First, the analysis of learning situation

The teaching and learning of these contents are carried out on the basis that students master the characteristics of rectangles and squares and can calculate the perimeters of rectangles and squares. The length of primary school students' learning area is a leap in the cognitive development of spatial form. Learning the content of this unit well will not only help to develop students' spatial concept and improve their ability to solve simple practical problems, but also lay a foundation for learning the area calculation of other plane graphics in the future.

Learn this unit well, make use of the characteristics of rectangles and squares that students already know, let students operate by hands, learn the knowledge of this unit through observation, measurement, estimation, induction and reasoning, and collect, analyze and deal with some common sense related to area units in students' lives, such as: my home area is 100 square meters, and the house price per square meter is 3,500 yuan. But the students don't have it in their heads. Therefore, when understanding the unit of area, let students find the surface similar to the size of the unit of area in their own body or life, so as to understand and remember the unit of area in connection with real life, which will enable students to quickly establish the representation of the unit of area in their minds. After students establish the representation of area units, let them use the area units they have learned to estimate the size of the surface of objects in life, so that students can have a deeper understanding of area units in the process of application.

Second, the teaching objectives

1. Make students know the meaning of area with examples, and estimate and measure the area of a graph with units of their own choice; Understand the necessity of introducing a unified area unit, understand the area unit square centimeter, square decimeter, square meter, square kilometer and hectare, and establish the expressions of 1 square meter, 1 square decimeter and 1 square centimeter; Familiar with the propulsion speed between two adjacent units, and can perform simple unit conversion.

2. The teaching case of mathematics "area" in the third grade of primary school: let students explore and master the area formulas of rectangles and squares, and gain the experience of inquiry learning; The formulas can be used to correctly calculate the areas of rectangles and squares, and the areas of given rectangles and squares can be estimated.

Third, the focus of teaching

1. Let students know the meaning of area, master the commonly used area units, and establish the representation of area units.

2. Let students discover the calculation methods of rectangular and square areas through hands-on practice and communication, and master them.

Formula for calculating area.

3. Understand the meaning of area, know the area unit, and grasp that the progress rate between adjacent areas is 100.

Fourth, teaching difficulties.

1. Make students establish the concept of area and the representation of area units.

2. Experience the necessity of introducing unified regional units into the operation.

3. Derivation of the formula for calculating the area of rectangle and square.

4. The concept of area and the formation process of common area units. The specific teaching process is as follows:

5. Grasp that the propulsion rate between adjacent areas is 100.

Five, the unit class arrangement

7 1-74 1 class, exercise 18, question 1 and 2.

Page 74-75 of Lesson 2: Example 1, Exercise 18, Questions 3 and 4.

Examples 2 and 3 on P77-78 of the third category; Exercise 19 question 1-4

Lesson 4 P80-8 1 page; Exercise 19 Question 5- 1 1

P82-83 is in Class Five.

Lesson 6 P84-85

P86-87 (sorting and reviewing)

Six, teaching materials and teaching suggestions

Textbook description

1. Content structure and status of this unit.

This unit mainly includes four parts: area and area unit, area calculation of rectangle and square, advancing rate of area unit and common land area unit. The structure of this part is as follows:

The teaching and learning of these contents are carried out on the basis that students master the characteristics of rectangles and squares and can calculate the perimeters of rectangles and squares. The length of primary school students' learning area is a leap in the cognitive development of spatial form. Learning the content of this unit well will not only help to develop students' spatial concept and improve their ability to solve simple practical problems, but also lay a foundation for learning the area calculation of other plane graphics in the future.

2. The characteristics of textbook compilation.

(1) shows the formation process of the concept.

This unit has many concepts and is also very important. In order to help students establish concepts, the textbook fully shows the formation process of concepts. For example, the concept of area is an important initial concept of this unit. The textbook starts with comparing the size of the cover and the size of the plane closed figure, and moves from direct comparison to indirect comparison. Through various comparison activities, on the basis of obtaining a variety of perceptual knowledge, it helps students abstract the concept of area.

(2) Pay attention to form a common area unit representation.

