The meaning and nature of decimals, the second volume of fourth grade mathematics.

Clearly define the teaching purpose, clearly define the tasks of imparting basic knowledge, cultivating basic skills, developing ability and ideological and political education, rationally organize teaching materials, highlight key points, solve difficulties, and facilitate students to understand and master systematic knowledge. The following is the teaching plan of the second volume of fourth-grade mathematics, the meaning and nature of decimals, which I carefully arranged for you. Welcome to read for your reference. Please pay attention for more details!

The meaning and nature of decimals, the interpretation of unit materials in the second volume of fourth grade mathematics (1).

1, material selection

In this unit, we use all kinds of eggs in nature as materials. Why choose such a material? Mainly based on the following two considerations:

(1) reflects the role of decimals in nature and real life.

The quality of some bird eggs and turtle eggs is provided in the textbook. These data are not only true and reliable, but also very magical and interesting. They are eggs, too. The weight of ostrich eggs is 1, 65 kg, while that of hummingbird eggs is only 0.46 g (two soybeans are almost 3000 times). Without decimals, it is difficult to describe the size of hummingbird eggs, which shows the necessity of generating decimals.

(2) Pay attention to subject integration and realize the multidimensional value of mathematics education.

Subject synthesis is a new curriculum view advocated by the new curriculum reform. In primary schools, they are inextricably linked and constitute the whole education and teaching system. How to organically combine the information elements of various disciplines and give full play to the overall function of education is a problem worthy of our study. This unit selects "all kinds of bird eggs, turtle eggs, etc." As a material, its purpose is to give full play to the joint efforts of science and mathematics, and to maximize the educational function. This is also the greatness of our textbook "encyclopedia".

2. Context strings

(B) unit knowledge analysis

(C) the focus and difficulty of unit teaching

Key points:

The meaning and nature of decimals

The change law of decimal size caused by the movement of decimal position

Approximate decimals by "rounding"

The meaning of decimals is the basis of reading and writing decimals and comparing decimal sizes, and the nature of decimals is the basis of simplifying and rewriting decimals; The change law of decimal size caused by the change of decimal position is the basis of rewriting names; Finding the approximate value of decimal by rounding method is an essential knowledge point in decimal application. Therefore, these three teaching points are grasped, and other knowledge will naturally come. ]

Difficulties:

The rewriting of names (especially the rewriting of compound names) [here involves the requirement of accuracy. The difficulty is not small. ]

Find the approximate number of decimals by rounding.

(four) the main writing characteristics of the unit

1, the combination of numbers and shapes turns abstraction into intuition and reduces the difficulty of teaching.

The meaning of decimal is an abstract mathematical concept, and the essence of decimal is also an abstract mathematical law. It is difficult for students to really understand and master these concepts. In order to break through these difficulties, teaching materials link abstract mathematical knowledge with concrete numbers, and tap and use intuitive components in concepts, which can effectively reduce the teaching difficulty and deepen the understanding and understanding of knowledge. For example, when learning the counting unit of decimals on page 50 of the textbook, a big square is used to represent the integer "1", and its decimal place and percentage are respectively expressed as a decimal and two decimals; On page 57, when learning the basic properties of decimals, a ruler shows that a few centimeters is a few tenths of a meter; On page 55, the relationship between a point and the corresponding two decimal places is established,,,,, which deepens students' understanding of the meaning and nature of decimals.

2. Always pay attention to the meaning of decimals in teaching.

The teaching contents of the five information windows arranged in this unit are step by step. The meaning of decimals is the basis of further teaching the properties of decimals, the rules of comparing decimal sizes, the rules of changing decimal sizes caused by decimal movement, and the methods of rewriting names. Every knowledge point in the last four windows is explored from the perspective of decimal meaning. With the teaching of these knowledge points, the concept of decimal is gradually clear and clear, and the understanding of decimal is further sublimated.

3. Choose a lot of meaningful realistic data.

When reading the materials, I said that the data in the clearing window are all real data. This feature is not only reflected in the information window, but also fully reflected in practice. Such as (54 pages, 6 questions) the most vegetables, (60 pages, 9) the main nutritional components of several foods per100g, (69 pages, 5) the Guinness Records of several plants, (70 pages, 9) the running speed of several animals, population data of several states, etc. , integrating knowledge, application and ideological education.

