Textbook analysis
The surface areas of cuboids and cubes are the second lesson of Unit 5 in Book 10 of the People's Education Press textbook. This part of the content is based on students' understanding and mastery of the characteristics of cuboids and cubes.
Teaching objectives:
1. Make students know the surface areas of cuboids and cubes according to the specific situation, and master the calculation methods of the surface areas of cuboids and cubes on the basis of understanding the concepts;
2. Develop students' spatial concept and cultivate their ability of analysis and generalization.
3. Cultivate students' awareness of independent exploration.
Emphasis: Mastering the calculation method of surface area of cuboid and cube can solve simple practical problems.
Difficulties: According to the length, width and height of a given cuboid, it is also the key to determine the length and width of each face.
Second, oral teaching methods
Analysis of learning situation
In the child's heart, there is a deep-rooted need to become a discoverer, researcher and explorer. Curiosity prompted them to try everything themselves. Only through their own exploration and practice can students truly understand what they have learned, and then internalize it for their own use, and gradually learn to learn in learning and practical activities.
Selection of teaching methods:
Teaching activity is a multilateral activity between teachers and students, which is teacher-led and student-centered. The fundamental purpose and task of teacher-led is to better stimulate students' subjectivity, push them to the main position of learning, and let them learn actively. According to the students' age characteristics and cognitive rules, I adopted the inquiry teaching method in this class. The experimental research topic of heuristic teaching method is a new teaching method for teachers to guide students to actively explore new knowledge. The core idea is to teach students to learn and improve their learning ability. It embodies the basic principles of modern teaching theory, conforms to the principles of primary school mathematics teaching, and is an effective method to cultivate students' active learning. By guiding, inspiring and cultivating students to form correct, stable and lasting learning motivation in teaching, we can ignite the spark of hope in students' hearts, constantly stimulate students' desire for knowledge, and make students change "want me to learn" into "I want to learn". At the same time, as far as possible to provide students with good opportunities for exploration and practice, mobilize their various sensory coordination activities, and participate in the process of "discovering" mathematical knowledge.
Teaching means: students operate by hand and cooperate with multimedia courseware demonstration.
Third, talk about procedures.
This part is divided into three classes for teaching. 1 class teaches the concept of cuboid and cube surface area and the calculation method of cuboid surface area. The second lesson teaches the calculation method of cube surface area, and determines its surface area according to the actual situation. The third class is comprehensively applied to improve students' ability to use what they have learned to solve practical problems.
The specific teaching links are as follows:
(A) cleverly set the situation, the introduction of life
"The best stimulus of learning is interest in what you have learned", and students' enthusiasm and initiative in learning are often diverted by their own interests, which is an important factor and internal motivation to promote students' active learning. Because most mathematics knowledge is boring, teachers should make full use of students' curiosity, create situations and stimulate students' interest in learning. Let students collect all kinds of packaging cartons before class, which leads to a new lesson. Firstly, two kinds of packaged facial tissues are displayed, one is beautiful carton packaging, which is generally more expensive, and the other is soft packaging, which is cheap and economical and suitable for ordinary families. But its appearance is not very beautiful. Is there any good way to make it beautiful? Students have come up with ideas to find ways. 1, packed in waste boxes; We can make a beautiful cuboid box of suitable size and put it in it. In this way, there is an urgent problem to be solved: how much cardboard do you need at least to make this rectangular box? This leads to the learning content of this lesson: finding the surface area of rectangular carton.
(B) independent exploration, image perception
The process of hands-on operation is a process of using both hands and brain. In the process of students learning with learning tools, multiple senses participate in learning activities, which can not only deepen students' understanding of knowledge, but also push students to the main position, so that they can take the initiative to do xxx, explore and think. This unit is the beginning for students to learn 3D graphics systematically. Therefore, we should strengthen hands-on operation in teaching, provide intuitive images and attractive perceptual materials. Through a series of exercises xxx, let them experience the process of perception, understanding and generalization of the concepts of cuboid and cube surface area, explore the calculation method of surface area independently, establish a clear representation in their minds and enrich their perceptual knowledge.
1, the concept of surface area of cuboid and cube
Guide the students to unfold the rectangular box and mark six faces in turn. Let the students know how many cardboard they need at least, that is, find the total area of these six faces on the rectangular box and establish the concept of surface area in xxx work.
