Lesson plan 1, unit 3, understanding of cylinders, sixth grade mathematics, People's Education Press;
Nine-year compulsory primary school mathematics volume 12 P3 1~32 pages
Teaching objectives:
1, through learning and operation, we can understand the characteristics of the cylinder, the three-dimensional diagram of the cylinder, the height of the cylinder and the unfolded diagram of the cylinder side.
2. Make students form a clear representation of the cylinder, know the cylinder according to its characteristics, know its height, and imagine its side development diagram, so as to cultivate students' spatial concept.
3. Cultivate students' ability to explore and solve problems through activities such as observation, operation, thinking and discussion.
Teaching emphasis: to understand and master the characteristics of cylinder and the side development diagram.
Teaching difficulties: By unfolding the side of the cylinder, students can understand the relationship between the length of the rectangle and the circumference, width and height of the bottom of the cylinder.
Teaching preparation:
Teacher: Courseware, cylindrical model, rectangle (length 30 cm, width 20 cm) and square made of cardboard.
Student: Each student brings a cylindrical object with a side bag, scissors.
Teaching process:
First, create a situation and introduce a topic:
Show a rectangular flag and spin it quickly. Let the students observe: What do you see? (cylinder)
Point out the topic: understanding of cylinders
We got a preliminary understanding of cylinders in the first grade. Today, we will study it further and believe that we will have a deeper understanding of the cylinder.
Second, learn new knowledge.
1. Understand the characteristics of the cylinder.
(1) Observe and compare, and establish the appearance.
Teacher: There are many jars in life. Where have the students seen them?
The courseware shows the cylinder pictures collected by the teacher and abstracts the three-dimensional graphics of the cylinder from the real thing.
(2) Operation perception, summarizing the characteristics of the cylinder.
Teacher: What are the faces of a cylinder? What are the characteristics of these faces? Next, we will use the prepared cylinder to study it by looking, touching and rolling. Focus on solving the following problems: (courseware display)
What faces does a cylinder consist of? What are the characteristics of these surfaces?
Are the upper and lower surfaces of the cylinder the same size? Please verify it by measurement and comparison.
After the activity is completed, report and exchange, and the teacher writes and guides on the blackboard in time to get the composition and characteristics of the column.
2. Know the height of the cylinder
Look, teacher, here are two columns. Note that their backgrounds are the same, so what's the difference? So what is the height of the cylinder? What do you think the height of a cylinder means? Who can point?
The courseware explains that the distance between the two bottom surfaces of a cylinder is called height.
Ask the students to point out a few more heights. There are countless experiences. And guide the students to understand that there is also a height inside. And use courseware to demonstrate that the height and length are the same. Courseware shows that there are countless columns of the same height and length.
Introduce different names of cylinder height in life.
Practice in time (courseware demonstration)
The children solved these problems easily. Seeing how great you are, the little pillar in the teacher's hand can't help asking you a favor. It wants to know how big the side wrapping paper is on it. What should I do?
3. Study the side development diagram of the cylinder.
(1) Thinking: How do you want to cut it? What shape will it be after cutting and unfolding? Think about it.
(2) Group cooperation and inquiry: (Courseware display and inquiry requirements)
(3) Report to the group after the activity. (Ask two groups of students to go up and explain while demonstrating. The teacher will ask questions and write them on the blackboard. ) The length of a rectangle is the circumference of the bottom of the cylinder, and the width is the height of the cylinder.
(4) The teacher demonstrates the operation, and sticks the profile on the blackboard.
(5) Courseware demonstrates the whole process so that students can understand and digest the whole process.
(6) Thinking: Is it possible that the side development diagram of a cylinder is square? When is a square? (Demonstration with square paper)
Summary: If the side of the cylinder is cut along the height, it will be rectangular or square; if it is cut obliquely, it will be parallelogram; if it is cut or removed along the broken line, it will be irregular.
In this lesson, we not only know the characteristics of cylinders, but also study the lateral expansion of cylinders. What is the learning effect of students? Let's look at ourselves.
Third, consolidate the practice.
1, concept discrimination
2. Identification (this is the development diagram of the cylinder)
Step 3 Create a cylinder
Conclusion: Students, in fact, there is a wonderful mathematical phenomenon hidden in the process of rotating the cylinder just now. Do you want to know? (Point moving into line, line moving into surface, surface moving into volume courseware display) Is it interesting? In the magical world of mathematics, there are many interesting phenomena like this, just waiting for you to explore and discover!
