved surfaces. It is a good choice for students Further develop the concept of space and learn the basic knowledge necessary for the surface area of ??a cylinder.

(2) Teaching objectives

(1) Knowledge and skills: Understand the names, characteristics and lateral expansion diagrams of each part of the cylinder, and be able to judge and make a cylinder model based on the expansion diagram.

(2) Process and method: In the activity of making a cylinder, further explore the characteristics of the cylinder, understand the relationship between the side and the bottom of the cylinder, and cultivate students' spatial concepts and hands-on ability.

(3) Emotions and attitudes: Experience the close connection between columns and daily life. Through cooperation among students in making columns, we can make progress together and experience success.

(3) My teaching philosophy is:

The sixth-grade students already have preliminary life experience in understanding the cylinder, but their perceptual understanding of the side expansion diagram of the cylinder is not rich enough. It is a leap in cognition. In order to break through this difficulty, I treat students as discoverers. They first understand intuitively, and then make cylinders by hand, allowing students to use their eyes, mouth, and hands to participate in the formation process of new knowledge, and guide students to "do it." math".

(4) My teaching tools for this lesson are as follows:

Each group prepares a compass, two pieces of colored cardboard, a pair of small scissors, and glue. Students bring their own cylinders Items etc.

2. Preaching method.

I will take students as the main body during the entire class, give full play to the teacher's guiding and organizational role, and use the following teaching methods to organize teaching.

①Situational teaching method; ②Inquiry and discovery method; ③Activity experience method.

3. Explain the method of learning.

Modern teaching theory emphasizes that teaching students to learn is a basic task of teaching. In order to implement the concept of students as the main body and teachers as the leader in teaching, I use the following learning method to organize teaching.

① Observation operation method; ② Cooperation and communication method.

4. Explain the teaching process.

Based on the above teaching concepts, I have designed the following teaching links:

1. Create situations and introduce topics.

2. Independent learning and preliminary understanding.

3. Hands-on operation to deepen knowledge.

4. Practical application, expansion and extension.

(1) Let’s talk about the first step: creating situations and introducing topics

As soon as the class started, I used courseware to show a large number of cylinders in life for students to appreciate and ask questions. Ask students, there are so many columns in our lives! Why are they designed to be cylindrical? At this time, students will speak one after another. Some students may say: because cylinders are more beautiful; some students may say: design rollers and wall brushes to make cylinders easy to roll, etc. The creation of such problem situations arouses students' interest and stimulates their thirst for knowledge. I took this opportunity to introduce the topic: today let us study cylinders together. Topic: Understanding of cylinders.

(2) Next, enter the second link: independent learning and preliminary understanding.

I asked the students to take out the prepared cylinders, touch them, compare them, and talk about them to arouse their existing knowledge and experience of cylinders and understand the differences between cylinders, cuboids, and cubes. The student’s language describes the characteristics of each part of the cylinder:

Two equal circular surfaces are the base of the cylinder, surrounded by a curved surface called the side of the cylinder. The distance between the two bases is the height of the cylinder. .

In this link, students have a preliminary understanding of the cylinder, a concrete perception, and an understanding of the characteristics of each part of the cylinder.

(3) The next step is hands-on operation and deepening of understanding.

This is an important step. I ask students to make their own cylinder models as required. In this process, I act as an organizer, patrolling and providing guidance, so that students can become the real masters of learning. At this time, I found that some students might do this: use an existing cylinder to first draw two circles, and then roll up the object to make the side; some students would roll the object on the paper for a week, measure the side first, and then Use a compass to draw two circles to make the base; some students rolled the sides first, and then used the sides to draw the base, but found that the drawings were not circles.

After finishing, I asked the students to report and display their works. At this time, students may have the following situation: for example, the side is too small and cannot be covered; the upper and lower bottoms are not the same size.

In this activity, students are allowed to fully experience the conversion between plane and curved surfaces;

The key point is to find that the seams between the side and the bottom are not easy to match;

And then Think about how to make the bottom edge of the side and the bottom surface just fit together.

After the problem was raised, I asked the team that made it better to talk about how to deal with this problem so that the sides and bottom of the cylinder can be just right together. Through students' repeated demonstrations, let students discover and summarize:

(1) The side of a cylinder is a rectangle;

(2) The length of the rectangle is equal to the circumference of the base of the cylinder; < /p>

(3) The width of the rectangle is equal to the height of the cylinder.

Then I asked the students to do calculations based on their knowledge:

The first situation: first make the side, and design the base based on the fact that the length of the rectangle on the side is equal to the circumference of the base of the cylinder.

Second case: Make the base first, and design the side according to the circumference of the base circle being equal to the length of the side rectangle.

Enable students to have a more accurate understanding of the side expansion diagram of a cylinder.

Finally, let the students redesign and do it:

Based on the calculation results, re-measure and make on new cardboard. After students have an in-depth understanding of the characteristics of cylinders, their goals are clearer, their methods are more scientific, and they use mathematical knowledge to solve practical problems. Finally, I will let the students go on stage to show their works, select a group of student works, expand them and paste them on the blackboard, and write the corresponding amounts.

In this link, through independent exploration activities such as hands-on operations, group cooperation, and problem solving, students gained a deep understanding of the cylinder, highlighted key points, and broke through difficulties. Improve students' interest in learning mathematics and awareness of cooperation and communication, and develop their spatial concepts, emotional values, etc.

(4) Practical application, expansion and extension.

In accordance with the spirit of the new curriculum standards and the principle of starting from the shallower to the deeper, and striving to ensure that everyone learns the necessary mathematics, I have divided the practice content into three levels:

1. Basic level: Determine which cylinders are and indicate the base, sides and height of the cylinder. (Through the training of this question, students can further understand the names of each part of the cylinder.)

2. Comprehensive layer: There are some circles and rectangles here. Which ones can be matched to form a cylinder? How many different types of cylinders can be made? (This exercise allows students to once again understand the key point of this lesson: the length of the rectangle expanded on the side of the cylinder is equivalent to the circumference of the base of the cylinder, and the width of the rectangle is equivalent to the height of the cylinder.)

　3. Open layer: In this level of practice, I extend students' exploration positions from classroom to extracurricular, and guide students to actively apply the knowledge and methods they have learned to solve practical problems.

The above is the teaching process of this lesson. This lesson is based on students’ existing life experience, allowing students to use imagination, description, cooperation and communication, from physical observation to hands-on operation to make cylinders, etc. way to understand cylinders and highlight the mathematical concept of "doing mathematics". It also enables students to make progress together and experience success in cooperation.