2. Explore the calculation method of cuboid surface area.
(1) instruct students to measure the length, width and height by hand, try to calculate the surface area through group cooperation, and then report to class. Finally, the calculation method of cuboid surface area is summarized.
In this process, we should pay attention to guiding students to truly understand the relationship between the length and width of each side of a cuboid and the length, width and height through observation and xxx work. Teachers should give guidance and guidance at key points to break through this difficult problem.
(2) After the box is finished, I want to find some beautiful wrapping paper to wrap it directly outside. How much wrapping paper do I need at least if the bottom is not attached? By solving this problem, students realize that sometimes in life, the total area of six faces is not required, but which faces should be calculated according to the actual situation.
(3) Try it: Work together at the same table to find out how much cardboard the rectangular frame needs at least. There are also reports and exchanges.
3. Explore the calculation method of cubic surface area.
After defining the calculation method of cuboid surface area, let the students explore the calculation method of cuboid surface area by themselves through cooperation, and find out how much cardboard the cuboid packaging box needs at least.
4. Asking questions is difficult
Fourth, consolidate practice and expand application.
Mathematics comes from life and serves life. Only through application can students truly understand and master the mathematical knowledge they have learned. Therefore, it is necessary to create opportunities for students to apply mathematical knowledge in practical activities, so that students can come into contact with more mathematical problems in life practice, apply what they have learned, and gradually learn to look at the world around them from a mathematical perspective and know the familiar things around them.
(A) the exercises in the book
Through purposeful basic exercises, consolidation exercises and comprehensive exercises, students have further deepened their understanding of new knowledge, strengthened their ability to solve practical problems with new knowledge, and formed certain skills. )
(2) Design tape packaging
1, single package: students design the outer package for a tape box and fill in the design plan in the design table.
2, two boxes of packaging: two boxes of a set of several display methods, preliminary estimation: which is the most material-saving, which is the most wasteful.
Which of the above three do you think is the most suitable for placing and designing outer packaging? Besides the above three kinds, are there any other ways to put them?
3. Exercise homework after class: Design and make two sets of tape packing boxes according to your favorite arrangement, and work out how much material to use at least. If you are interested, you can also design and make multiple boxes of tape packaging, and we will give a report, exchange and display next class.
Mathematics Lecture Notes "Surface Area of Cuboid and Cube" Part II I. Analysis of Learning Situation
1, teaching material analysis:
Zhejiang Education Press, Book 10, Primary Mathematics Unit 1, The surface area of cubes and cubes is the third lesson of this unit. The unit "cuboid and cube" is the beginning for students to systematically learn three-dimensional graphics. This lesson mainly teaches the concept and calculation method of surface area of cuboid and cube. Textbooks first help students understand the concept of surface area by unfolding the six faces of a rectangular box or a cubic box. In this way, the concept of surface area can be well related to the characteristics of cuboids and cubes that have just been established, so as to prepare for the later study and calculation of surface area. Then through the example 1, the calculation method of cuboid surface area is taught. Then arrange a "try" to learn the calculation method of cube surface area.
There is no formula for calculating the surface area of a cuboid in the textbook, but it inspires students to calculate it in different ways. This arrangement is helpful for them to better grasp the concept of surface area and related calculations, and to better develop students' spatial concept.
2. Learner analysis:
The knowledge of the surface area of cuboids and cubes is taught on the basis that students have mastered the area calculation of rectangles and squares and have a preliminary understanding of the characteristics of cuboids and cubes, that is, students have made it clear that cuboids and cubes have six faces, the areas of the opposite faces of cuboids are equal, and the areas of the six faces of cubes are equal. Calculating the surface area of cuboids and cubes is widely used in life. Through this part of the study, students can deepen their understanding of the characteristics of cuboids and cubes and develop the concept of space.
Second, the teaching objectives and difficulties
Teaching objectives:
1. Understand the meaning of the surface areas of cuboids and cubes.
2. Understand and master the calculation method of the surface area of cuboids and cubes.
3. Cultivate and develop students' concept of space.
Teaching focus:
Significance and calculation method of surface area of cuboid and cube.
Teaching difficulties:
Determines the length and width of each face of the cuboid.
