1, by exploring the process of fractional multiplication calculation method, we can understand the significance and calculation method of fractional multiplication, and we can calculate fractional multiplication correctly and skillfully, thus improving the calculation ability.

2. Under the guidance of the teacher, abstract the quantitative relationship of finding the score of a number by multiplication, solve the mathematical problem of finding the score of a number, and improve the problem-solving ability.

3. Understand the function of fractional multiplication in real life, understand the application value of mathematics, and enhance the confidence of learning mathematics well.

(2) Description of teaching materials

Fractional multiplication is taught on the basis of learning integer multiplication, decimal multiplication, the meaning and basic properties of fractions, and the addition and subtraction of fractions. At the same time, fractional multiplication is an important basis for learning fractional division and fractional mixing operations.

The main contents of this unit include: unit theme map, calculation of fractional multiplication and problem solving. The arrangement idea is that the unit theme map presents the problem situation solved by fractional multiplication in life, stimulates learning interest and starts learning motivation for unit teaching; Fractional multiplication includes derivation, induction and summary of calculation rules, and simplification techniques should be used in the calculation process. The problem-solving part mainly arranges the problem of finding the score of a number. In the design and arrangement of problems, we should jump out of the previous single problem presentation mode and present real-life problems to students with multi-angle and radial problem orientation, so as to exercise and cultivate students' problem-solving ability.

Fractional multiplication includes fractional multiplication of integers and fractional multiplication of fractions. Compared with traditional textbooks, the significance of fractional multiplication is relatively diluted. The meaning of fractional multiplication by integer and integer multiplication by fraction should be understood in combination with specific problems, and generally no separate distinction is made. The meaning and calculation rules of fractional multiplication by integer or integer multiplication by fraction are easy to understand, while the derivation process of fractional multiplication by fraction is complicated, which is difficult for students to understand. Therefore, the calculation method of fractional multiplication is both the focus and the difficulty of this unit. The textbook first arranges the calculation rules of multiplying fractions by integers, and then teaches the calculation rules of multiplying fractions by fractions. Diffuse difficulties by knowledge transfer.

The content of solving the problem is mainly to find out what the score of a number is, which is the basis of solving the problem of "knowing what the score of a number is and finding this number" in Unit 3, and further solving the more complicated score problem. When arranging teaching materials, we should pay attention to the reality of life, choose the pictures of cars driving in the theme map, put forward the question of "what is the score of a number" and directly give the standard quantity (the quantity of unit "1"), and ask students to analyze the quantitative relationship of items to make clear what the corresponding quantity is, and then contact the strategy of "finding the score of a number and calculating it by multiplication" in fractional multiplication. In this way, students can not only master the analytical methods and solutions of fractional multiplication, but also deepen their understanding of the significance of fractional multiplication.

In class activities and exercises, a large number of practical problems in life are selected to make students feel the connection between fractional multiplication and life. Knowledge related to social production, life, economy, geography and physiology broadens students' horizons and strengthens the comprehensive and interdisciplinary application of knowledge.

This unit highlights the following four aspects in writing.

1. Choose teaching content close to real life and highlight the application value of mathematics.

Fractional multiplication is a content in the field of number and operation, which is closely related to real life. Almost every fractional multiplication formula can find its prototype in real life. Therefore, the selection of this textbook highlights the existence and application of fractional multiplication in real life. From the combination diagram of bus running, watermelon separation and cake eating presented in the unit theme diagram, to the sales of cultivated land and farm tools in examples, and even to practical problems such as production, life, geography and humanities in practice, the significance and value of fractional multiplication are reflected. In the process of exploring these contents, students can not only master the calculation method of fractional multiplication, but also feel the role of mathematics in human social life and production.

2. Let students experience the process of exploring the law of fractional multiplication, and highlight students' sense of independence.

The editor used "how to calculate the score multiplied by the integer?" "How to calculate the score multiplied by the score?" And so on, let students actively participate in learning activities and experience the whole process of exploring the law of fractional multiplication. In the process of exploring laws, we should highlight students' main role, let students experience every link of observation, analysis, deduction, induction and summary, and make students' mathematics learning activities a lively, proactive and personalized process.

