The area of the comparison graph is 1. Let's start with teaching material analysis.
"Combined Graphic Area" is the first lesson in Unit 5, Grade 5, the experimental textbook of compulsory education standard published by Beijing Normal University. Grade three students have learned the area calculation of rectangle and square, and Unit 2 of this book has learned the area calculation of parallelogram, triangle and trapezoid. This lesson is the development of these two aspects of knowledge, and it is also a practical problem that often needs to be solved in daily life. On this basis, learning combined graphics can not only consolidate the basic graphics that have been learned, but also integrate the knowledge learned, pay attention to infiltrating thinking strategies to solve problems, and improve students' comprehensive ability. The content of the textbook highlights two parts, one is to feel the necessity of calculating the area of combined graphics, and the other is to emphasize students' independent exploration and learning according to the characteristics of combined graphics.
Second, the analysis of speaking and learning.
Although there are some differences in mathematics learning, the students in our class have good comprehensive quality, active thinking and strong interest in exploring mathematics problems. Then, according to students' existing life experience, through intuitive operation, there will be no difficulty in understanding the combined graphics, and in the second unit of the textbook, students have systematically learned the calculation methods of parallelogram, triangle and trapezoid areas, especially the infiltration of transformation ideas. On this basis, students should explore the calculation method of combined graphic area, and through independent exploration and cooperative communication, they should be able to realize the diversification of methods. However, it needs the exchange, reference, reflection and optimization of teacher guidance methods. Therefore, we should pay attention to let every student actively participate in the activities, make the activities fruitful, and really let students develop their mathematical methods and ideas.
Third, talk about teaching objectives.
According to the requirements of the new curriculum standards and the characteristics of teaching materials, combined with the cognitive ability of fifth-grade students, I set the following goals in this class:
1. Knowledge and skill goal: In the activities of independent exploration, various methods for calculating the combined graphic area are summarized.
2. Process and Methods Purpose: According to the situation of various combination diagrams, effectively choose calculation methods to answer and solve related practical problems.
3. Emotional attitude and values goal: Infiltrate the reformed teaching ideas, improve students' ability to use new knowledge to solve practical problems, and cultivate students' innovative spirit in independent exploration activities. Cultivate students' enthusiasm for exploring mathematical problems and enhance their confidence and interest in learning mathematics.
Four, said the teaching emphasis and difficulty:
Teaching emphasis: Students can master the method of dividing and adding to find the combined graphic area through their own hands-on operation.
Difficulties in teaching: Understand various calculation methods for calculating the area of combined graphics, and choose the appropriate method to calculate the area of combined graphics according to the relationship between combined graphics.
Verb (abbreviation of verb) oral teaching method and learning method
Teaching methods: In order to highlight the key points and difficulties, I mainly designed the teaching methods of independent exploration and cooperative communication. Hands-on practice, independent exploration, cooperation and communication are important ways for students to learn. Change the role of teachers, give students more space, carry out inquiry learning and let them
Think independently in specific operational activities, communicate with peers, experience the process of problem raising and problem solving, and experience the fun of learning success.
Learning style: The new curriculum emphasizes students' dominant position in classroom teaching, and students' participation in learning activities is an important factor to determine the teaching effect. Therefore, in the choice of learning methods, I adopt independent observation and thinking, group cooperation and communication, and learning and induction. In the teaching of the whole class, I combined the learning methods of observation, operation, cooperation and communication, paid attention to the cultivation of students' spatial concept, and highlighted students' operating experience, which not only reflected the characteristics of the new textbook, but also gave full play to students' main role and closely linked mathematics with life.
Sixth, talk about teaching preparation.
Rectangular, square, parallelogram, trapezoid and triangle paper; Homework paper; Small blackboard; color pen
Seven, talk about the teaching process.
In order to complete the teaching objectives of this section, highlight the key points and break through the difficulties, and link mathematics with real life according to the new curriculum standards of primary school mathematics, so that students can fully realize that mathematics is around and feel the interest of combined graphics, I have formulated the following teaching links:
The first link: create the situation and review the introduction.