Third, teaching ideas
1, create problem scenarios and stimulate learning desire.
According to the characteristics of teaching materials and the students' reality, at the beginning of the new class, I created a "carton factory to make a rectangular box with a length of 8 decimeters, a width of 2 decimeters and a height of 4 decimeters and a cubic box with a length of 4 decimeters." Which box needs less cardboard? " This question scenario, and then ask: "Where do you want to make cuboids and cubes out of cardboard?" It not only stimulates students' interest in inquiry, but also establishes a clear representation of the concept of "surface area of cuboid or cube", which makes full preparations for learning the calculation method of surface area.
2, with the help of teaching media, improve the effectiveness of learning.
The unit of "cuboid and cube" is the beginning of students' systematic study of three-dimensional graphics knowledge. In teaching, students should enrich their perceptual knowledge as much as possible and establish clear representations. I asked, "Can you see the surface area of this cuboid at a glance? Is there any way to read it all at once? " Guide students to think about changing three-dimensional graphics into plane graphics. After that, the multimedia computer demonstrates the unfolding process, so that students can find six faces in the unfolded figure. Strengthen the concept of space and increase interest in learning.
On this basis, "ask": What is the relationship between the length, width and height of a cuboid and the length and width of each face? Let the students try to solve the problems around the difficult problems in this class, while the teacher only explains and guides the key points. Reflect students' dominant position and cultivate students' ability to solve problems independently. Through independent exploration, students discover the calculation method of the surface area of a cuboid. However, due to the difference of students' cognitive level, all kinds of students are allowed to put forward their own methods, and then through comparison, the general method of surface area calculation is realized, so that students can consciously combine the teaching content and reflect the thinking method, realize that they should grasp the key to solving problems and carry out appropriate thinking training.
3. Appropriate application and expansion to develop the concept of space.
Students use physical objects to solve the above problems. In the exercise part, I first arranged a set of judgment questions. The third sub-topic is that the routine of students' thinking has been broken. Compared with independent objects, what about the surface area of combined objects? I leave more time and thinking space for students to think for themselves, which further deepens new knowledge. Then, the second big question arranged the practice of calculating the area by numbers, which made the students' thinking transition from concrete image thinking to abstract logical thinking. However, whether it is the physical object of the packaging box, the specific graphics or just the surface area calculation of the data, the calculation of six complete surface areas has been solved, but there are also six surface areas in real life, so how to calculate the incomplete packaging area? I sorted out "how to find the surface area of the same size plastic box without cover?" Its purpose is to cultivate students' ability to use knowledge to solve problems flexibly. Here, we pay attention to the divergence of students' methods, diversification and optimization of problem-solving strategies, and cultivate students' personality. Finally, I think students' understanding should not only stay at the level of perception, but also rise to rational understanding. In clever questions, I leave students more time to think about the packaging of combined objects. They compare and communicate in groups, solve problems and discover new problems. This connection not only pays attention to students' dominant position, but also creates a space for cooperation. Finally, guide students to find the law according to the calculation results. "The more overlapping surfaces, the closer the figure is to the cube, and the smaller the surface area. Encourage students to use this law to further explain the packaging phenomenon in life, so that students can clearly choose the appropriate materials according to the actual situation, either to make the packaging attractive or simple and compact, and save paper as much as possible. So that students can feel that mathematics comes from life and is applied to life, and enhance the application consciousness of mathematics.
Teaching materials of mathematics "Surface area of cuboids and cubes" Part III I.
(1) Lecture content of "Surface area of cuboids and cubes" on pages 25-26 of the tenth volume of mathematics in nine-year compulsory education.
(2) The position, function and significance of teaching materials This course is based on students' understanding and mastery of the basic characteristics of cuboids and cubes. Calculating the surface area of cuboids and cubes is widely used in life. Learning this part can deepen students' understanding of the characteristics of cuboids and cubes and solve some practical problems. At the same time, it can also enable students to form a preliminary spatial concept about the surrounding space and objects in the space, which is the basis for further learning other three-dimensional geometric figures.