3. Pay attention to the existing knowledge and experience, and leave room for students to study independently.

When compiling teaching materials, we should pay attention to the formation process of knowledge, leave enough space for students to study independently, and consciously guide students to actively explore and communicate. For example, the discussion on page 2 guides students to explore, communicate, summarize and improve, and then gives the calculation rules. In addition, the presentation of teaching content is enlightening and helpful for students to think further. For example, in the dialogue between two students on page 12, after the first student understood that "6 10 is the original price", the second student proposed "Calculate the total price of three farm tools before discount, and then …". These are tips to guide students to think and solve problems further in teaching. Furthermore, after the textbook guides students to master the basic operation of fractional multiplication through examples, the understanding of the significance of fractional multiplication and the understanding of fractional multiplication operation are explored and strengthened through a large number of classroom activities and exercises.

4. Pay attention to practical application and cultivate application awareness.

The textbook of this unit not only focuses on selecting topics from real life to build mathematical models, but also focuses on guiding students to solve practical problems in real life, so that students can acquire knowledge and skills and cultivate their application awareness and ability. The specific manifestations are as follows: 1. In the teaching of examples, the fractional multiplication formulas are all derived from examples in actual production and life, such as examples 1 on 2-4 pages, examples 3 and 4. The second is the choice of problem-solving materials, which is an example of current social life that students are very familiar with or concerned about, such as the travel problem of example 1 on page 8 and the sales problem of farm tools on page 12. These contents are very realistic, and the strategies and calculation methods of solving problems need students to explore and choose independently, so as to better cultivate students' openness of thinking and ability to solve simple practical problems, and enable students to develop good application consciousness in the process of learning these knowledge.

Teaching skills

The study of this unit is mainly carried out through activities such as observation, thinking, conversation and calculation. Although it is a traditional teaching content, the compilation of teaching materials has changed a lot compared with traditional teaching materials. In teaching, we should grasp the intention of compiling teaching materials, embody the new curriculum concept, let students experience the process of exploring and deducing laws, make use of existing knowledge and experience for independent thinking and cooperative exchange, and cultivate students' application consciousness and practical ability.

1, pay attention to the leading role of topic diagram and situation diagram.

The unit theme diagram and situation diagram in examples and exercises not only play the role of presenting information, but more importantly, create problem-solving situations for students' learning and stimulate students' interest in learning. In teaching, students can not only make multimedia courseware with dynamic effect according to the situation map, but also directly observe the situation map in the teaching wall chart or teaching material, get relevant information from it, feel the reality of the problem, arouse memories of existing life experiences and stimulate curiosity of learning new knowledge. When teaching the theme map on page 1, let students observe and understand which life cases are involved in the map. What information have you learned from the situation? What math questions would you ask? How to solve these problems? What are the difficulties in solving these problems? This leads to the content to be learned in this unit, so that students can have a general impression of the content of this unit and get ready for learning fractional multiplication.

2. Pay attention to students' independent exploration of the law of fractional multiplication.

In the teaching of this unit, students should be given sufficient space for independent activities, and the existing knowledge and experience should be used to explore the calculation law of fractional multiplication. For example, when teaching the example of 1 on page 2, after constructing the formula of 15×4 through situational understanding, how to calculate 15×4 can be completely solved by students' existing calculation experience. In the future, the calculation rules of multiplying scores by scores should be summarized by students themselves, without too much intervention and arrangement from teachers.

3. Pay attention to the combination of independent thinking and cooperation.

In teaching, on the one hand, we should make full use of students' cognitive level, let students explore the calculation method of fractional multiplication, reflect on the learning process and results, and realize independent construction on the basis of original knowledge and experience; On the other hand, it is necessary to strengthen the communication within the group and class, so that students can express their own calculation methods and problem-solving thinking process in language. Through communication, students can experience the diversification of calculation methods and problem-solving strategies, promote the development of thinking ability, and cultivate students' sense of cooperation and communication ability.

