On the area of parallelogram in PEP
First of all, talk about textbooks.
Teaching content:
The teaching content of "Calculation of parallelogram area" is pages 80-83 of the first volume of Primary School Mathematics, the standard experimental textbook of compulsory education curriculum of People's Education Press. The preliminary understanding of geometry knowledge runs through the whole primary school mathematics teaching in the order from easy to difficult. The textbook in this chapter undertakes the task of making students learn to calculate the area of parallelogram, triangle and trapezoid. The first lesson of this unit is based on students' mastery of rectangular area calculation. The application of this part of knowledge will lay a good foundation for students' later geometric knowledge. It can be seen that this lesson is an important link to promote the development of students' spatial concepts and the study of solid geometry knowledge.
Teaching objectives:
Knowledge and skill goal: to understand and master the calculation formula of parallelogram area.
Process and Method Objective: To be able to use formulas to solve practical problems.
Emotion, attitude and values: through the deduction of formulas, the universal connection between things is infiltrated into students; By solving practical problems, students can improve their understanding of mathematics anywhere in their lives.
Teaching emphases and difficulties:
(1) teaching emphasis: derivation and application of parallelogram area calculation method.
(2) Teaching difficulties: How to make students really understand the relationship between the length and width of the rectangle and the base and height of the parallelogram after the rectangle is cut into rectangles.
Second, oral teaching methods
In this lesson, I will use. Independent practice, cooperation and exchange? Through demonstration and practical operation, this teaching method stimulates students' enthusiasm to participate in learning and allows students to show their personality in the learning state of seeking knowledge.
The learning methods of this lesson are: independent discussion, group cooperation, practical operation, observation and imagination, etc. Let students explore in person, take the initiative to discover, and let them study easily and happily!
Preparation of teaching AIDS: parallelogram cards, rectangular cards, inspection paper, scissors, etc.
Third, talk about the teaching process
(A) combined with life doubts, stimulate the introduction of interest
At the beginning of the new class, I will use a story to ask questions and lead in, so that students can carry out inquiry activities in a vivid teaching atmosphere.
Once upon a time, there was a farmer's uncle who divided the land among his two adult sons. He gave the land to his eldest son and the land to his second son according to the usual harvest and the size of the ridge. But both sons felt that the land allocated to them was small, and they all said that the farmer's uncle was eccentric. This can make the farmer's uncle angry, but he can't understand it. I only know that the number of ridges and harvest in these two fields are the same, so the farmer's uncle wants to find a wise man to help him solve this problem. Students, can you help him?
Through such an interesting story, it naturally leads to the key content of this lesson and makes students unconsciously start thinking about the theme.
(2) Organize hands-on practice and try multi-dimensional exploration.
I will take the story as the main line, further guide and organize students to practice and help farmers find ways.
First of all, I will guide students to find ways to prove that the two plots are the same. To this end, I prepared two school cards for my classmates. Suppose these two plots are the school cards in everyone's hands. What should you do? We can discuss it in groups. ? Such guidance can make students use their brains and do their best without any constraints. This stimulates students' thinking and guides them to determine the credibility of the method. Students may come up with many methods, such as counting squares, comparing overlapping cards, cutting and splicing, etc. Not all of them are valuable, because they are not forced by teachers, but the results of students' own discussion and research, which is the harvest produced in the classroom.
Finally, on the basis of students' various answers, I will organize students to practice various methods in groups and ask them to explain the practice process reasonably. Students will experience the connection between rectangle and parallelogram in careful operation. Make full preparations for the next step to derive the parallelogram area calculation formula!
(C) grasp the key links, in-depth derivation and combing
Students' understanding is from the shallow to the deep. Through hands-on practice, they already know that the areas of the two cards are equal, the length of the rectangle is equal to the base of the parallelogram, and the width and height are equal. But in students' thinking, there is no connection between the three. I seize this key point and organize students to make in-depth deduction. That's what I did. I used the report of the practical excavation and filling method group to guide students to think: area = length of rectangle? Width, how to find the area of parallelogram? The students deduced that the area of parallelogram is equal to the bottom. Tall man. The formula comes from the actual operation of the last link, so it comes naturally, breaks through the teaching focus and completes the teaching goal of this lesson. At this point, I didn't stop. I still give two figures of individual data with the help of the farmer's uncle's land distribution, so that students can use the formula to calculate and get the exact answer with the same area, which completely solves the problem for the farmer's uncle. The farmer's uncle smiled happily Students not only consolidate the calculation of parallelogram area, but also gain the joy of success.
(D) layered application of new knowledge, and gradually understand the internalization.
Only by organizing students to consolidate and apply new knowledge in time can we get the internalized effect. Do I meet the requirements? Pay attention to the foundation, practical ability, expand thinking and connect with life? Principles, arranged four groups of exercises. (Basic exercises, fun exercises, practical exercises, promotion exercises)
Basic exercises:
The positions of several parallelograms are different, which enables students to deepen their understanding of the corresponding base and height of parallelograms and consolidate the application of its area calculation method.
Interesting exercise:
The design of interesting questions further consolidates the use of parallelogram area method and broadens students' horizons of knowledge understanding.
Practice: Teaching comes from life, and there is mathematics everywhere in life. This kind of practical exercise, in the process of learning and strengthening the application of knowledge, enables students to experience the happiness of mathematics everywhere in their lives.
Weightlifting exercises:
The promotion exercise not only examines the accuracy and rigor of students' understanding of knowledge, but also examines students' imagination and spatial concept.