(3) Determination of teaching objectives According to the requirements of mathematics curriculum standards, the objectives should be diversified. According to the textbook of this course and the actual situation of students, I have set the following goals: cognitive goal, skill goal, emotional goal, understanding the meaning of cuboid and cube surface area, and mastering the calculation method of cuboid surface area. Learn to cooperate and communicate in the learning process, cultivate and develop students' spatial concept, cultivate students' spirit of exploration and attempt, and use what they have learned to solve some practical problems. By guiding students to establish the concept of space, we can cultivate their interest in learning geometry knowledge and let them feel the charm of mathematics.
(4) Teaching emphasis and difficulty: establish the concept of surface area, and understand and master the calculation method of cuboid surface area. Difficulties: Imagine the length and width of each face according to the length, width and height of a given cuboid.
Second, talk about teaching methods and learning methods.
(1) teaching methods in order to understand and develop students' mathematical knowledge, ideas and methods in their mathematical practice, I mainly adopt "trying teaching method" in this class, supplemented by "situational inquiry" teaching method and "observation method" to realize the interaction between teachers and students, train students in ways of thinking such as analysis, synthesis, comparison, abstraction, generalization and induction in a planned way, and strive to explore new strategies in mathematics classroom under the guidance of new curriculum standards.
(B) Learning Method "New Curriculum Standard" advocates students to "actively participate, be willing to explore and be diligent in hands-on" and build a harmonious classroom atmosphere. Therefore, hands-on practice, independent exploration and cooperative communication are the main learning styles of the students in this class.
Third, say teaching AIDS, learn tools and prepare teaching AIDS:
Multimedia courseware. Learning tools: bring a cuboid or cube carton and a pair of scissors.
Fourthly, talk about teaching design.
Revisit old knowledge, pave the way and bridge the bridge.
Oral answer. 1, a cuboid has () faces, () edges and () vertices; The length of the opposite side () and the length of the opposite side ().
2. A cube has () faces, () edges and () vertices; Its sides (), each face (). It is very special ().
3. Look at the picture and point out the length, width and height of each cuboid. The students answered. Give play to the transfer function of old knowledge and pave the way for new knowledge.
Second, create a situation to cut into the theme
1, animation demonstration situation map. Mom's birthday is coming, and Xiao Ming chose a beautiful gift. In order to make the gift more beautiful, he plans to pack the box himself. Xiaoming bought a beautiful wrapping paper. In order to save paper, he wants to cut a piece of suitable size before packaging. How much paper should he cut at least? What should Xiaoming do? Can you give him advice? Introduce a new lesson: this requires a new mathematical knowledge, the surface area of cuboids and cubes. 1, students think while watching. 2. Students express their ideas: Student 1: You must first know how big the box is. Health 2: You must first find out how big each side of the box is. ..... The new curriculum standard emphasizes that teaching materials must obey and serve the needs of students. We should proceed from the students' existing life experience and reality, apply teaching materials and deal with them flexibly. So I optimized the combination of example 1, which really made mathematics glow with rich life breath. The design of this situation is intended to ignite students' thinking sparks, stimulate students' strong desire for knowledge, and feel a humanistic feeling at the same time.
Third, establish the actual operation of representation.
Show "Operation Tips" and "My Discovery". Operation skills: ① Take out the prepared cuboid or cube, cut it along the edge, and then flatten it to see the shape of the unfolded carton. ② In the expanded drawing, it is marked with "up", "down", "front", "back", "left" and "right" respectively. My discovery: Do you find out which faces of the unfolded figure have the same area in the cuboid? What is the relationship between the length and width of each face and the length, width and height of a cuboid? What about the cube?
1, students begin to operate.
2. Observe, find and complete the form. (one for each person)
3. Group communication. (Guidelines for District Patrol)
4. Report. 1: I found that the areas of two sides of a cuboid are equal. Health 2: I found that the top and bottom of a cuboid are equal, the front and back are equal, and the left and right are equal. "New Curriculum Standard" points out: "Hands-on practice, independent exploration and cooperative communication are important ways for students to learn mathematics." I think the design of this link can better interpret this concept. Giving students enough time and space to engage in mathematics activities, allowing students to find problems, solve doubts and doubts in a harmonious classroom atmosphere, and cultivating and developing students' concept of space play a decisive role in establishing the appearance of products.
Fourth, explore independently and deepen the theme.
Animated demonstration and explanation show that a cuboid is decomposed into a plane expansion diagram to guide students to establish a representation of surface area.
