? "Area unit conversion" is the last teaching content in Unit 6 of Grade Three of Beijing Normal University Edition. This part of the content is taught on the basis that students have established the concept of "area", initially formed the representation of the actual size of commonly used area units, and learned the calculation of rectangular and square areas, which also paves the way for students to learn the knowledge of "hectare" and "square kilometer" in grade five. The textbook allows students to practice with questions, independently construct the mathematical model of "1 square decimeter = 100 square centimeter", and then transfer and classify "1 square meter = 100 square decimeter". Finally, through "doing one thing", guide students to apply the learned progress rate to the conversion between common area units, and further understand the progress rate between area units.

Through the study of the previous knowledge in this unit, students have experienced the construction process of "area" and "area unit", and have a preliminary representation of "1 square meter", "1 square centimeter", mastered the calculation methods of rectangular and square areas, and have the ability to calculate rectangular square areas. It can be said that students have enough experience to explore and discover the progress between area units.

Taking this course as an example, it helps students to gradually establish the awareness of quantity, tap the core literacy contained in the teaching content of quantity, explore the value and significance of "awareness of quantity", enrich students' learning experience activities, cultivate students' awareness of quantity, and cultivate students' spatial thinking ability and estimation ability.

First of all, with the help of experience, a variety of methods-to build a "sense of quantity."

The first part:

Teacher: (courseware demonstration: 1 square decimeter is how many square centimeters? )

Health 1: equal to 10 square centimeter, because 1 decimeter is equal to 10 centimeter.

Health 2: No, it should be 100. When you say the length, this is the area, and it can't be 10.

Teacher: Who is right? Can everyone try it in their own way? You can use the school tools 1 cm2 and 1 cm2 in your hand. (Students report after trying independently. )

Method 1: Swing.

Health 1: I used the pendulum method. The first line is 10, and then only the first column is 10. You don't have to fill it up. Each row is a small square of 10 1 cm2, and you can put 10 rows. 10× 10= 100, that is, 1 square decimeter is equivalent to 100 square centimeter.

Method 2: Draw a picture.

Health 2: I think it is more troublesome to put a small square of 1 square centimeter. I use the method of drawing. The side length of 1 decimeter can be divided into 10 blocks 1 cm. After horizontal and vertical lines are drawn respectively, there are small squares of 10 1 cm in each row, 10× 10= 100.

Method 3: Push.

Health 3: I did it with the square area calculation method. 1 square decimeter is a square with a side length of 1 decimeter, and 1 square centimeter is a small square with a side length of 1 cm. 1. The side length of a big square is converted into 10 cm, and the area of a big square can also be10cm×10cm =100cm 2, that is,1cm 2 is equal to100cm.

Teacher: Your method is very good. It is clearly proved by operation and reasoning that 1 square decimeter = 100 square centimeter.

[My Thinking] Students independently use their existing experience to build mathematical models, which is the process of "sense of quantity" accumulation. In this link, students experience the mathematical activities of guessing, verifying and summarizing, and through the cooperation of hands, mouth, eyes and ears, they enrich their perceptual knowledge and gain real direct experience. Guide all students to experience learning through students' display, drawing and promotion. It is proved by various methods and forms that 1 square decimeter is equal to 100 square centimeter. So as to naturally construct the meaning of the most basic quantity in the conversion of area units. Last lesson, the students' operation method in the process of finding the rectangular area is just right here. The operation method of drawing a picture is more intuitive, and drawing is actually an upgrade of the pendulum. Guide the students to observe and find that the result is 10 per line, a total of 10 lines. In addition, the first and second methods are associated with a third-party method for observation. The above two figures just intuitively demonstrate the process of transformational reasoning. From intuition to reasoning, the progressive rate between square decimeter and square centimeter is calculated step by step, which provides positive experience for learning the progressive rate between square meter and square decimeter.

Second, transfer reasoning, generalization and abstraction-explore the "sense of quantity"

The second part:

Teacher: (The courseware shows: 1 square meter is how many square decimeters? At the same time, it produces 1 m2 paperboard and 1 m2 decimeter small paperboard. Students are required to think independently before reporting and communicating.

Health 1: I think 1 square meter is equal to 100 square decimeter. Think of the above picture as 1 square meter and 1 square centimeter as 1 square decimeter, and you will know that 1 square meter has 100 square decimeter.

Teacher: With the help of the picture above, imagine a good way. Wonderful! !

