Question 2: The meaning of the score. Fraction indicates the fraction of one number to another, or the ratio of one event to all events. Divide the unit "1" into several parts on average, and the number representing such a part or parts is called a fraction.
Question 3: The meaning of the score divides the unit 1 into several parts on average, and the number representing such one or several parts is called the score.
For example, the unit 1 is divided into five parts, that is, the number of such a part is 1/5, and the number of such three parts is 3/5.
Question 4: Generation and significance of decimals 1. Explore the generation of decimals.
1, game: estimate, test.
Do students like playing games? Today, the teacher will play an estimation and test game with you. This is a rope. Let's estimate how long it is
Ask a classmate to measure and verify the answer.
② Who will estimate the length of the desktop?
Ask the students to measure and reveal the correct answer.
What if it is less than 1 meter?
2. Reveal the generation of decimals:
There are many examples in life where you can't get integer results. Therefore, people thought of using fractions and decimals to express them, so decimals came into being. Let's study the mystery of this lesson!
Second, explore the significance of decimals
(A) to explore the meaning of decimal places
(Showing courseware) We can learn with the help of the meter ruler.
1, 0. 1 m.
① Divide 1m into several parts, and each part is decimeter long.
(2) What is the fraction in meters and its denominator?
Write down how many meters are decimals and introduce what decimals are.
④ Summary: Divide 1 m into 10 parts, each part is one tenth of a meter, one tenth is a decimal counting unit, and the decimal is 0. 1.
2, the group knows 0.3 meters and 0.7 meters.
Please complete the blank space on page 50 of this book in groups.
3. Student report.
4. Summary: Just now, we divided 1m into 10 parts on average, and used a few tenths of a meter or a decimal place to represent such a part or parts, so a few tenths can be represented by a decimal place.
(B) to explore the meaning of two decimal places
1, look at the courseware, and perceive that 1 meter is divided into 100 on average.
Just now we divided 1 meter into 10 parts, and each part is 1 decimeter. If we divide every 1 decimeter into 10 parts, how many points will we divide 1 meter into?
2. Know 0.0 1 m.
① We divide 1m into 100 blocks on average. How long is each piece?
② Summary: Divide 1 m into 100 parts, each part is 1% m, 1% is a counting unit with two decimal places, and the decimal number is 0.0 1.
3, self-study: know 0.03m and 0.07m m.
Please follow the method of learning one decimal place, explore by yourself, and fill in the blanks on page 5 1 in the book.
4. Student report.
5. Summary: Just now, we divided 1m into 100 equally, and expressed such one or several copies with a few meters or two decimal places, so the percentage can be expressed with two decimal places.
(C) explore the meaning of three decimal places
1, (showing courseware) If 1 m is divided into 1000 copies on average, how many meters of works is this 1 copy, 6 copies, and 13 copies? Please follow the method of learning two decimal places, explore by yourself and fill in the blanks on page 5 1 in the book.
3. Student report.
4. Summary: Just now, we divided 1 meter into 1000 parts on average, and expressed such one or several parts with a few thousandths of a meter or three decimal places. So a few thousandths can be expressed by three decimal places. Each part is one thousandth. So one thousandth is a counting unit with three decimal places, which can be written as 0.00 1.
(4) expansion
If 1 meter is divided into 10000 parts, you can write a fraction with denominator and get several decimal places.
Summary: If you keep dividing like this, you can get many different fractions and decimals.
(5) Summarize the meaning of decimals.
1, group discussion: Look carefully at the scores and decimals we wrote. What did you find?
2. Group Report
3. Summary: A few tenths can be expressed with one decimal place, a few percent can be expressed with two decimal places, and a few thousandths can be expressed with three decimal places. Therefore, fractions with denominators of 10, 100, 1000 can be expressed in decimals. This is the meaning of decimals.
4. What does the ellipsis mean here?
(6) Inductive counting device
1, what are the decimal counting units? Please read the textbook and learn the decimal counting unit.
2. Student report
3. Summary: Counting units of decimals are one tenth, one hundredth, one thousandth ... written as 0. 1, 0.0 1, 0.005438+0 respectively. ...
(7) Learning rate
1, think about it: what is the propulsion rate between 0. 1 and 0.0 1? What is the lead time between 0.0 1 and 0.00 1? What is the forward speed between two adjacent counting units?