4. When designing teaching, teachers should not only walk into the teaching materials, but also walk out of them.

When teaching, we should carefully read and understand the textbook, thoroughly understand the intention of compiling the textbook, grasp the requirements of the textbook, and properly complete the unit teaching task. On the other hand, teachers should not be too rigid about teaching materials, and should use them flexibly. For example, the textbook does not require knowledge and understanding of fractional multiplication, but it does not object to the necessary understanding of the significance of fractional multiplication. However, because there is no requirement for the order relationship of factors in the multiplication formula, the formula corresponding to the meaning of fractional multiplication is not unique. On the contrary, the corresponding meaning of a fractional multiplication formula is not unique, and it becomes a one-to-many relationship. This is different from the cognitive view in traditional textbooks. If we leave the problem situation to discuss the significance of fractional multiplication, it may complicate simple problems. However, this does not exclude students from knowing and understanding the significance of fractional multiplication from a certain angle or aspect, especially returning the abstract formula to the original problem situation to understand. For example, after teaching the summary of example 3 on page 3: "What is the score of a number? Multiplication calculation "is a problem-solving strategy refined and generalized on the basis of deeply understanding and understanding the meaning of 100×45" What is the 45 of 100 ". This conclusion is the basis of solving the problem of fractional multiplication and division and must be understood and mastered.

(d) Teaching content analysis and teaching suggestions of each part.

Fractional multiplication (page 65438 +0 ~ 7)?

1, teaching content analysis

The teaching contents of this section include unit theme map, 4 examples, 1 classroom activities and exercises 1.

The upper part of the unit theme diagram is to find the fraction of a number, and the lower part is to find the sum of several identical addends. Students can also ask some math questions through observation and reading. Some of the contents in the picture directly become the contents of later study and discussion. Through this arrangement, the textbook strengthens the connection between the unit theme map and the subsequent learning content, and strengthens the integrity and systematicness of the unit knowledge.

The functions of the four examples in this section are as follows: Example 1 teaches the calculation rules of multiplying fractions by integers; Example 2 consolidates the law and emphasizes how to subtract points in the calculation process to make the calculation simple; Example 3 teaches different forms of integer fractional multiplication, and summarizes the problem-solving strategies of fractional multiplication through understanding and understanding the significance of integer fractional multiplication; Example 4 teaches the calculation rules of fractional multiplication and illustrates the calculation principle of fractional multiplication with examples.

Example 1 is introduced from the problem situation that everyone eats 15 cakes, and a formula for finding the sum of scores with the same denominator is obtained. Then, with the help of the original multiplication knowledge, it becomes the form of fractional multiplication by integer, and then explores the calculation method of fractional multiplication by integer. Exploring calculation rules is the focus of example 1, and then strengthening the understanding and operation of calculation rules by trying to train the content. Finally, through discussion, the calculation rules of fractional multiplication by integer are summarized.

Example 2 is formative training after students have mastered the calculation rules of fractional multiplication by integer. Focus on how to reduce points in fractional multiplication calculation, one is to reduce points after calculating results, and the other is to reduce points during calculation. We advocate the latter. The advantage of this reduction is more obvious in the mixed operation of fractional multiplication or multiplication and division.

Example 3 is the most important example in fractional multiplication, and its quantitative relationship is the basis for solving fractional problems. Here, students can be properly required to have a necessary and meaningful understanding of 100×45, and can use 100 as an integer to make the transition, that is, how many times is 100 and how much is the transition from 100 to 45, but the key point is to understand that 45 is 1 hour.

Example 4 is the content of the method of multiplying teaching scores by scores. Instead of simply telling students to multiply numerator by numerator and denominator by denominator, let students understand the operation of fractional multiplication. In this way, students can not only deepen their understanding of fractional multiplication, but also prepare for studying fractional division in the future. According to the illustrations in the textbook, teaching can be divided into three steps. It is important to guide students to understand the practical significance of 35× 12, that is, what is 35 hectares 12. It is similar to the understanding in Example 3, except that the unit "1" in Example 3 is an integer (100 km), while the unit "1" in Example 4 is a fraction (35 hectares). The first step is to map 35 hectares of cultivated land at 1. Step 2, find out 35 12, that is, 35×2 of 1 hectare. The third step is to find 34 of 35, which is 3×35×4 of 1 hectare. Then consolidate and master this calculation method by "trying" and extend it to the calculation formula of fractional multiplication. Finally, let the students use a discussion to summarize the calculation rules of the score multiplied by the score.