(5) Interpreting the unit information window

Information window 1(49 pages)

1, situation diagram (see page 49 of the textbook)

(1) Scene Interpretation: The scene title of this information window is "Bird Egg Quality". The eggs of red-crowned crane, albatross, ostrich, chicken and four kinds of birds were displayed on the spot, and the quality of the eggs of four kinds of birds was marked.

(2) The information carried by the scene map: There are four items: (1) The mass of the red-crowned crane is 0,25 25kg；; (2) The mass of albatross eggs is 0.365 kg; (3) The mass of ostrich eggs is1.65kg; (4) The mass of the egg is 0.06kg. ..

2. Knowledge points

There are three examples in this information window * * *, and the knowledge points included are (1) the meaning of decimal (the understanding of two decimal places) (2) the meaning of decimal places (the understanding of three decimal places, the counting unit and digits of decimal places) (3) the reading and writing of decimal places.

3. Teaching suggestions

(1) focuses on the meaning of two or three digits after the decimal point, and gradually forms a relatively systematic and complete decimal concept and counting method.

With regard to the teaching of decimal meaning, the textbook is arranged as follows: first, learn to read and write decimals, and then learn the understanding of two-digit decimals and three-digit decimals. At the same time, take two-digit or three-digit decimals as an example to understand counting units and digits and summarize the meaning of decimals. The example does not involve more than three decimal places, and it is basically not involved in the exercise. The purpose is to reduce the difficulty, focus on two or three decimal places, and fully understand the meaning of decimals. Therefore, in teaching, teachers should refine the teaching process and make full use of intuitive means so that students can get full perception and experience. Fractions with denominator of 10 can also be written as decimals, and a decimal represents a few tenths; Fractions with a denominator of 100 can also be written as two decimal places, representing a few percent. By learning examples and doing basic exercises, we can gradually deepen our understanding of decimals. On this basis, if you encounter a page of 0297 kg; Page 64 0,0528; 72 pages 1, 3,295 hectares; When you encounter four decimal places on 74 pages, such as 40075 and 5696 kilometers, or many decimal places, you can draw inferences from others, migrate independently and pretend to be reasonable, and gradually form a relatively systematic and complete decimal concept.

(2) Understand the relationship between decimal places and digits in the activity of sorting out the digital sequence table independently.

For example, on page 5 1 of the textbook, when learning the numerical order representation of decimals, teachers can remove a line from the numerical order table, so that students can sort out the numerical order and counting units of decimals by themselves through independent exploration and deepen their understanding of numbers and counting units. (Let students fill in independently and let go completely)

(3) Help students understand the meaning of numbers and bit values with the help of counters.

It is an effective method to help students understand the meaning of numbers and bit values with the counter on page 53 of the textbook. Due to the limitation of space, the textbook does not arrange this content in exploration, but in practice. It is suggested that the teacher regard it as an example exercise. Can you dial the following decimals on the counter? Fully understand its importance and can't treat it as ordinary exercise.

4. Pay attention to the problem

(1) Combine the examples around you to deepen the understanding of the practical meaning of decimals.

The green textbook divides the teaching of decimals into two stages. The third unit in the first volume of Grade Three is "Learning at Home-Preliminary Understanding of Decimals". This unit in the book "The World of Eggs-Significance and Properties of Decimals" is the beginning of systematic learning of decimal knowledge, and its content is the most basic knowledge in decimals, which is the basis for learning four decimal calculations. So this unit is the focus of the whole decimal teaching. Therefore, in this part of teaching, teachers should use examples around them to guide students to deepen their understanding of the practical significance of decimals. Can summarize the meaning of decimal in language.

For example, after learning examples, let students talk about the application of decimals in life.

Students can cite many examples according to their own experiences, such as: going to the bookstore to buy books and "talking about new learning methods" 5. 35 yuan; New 100,000 Why 10, 95 yuan; "Fairy Tale King" 3, 85 yuan; "We love science" 8, 10 yuan; And measure the height, Xiaohong 1, 46 meters, Xiaoming 1, 52 meters.