Health 2: Because 1 decimeter = 10 cm, 1 decimeter square = 100 cm square, then 1 m = 100 decimeter square.

Teacher: Be reasonable, be reasonable!

Health 3: I think 1 m2 is equal to 100 square decimeter, and the orthomorphic area with side length of 1 m2 is a square area with side length of10 =100 square decimeter.

Teacher: It's a good idea to convert the unit of side length first and then calculate the area of the square.

Teacher: Observe these two relationships, "What did you find? What will you think of from this? " Students summarize themselves and then communicate. With the help of blackboard writing, students can intuitively understand that "the advance rate between two adjacent area units is 100".

Blackboard writing:

Square meters? Square decimeter square centimeter? square millimeter

? \ / ? \ / ? \ /

100 ? 100 ? 100

[My Thinking] This part of the learning process makes full use of intuitive perception, migration, analogy and other methods for students to explore and find that: because 1 m is equal to 10 decimeter, the square area with a side length of 1 m is 1 m2, which is equal to the square area with a side length of 10 decimeter. When communicating, let the students understand the essential relationship between square meters and square decimeters. After experiencing the generation and accumulation of units, students gradually form the concept of units in their minds, and use this as a standard to learn estimation, thus cultivating students' sense of quantity and accumulating measurement experience. Connecting with imagination, comprehensive perception, expanding and extending, summarizing and abstracting "the advancing rate between two adjacent area units is 100". Through induction and generalization, we not only sublimated our understanding, but also naturally grasped the law of unit propulsion rate. Accumulate "sense of quantity" in students' minds.

Third, the wonderful memory and flexible use of the image-the "sense of quantity" of the product

Although there is reasoning learning based on the conversion of upper area units, the "sense of quantity" accumulated by each student in learning is different. We can also "apply what we have learned", and it is a very effective method to accumulate "sense of quantity" in application. However, in the process of solving problems, there will always be students who are biased and have a poor grasp of the progress between area units. How can we use it flexibly? I tried "finger memorization" in teaching. This method is very effective when students use it to assist the conversion of learning length units.

The third part:

When students are practicing, they have some problems, such as 18 square decimeter =( 180) square centimeter, and 3 square meters = (? 300? ) square centimeters, 2400 square decimeters =(240) square meters. It seems that I can't grasp the law between the speeds. What should we do?

In class, a boy named Xiao Xuan stood up and said, Teacher, we can remember the progress rate between "area units" with our fingers just like learning "length units". When the hand is open, the first knuckle is the length unit, and one knuckle is regarded as the adjacent propulsion rate of 10, and the gap between fingers is small. Then the two knuckles are units of area, and the distance between fingers is larger, with two knuckles. It seems to be 10× 10= 100, and the adjacent permeability is 100. According to the conversion method of length units, from left to right, the large unit becomes smaller and the small unit becomes larger, so there is nothing wrong. Such as: 3 square meters = (? ) square centimeter, click the second knuckle of the second finger "square centimeter", then click the second knuckle of the fourth finger "square centimeter", and add a "square decimeter" in the middle, then the propulsion rate between them is100×100 =10000, both of which are What a wonderful method, intuitive and easy to understand.

According to what the students said, we improved it and formed a special "finger unit exchange algorithm", and there is also a special name called "announcement point and point area exchange algorithm" As shown in the figure, it can help us remember the conversion of length, area, volume and even mass unit rate. As shown in the figure:

[My Thinking] I am very happy to find that the students have made reasonable improvements and creations on the methods they have learned, and formed a new strategy of skillfully converting area units. From then on, as long as we learn to convert units, we all try to use similar methods. This ingenious image connection memory through vision or touch is very beneficial for students to accumulate "sense of quantity" in the whole primary school study. In this process, students can truly "learn and gain, think from what they gain, think and create, and create and enjoy".

? The cultivation of students' "sense of quantity" is an accumulation process. In addition to the above methods, there are many strategies, such as comparative estimation: knowing the size of basic units, we can imagine multiple basic units, compare perception and realize rationality. Immersive experience method: create real situations, so that students can actually experience and have perceptual knowledge of various quantities. Only by knowing more about students' experience of "sense of quantity" in teaching can we guide students to accumulate "sense of quantity" and gradually improve it, so that students' intuition and sensitivity to quantity are constantly enhanced, and students can actively and consciously understand and use sense of quantity in actual situations.