What is the area of the first section of Unit 4 in Volume II of Grade Three of Beijing Normal University Edition?
Analysis of teaching materials
"What is area" is the first lesson in Unit 4 of Book 6 of Beijing Normal University Edition. This course belongs to the field of "space and graphics" and is taught on the basis that students have mastered the characteristics and perimeters of rectangles and squares. Mastering this part will lay a good foundation for them to learn the area calculation of rectangles and squares in the future, and also lay a foundation for the whole knowledge of mathematical geometry. Students have rich experience in understanding the surface size of objects. In order to understand the meaning of area intuitively, the teaching materials are arranged in three levels to guide students to understand and experience step by step. At the first level, let students have a perceptual knowledge of the area by comparing the area ratio of mathematics textbooks with Chinese textbooks, coins, palms and leaves. In the second stage, students are allowed to compare the areas of squares and rectangles in different ways. Through comparison, students can further understand the concept of area, experience the diversity of strategies for comparing the size of area, especially the advantages of measuring and comparing squares, and pave the way for studying area units in the future. The third level is to further understand the meaning of area through the activity of drawing on square paper and realize a mathematical fact that graphics with the same area can have different shapes.
Analysis of learning situation
Students have mastered the characteristics of plane figures such as rectangles and squares, know the perimeter of the figures, and can calculate the perimeter of rectangles and squares. But also has the ability of preliminary observation, evaluation and verification, and the ability of touching and comparing.
Teaching objectives
1. Participate in cognitive process activities and know the meaning of graphic areas.
2. Experience the diversity of comparison strategies by comparing the sizes of two graphs.
3. Improve hands-on operation ability, comprehensive analysis ability, preliminary space concept and the ability to cooperate and communicate with people in activities.
Teaching focus
Understand the meaning of area with examples.
Teaching difficulties
Explore the method of comparing the sizes of two graphs and experience the diversity of comparison strategies.
Teaching assumption
The focus of this lesson is to understand the meaning of area, which is based on the fact that students have mastered the perimeter of rectangles and squares. From learning length to learning area, students are transitioning from line to surface, and from one-dimensional space to two-dimensional space, which is a leap in understanding. Learning this lesson well is not only conducive to developing students' spatial concept and improving their ability to solve problems, but also lays a foundation for the area calculation of plane graphics in the future. Therefore, in teaching, I pay attention to strengthening children's hands-on operation ability, enriching students' perceptual knowledge and effectively improving the effect of knowledge intake.
1. In class, I cooperated with students to complete the lead-in, which not only narrowed the distance between teachers and students, but also created harmony.
The classroom atmosphere naturally leads to the learning content of this lesson, and I realize that the surface of the object is big and small. For the understanding of closed graphics, I demonstrate closed graphics in the courseware, let children point out the area, perceive the area of closed graphics, and explain the activities of closed graphics without area with endless grass planting, so that students can experience the process of area formation.
2. When exploring the comparison of rectangular and square areas, students should first experience observation and overlapping methods, and then explore different methods through group cooperation to optimize grid drawing. This link not only cultivates students' hands-on operation ability, but also makes students experience the joy of success.
3. The exercise design of this class is to grasp the key points, face the whole class and teach students in accordance with their aptitude. Finally, the creative contest aims to make students understand the meaning of area and understand that the same area can have different shapes.
Training/teaching AIDS
Multimedia courseware, two leaves.
Learning tool
Coins (dimes and one yuan), a square centimeter plastic sheet, 10× 10 transparent film, a plastic disc with a diameter of 2 cm, colored pencils, a rectangle and a square (6 in Appendix 2).
teaching process
(A) create a situation
Teacher: (showing math books and information books) Are the students familiar with these two books? What do they have in common? Students will say it's the same size and ask: what size? What does this mean? Students will try to tell whether it is the same size, or they will touch the cover of the book to explain it. Then, the teacher said to all the students: Let's all touch it. In addition, the cover of the math book is as big as that of the information book.
Student: Take the initiative to touch it, and then other students will touch it.
Design intention: guide students to pay attention to "face"
Teacher: What about these two coins? What is the difference? Whose face is bigger and whose face is smaller?
Teacher: This is the teacher's palm. Where's your palm? Who wants to compare the palm size with the teacher? Haha, I have big palms. Do these two leaves have faces? (Showing a student touching his face at the booth) Whose face is bigger and whose face is smaller?
Design intention: to draw out the opposite preliminary understanding from the familiar life things of students, to stimulate students' desire for knowledge and pave the way for exploring new knowledge.
(2) Explore new knowledge
1. Preliminary concept of perception area
(1) Understand the meaning of area.
Teacher: What we met just now were all objects. What? What is the contrast? (Size of the surface of an object)
Design intention: Although this course does not require exploring the concept of the surface of an object, it is still guiding students to realize that the size of the surface of an object is its area. Starting from a surface of an object, students can realize that the size of a surface of an object is its area, and on this basis, they can realize that the surface of an object is sometimes composed of multiple surfaces. Lay a good foundation for students' follow-up study.