2. Student report.
3. Summary: The propulsion rate between every two adjacent counting units is 10.
5. Emphasize: What do you mean by adjacent?
Third, practice to consolidate and deepen understanding
1, do it on page 5 1 in the textbook.
2. Use of decimals. Do exercises ... >>
Question 5: What problems should we pay attention to in understanding the meaning of scores?
Problems and solutions in the construction of fractional meaning
Feng Gang ethnic primary school
In primary school mathematics, the study of fractional knowledge is an abstract but important content. Students begin to learn grades in the third grade, and most students feel very eager to learn. However, when they further studied the meaning of fractions in the fifth grade and initially began to use fractions to solve problems, many problems were exposed. Students are confused about the use of grades and are at a loss to solve problems. There is a common phenomenon in students' practice: when students do single questions like "how much is the total share", the correct rate is higher; When students learn the relationship between fractions and division, they do a single question of "how many meters is each part", and the correct rate is also very high. But when these two problems are combined into one, for example, a rope is 2 meters long and divided into five sections on average, with each section being full () and each section being long (). At this time, only one third of the students in the class can correctly understand the meaning and answer. And often after repeated explanations by teachers, the effect is still very unsatisfactory, and even some students have been confused. This phenomenon caused me to think. What problems should be paid attention to in understanding the meaning of fractions in teaching?
On the arrangement of the content of fractional learning. The textbook of primary school mathematics published by People's Education Press is mainly divided into three stages: the first stage is to make a preliminary understanding of scores in the first volume of grade three, including cognitive scores, comparative scores, cognitive scores, comparative scores and denominators, etc. The meaning of fractions mainly depends on concrete objects and intuitive graphics. An object or a graphic is divided into several parts on average, and one or several of them are represented by fractions. The second stage is the second volume of grade five. The main contents include the meaning of fractions, false fractions of true fractions, basic properties of fractions, reduction, general fractions, reciprocity between fractions and decimals, addition and subtraction of fractions with different denominators and so on. The meaning of fraction is to treat multiple objects or numbers as a whole, sum up the meaning of unit "1" and fraction, and then learn the relationship between fraction and division, and initially learn how to solve the problem that "one number is the fraction of another number". At this point, the score has two meanings: (1) indicates a relationship (unit "65438+); (2) indicates a specific quantity (the actual quantity of each share after a quantity is averaged). The third stage is the sixth grade, which mainly includes the understanding of reciprocal, the multiplication and division of fractions and the solution of related problems, and the relationship between fractions and ratios. The significance of the score is mainly related to the ratio. Throughout the arrangement of the whole textbook, the content about the meaning of the score rarely involves the specific number of the score, and the generalization of the meaning of the score only emphasizes "dividing the unit 1 into several parts on average to indicate the number of one or several parts", and does not summarize the meaning of the score at the same time. However, teachers do not pay attention to it, so students' further construction of the meaning of fractions cannot be effectively realized when the knowledge they have learned is deeply rooted. Students can't tell the meaning of this somewhat similar question and can't answer it correctly.
About the subject students. The fundamental reason is that students don't fully understand the meaning of scores. It is this ignorance that leads students to confuse scores as the root of a specific quantity and score rate. Therefore, the significance of scores and the significance of scores are the difficulties for students to learn. As a fifth-grade student, his thinking characteristic is that he is in the transition stage from visual thinking in images to abstract logical thinking, and visual thinking in images still occupies a dominant position to some extent. If you leave a specific number or object, students will have difficulty in understanding and cannot answer correctly according to the meaning of the score.
About teaching. Teachers lack the overall concept in teaching. When teaching "the meaning of fractions", we often fail to focus on the overall situation and grasp the development of the meaning of fractions, and often teach in class, focusing on solving the knowledge objectives of this lesson and ignoring the integrity of knowledge structure. This is the root cause. The common occurrence of this phenomenon shows that when we teach the relationship between fraction and division, we do not understand it as another level of meaning of fraction, nor do we compare it with the meaning of the previous fraction. Students' understanding of the meaning of fractions is limited to dividing the unit "1" into several parts on average, indicating the number of one or several parts. Ignoring fractions can also represent the quotient (that is, the specific quantity) of dividing two numbers.
About coping strategies.