1, observe carefully to deepen the understanding of the relationship between the unfolded figure and the original cuboid.
2. Establishing the representation of surface area Proper use of modern multimedia information technology is a powerful tool for students to learn mathematics and solve problems. The cuboid is displayed visually through the courseware, thus prompting students to establish the representation of "surface area" and preparing for later learning to calculate the surface area of cuboid. Reproduce the situation diagram and ask a tentative question: Can you help Xiao Ming figure out how big the paper should be cut? Example of self-study textbook 1. Try to practice, so that students can actively try to use the knowledge and methods they have learned when facing practical problems, and explore strategies to solve problems from the perspective of mathematics, so as to change "teaching mathematics" into "using mathematics" and at the same time let them enjoy the joy of success.
Show discussion outline:
1, how to calculate?
2. What is the key to correctly calculate the surface area of a cuboid?
Group cooperation and communication Group cooperation and communication can make students more, 20 cm wide and 30 cm high. Please help him figure out how much glass he needs at least. In real life, we often encounter such a situation that we don't need to calculate the total area of six faces of a cuboid. Can you give another example? Students should consider which areas need to be calculated according to the specific situation, complete the exercises and give feedback in time. Examples, such as calculating the surface area of swimming pool, drawing columns, etc. The purpose of improving exercises is to arouse students' memories of existing life experiences, to know how to solve problems according to reality, and to truly feel that mathematics is "useful" everywhere in life.
Fifth, summarize and evaluate classroom development.
Summarize the evaluation. What did you learn today? How does it help you? Students evaluate themselves. Let students evaluate themselves, which can not only sort out what they have learned, but also cultivate students' self-reflection consciousness. Classroom extension. Students, a cube is a special cuboid. How to calculate its surface area is relatively simple. Why? Think after class. This "challenging" task can better extend the classroom, stimulate students' curiosity and make them move after class.
Five, say blackboard writing
The surface area of a cuboid or cube The total area of six faces of a cuboid or cube is called its surface area. Method 1: Method 2: 6× 5× 2+6× 4× 2+5× 4× 2 (6× 5+6× 4+5× 4) × 2 or so.
Mathematics "Surface Area of Cuboid and Cube": Lecture 4: Textbook;
1) Teaching content: The surface areas of cuboids and cubes are the second lesson of Unit 5 in Book 10 of the People's Education Press textbook.
2) The position and function of this course: This part of the content is taught on the basis that students have learned the calculation method of the area of rectangles and squares, fully understood the representation of cuboids and cubes, and mastered the characteristics of cuboids and cubes.
3) the establishment of teaching objectives:
1, knowledge and skills:
1), master the definition of surface area: the total area of six faces of a cuboid or cube is called surface area.
2) Master the calculation method of the surface area of cuboids and cubes, and solve practical problems about the surface area of cuboids or cubes in real life according to specific conditions. (e.g. a cuboid or cube with five or four faces)
3) Cultivate students' exploration consciousness and innovative practice ability, further develop students' spatial concept, cultivate students' awareness and ability of independent participation, and enhance students' strong thirst for knowledge.
2, process and method:
1) the process of knowledge generation: in actual production and life, there are many problems that need to require the surface area of cuboids and cubes, such as packaging boxes needed in industrial production, packaging cuboids or cubes in decoration, painting walls in construction, etc.
2) The process of mastering knowledge: introduce the scene, perceive the necessity of calculating the surface area of cuboid and cube, discuss the calculation method of cuboid surface area in groups, sum up the calculation method of cuboid surface area in the whole class, choose the best scheme to discuss the calculation method of cube surface area, practice independently, and consolidate the ability of knowledge extension and formation.
3, emotional attitudes and values:
1) cultivate students' abilities of observation, analysis, induction and language expression, carry forward the spirit of coordination of trying and cooperation, and promote the development of thinking ability.
2) Enhance students' interest and confidence in learning activities.
4) Establishment of key points and difficulties:
1, key point: master the calculation method of surface area of cuboid and cube, and solve related practical problems.
2. Difficulties: According to the length or width of a given cuboid, it is difficult to determine the length and width of each face.