There are three problems in classroom activities. The question 1 is a variant of the example 1 and the association and consolidation of related knowledge. By finding the sum of several identical fractions, converting it into the form of multiplying the number of components by integers, and then calculating it, we can skillfully consolidate the calculation law of multiplying fractions by integers. The second question is the auxiliary exercise in Example 3. The difference is that the unit "1" corresponding to 14 here is the height of a student, which should be obtained through actual measurement, and then the problem-solving strategy provided in Example 3 is used to solve the problem. The third question is the supporting exercise of Example 4, which requires students to use a grid diagram to represent the calculation of the score multiplied by the score. The premise of completing this problem is whether students can correctly understand the meaning of multiplying the score by the score and how to express it on the grid.

Exercise 1 arranged 15 questions, 1 thinking questions. Among them, 1~9 is an exercise about multiplying fractions by integers. Question 8: Based on the knowledge of the meaning of the fraction in the second volume of the fifth grade, the unit "1" is divided into several parts, and the number representing several parts is expressed by the fraction. Then, combined with the problem-solving strategy of this unit: "Find the fraction of a number and calculate it by multiplication", list the formulas. In the problem 15, we need to borrow the formula for calculating the volume of a cuboid to construct a formula, which is a formula for multiplying a fraction by a fraction. In the concrete calculation, we can simplify the operation by reduction.

2. Teaching suggestions

1, the teaching content of this section is suggested to be completed in 3 class hours.

2. When teaching example 1, let students experience the whole process of data information collection, collation, analysis, presentation and calculation law exploration. Students should be reminded to pay attention to the analysis and understanding of key words before the demonstration. The key word of this question is "* * * how much to eat", which tells us that we are seeking the sum of several numbers. Because these numbers are the same, they are all 15, which is a problem of "finding the sum of four 15". In this way, a real problem is abstracted into a pure mathematical problem, which is the meaning of 15×4. The meaning of 15×4 is not given in the textbook. In teaching, students can understand it from the perspective of integer multiplication, such as: "What is the sum of four 15, and what is the multiple of four 15". In15× 4 =145, there should be15× 4 =15+65438+65438+15 = 65438. Ask the students to summarize the calculation rules of multiplying fractions by integers.

In the teaching of Example 2, we should highlight the contrast and difference between the two calculation processes. The first calculation method is to calculate first and then reduce the score. The purpose of reducing the score is to simplify the score. The second calculation method is to reduce the score before calculation. The purpose of reducing the score is to simplify the calculation and let students know that when the score is multiplied by an integer, it must be an integer and a denominator.

In the teaching of Example 3( 1), it is easy for students to list formulas according to the relationship of "speed × time = distance". The key point is to guide students to understand the meaning of the formula. You can ask questions at different levels to understand what the corresponding unit "1"(1class hour) and the corresponding unit "65440" are.

As can be seen from the line graph, the distance of 45 points is 45 of 100 km, and the distance of 45 points is 45 of 100 km. So how to find the 45 of 100 km? The formula 100×45 has been listed as "speed× time". When the formula 100×45 holds, teachers can guide students to make a reflective understanding, that is, what is the meaning of 100×45? (You must spend more time here to understand) In order to effectively inspire students, you can also use the integer 100 (greater than 1, equal to 1) to pave the way for the transition. For example, ask students to explain the meanings of 100×3 and 100× 1, that is, what is three times of 100, and what is 1 multiplied by 100, so as to guide students to explain100.