These four levels of exercises are designed from the shallow to the deep, which can cover all the knowledge points of this lesson, integrate practicality and fun, let students acquire knowledge in pleasure, and effectively cultivate their innovative consciousness and problem-solving ability. It can be said that the teaching of this course is interlocking, clear and orderly, and will certainly achieve satisfactory results.
At the end of this class, in order to let the students have a systematic and complete understanding of what they have learned, I will first ask the students to talk about what they have learned in this class. Then it is put forward: can the parallelogram area formula be proved by origami or other methods? As homework after class, it provides students with a space for multiple thinking and further cultivates their innovative spirit. Do it. At the end of the song, people are scattered, and the sound is lingering? .
Fourth, write on the blackboard
I adopt the principle of clear organization, which not only embodies the learning goal, but also highlights the learning focus, which can help students understand the knowledge points of this lesson more clearly. Specially designed as follows:
Area of parallelogram
Area of triangle = bottom? high
Area of four parallel sides = bottom? high
S = ah
Area evaluation diagram of parallelogram in PEP.
"Mathematics Curriculum Standard" points out:? Students are the masters of mathematics learning, and teachers are the organizers, guides and collaborators of mathematics learning. ? Teacher Ye fully embodies this point in the process of mathematics teaching, gives full play to students' main role, pays attention to cultivating students to actively explore the parallelogram area calculation formula through cutting, spelling and measuring, and master the parallelogram area calculation formula to solve practical problems. In the whole teaching process, Mr. Ye always encourages students to discover, think and find the best solution by themselves, which stimulates students' enthusiasm for learning and enlivens students' thinking, and enables them to gain some vivid experiences and beneficial enlightenment. To sum up, there are the following points.
First, the teaching ideas are clear, the objectives are clear, and the difficulties are outstanding.
According to the teaching content, teachers teach students in accordance with their aptitude and formulate teaching ideas. This course is based on. Create a situation? Guide the practice of exploring and discovering laws? As a clue, the whole teaching idea is clear.
The content of this lesson is taught on the basis that students have mastered the characteristics of parallelogram and the area of rectangle. According to the requirements of teaching materials and students' reality, teachers have established three teaching goals according to the concept of curriculum standards: the goals set by teachers are specific, clear, comprehensive and operable, paying attention to students' life experience and solving practical problems in life.
In this lesson, the teacher emphasizes the training of students' hands-on operation and active inquiry, deepens the understanding of area calculation through activities such as cutting, spelling and measuring, and organically uses the teaching strategy of conversion to make students deeply understand the meaning of parallelogram area formula, highlight the teaching difficulties, and make the whole teaching detailed and accurate. This design conforms to students' age characteristics and cognitive laws, embodies the student-centered learning process and cultivates students' learning ability.
Second, attach importance to students' existing knowledge and experience, attach importance to operational inquiry, and give play to the main role.
Students' existing knowledge and experience are the basis for students to learn new knowledge, the growing point of classroom teaching and the starting point for teachers to guide students' learning. Teacher Ye showed a rectangle at the beginning of the class, then pressed it into a parallelogram and asked what had changed. What hasn't changed? Has the area of the parallelogram changed? Students express their opinions, some think that they have changed, and some think that they have not changed. Then the parallelogram is transformed into a rectangle, and the area of the rectangle is calculated to arouse students' memory of the existing knowledge. The design of this process fully shows students' original knowledge and experience, exposes students' prototype of new knowledge, and lays a good foundation for guiding students to further discuss and communicate and clarify the calculation method of parallelogram.
The whole teaching process has distinct levels. By cutting, moving, spelling and measuring, students can use their hands, brains and mouths. Everyone participates in the learning process, not for operation, but to organically combine operation, understanding concepts and mathematical expression. Let the students look at the pictures they cut and paste to explain mathematics, which reduces the difficulty of mathematical expression. Through operation, students can learn happily, fully understand knowledge, intuitively deduce the concept of parallelogram formula, and cultivate their ability to acquire knowledge, observe and operate.
Third, pay attention to the infiltration of mathematical methods and ideas.
It is a very important task to infiltrate scientific mathematical methods and ideas in mathematics classroom, which is related to the cultivation of students' good thinking qualities such as rigor and logic. When designing a class, we should pay special attention to the content that runs through the whole class and forms clues. For example, in this lesson, what is the significance of the diversification of thinking methods in the shearing and splicing of the bottom and the height and the resulting transformation from change to invariance? Wait, there's a lot to consider. Students of several important ideas in mathematics have been well trained, laying a good foundation for the development of students' logical thinking and problem-solving ability in the future.
Worthy of discussion
Teaching itself is an art, only better, no best. A class without problems is not a good class in itself. So this lesson also has the following points worth discussing.
1, the preparation of teaching AIDS is still insufficient. When discussing the area of parallelogram and the area of converted rectangle, we should put the converted rectangle on the blackboard instead of the original rectangle. So when the teacher said that the area of a rectangle is equal to the area of a parallelogram, the students hesitated.
2. When converting a parallelogram into a rectangle, it is necessary to know what it follows. In order to reflect the rigor of mathematical language, students should be given enough time to speak and let them feel that the height of parallelogram is the width of rectangle after conversion.
3. The design of exercises should be gradual. I think the third exercise designed by Teacher Ye is the area of parallelogram, which is only the application of the parallelogram area formula and should be put in the second place. In the second exercise, show two heights and a base in the parallelogram, let the students make a choice and then calculate. Which height should I use to calculate? What needs to be highlighted is that the area of parallelogram multiplied by the base must be corresponding, so that students' thinking ability can be further improved and should be placed in the third place. Put these before practice? Are the areas of parallelogram equal? This should be placed in the fourth question, as a promotion, stretching students' thinking to a higher level.