(2) Guide students to summarize the meaning of decimals and improve their ability of abstract generalization.

Abstraction is the essence of mathematics. It is one of the main goals of concept teaching to guide students to abstract and summarize mathematical concepts in relatively standardized and concise language and to raise perceptual knowledge to rational knowledge. Therefore, we should cultivate students' ability of abstraction, induction and generalization in concept teaching and improve their mathematical literacy.

(3) Establish the concept of decimal with the help of intuitive model.

In the exploration of learning the meaning of decimals, the textbook provides us with some intuitive models (see page 50 of the textbook, where two digits are plane figures and three digits are three-dimensional figures). These mathematical models will greatly help students intuitively understand the meaning of decimals. I hope that teachers can dynamically show the process of average score with pictures or multimedia, so that students can deeply understand the meaning of decimals.

(4) Flexible handling of teaching scenarios in textbooks to improve the effectiveness of teaching.

For the original teaching situation in the textbook, my personal views are as follows: First, we should respect it. Second, we should treat it rationally. The reason why we should respect it is because the materials selected in the Youth Edition textbooks should be said to condense the wisdom of many experts, scholars, researchers and front-line backbone teachers. After several years of teaching practice, it should be said that it is more practical and effective. Therefore, teachers should dig deep into its connotation, make full use of it, and in the words of teachers, don't betray her cheaply. On the rational treatment of situations in textbooks. Because, influenced by teaching conditions, students' living environment and regional characteristics, even the best textbooks can't adapt to all teaching objects. Therefore, teachers can extensively explore real, effective and vivid teaching situations with strong "mathematical flavor" in real life according to the specific conditions of their students, so as to replace the original situations, thus meeting the learning needs of students and realizing the due value of situation introduction.

Step 5 practice independently

Page 53 Question 2 Page 55 Cabin

Information Window 2 (page 56)

1, situation map (see page 56 of the textbook)

(1) Scene Interpretation: The scene title of this information window is "Quality of Turtle Eggs". The scene map shows the eggs of flat-breasted turtles, snake turtles, green-haired turtles, money turtles, small crocodiles and five kinds of turtles, and also marks the quality of the five kinds of eggs.

(2) The information carried in the scene map: There are five groups: (1) The mass of the flat-breasted turtle is1,84g0 and 4 decimeters long (2) The snake turtle is 24, 185g (43) The green turtle is1/.

2. Knowledge points

There are five examples in this information window * * *, and the knowledge points included are (1) the comparison of different decimal sizes in integer parts (2) the comparison of the same decimal size in integer parts (3) the law of decimal size invariance (basic properties of decimals) (4) the simplification of decimals (5) the rewriting of decimals.

3. Teaching suggestions

(1) Guide students to ask questions of "research value" for learning new knowledge.

There are five messages in the message window. From the perspective of combination, students can ask many questions, such as the addition and subtraction that students are used to. Generally speaking, for this information, they will also ask "who is heavier than who". Here, teachers must pay attention to guiding students. Guide them to ask questions about this class (can you ask the question of comparing the two quantities? ) to ensure the effectiveness of study time.

(2) Teaching the nature of decimals and highlighting the experience of natural connotation.

Experience the rationality of nature first, and then experience the application of nature. The nature of decimal is one of the important contents of decimal concept. Teaching the nature of decimals can help students further understand the meaning of decimals and make necessary knowledge preparation for teaching the calculation of four decimal places. The textbook is divided into two sections to teach the nature of the decimal system. The first paragraph is to understand the content of nature (the second red dot in 57), and the second paragraph is to rewrite decimals by using natural simplification (a small computer with 58 pages). When summarizing the nature of decimals, due to the limitation of space, only one example is listed in the textbook. From the perspective of discovering and summarizing the laws, the examples are a little thin and unconvincing. Therefore, before students sum up the rules, it is suggested that students can be guided to supplement some similar examples to verify their findings. Example 2, 5 yuan =2, 50 yuan. 0, 1 m =0, 10 m =0, 100 m and so on. These examples can provide rich perceptual materials for the nature of decimals, so that students can experience the law of adding "0" or removing "0" at the end of decimals and keeping the size of decimals unchanged in many examples.