Form the appearance of common area unit, that is, form the concept of actual size of common area unit. This is of great significance for students to consolidate the concept of area, learn to choose the appropriate area unit according to the actual situation, and further form the ability to estimate the area. In addition to introducing each area unit and explaining its meaning, the textbook also guides students to feel the actual dimensions of 1 cm2, 1 decimeter square and 1 square meter through observation and gestures, and initially forms the appearance of the actual dimensions of the area unit. In addition, let students experience various practical activities of estimating the area to consolidate the appearance.

(3) Comparative analysis of strengthening concepts.

This is an effective measure to prevent concept confusion, promote accurate distinction of concepts and strengthen memory. Taking the area unit as an example, the measures taken in the textbook are as follows: first, strengthen the comparison between different size area units; Second, strengthen the distinction between area units and corresponding length units. These measures are helpful for students to establish a clear concept of area unit.

(4) Let students experience the process of inquiry.

When discussing the area calculation of rectangles and squares in textbooks, we should pay attention to creating appropriate problem situations, so that students can experience a relatively complete inquiry process driven by tasks. In addition, when discussing the progress rate between units with common area, and in some exercises, we should pay attention to leaving students with appropriate exploration space so that they can gain exploration experience while completing the exercises.

Teaching suggestion

1. Change the mechanical learning of concepts into meaningful learning.

In the learning of mathematical concepts, mechanical learning means that students can only remember the descriptions and symbols of mathematical concepts, but they don't understand their internal meanings, let alone their relationship with related concepts. Meaningful learning means that students can not only remember the descriptions or symbols of the concepts they have learned, but also understand their internal meanings and substantive connections with related mathematical concepts. In layman's terms, it is to master concepts on the basis of understanding. As far as the study of area units is concerned, students can be promoted to understand concepts from three aspects. First, why did the initial perception choose a square as the shape of the area unit? The second is to know how each area unit is stipulated; The third is to understand the internal relationship between area units and corresponding length units.

2. Strengthen intuitive teaching and enrich students' direct experience.

In the teaching of space and graphics, providing intuition is often the starting point of understanding and learning. Making good use of intuitive means and strengthening intuitive teaching are of great significance for mastering the knowledge of space and graphics.

In the teaching of this unit, we should strengthen hands-on activities, and let students learn while doing through hand, mouth, eyes and ears, especially through hands-on experiments, which is conducive to enriching students' perceptual knowledge and effectively improving the effect of knowledge intake.

In the teaching of this unit, we should also pay attention to giving full play to the advantages of various intuitive means to foster strengths and avoid weaknesses. Some contents, such as making multimedia courseware, are of course good. But there are also some contents, such as understanding the area unit. Instead of using multimedia, it is better to use conventional teaching AIDS and learning tools, so that students can truly feel the actual size of area units and get real direct experience, which is more conducive to the formation of representations.

3. Let students explore and take the initiative to draw conclusions.

In order to change the tendency of overemphasizing simple acceptance and passive acceptance in previous teaching, it is necessary to choose appropriate content, provide certain space and guide students to actively explore and learn.

In this unit, the calculation of rectangular area is not difficult to explore, the conclusion is easy to find, and it is convenient for intuitive operation experiments. It is a subject suitable for students to explore in primary school mathematics. Teachers should make full use of these characteristics of teaching content and organize students to carry out inquiry learning.

4. Pay attention to the cultivation of estimation ability.

Although estimation is a rough measurement method, it is widely used in real life. People usually have more opportunities to estimate the area than to measure it accurately. Therefore, the textbook of this unit pays more attention to the estimation of area, which is not only reflected in "doing something", such as "estimating the area of the classroom in this class is about how many square meters." "Estimate the area of the textbook cover, and exchange the estimation method in the group." There are also many reflections in the exercises. For example, many exercises to calculate the area require students to estimate first and then measure the length, width (or side length) to calculate the area. Paying attention to the cultivation of estimation ability is also helpful to improve the ability to solve practical problems.

5. The content of this unit can be completed in 7 class hours.

Four, the specific content of regional and regional units and teaching suggestions.