Teaching reflection:
Cylinders are common three-dimensional figures. There are many cylindrical objects in real life, and students have a preliminary understanding of cylinders. Therefore, in the lead-in session, I guide students to connect plane graphics with three-dimensional graphics and feel that "face-moving body" is introduced into new lessons. The focus of this lesson is to understand the characteristics of cylinders. In teaching, I guide students to explore and study the basic characteristics of columns.
In the process of inquiry, I strive to create practical opportunities for students, give them enough time to operate and think, and let them gain rich experience in activities. The activity is divided into two levels: activity one studies the characteristics of the cylinder, so that students can explore the main characteristics of the cylinder by looking, touching and rolling; Activity 2: Explore the side spread. Through this kind of activity experience, let students experience the process of learning mathematics, and let students fully understand, form appearances, observe, compare and explore laws in hands-on operation.
This course belongs to the teaching of space and graphics, and its other important role is to cultivate students' spatial imagination. Therefore, I cultivate students' spatial imagination through multiple links:
1. Introduce a new lesson from a cylinder rotated by a rectangle.
2. Before unfolding the profile, let the students imagine the shape after unfolding, and then operate.
3. In the practice of consolidating the creation of columns, encourage students to boldly imagine and create columns. In order to cultivate students' spatial imagination and develop the concept of space.
People's education printing plate sixth grade mathematics third book cylinder understanding teaching plan 2 teaching content:
Unit 3 P 17- 18 and Do It.
Teaching objectives:
1. Know the cylinder and master the names and characteristics of each part of the cylinder.
2. Be able to establish the geometric model of cylinder and experience the learning method of abstracting graphics from objects.
3. Make students experience the process of operation, observation, comparison and exploration, and improve their ability of analysis, reasoning and judgment.
Teaching emphasis: Understand and master the basic characteristics of cylinders.
Difficulties in teaching: develop the concept of space and master the basic characteristics of columns.
Teaching preparation: cuboid, cube, cylinder, triangle ruler, ruler, study list.
Teaching process:
First, introduce "new" standards-introduce new courses and define goals.
1. Create a situation
The teacher took out the chalk box and asked, "What is this figure?" ? Arouse students to review their existing experience and pave the way for learning new knowledge.
2. Expose the topic and make it clear.
After revealing the topic, inspire the students to think and answer: What do you want to know about the cylinder? Students are free to answer, and the teacher will sort out the questions on the blackboard and grasp the key words to read, write and speak.
Second, explore the "new" according to standards-guide learning according to standards and explore new knowledge.
(1) Self-study-discover cylinders.
1. Find out: Where else have you seen a column in your life?
2. Exhibition: Show the columns in life in kind: thermos cup, lipstick, battery, round pen holder.
3. Take a look and think:
Read the textbook P 17 carefully, focusing on what parts the cylinder is made of. Observe and think:
(1) What are the parts of this cylindrical object, and what are their characteristics?
② What are the shapes of the upper and lower planes of the cylinder?
What do you think are the characteristics of the two bottom surfaces?
Talk about it
Let the students talk about their own thinking results and verify that the upper and lower bottom surfaces of the cylinder are two circles of equal size.
read
A cylinder is surrounded by three faces. The upper and lower sides of a cylinder are called bottom surfaces, and the surfaces around the cylinder (except the upper and lower sides) are called side surfaces. The distance between the two bottom surfaces of a cylinder is called the height.
(B) * * * learning-teamwork, understanding the cylinder
1. Cut it, measure it and discuss it.
Take out your cylindrical model and discuss it in groups of four:
① Circle: Cut your cylindrical model.
② Measurement: measure the radius and diameter of the upper and lower bottom surfaces of the cylinder; And the heights of columns of different sizes.
(3) Say: Tell me what are the characteristics of the two bottom surfaces of the cylinder you found? What is the shape around the cylinder? What does the height of a cylinder have to do with it?
2. Show an exhibition and comment on it
Explain the requirements:
(1) What features do you find on the upper and lower surfaces of the cylinder?
② What is the shape of the surface around the cylinder (except the top, bottom and bottom)?
③ What does the height of a cylinder have to do with it?
Summary: A cylinder is surrounded by three faces. The upper and lower sides of a cylinder are called bottom surfaces, and the surfaces around the cylinder (except the upper and lower sides) are called side surfaces. The distance between the two bottom surfaces of a cylinder is called the height.
4. Explore and expand
Stick a rectangular piece of hard paper on the stick and turn the stick quickly to see what shape it becomes.
Summary: Rectangular cardboard can be turned into a cylinder by rotating quickly around a stick.
Third, the "new" bid evaluation-standard testing, bid evaluation objectives
1. "Do it" on page 18 of the textbook 1
(1) indicates the bottom surface, side surface and height of the cylinder below.
(2) How many bottoms does a cylinder have? What shape is it?