(3) In the practice of comparing sizes, compress the thinking process and master the comparison essentials.

In the process of red dot teaching, students are exposed to some situations that are often encountered when comparing decimal sizes (the integer parts are different, the integer parts are the same, and there is a zero at the end of the decimal), and they experience the comparison method in detail. Then, in the independent practice, students can apply the preliminary experience, and through a certain number of exercises, further experience the method of comparison and master the essentials of comparison. For example, if you compare the sizes of 0, 604, 0, 64, 0, 064, 0, 46, 0 and 6 on page 2 of page 59, they are all pure decimals. Just look at the decimal place of 6 and compare it with 0,604,0,64,0 and 6. From small to large, they are 0, 6 and 6 respectively. The order of five numbers is 0,064, 0,4,0,6,0,604,0,64. Doing problems in this way can guide students to compress their thinking process, experience the essentials of comparison and cultivate the flexibility and sensitivity of thinking.

(4) In the open questions, discover and master the general rules of comparing decimal sizes.

6 1 Page 65438 +0 1 Question. At 8 o'clock, □ 7 > 8, 47, the box can hold 0, 1, 2, 3; 56、24? 56, 2□ box can be filled with 5, 6, 7, 8, 9; By filling in these figures, if the integer parts of the two decimal places are the same, the decimal place with the largest tenth digit is larger, and if the tenth digit is the same, the decimal place with the smallest digit in the percentile is smaller. In exercise 12, the composition card is divided into six different decimal places, which are arranged in order of size. The students experienced the findings in the question 1 1 again. These findings are general rules for comparing decimal sizes. If we master these laws, we can quickly compare the sizes of decimals and make correct judgments.

4. Pay attention to the problem

The teaching order of (1) red dot 1 and red dot 2 can be changed by asking.

See page 56 of the textbook. Which is more important for teachers to guide students? After the light topic, students can first mention which is heavier, the green turtle egg or the golden turtle egg. It is also possible to mention first which is heavier, the small crocodile turtle egg and the flat breast turtle egg? Because there is no order between these two knowledge points, teachers can randomly determine the order of knowledge learning according to the order of students' questions.

(2) Discover the essence of decimals by intuitive methods.

The nature of decimals is actually reflected in the nature of decimals, because adding 0 at the end of decimals is reflected in fractions, that is, adding 0 to both numerator and denominator, and removing 0 at the end of decimals. This is also the case. The nature of decimals is very important. Students know that adding "0" to the "0" at the end of the decimal does not change the size of the decimal and deepens their understanding of the meaning of the decimal. It is also the basis for calculating four decimal places, simplifying and rewriting decimals, and comparing decimal sizes. Therefore, students must have a deep understanding of the nature of decimals. The nature of decimals is essentially to explain when decimals are equal. It is related to the basic properties of fractions. Because students have not learned the basic nature of fractions, they can only explain them in an intuitive way. (See page 57 of the textbook) These two pictures are very important and students must understand them.

(3) Set aside time and space for students to discuss the key issues set in the textbook. For example, when learning the simplification of 58 pages of decimals, a key question is thrown in the textbook: "Can this 0 be removed?" When learning how to rewrite decimals, the textbook throws a key question: "How to rewrite 5 to three decimal places?" For these key issues, teachers must pay attention to them, do not pass them by, and provide students with enough time and space for independent thinking and cooperative exploration, fully mobilize their thinking, and deepen their understanding and internalization of knowledge.

Step 5 practice independently

6 1 Page 10,1/Question

Information Window 3(62 pages)

1, situation map

(1) Interpretation of scene diagram: The scene title of this information window is "Quality Relationship of Four Birds' Eggs". The scene map shows cuckoo, hummingbird, golden pheasant and kiwifruit, and also shows the quality of kiwifruit eggs and the multiple relationships between kiwifruit eggs and other three birds.

(2) The information carried in the scene map: There are four items: (1) The kiwi egg has a mass of 460,5g; (2) The quality of a kiwi egg is equivalent to that of 10 golden eggs, 100 cuckoo eggs or 1000 hummingbird eggs.