When teaching Example 3(2), we can directly solve it with the method just obtained. For example, "How much is the 45 of 100 km to be solved by 100×45, then how to solve the 95 of 100?" Finally, the problem-solving strategies extracted from this example are summarized and conceptualized, and it is concluded that "how much is a fraction of a number, and it is calculated by multiplication". At this time, let the students summarize, for example, "What is the 35 of A? The formula is a × 35; The formula for finding the number of m 1n is m×1n; The formula for finding cb of a is a×cb ".

In teaching, on the one hand, we should continue to consolidate multiplication to calculate the fraction of a number, on the other hand, we should pay attention to let students understand that the product of numerator multiplied by numerator is numerator and the product of denominator multiplied by denominator is denominator. It is difficult for students to understand this theory, and the textbook uses the effective "schema combination" in traditional teaching to help students understand it.

The first step is to multiply the number of hectares of cultivated land when 1 is passed, and also multiply the number of hectares of cultivated land when 12 is introduced. The formula is 35× 12, which further makes students understand that 35× 12 is 35 hectares.

Step 2, find out how many hectares of cultivated land are at 12, that is, how much is 12 of 35 hectares, that is, divide 35 hectares into two parts on average and take 1 of them. Teachers can put a picture on the left of Example 4 in the textbook on the blackboard, then divide 35 hectares into two parts, take 1 part, and then extend the dotted line of the bisector (turn it into the picture on the right in the textbook), so that students can realize that this is actually dividing 1 hectare into (5×2) equal parts and taking 3 parts, and the result is 3×/kloc-0. The denominator part "5×2" is the denominator multiplication of the original two fractions. Finally, the complete formula 35×12 = 3×15× 2 = 310 (hectare) is listed, and then students are asked to observe and reflect on this complete formula. Through the calculation of 35 × 12, the fraction can be multiplied by the numerator and the denominator by the denominator.

The third step is to find out how many hectares of cultivated land there are at 34: 00. Can inspire students to think, can it be formulated directly according to the experience of solving the first problem in Example 3 and Example 4 (what is the score of a number, calculated by multiplication)? Students can transfer general problem-solving strategies to deal with this example. They can think that 1 hour has cultivated 35 hectares, and at 34 o'clock, 1 hour is 34, so the cultivated land at 34 o'clock is 34 of 35 hectares. Then the multiplication formula of 35×34 is listed according to "What is the fraction of a number? Calculate by multiplication". Then, students can imitate (1) a small question, express 35×34 with dot matrix graphics, and deduce the calculation method of 35×34. Get 35×34=3×35×4=920 (hectare), and then ask students to review and reflect on this calculation method. Then, let the students complete the practice of giving it a try to consolidate and expand the application of this calculation method. Finally, through a discussion, guide students to summarize the calculation rules of multiplying scores by scores.

When teaching class activity problem 1, it is suggested to add a+sign between each square figure and connect the last one with the penultimate one with an = sign. In fact, this is also a formula. By comparing up and down, the above is a graphic formula, and the following two are symbolic formulas, both of which represent quantitative relations. Let the students know that some relations between some quantities are certain, but the expression form is optional. The measurement of the second question can be prepared before class, because the class time is limited, which does not affect the consolidation and proficiency of classroom knowledge. Question 3 not only requires students to draw, but also organizes students to communicate with each other to judge whether the drawing is correct and explain the basis and reasons for drawing.

The 8 11problem in exercise1should be abstractly summarized as the problem-solving strategy of "what is the score of a number". On the basis of students' careful reading and understanding of its practical significance, multiplication calculation lists formulas according to problem-solving strategies. Question 5, 15 is a comprehensive question. When analyzing and understanding the meaning of the problem, we should build a mathematical model with the help of the relevant knowledge of space and graphics. The fifth question lists the formula of 45×4 with the formula of finding the perimeter of a square, and the 15 question lists the formula of 35×25× 13 with the method of finding the volume of a cuboid, instead of using the new knowledge of "finding the fraction of a number by multiplication".

Think about the problem and ask the students to make it clear that the product is between 14 and 78, that is, greater than 14 and less than 78. You can calculate the product of each question first, and then find the answer by comparing the general points. In order to let students see the answer to this question clearly, you can draw a number axis and see that only 12, that is, the product of 23×34 is between 14 and 78.