Area and area unit (pages 70-76)

Generally speaking, the order of this part is: understanding the area → introducing the area unit → comparing the length unit with the corresponding area unit. Separately, the concept of (1) area includes two aspects: the surface size of an object and the size of a plane closed figure; (2) Area units, including the necessity of unifying area units, and why a square with a side length of "1" is used as the area unit; (3) Comparison between 1 cm and 1 cm2, 1 decimeter and 1 decimeter 2, 1 meter and1square meter.

1. Theme map.

This is a picture of a classroom scene, which provides a lot of learning information about area and area unit. For example, the blackboard on the wall and the TV screen can be distinguished by observation. In the classroom, the students are doing their homework. Some use overlapping method to compare the size of the cover of textbooks and exercise books, some put a disk or triangle on a rectangle, some put a small square of 1 square centimeter on the thumb to compare the size, and some use a square of 1 square decimeter to measure the desk area. Two other students are sorting out the wall newspaper. In this way, presenting relevant learning content in the real life background will help to stimulate students' interest in learning, and also help students to learn with the help of existing knowledge and experience in specific situations, from which they can gain rich perceptual knowledge and understand it.

2. The concept of area.

The concept of area can be introduced from two aspects: comparing the surface area of an object and comparing the size of a plane closed figure. The former can find the object of observation and comparison from the theme map, such as comparing the blackboard with the TV screen, and can also let students compare the cover sizes of math textbooks and exercise books according to the tips of textbooks. From this, we can naturally draw two methods to directly compare the size of closed figures on the surface or plane of objects, one is observation comparison method, and the other is overlapping comparison method. Generally speaking, we can observe and compare when there are obvious differences in the size of the surface or plane figure of the object; When the size difference is not too big to draw a conclusion, and the objects are easy to overlap, the overlapping method can be used to compare the sizes.

In addition, there is an indirect comparison method, that is, based on a unified figure, a pendulum is made in the plane part to be compared and several such figures are counted. The two rectangles on page 7 1 of the textbook can be compared by indirect comparison method. This arrangement paved the way for the introduction of area units.

In teaching, the concept of area can be introduced according to the following steps.

Take a look. Which is bigger, the blackboard or the screen?

Compare, which cover is bigger, the math textbook or the exercise book?

Guess, two rectangles, which is bigger?

On this basis, the description of the concept of area is introduced. Then ask the students to say the results of the above two comparisons with "area". You can also let students look at the objects around them, for example, comparing the areas of two surfaces. For example, compare the size of blackboard surface and class table surface, and the size of class table surface and chair surface.

3. Area unit.

In order to make students understand the necessity of introducing area units, the textbook compares the sizes of two rectangular areas on page 70, creates a problem situation and designs a series of contradictions and conflicts. First of all, it is difficult to see which of the two rectangles is bigger by observation. Secondly, because of the different shapes, it is difficult to compare the sizes by overlapping method. This has caused cognitive conflicts and prompted students to try to use indirect comparison method, that is, to compare with other graphics as the standard. Therefore, students can choose their own measurement standards for comparison, and may choose different standards: different graphics (such as disks and squares); Graphics with the same shape but different sizes (such as squares with different sizes); Graphics (such as squares) with the same shape and size, etc. Through personal experience, students can find that it is not good to have different shapes or sizes as a relatively standard figure to get consistent measurement results. It is concluded that "to compare the sizes of two figures, we should use a unified area unit to measure them." Further, let the students think about what kind of graphics are suitable for representing area units. In this regard, students generally choose a square from the perspective of convenient pendulum and measurement. This is of course reasonable and practical. But teachers should understand that it is purely artificial to define the area unit as a figure of what shape and size. Other shapes can also be selected as required, such as regular triangles.

Next, the textbook introduces the provisions of common area units of square centimeter, square decimeter and square meter, and through various activities: "Which fingernail is closest to 1 square centimeter?" "Hand-painted size of 1 square decimeter." "Try it, how many students can stand in a square of 1 square meter?" Let students perceive the actual size of these area units.