2. Knowledge points

There are three examples in this information window * * *, and the knowledge points included are (1) the change law of decimal size caused by moving the decimal point to the left (2) the change law of decimal size caused by moving the decimal point to the right (3) the change law of decimal size caused by moving the decimal point to solve problems.

3. Teaching suggestions

(1) Explain the new expression.

In the previous primary school mathematics stage, the conventional understanding was: expanding several times means multiplying several times, and shrinking several times means dividing by several times. However, some people have different views on this. Some people think that if the number A is expanded by n times, it should be a+na times, not na times. Some people think that the number of times only applies to the expansion of numbers, not to the reduction of numbers (some people think that doubling the original number is 0a-na). Considering the above problems and the connection with middle schools, our textbook has changed its expression (see page 63 of the textbook) and moved at the decimal point. Change "expand,,,,, and times" and "shrink,,,, and times" to "expand to its,,,,, and times" and "shrink to its,,,,

Expand to 10 times the original number.

Expand to its 10 times.

Reduce to the original number of110.

Reduce to110.

(2) Deal with the problem of "zero padding".

It is important to solve the problems of "zero-filling" and "zero-removing" when applying the law that the decimal position changes, especially when the decimal point moves to the left, if there are not enough integer digits, the zero-filling problem can be divided into two cases. A non-integer number, such as 1 reverts to the original 65438+. Second, after the decimal point is moved to the left, the zero behind the decimal point should be removed, for example, 250 should be changed to the original11000 (the last green dot on page 63 of the textbook only indicates the problem, not the calculation process. The teacher here must deal with the problem of "filling in zeros" in place)

4. Pay attention to the problem

(1) Handle the choice of old and new expressions.

As mentioned above, the expression of expanding or shrinking a number is different from before, so we will take the expression of one line as the criterion in future study and abolish the original unscientific statement. In particular, some nonstandard books for students may contain old sayings. Teachers should pay attention to explaining them to students to avoid unnecessary confusion.

(2) Determine the function of the example according to the cognitive needs.

For the case, see People's Education Edition "Decimal Change Law".

Step 5 practice independently

Question 9 on page 66

Information Window 4(67 pages)

1, situation map

(1) Scenario Interpretation: The scenario title of this information window is "The Growth of Swan". The scene shows newborn swans and adult swans, and the weight of swans in these two periods is also marked in the picture.

(2) The information carried by the scene map: There are two items: (1) The newborn swan weighs 200 grams; (2) Adult goose weight10,5 kg.

2. Knowledge points

There are two examples in this information window * * *, which contains the knowledge points of (1) singular rewriting (2) complex rewriting.

3. Teaching suggestions

(1) Master the three main steps of name-number interconversion.

First, it is discriminated whether the number of low-level units is rewritten as the number of high-level units or whether the number of high-level units is rewritten as the number of low-level units, so as to decide how to calculate.

B ensure that the propulsion rate between two units is 10, 100 or 1000.

C according to the above two aspects, determine whether the decimal point should be moved left or right, and move a few places.

(2) Guide students to summarize the rewriting methods.

After learning the rewriting of single numbers of red dots and compound numbers of small computers, students have some understanding of the rewriting methods of names. Although students are not required to summarize the rewriting methods in textbooks, my personal opinion is to allow students to tell the basic steps and methods of rewriting in their own language and improve their ability of induction and generalization.

4. Pay attention to the problem

(1) reflects the necessity of rewriting to the same company.

The question raised on page 67 of the textbook is how much weight the swan has gained when it grows up. To solve this problem, we must rewrite different units into the same unit. The intention of the textbook itself is to start with solving problems, leading to the rewriting of decimals and names, and highlighting this rewriting is the need to solve problems. In teaching, teachers should pay attention to this point.

(2) Encourage the diversification of rewriting methods.

On the issue of diversification, first, the example itself embodies the characteristics of diversification. For example, in the exploration section, the first child rewrites the name of the senior unit into the name of the junior unit, and the second student rewrites the name of the junior unit into the name of the senior unit.

