Understanding and mastering the relationship between fraction and division can not only deepen the understanding of the meaning of fraction, but also lay the foundation for later learning pseudo-fraction, with the basic properties, ratio and percentage of fraction. Therefore, the relationship between fraction and division plays an important role in the whole textbook. Next is the reflection on the teaching of fractions and division brought by learning. I hope you like it. ? Reflections on the teaching of fractions and division? ? Mathematics teaching should start from students' life experience and existing knowledge background, so that students can feel that mathematics is around and learn mathematics in life. Let students know the importance of learning mathematics and improve their interest in learning mathematics? Fraction and division are abstract contents for primary school students. The reason why mathematics knowledge can be understood and mastered by primary school students is not only the result of knowledge deduction, but also the result of the interaction of specific models, graphics, scenarios and other knowledge. So when I designed the course of fraction and division, I considered the following two aspects:? 1. Start with solving the problem and feel the value of the score. ? Starting with the problem of dividing the cake, let the students feel that when the quotient can't be expressed in integers, it can be expressed in fractions. This lesson is mainly conducted from two levels. First, with the help of students' original knowledge, the problem that 1 cake is divided into several parts according to the meaning of score is solved, which is expressed by business score; Secondly, with the help of physical operation, it is understood that several cakes are divided into several parts on average, and quotient can also be expressed by scores. And these two levels are designed from the perspective of solving problems. ? 2. The expansion of the meaning of fractions is synchronized with the understanding of the division relationship. ? When the quotient of integer division is expressed by fraction, the divisor is the denominator and the dividend is the numerator. Conversely, a fraction can also be regarded as the division of two numbers. Can be understood as? 1? Divided into four parts on average, that is to say, three parts like this; Can also be understood as? 3? Divide it into 4 parts on average, that is, 1 part. That is to say, the process of understanding and establishing the relationship between fraction and division is essentially synchronous with the expansion of the meaning of fraction. ? After teaching, I reflect on my own teaching, and find that the state of primary school mathematics knowledge stored in students' minds can be transformed from abstract to concrete mathematics knowledge, except abstract. The whole class teaching has the following characteristics: 1. Provide rich materials and experience? Math? Process. ? Understanding the relationship between fraction and division is a process of gradually enriching perceptual accumulation and abstract modeling with tangible objects and pictures as the media, hands-on operation as the way and rich appearances as the support. In this process, we pay attention to the following aspects: first, provide rich mathematics learning materials; Secondly, on the basis of making full use of these materials, students gradually improve their own conclusions, from literal expression to equations expressed in words to letters, from complex to concise, from life language to mathematical language, and from concrete to abstract. ? 2. The problem lies in the method, and the content carries ideas. ? Mathematics learning is a problem-solving process, and methods naturally reside in it; The learning content contains mathematical ideas. In other words, mathematical knowledge itself is only one aspect of our study of mathematics, and it is more important to infiltrate mathematical thinking methods with knowledge as the carrier. ? As far as fractions and division are concerned, the author thinks that if we teach only to get a relationship, we just catch the tip of the iceberg. In fact, with the help of this knowledge carrier, we should also pay attention to thinking methods such as induction and comparison, and how to use existing knowledge to solve problems, so as to improve students' mathematical literacy. ? Reflections on the teaching of fractions and division? The relationship between fraction and division is not taught until students learn the meaning of fraction. The purpose is to let students know that the quotient of two integers can be expressed by fractions, no matter whether the dividend is less than, equal to or greater than the divisor. ? The teaching of this part of the content can not only deepen students' understanding of the meaning of fractions, but also be the basis for later learning the basic properties of pseudo-fractions, including fractions, fractions and ratios, and percentages. Therefore, the relationship between fraction and division plays an important role in the whole textbook. If we simply teach the relationship between fractions and division in form, students can learn it firmly, but in this way, we can work out 3? The arithmetic of 4=3/4 is often ignored. In order to let students know what it is and why, I organize teaching in this way. 1. Feel new knowledge through practical operation? In teaching, I designed such a teaching situation, and divided a piece of cake among four children equally. How much did each child get? Let the students take a round piece of paper to represent a cake, and divide it for themselves to arouse the understanding of the meaning of the score. Then show that three cakes should be distributed equally to four children. How much should each child get? Try to give three round pieces of paper to four children, four in each group. And let the group send representatives to the stage to show the scoring process. Through hands-on operation, students get two different points and two meanings, that is, each person gets three quarters of 1 cake, which can also be said to be one quarter of 3 cakes. Through this process, students fully understand the 3? 