Oral teaching methods and learning methods;
Modern mathematical theory holds that students' mathematical activities should be increased in primary school mathematics classes. According to the characteristics of this unit textbook and students' cognitive rules, I mainly use review introduction method, situational teaching method and heuristic analysis method to teach this lesson.
Teaching and learning are inseparable, and teaching is to learn better. According to students' learning rules, in the teaching process, students are mainly guided to master the following learning methods: transformation and migration, comparative analysis and summary and induction.
Talking about the teaching process:
(A) cleverly set the scene, the introduction of life:
Teacher: Students, the school wants to donate money to the children in the disaster area and decided to hold a fundraising ceremony on the school playground this Wednesday. Teacher Liu from the General Affairs Office wants to make a decent donation box. He heard that we were studying cuboids and cubes, so he asked us for a favor. Please think about what we should do. (Student A) What other information do we need to know? There is cardboard in the general affairs office, so how much should we take? This leads to the content to be learned in this lesson: the surface area of a cuboid.
(2) Independent exploration and image perception.
The process of hands-on operation is a process of using both hands and brain. In the process of students' operational learning with school tools, multiple senses participate in learning activities, which can not only arouse students' learning enthusiasm, but also enable students to actively operate, explore and think.
1. Guide the students to expand the cuboid that they can make in the last lesson, and mark six faces in turn, so that the students can determine how much cardboard they need at least and find the total area of the six faces. Establish the concept of surface area in students' minds.
2. Explore the calculation method of cuboid surface area.
(1) instruct students to measure the length, width and height by hand, try to calculate the surface area through group cooperation, and then report to class.
(2) Discuss the calculation method of cuboid surface area in groups. In this process, we should pay attention to guiding students to truly understand the relationship between the length and width of a cuboid through observation and operation. Teachers must guide and guide at key points to break through this difficult problem.
(3) Communication with the whole class. Students' possible methods include adding the areas of six faces; Multiply the respective areas of three different faces by 2, and then add them; The areas of three different faces are added and multiplied by 2. Let the students choose the best scheme by comparison. So the surface area of a cuboid is abstracted as = (length and width+length and width+width and height) 2.
After the donation box is finished, I want to find some beautiful red paper to stick on the outside of the box and observe which faces need to be decorated. How much red paper do you need? (Group discussion and answer)
Through the solution of this example, let students know that sometimes the total area of six faces is not needed in life. At this time, inspire students to talk about similar situations in life, such as wooden chalk boxes and coal boxes. ) to guide them to solve practical problems.
The teacher showed the specific data of the length, width and height of the donation box, and worked out how much cardboard and red paper were needed respectively.
5. Discuss how to calculate the surface area of the cube in groups.
6. communication. Students may have calculated the surface area of a cuboid according to the calculation method. When communicating, pay attention to guide students to compare which method is the simplest, and at the same time, make clear why they should multiply by 6 in the calculation formula of cubic surface area.
7. It's hard to question.
(3) Consolidate practice and expand application. Mathematics comes from life and serves life, and what students have learned can be truly understood and mastered through application.
1, the exercises in the book. Through purposeful basic exercises, consolidation exercises and comprehensive exercises, students have further deepened their understanding of new knowledge. It strengthens students' ability to use new knowledge to solve practical problems and enables them to form certain skills.
2. Design tape packaging
1) Single package: Students design the outer package for a tape cassette and fill in the design plan in the design form.
2) Two-box packaging: There are several ways to set two boxes. Preliminary estimation: which is the most material-saving and which is the most wasteful.
Which of the above three do you think is the most suitable for placing and designing outer packaging? Besides the above three kinds, are there any other ways to put them?
3. Practice homework after class:
1) According to your favorite arrangement, design and manufacture two sets of tape outer packaging boxes, and calculate how much materials are needed at least. If you are interested, you can also design and make multiple boxes of tape packaging, and we will give a report, exchange and display next class.
2) Thinking after class: If we get the right cardboard according to our calculated cardboard area, can we make the donation box we need? Why?
Reflection after preaching:
Learning this lesson, if students can find the area of a certain surface of a cuboid in the last lesson, there is no problem in learning this lesson. It is estimated that some students will have some difficulties in learning this course. It is necessary to strengthen individual counseling for these students, make more use of physical objects for students to observe, and gradually establish the concept of space.