First, teaching material analysis:
The calculation of cylindrical lateral area is the learning content of Unit 2, Book 12 of Nine-year Compulsory Education Six-year Primary School Mathematics, and should be taught on the basis that students have mastered the area calculation of rectangles and circles. This part of the study lays the foundation for learning some solid geometry knowledge later. In the textbook, Example 2 and Example 3 are studied together to directly study the surface area of a cylinder. I'm here to separate it, disperse the difficulties and make it easy for students to master.
Second, the teaching objectives:
According to the concept of mathematics curriculum standards, students' learning objectives should integrate knowledge and skills, processes and methods, emotional attitudes and values. In order to implement these points, the teaching objectives of this lesson are as follows:
1, knowledge and skills.
Through imagination, operation and other activities, we can deepen our understanding of the characteristics of the cylinder and understand the meaning of the cylinder lateral area. As we know, after the cylinder is unfolded, the side can be rectangular or square.
2. Process and method.
By guessing, observing and watching videos, students can improve their ability of analysis and generalization, understand the concept of space, and use knowledge to analyze and solve practical problems reasonably and flexibly. Combined with the specific situation and hands-on operation, explore and master the calculation method of cylinder side area, and correctly calculate the side area and surface area of cylinder.
3. Emotional attitudes and values
It is full of exploration and challenges to let students experience mathematics activities personally. Through independent exploration and cooperative exchanges, they dare to express their opinions and benefit from exchanges. Setting teaching objectives through students' own understanding conforms to students' cognitive law of learning mathematics, allowing them to experience the process of solving problems personally, improving their perceptual knowledge of problems, and improving their rational understanding of problems through a series of exercises and calculations. He can flexibly use the calculation method of cylindrical lateral area according to the specific situation, solve some simple practical problems in life and experience the connection between mathematics and life; Cultivate students' ability of observation, operation and imagination, develop students' concept of space, and infiltrate the idea of transformation. It can also cultivate students' good personality, including the innovative spirit of daring to guess and explore, and tenacious learning perseverance.
Third, the teaching emphasis and difficulty:
Lateral area and surface area of cylinder occupy an important position in the teaching material of this course, which is the basis of learning other geometric knowledge. Therefore, the focus of this lesson is to discuss the calculation method of cylindrical lateral area and solve some simple practical problems in life by using the calculation method of cylindrical lateral area.
Because the lateral area calculation of cylinder is abstract, students' spatial imagination is not rich enough, so
The difficulty of this lesson is to understand the diversity of cylinder lateral bulge, and to link the bulging diagram with each part of the cylinder, and to derive the calculation formula of cylinder lateral area. The key to solve this difficulty is: the relationship between the parts of the rectangle obtained by expanding the edges of the cylinder and the parts of the cylinder.
Five, learning methods:
In the learning activities of this class, we should pay attention to cultivating students' spatial concept, imagination, hands-on operation ability, exploration ability and reasoning generalization ability. Therefore, students learn to operate, observe and imagine under the guidance of teachers. Through observation, comparison, reasoning and generalization, fully mobilize students to participate in the occurrence, development and formation of new knowledge, learn to operate, learn to observe, compare, analyze and generalize, and learn to imagine. Get a successful experience in the activity, so as to cultivate students' interest in learning mathematics and achieve the goal of "everyone learns valuable mathematics".
Sixth, the teaching process:
(a) review the old and learn new, cleverly introduced.
In this process, I showed three aspects of review content:
(1) I know the characteristics of a cylinder are
(2) How to calculate the circumference of a circle? How is the area of a circle calculated? Say it, express it in letters.
Do you know how to calculate the area of a rectangle?
The above design allows students to complete the questions one by one in the form of personal report-collective evaluation. Let the students further master the characteristics of the cylinder and review the calculation methods of the circumference and area of the circle and the area of the rectangle. This knowledge is completely related to the calculation of lateral area and surface area of cylinder, which paves the way for the next step to explore the lateral area and surface area calculation method of cylinder. At the same time, it also enables students to understand the relationship between old and new knowledge and fully embodies the consistency of mathematical knowledge.
(2) Set suspense, create inquiry situations, stimulate students' inquiry desire, and lead to the inquiry theme of this lesson.
1, create situations and introduce new lessons.
In our daily life, we often see some cylindrical packaging boxes. This is a cylindrical potato chip box. Now the teacher wants to stick a piece of wrapping paper around him, design it into a beautiful pattern and make it into a small ornament. Is there any way to tell the teacher how big a piece of paper you want? How many square centimeters is the area?
Students discuss and communicate.
Most students can understand and imagine, and then sum up the calculation method of the side area of the cylinder by operating and watching the video.
This design makes students understand the necessity of inquiry, makes students clear the purpose and direction of inquiry, and is challenging and can stimulate students' interest in inquiry.
2. Because of the above inquiry process, students will naturally sum up the calculation method of lateral area of a cylinder: the perimeter of the bottom times the height, that is, the perimeter of a circle times the height. After summing up the formula, ask the students to write it down, read it and show it on the blackboard. Then let the students think: "If lateral area needs a cylinder, what conditions do you need to know?"
3. verification. Is it possible for the unfolded shape to be square? When will it be a square? Teacher: Is that right? Let's verify it together! Please take out a square piece of white paper and see if it can be rolled into a cylinder.
Hands-on verification.
4. Derivative Example 2.
5. Induce new knowledge.
"Do you know how to find the cylindrical lateral area now? Write your research results first, then communicate with your peers, and then show your results to everyone so that everyone can share your success. "
6, contact life, consolidate practice, cultivate ability.
This link is an important link to consolidate the basic knowledge of internalized space, cultivate and expand spatial thinking, form students' ability to feel space, and learn some simple knowledge points about spatial geometry. Therefore, under the premise of paying attention to the application of knowledge, the exercises I designed pay attention to the connection with students' real life, so that students can apply what they have learned to solve practical problems in life. Let them feel the close connection between mathematics and life-mathematics comes from life and acts on life.
(4) Summarize the whole class and promote construction.
This is an essential part of the new curriculum. Through students' own summary and evaluation, it not only deepens students' understanding and digestion of new knowledge, but also makes students experience the value and interest in learning mathematics. Let the students talk about what they learned in this class and how they learned it.
The purpose of this link is to let students have a systematic understanding of what they have learned in this lesson, to cultivate students' ability to sort out knowledge, to guide students to summarize their learning methods, and to achieve the goal of learning to learn.