4=3/4.？ 2. Let the students know why they use fractions to represent the results of division. After the students understood the relationship between fractions and division, I consciously designed these exercises. 1? 3= 8? 9= 2? 6= Let the students write the calculation results in their exercise books to see who finishes the calculation first. As a result, some students raised their hands in a second or two, and some students took a long time to write the calculation results. After the report, guide the students to think: 1? 3=0.333 and 1? 3= 1/3 8? 9= 0.88 and 8? What's the difference between 9= 8/9? The students' most direct answer is that it is too troublesome to express quotient with cyclic decimals, but it is not quick and simple to express quotient with fractions. At this time, tell the students that it is simple and quick to calculate the quotient divided by two integers in the future, and it is not easy to make mistakes when the division is infinite or there is a decimal in the quotient. ? 3. Take the opportunity to extend and pave the way for follow-up study? Introduce the difference between point and quantity to students for the first time. For example 1? Divide a cake into four parts on average. How much will each cake get? How many cakes do you get for each piece ② "Divide the 2m-long rope into 7 sections on average. How much is this rope for each section? How long is each section? ③ Divide 4 kilograms of salt into 5 parts on average. What is the weight of each part/how many kilograms does each part weigh? Let the students understand the first question of these three questions? Integral? Percentages have no units, but the sum is the unit? 1? Divide the unit 1 into several parts and find that one part is a fraction of the total. Are they all units? 1? Divided by the average number of copies, for example, the scores of the first three questions are 1 respectively. 4= 1/4 1? 7= 1/7 1? 5= 1/5。 The second question is how much each copy costs. Each copy has one unit, which is obtained by dividing the total number by the average number of copies. The number must have the name of the unit. The algorithms for the first three questions and the second question are 1 respectively. 4= 1/4 (Zhang) 2? 7=2/7 (meter) 4? 5=4/5 (kg)? Here, after students know the scores and the number of copies of each copy, they have made a good preparation for the application of scores and percentages in the future. ? 4. Let students construct new knowledge independently? When students find that the dividend in division is equivalent to the numerator in the fraction and the divisor is equivalent to the denominator in the fraction, guide them to change the number to their own name: dividend? Frequency divider = frequency divider/frequency divider. At this time, let the students use the letters A and B to indicate the relationship between division and fraction in their exercise books. Most students write: a? B=a/b, the teacher took out a slightly worse student's blackboard and deliberately praised the student. When praising, he suddenly turned around and gave the student a big cross at the back of his homework. Just when the students were surprised? Why is it wrong? At this time, several flexible people cried and said: B can't be equal to 0! ? I immediately seized this opportunity to ask: Why can't B be equal to 0? I continued to use the example in class, and gave the cake of 1 to four people, and each person got the cake of 1/4 as an example. Let the students talk about this score. 4? What does this mean? If you put? 4? Replace with? 0? Students suddenly realize: denominator refers to the unit? 1? Average number of shares, average share? 0? There is no point in serving. When letters are used to express the relationship between fractions and divisions-? Answer? b=a/b(b？ 0)? Students often forget that b here can't be 0. Through this analysis, students can understand more deeply that the divisor in division can't be 0, so the denominator in fraction can't be 0. This does not directly tell students that the divisor in division cannot be 0, and the divisor in fraction is equivalent to the denominator, so the denominator cannot be 0. But by analyzing the actual meaning of a score, students can fully understand that the denominator in the score represents the average number of copies, so the denominator cannot be? 0? The truth. ? Disadvantages of this lesson: Although students have a thorough understanding of the relationship between fractions and division, there are still some differences between them that do not guide students to sum up. Division is the division of two numbers, which is an operation