In addition, students may have other algorithms, ① 200 g = 0,2 2kg；; ② 0，5 kg-0，2 kg = 0，3kg； ③ 10 kg+0，3 kg = 10，3 kg。

(3) The mutualization of complex numbers is a difficult point, which needs to be broken through.

The interconversion between decimals and complex numbers is a teaching difficulty, mainly due to two reasons: First, students often make mistakes in the rate of progress (the rate of progress is 100, but it is very difficult if the rate of progress is 100, 1000 or 60), and second, students don't know enough about odd complex numbers, and they haven't been exposed to many integers in the past. The 68-page microcomputer shows the topic of rewriting composite numbers, which is the teaching difficulty of this information window. The textbook only shows the problem, not the rewriting process. Its purpose is to increase its openness, but it does not mean that it can be weakened. Teachers should not make light of it, but must explain it to students step by step, especially 2,39kg = _ _ _ kg _ _ _ g, which involves a problem of filling in zeros.

Step 5 practice independently

Page 68 Question 1

Information Window 5 (Page 7 1)

1, situation map

(1) Scene Interpretation: The scene title of this information window is "Measuring Birds' Eggs". This scene shows two children measuring the length of a bird egg.

(2) The information carried by the scene map: There are two groups: (1) Xiaohua read that the length and diameter of bird eggs are 3 or 9 cm, and Xiaoming read that the length and diameter of bird eggs are 4 cm; The width and diameter of a bird's egg are 2. 04cm.

2. Knowledge points

There are two examples in this information window * * *, which contains the knowledge point of (1) finding the approximate number of decimals by rounding (2) consolidating the method of finding the approximate number of decimals (taking the approximate number in special cases). (In autonomous exercise: rewrite the decimal into a number in units of 10,000 or 100 million; A reserved decimal number with exactly 0 at the end. )

3. Teaching suggestions

(1) In the exploration session, we should grasp the key issues and discuss them.

See page 7 1 of the textbook and set two key questions. As long as we grasp these two key points, the problem of divisor will be solved.

(2) Clearly preserve the relationship between decimal places and precision.

In the process of finding the approximate number of decimals, guide students to understand the meaning of keeping a few decimals, that is, keeping a decimal accurate to the tenth place and omitting the mantissa after the tenth place; Keep two decimal places accurate to hundreds, omit the mantissa after hundreds, and so on.

In addition, it is particularly important to point out that when calculating the approximate number of decimal places, students should be guided to understand the accuracy of keeping different decimal places. For example, can the 0 in the green dots 2 and 0 on page 72 of the textbook not be written? This green dot is set to let students experience the accuracy. If you don't write, it means that 2 and 04 are reserved to integers, and if you write 0, it means that one decimal place is reserved, and the precision to the tenth place is higher than that to the integer. Although 2, 2 and 0 are equal in size from the perspective of decimal nature, they represent different degrees of accuracy from the perspective of accuracy. Therefore, the "0" at the end of approximate numbers 2 and 0 cannot be removed here.

4. Pay attention to the problem

(1) Let students feel the significance of seeking divisor by combining the real situation around them.

For example, when measuring the length and weight of an object, due to the limitation of tools, errors will inevitably occur, and the results obtained are approximate (height 1, 63 meters); For example, the length of the desk measured by a ruler is 1 and 12 meters, and the weight of the nickname measured by a scale is 25 and 5 kilograms. Here, 1, 12 and 25, 5 are approximate values, but when counting large numbers, they are generally approximate values, such as 13 in a city. Here 13,50,000,13 and10 billion are approximate figures. Through these examples, students can realize that data that are generally consistent with reality or numbers that are close to reality are called approximations, and further understand the meaning of approximations.

(1) Exercise with "√" appropriately.

There is no practice for students to write "≈≈≈≈≈≈≈≈≈≈".

Step 5 practice independently

Page 73, question 5, question 74, have you learned?

(vi) Several questions raised in this unit.

1. How to help students build a model of decimal meaning?

2. The conversion between the nature and name of decimals is the teaching difficulty of this unit. What effective measures do you think can be taken to break through these difficulties?

3. How to play the role of calculator in the teaching of exploring mathematical laws?

4. The new curriculum advocates students' autonomous learning, so how to grasp the guiding role and promoting role of teachers?