This is the focus and difficulty of this lesson. How to break through this difficulty? This is how I arranged it. At the beginning of this lesson, students can immediately recognize squares, rectangles, parallelograms, triangles and trapeziums by opening the gift bags given by the teacher, so as to review the area formulas of these figures and lay the foundation for ensuring the correct calculation of the area of the combination diagram. Ask the students to spell out their favorite patterns with these figures. Please show your work to everyone and tell them what the spelled pattern looks like. What are the basic graphics? This makes it clear that the combination figure is composed of several basic figures, which leads to the topic: the area of the combination figure (blackboard writing)
(Design concept: The purpose of this link design is to let students fully mobilize various senses to participate in learning in the process of speaking, spelling and taking a look, feel that knowledge comes from life and serves life in a strong learning atmosphere, and make it clear that many problems in life are related to the area of combined graphics. )
The second link: independent exploration, cooperation and exchange.
This link is the main part of classroom teaching, one of the main ways to learn knowledge and cultivate ability, and also the key link of this course. According to the development of students' learning ability, I have arranged three levels:
The first level: show the theme map.
The teacher shows the floor plan of the living room, guides students to observe, gives data and information, asks questions, and helps me calculate how many square meters of floor I should buy according to this information.
Design concept: in solving this life problem, give students enough time and space to actively participate in learning, and let them have successful experiences and experience gains in group activities through independent exploration and group communication. )
The second level: the group reports the learning situation.
The report will show the students' academic achievements, and the following situations will occur:
(1) Divides the combined graph into two rectangles.
(2) Divide the combined graphics into squares and rectangles.
(3) Divide the combination diagram into two trapezoids.
(4) Fill a small square in the combination diagram to make it a big rectangle, and then subtract the area of the small square from the area of the big rectangle.
(5) Divide the combined figure into two rectangles and a square (or other cases).
Design concept: In this process, I respect students' dominant position, actively create opportunities for students to learn actively, provide them with space to try and explore, make students happy and be good at autonomous learning, actively think about problems from different aspects and angles and seek solutions to problems. Through the discussion and cooperation among groups, a conclusion is drawn. )
The third level: teachers and students summarize the subdivision methods and supplement and improve the optimization of the methods. By allowing students to observe and compare the differences of the above methods independently, the calculation method of calculating the area of combined graphics is summarized, and the method of transforming into basic graphics through "division" and "addition" is mastered, so that students can make it clear that when dividing combined graphics, the simpler the dividing graphics, the simpler the problem-solving method.
The third link: comprehensive application, consolidation and improvement.
In order to consolidate new knowledge, I designed exercises at different levels to improve students at different levels.
In this part of the teaching, I pay attention to the cultivation of students' self-confidence, so that different students can improve in different degrees, so that they can fully experience the happiness of success, so as to be confident and dare to challenge difficulties. At the same time, I also pay attention to the cultivation of students' interest in learning and thinking ability. )
The fourth link: summarize the harvest and reflect on the promotion.
I ask a question: What have you gained from learning this lesson?
I want to feedback the teaching effect of this course in time through this link, and guide students to improve their summary, whether in knowledge or in mathematical methods and ideas. )
In the design and implementation of this class, I made a bold attempt according to the concept of the new curriculum and achieved good teaching results. There are mainly the following points:
1. Give full play to students' main role, trust students' ability, enthusiastically encourage students' exploration activities, and give students enough time and thinking space. Maximize the development of students' observation ability, thinking ability and inquiry ability, and enhance students' interest in learning mathematics.
2. Pay attention to the development of students' mathematical knowledge and ideas. In independent exploration or cooperation and communication with peers, students can let go of their thinking, publicize their personality, get the same improvement in complementary reflection, and fully experience the fun of success, thus becoming the real master of learning.
Compare the areas of the figures and say draft text 2. First of all, teaching materials
This lesson is selected from Lesson 1, Unit 4, Volume 5, Beijing Normal University Press, and belongs to the category of graphics and geometry. It is a further development on the basis of students mastering the characteristics of basic plane graphics and finding rectangular and square areas. The purpose of arranging teaching materials in this way is to let each student know the diversity of area comparison method through students' observation and comparison activities. At the same time, with the help of grid paper, let them know that the size of a graphic area is not only determined by the shape of the graphic, but more importantly, by the number of area units occupied by the graphic. This also lays a foundation for students to explore the calculation of basic graphic area themselves. So this lesson plays a connecting role in this unit.
According to the new curriculum standards and the main contents of this course, combined with my actual teaching experience, I have determined the following teaching objectives:
Knowledge and skills:
1, with the help of grid paper, you can directly judge the size of the graphics area.