(3) How many sides and how many heights does a cylinder have?
2. Textbook page 18 "Do it" Question 2
(1) Where is the axis of rotation in the diagram 1?
(2) Where is the axis of rotation in Figure 2?
(3) Why does the same rectangle rotate different cylinders?
3. Exercise 3 Question 1
According to your understanding of cylinders, can you accurately determine which of the following figures is a cylinder? Think about why other shapes are not cylinders. What are the characteristics of cylinders?
Fourthly, the extension of the "new" standard-the summary, expansion and extension of the whole library.
What did you learn and gain from this lesson?
Blackboard design:
column
Bottom 2
1 side
As tall as a dragon.
People's Education Press Sixth Grade Mathematics Book 3 Unit 3 Understanding of Cylinders Teaching Plan 3 Teaching Objectives
In the animation hands-on operation, always understand the relationship between the side development diagram of the cylinder and the perimeter and height of the bottom surface, and cultivate mathematical literacy.
Difficulties and difficulties analysis
Focus on the analysis and understanding of the relationship between the side development diagram of the cylinder and the perimeter and height of the bottom surface. It is difficult to understand the relationship between them literally. It is difficult to turn a static picture into a dynamic picture because it requires a certain degree of spatial understanding and hands-on thinking ability.
Difficulties: It is difficult for students to understand the relationship between the side development diagram of the cylinder and the perimeter and height of the bottom surface.
teaching method
1. Through hands-on operation and animation demonstration, understand the relationship between the side development diagram of the building cylinder and the perimeter and height of the bottom surface.
2. Through the close connection between experience cylinder and daily life, empirical mathematics originates from life and is higher than life.
teaching process
First, import
1. Explore the composition and characteristics of each part of the cylinder.
2. What exactly is a cylinder like? (Courseware demonstration)
Second, knowledge explanation (difficult breakthrough)
3. Know the bottom, height and side of the cylinder.
(1) Group cooperation: Explore the composition and characteristics of each part of the cylinder.
Teacher: So what exactly is a cylinder like? (Courseware demonstration)
1. Touch and scroll by hand. What's the difference between a cylinder and a cuboid or cube? What did you find?
② How many faces does a cylinder consist of?
③ Group discussion and verification: What is the relationship between the two bases?
④ What are the characteristics of measuring the distance between the two bottom surfaces of a cylinder?
(2), the group report:
Students operate by hand and communicate in groups.
Teacher: Which group of students will tell you the characteristics of cylinders? How did you verify it?
(Students report, the teacher immediately added)
Group A: It is pointed out that the cylinder consists of three faces, two bottom faces and one side face, and the two bottom faces are equal.
Group B: The cylinder is known to consist of three faces, two bottom faces and one side face.
Group C: Point out the three faces of the cylinder with help.
Health: We know that a cylinder has three faces, and both a cuboid and a cube have six faces.
Health: The upper and lower surfaces are round.
Health: The distance between the two bottoms of a cylinder is the same.
Teacher: Point to the bottom and side of the cylinder with your fingers.
(Blackboard: 2 bottom faces, 1 side faces)
What are the characteristics of these faces of a cylinder?
(3) Observe and compare the characteristics of the cylinder bottom.
Group A: Both bottom surfaces of the cylinder are circles with equal size.
Teacher: How do you know that the two bases are equal?
Preset: cut it out for comparison, measure the diameter, and draw it on paper upside down to see if it coincides. (Ask students to demonstrate and verify separately)
Teacher: Which method is the easiest to verify?
Group A students: Draw on paper and observe it upside down.
(4) Height of cylinder.
Teacher: What happened to the height of the cylinder?
Guide: Which distance represents the height of a cylinder?
Look at the screen The distance between the two bottom surfaces of a cylinder is called the height of the cylinder.
Courseware shows that the distance between two bottom surfaces of a cylinder is called height.
Teacher: Where can I find the height of the cylinder?
According to the students' answers, the courseware displays and flashes colored lines.
Teacher: Can you point out the height of your post?
Teacher's explanation: the height is the distance between the two bottom surfaces and should be perpendicular to the two bottom surfaces.
(5), the cylinder side
(1), organize students to touch the cylinder model, see where the side of the cylinder is, and guess what the shape is after the side is unfolded.
Organize students to operate in groups: cut the side of a cylindrical model and observe it.
Results: group AB: the side of the cylinder was rectangular after deployment.
(2) cut.
What shape is the wrapping paper cut along the side of the can?
(Pay attention to the safe use of scissors)
(6) knowledge summary
A cylinder consists of two identical bottoms and 1 sides. The distance between the two bottom surfaces is the height of the cylinder.