Summary: Through observation, operation and comparison, we know that the surface of an object is large and small.
Teacher: We say that the size of the surface of objects is their area. (blackboard writing)
Design intention: Let students fully touch the surface of the object, compare the size of the surface of the object, infiltrate the mathematical thought of the relativity of area size, establish perceptual knowledge for students to learn "area", and reflect the main position of students in classroom teaching.
(2) Understand the meaning of area with specific examples.
The teacher said slowly: the size of the blackboard surface is the area of the blackboard surface. Who can say this sentence completely?
Teacher: What is the size of the textbook cover? (Name a few more people)
Who can talk about the area of other faces like a teacher? Compare the size of the surface with the examples given by students.
(3) Look at the picture and speak.
The screen shows the process of abstracting the four pictures in the book into plane graphics.
Teacher: Can these figures feel their size by touching them? Do these figures have sizes? That is to say, these closed plane shapes also have areas. Who can tell where their area is? Is there any way to present this area?
Student: Point out the area and demonstrate it with courseware (color it with a single color).
Teacher: Why is it a closed figure? (Courseware demonstration: wipe a picture slightly. ) If you plant grass here, can you finish it?
Design intention: to help students understand the word "closed"
Teacher: Who can tell me what the area is? (Point out the descriptions of several students)
Complete blackboard writing: the size of the surface or closed figure of an object is their area.
(Students read together and the teacher writes on the blackboard)
(4) contact life development.
Who can give an example to illustrate which surfaces and closed graphic areas have you seen in your life and study?
Talk in groups first, and then communicate in groups. (Help students express themselves completely)
Summary: It seems that the application of area in our daily life is still very common. As long as we pay more attention to observation, we will find that mathematics is around us.
Design intention: Make full use of students' existing life experience, understand the concept of area through a series of practices of "meeting teachers-trying by yourself-innovating examples", from intuitive image to abstraction, and help students to deeply establish the appearance of area under the support of perceptual experience.
2. Hands-on operation, size comparison and correct understanding of the meaning of area.
(1) direct observation and comparison
Show two triangles with different sizes to compare areas (observation method and overlapping method)
Show me page 4 1 and practice the first question.
Design intention: Students should consolidate new knowledge in time, cultivate intuitive estimation ability and develop spatial concepts.
(2) tool comparison
Teacher: We can compare the sizes of some figures by direct observation. Now, please look at these two figures (Figure 6 in Appendix 2). Which area is the largest?
① Question: Guess, which figure has a larger area?
(2) Looking for the verification strategy:
A. which conclusion is correct? Can you find a way to verify it with the school tools in your schoolbag?
B. Personal attempt
C. communicate in groups and talk to each other. Inductive grouping method.
D. the group representatives demonstrate the verification and explain the reasons or ideas.
At least four methods can be presented: folding, placing with circular pictures, placing with small squares, and comparing with the grid of transparent film. Guide students to learn to appreciate, reflect and evaluate. (When reporting various comparison methods, the order is from complex to simple, such as: cut the overlap ratio first; Then put it together with the disc; Finally, the number of grids is calculated; ..... This reporting order is decided by the teacher's patrol during the student activities. )
(3) Teacher's summary: When comparing the size of two graphs. Different methods can be used, but the verification process must be scientific and serious. Which method do you think is better?
Design intention: Through hands-on operation, students gain their own experience in exploring mathematics and cultivate their own exploration consciousness. By grouping and using various comparison methods (observation, cutting and spelling, drawing, counting grids and unifying standards), let students participate in cooperative exchange activities. In the communication, the students realized that there are various methods of comparison, but they should unify the standards, so as to successfully verify the answers of guessing and experience the diversity of comparison strategies. Students communicate and show their own methods on the stage, which not only exercises their oral expression ability, but also gains a successful experience with the affirmation of teachers and classmates, paying attention to students' emotions, attitudes and values.
(3) Practical application
1. Feel the size of the graphic area intuitively.
4 1 page exercise 2 questions.
Design intention: Comparing the graphic area is the basic method for students to consolidate new knowledge and infiltrate the grid proportion in time.
2. Creative Competition
Practice drawing a picture on 40 pages.
Let the students talk about what should be paid attention to in the requirements. What are the similarities? What is the difference? The students try to draw by themselves. Students who finish first can look at each other and share different painting methods. Then in the class demonstration, I will experience different shapes of graphics, and the area may be equal.
Design intention: let students further consolidate their understanding of the area, let them imagine freely, draw various figures, and then organize exchanges, so that students can intuitively perceive that figures with the same area can have different shapes.
(4) Summing up the harvest
What did we learn in this class?
Design intention: to enable students to consolidate what they have learned again and achieve the goal of fully absorbing and mastering.