and an expression. Fraction can not only represent the division of numerator and denominator, but also represent a numerical value. ? Reflections on the teaching of fractions and division? Understanding and mastering the relationship between fraction and division can not only deepen the understanding of the meaning of fraction, but also lay the foundation for later learning pseudo-fraction, with the basic properties, ratio and percentage of fraction. Therefore, the relationship between fraction and division plays an important role in the whole textbook. The new curriculum standard points out:? The content of students' teaching and learning should be realistic, meaningful and challenging, which is conducive to students' active observation, speculation, verification, speculation and communication. This shows that creating effective learning situations can guide students' development? Autonomy, exploration and cooperation? Learning activities to promote students' active participation. ? Therefore, in the process of introducing new lessons, I intentionally designed two division calculation questions: 8? 9= 4? 7= ? When the students saw these two division formulas, they all breathed a sigh of relief and said, such simple two questions! ? So I started a competition between men and women in my class. Boys count the first question and girls count the second. On hearing the order, the boy buried himself in calculation. Hu Wenxin, who is quick-thinking, already knows the answer and doesn't write at all. I motioned to her not to tell the answer. I turned around, and most of my classmates got the answer at the prompt of the classmates who had already done it. Only a few boys were still counting. ? Make students think after the report: 8? 9= 0.88 and 8? What's the difference between 9= 8/9? The students' most direct answer is: it is quick and simple to use circular decimals to indicate that there is no score. This introduction makes students understand that the division of two numbers can be expressed by fractions, which lays the foundation for further learning the relationship between fractions and division. ? After that, the formula of dividing two numbers is shown, and students can quickly express quotient with scores. ? Take 1 in the example? 3= 1/3 Guide the students to find that the dividend in division is equivalent to the numerator in the fraction, and after the divisor is equivalent to the denominator in the fraction, let the students change the number into their own name: dividend? Divider = numerator/denominator. At this time, I asked students to use letters A and B to express the relationship between division and fraction. Xue Longfeng walked to the blackboard and carefully wrote: A? B=a/b, I saw this student writing seriously, and immediately praised her and asked the students to applaud her. Just when everyone was happy for Xue Longfeng, I made a small note behind the formula she wrote? . The student immediately expressed incomprehension. The teacher praised her just now. What's the sentence now? . Or a few people with flexible minds cried first and said: B can't be equal to 0! ? I immediately seized this opportunity and asked:? Why can't b be equal to 0? The whole class was suddenly quiet, and no one could say why. I'm a little excited that this difficulty is about to break through. I will continue to use 1 as an example to ask:? Who can tell me this score? 3? What does it mean that some students raise their hands to answer? Treat the cake as a unit? 1? ,? 3? Represents the number of cakes divided equally. If you put? 3? Replace with? 0? Students finally understand that the denominator is the unit? 1? Average number of shares, average share? 0? There is no point in serving. That's it? Answer? b=a/b(b？ 0)? Students often forget that b here should not be 0. Through this analysis, students can more deeply realize that the divisor in division cannot be 0 and the denominator in fraction cannot be 0. ? I think I handled this link better. I didn't tell the students directly that the divisor in division can't be 0, and the divisor in fraction is equivalent to the denominator, so the denominator can't be 0. But by analyzing the actual meaning of a score, we can fully understand that the denominator in the score represents the average share number, so naturally it cannot be divided equally? 0? Share it. ? There are successes and shortcomings. After-class reflection, students have a thorough understanding of the relationship between fractions and division, but what differences between them have not guided students to find and summarize in class. Division is the division of two numbers, which is a formula and the fraction is a number. This shows that I didn't understand the textbook deeply enough before class, and I haven't grasped the integrity and coherence of knowledge. In the future teaching, we should try our best to deeply understand the teaching materials, and at the same time consult more materials to expand and extend the knowledge of the teaching materials.

Reflections on the teaching of fraction and division;

1. Reflections on the Teaching of Fraction and Division

2. Reflections on the teaching of fractional division

3. Reflections on the teaching of fractional division under the new curriculum standard

4. The fifth grade mathematics volume 2 scores and division teaching plan

5. Reflections on the teaching of mathematical fractional division