Third, classroom exercises (consolidation of difficulties)
4. Knowledge expansion
(a), the height of the cylinder and other expressions.
Look: A well is cylindrical, and the height of this cylinder can be said to be "deep". A 1 yuan coin is cylindrical, and the height of this cylinder can be said to be "thick". Water pipes are also cylindrical, and the height can also be called "long".
(2) Teacher: Why are tree trunks all cylindrical?
The cylindrical support is large. Canopys are supported by trunks. Especially the fruit-bearing fruit trees, with many fruits hanging on them, need strong trunk support to survive.
The cylindrical trunk has no edges and corners. When the wind blows, no matter which direction the wind blows, it carries dust and debris, and only a small part of it is affected, so it is not easy to be injured by the blast. Therefore, the shape of the trunk is cylindrical, which is the result of trees adapting to the natural environment, the result of long-term evolution and the need to adapt to growth.
Four. abstract
We know a new three-dimensional figure-cylinder, which has several common characteristics: for example, their upper and lower bottoms are completely equal circles, and their sides are rectangular after expansion.
People's education printing plate sixth grade mathematics volume 3 unit cylinder understanding teaching plan 4 teaching goal
1. Make students know the bottom, side and height of the cylinder, master the basic characteristics of the cylinder, and develop students' spatial concept.
2. Let students experience the process of exploring the basic characteristics of cylinders and improve their ability of observation, operation, analysis and generalization.
Focus on the basic characteristics of the cylinder.
The relationship between the lateral area of a difficult cylinder and its expansion diagram.
Teaching methods include observation, analysis and induction.
Analysis of learning situation
Cylinders are geometric shapes that people often encounter in production and life. Students are no strangers to cylinders, but they don't have a deep understanding. Teaching this part is conducive to developing students' concept of space and laying a foundation for further applying geometry knowledge to solve practical problems.
teaching process
First, create situations and introduce new lessons.
Question: What 3D graphics have you studied? (cuboid, cube).
Today, the teacher will teach students to know a new three-dimensional figure-cylinder, or cylinder for short.
Please take out the column you prepared and the teacher will check it.
The teacher also collected some pictures of columns, please enjoy them.
You've also seen those cylindrical objects in your life.
We have known about cylinders since the first grade. What kind of figure do you think is a cylinder? Tell me.
Second, explore new knowledge.
1. Extract the 3D figure of the cylinder from the cylinder picture.
Teacher: What if they are drawn into three-dimensional figures? Want to see it?
Courseware demonstration: abstract a cylinder from a picture.
Q: How many faces can a cuboid and a cube see at most? How many faces can we see in a cylinder?
2. Explore the basic characteristics of the cylinder.
(1) Thinking: What are the upper and lower sides of a cylinder? What's it called?
Students draw a conclusion after observation.
Teacher: Work in groups, using hands and brains.
What are the dimensions of the two bottom surfaces of the cylinder? How do you prove it?
Draw, cut, compare and so on.
(2) What is the difference between fat and thin cylinders? What is the reason?
Let the students discuss and think with each other. The results show that, due to the different radii at the bottom of the cylinder, the cylinder with larger radius is fatter under the condition of equal height.
(3) Thinking: Touch the surface around the cylinder with your hands. What did you find?
Conclusion: It is a smooth surface.
(4) Thinking: What is the distance between the two bottoms of a cylinder? Where is it? How many/much?
The students first draw the height of the cylinder by hand, and then draw the height of the cylinder by crayon. Just try it. How many can you draw?
Whiteboard demonstration, there are countless columns,
3. Expand application and develop new knowledge.
In life, the height of a cylinder has different names, do you know? (whiteboard display)
Thick coins, deep wells and long steel pipes.
Third, consolidate and improve,
1, complete the question 1 of P 18.
Students do it independently and the teacher checks it.
2. Complete the second question of P 18.
Analysis: What are the radius and height of the rectangular bottom? Guide the students to use a rectangular piece of paper to help them understand.
Project summary
What have you learned from today's study? Please use "1, 2, 3, countless" to summarize the content of today's study, ok? Tell me.
Page 13- 14 of the work ability workbook. When you get home, you will understand the memory formula.
blackboard-writing design
Understanding of cylinder
Bottom height
2 1 countless articles
A circular surface of the same size
Teaching reflection
Cylinders are common three-dimensional figures. There are many cylindrical objects in real life, and students have a preliminary perceptual understanding of cylinders. In teaching, I pay attention to the combination with students' real life, so as to lay the foundation for developing students' spatial concept and solving practical problems. In teaching, it is important to understand that a cylinder has countless heights, not just a line connecting two bottom centers. Also let students realize that the three-dimensional figure of a cylinder has only two sides.