(1) Grasp the teaching materials as a whole and rationally integrate the teaching contents. Read through the textbook, develop the meaning of music score, arrange the content and knowledge ... >>
Question 6: What does Wu Zhengxian think of the meaning and essence of scores? Generation of scores of new knowledge points. The meaning and significance of a score are different from the division of true score, true score and false score, false score and score, false score and score or integer score. Reduce the greatest common factor of a fraction with constant size, find the greatest common factor simplest fraction reduction and its method: divide the least common multiple to find the least common multiple. Division of fraction ratio and its method. The requirement of fractional teaching is 1. Know how the score is produced, understand the meaning of the score, and clarify the relationship between the score and division. 2. Knowing the true fraction and the false fraction, knowing that the decimal part is another writing form of the false fraction, you can turn the false fraction into a decimal part or an integer. 3. Understand and master the basic nature of the score and compare the size of the score. 4. Understand the common factor, maximum common factor, common multiple and minimum common multiple of two numbers, find out the maximum common factor and minimum common multiple of two numbers, and be proficient in division and division. 5. The reciprocal of fractions and decimals. Teaching suggestions 1. Make full use of teaching materials and intuitive means. The textbook of this unit has made a lot of efforts in strengthening the connection between teaching and the real world. At the same time, the textbook also uses various forms of intuitive schema and the combination of numbers and shapes to express the geometric meaning of mathematical concepts. So as to provide rich learning resources for teachers and students. In teaching, we should make full use of these resources and give full play to the supporting role of image thinking and life experience in abstract thinking. One of the characteristics of this unit is that there are many concepts and they are abstract. The thinking characteristic of senior pupils is that their abstract logical thinking needs the support of intuitive thinking to a great extent. Therefore, when introducing new mathematical concepts, in order to carry out teaching smoothly, it is necessary to appropriately increase the visualization of thinking, turn abstraction into concreteness and turn abstraction into intuition. The so-called turning abstraction into concreteness is to mobilize students' relevant life experience and help them understand through concrete reality. The so-called turning abstraction into intuition means explaining the meaning of mathematical concepts with appropriate figures and schemas, which is the most commonly used and main intuitive teaching method of primary school mathematics. 2. Time abstraction is carried out at an appropriate level to construct the meaning of mathematical concepts. To do a good job in the teaching of wood units, we should pay attention to timely abstraction while strengthening intuitive teaching, and we should not let students' understanding stay at the intuitive level. Otherwise, it will also hinder students' understanding and application of what they have learned. For example, comparing the size of sum, some students may not necessarily answer who is bigger or smaller, but depend on which circle they divide and which is bigger, so they may be bigger or smaller, which is equal to sum. The main reason for this error is that it relies too much on intuition and does not abstract in time. Therefore, on the basis of fully intuitive teaching, let students get enough perceptual knowledge, seize the opportunity, guide students to summarize through examples and diagrams, and construct the meaning of concepts. 3. Reveal the internal relationship between knowledge and method, and master the method on the basis of understanding. In this unit, you need to master the methods of simplification and general fractions, the methods of converting false fractions into fractions or integers, and the methods of exchanging fractions and decimals. These methods seem to have many clues, but if they boil down to basic knowledge, that is, revealing the relationship between relevant knowledge and methods, it is easier to master methods on the basis of understanding. Take reduction and general division as examples, they are both applications of the basic properties of fractions. Although the numerator and denominator are divided by an appropriate number and multiplied by an appropriate number, they are all based on the basic properties of fractions, so the size of fractions remains unchanged. Therefore, it is not appropriate to focus on methodology in teaching, but to highlight the process of obtaining methods, so that students can understand the logic behind the operation methods. In this way, you can master the method through understanding, rather than learning the operation by memory.
Question 7: Does anyone know that there is a long-distance bus to Wuhan at Jiangmen City Bus Station? If so, how much will it cost? There is no direct train from Jiangmen to Wuhan. .
There are no cars in Guangzhou either. Only trains.
Question 8: What is the natural score of a score? Dividing the unit of 1 level into several parts to represent such a part or parts is called a fraction.
The basic nature of a fraction: the numerator and denominator of the fraction are multiplied or divided by the same number at the same time (except 0), and the size of the fraction remains unchanged.
And add them together:
The properties of constant quotient: dividend and divisor expand or shrink by the same multiple at the same time, and the quotient remains unchanged.
Decreasing score: when a score is equal to it, but the numerator and denominator are small, it is called lowering score.
Comprehensive score: it is called comprehensive score when the scores of different denominators are changed into the scores of the same denominator and the original scores are equal.