2, through communication, know the basic method of comparing the size of graphics area.
3. Experience the relationship between the change of graphic shape and the change of area.
Process and method: Through observation, imagination and hands-on operation, students' activity experience is accumulated, students' spatial concept is cultivated, and their ability of induction and summary is improved.
Emotional attitude and values: through exploring cooperative learning, stimulate students' enthusiasm for learning and cultivate their cooperative spirit.
Explore consciousness and gain successful experience.
Combining the teaching content and teaching objectives, I have determined that the teaching focus of this class is: mastering the basic method of comparing the size of graphics. The difficulty that may be encountered in teaching is to understand the relationship between the change of graphic shape and area. In teaching, I will grasp the key points and break through the difficulties to help students further improve their spatial imagination.
Second, preach the law.
The new curriculum standard requires teachers to be organizers and guides of teaching activities, and students to be the main body of learning and development. Teachers should not only teach students knowledge, but also teach them the skills to acquire knowledge. Therefore, according to the content of this lesson, I mainly adopt the following teaching methods:
1, hands-on operation to accumulate activity experience. The study of this lesson plays an important role in students' understanding of the surrounding plane graphics and forming the concept of space. It should be aimed at students from different starting points, with full participation and full experience. Design different levels of activities to cultivate students' spatial concept.
2. Master the mathematical methods in AC collision. It is not difficult for students to compare the area of independent graphics, but it is difficult to compare the area of combined graphics. Some students already have some consciousness of equal product transformation (that is, the transformation that only changes the shape of the graph without changing the size of the graph). They should learn from each other, guess, reflect and verify in operation, and finally achieve understanding and application, and fully mobilize students' enthusiasm for inquiry.
3. Evaluation, motivation and interest in learning. In teaching, students' thinking is always very clever and their language is always colorful, so as long as they are reasonable, I will give them recognition and encouragement, so that students can feel the joy of success.
Third, talk about link design and intention.
In the design of this class, I run through the activities. First, let the students independently find two figures with the same area; Then the group cooperates to find the combined graphics with equal area; Then, the introduction and expansion of the principle of complementary entry and exit, and finally, the further development of students' spatial imagination ability in consolidation exercises. The design of these activities builds a bridge for students' thinking, thus realizing the promotion of the concept of space. At the same time, my design tries to embody the following three points:
(A) mathematical methods as the bright line, mathematical thinking as the dark line, to cultivate students' mathematical core literacy.
This lesson takes observation, square counting, translation, flip, axial symmetry, equivalent replacement and other methods of comparing graphic areas as a bright line. Through observation, conjecture and operation verification, students find various methods to compare graphic areas.
(2) Strengthen operation perception, accumulate activity experience and cultivate students' spatial concept.
This lesson provides students with two hands-on opportunities. One is to explore independently that "the area of one graph is equal to the area of another graph"; The second time is to explore "the area of the combination of two graphs is equal to the area of the other graph". In class, students can imagine space by cutting, moving and spelling. Only through hands-on operation can they accumulate perceptual knowledge, gradually acquire relevant appearances, visually perceive the concept of space and deepen the concept of space.
(3) Enrich the space imagination and enhance the concept of space.
In the teaching process of graphic geometry, we should not only cultivate students' observation and operation ability, but also cultivate their rich spatial imagination. Spatial imagination is gradually formed on the basis of rich spatial perception, which is a further sublimation of spatial concept. In the design of this class, I try to create as many opportunities for students to imagine and constantly stimulate their thinking. For example, when students suggested that 1 and No.3 could be compared by translation, I immediately said, "Please imagine what would happen if 1 was translated to No.3 position?" Let the students think first and then verify. Especially in the handling of exercises, I pay more attention to the cultivation of imagination. There is a multiple-choice question: "Which of the following figures can be composed of two figures on the left?" I didn't give the students a choice directly, but first I asked this question, "Imagine what these two figures can be made into?" Give students time and space to give full play to their imagination, thus enhancing the concept of space.
Fourth, talk about blackboard design.
Writing on the blackboard is the soul of a class. In order to make students fully understand the knowledge and highlight the key points, I try to write it on the blackboard reasonably, beautifully, concisely and clearly.
These are my ideas about the teaching of this class. There may be more wonderful classes, and I will adjust flexibly according to the learning situation to create a democratic and harmonious class and give each student more room for learning and development.