Help me sort out the first volume of the fifth grade of Hebei Education Press, and review the things at the end of the math period. Focus on sorting it out! 3Q

1, "Trust often creates a beautiful realm." This sentence comes from Feng Jicai, the author of Pearl Bird, which means that as long as people and animals trust each other, people or animals will live in harmony.

2. Friends of Man tells us that nature is the environment for human survival and the habitat for all living things. Animals and humans live on the same planet. Animals are friends of humans, and humans are friends of animals.

3. In Hello Nature, Sister Zhang Haidi is a physically disabled and determined person. She told us that there is endless knowledge in nature. Going to nature can broaden our horizons, cultivate our sentiments and strengthen our physique.

4. In the article "Hurry", Zhu Ziqing told us that time comes and goes in a hurry, so we should know how to cherish it. The famous sayings about cherishing time are: young people are easy to learn, old people are difficult to succeed, and an inch of time is not light.

5. The author of "If there is only three days of light" is Helen. Keller, she has a very positive attitude towards life.

6. A Bing in Two Springs Reflecting the Moon is a person who loves music, dares to fight against fate and strives for a better ideal.

7. Long Songs tells us to cherish time and work hard as soon as possible.

8. Cheng Wei Qu expresses the poet's farewell to his friends, and Don't Move Big expresses the poet's encouragement and encouragement to his friends. The first two sentences of these two poems are all about scenery, and the last two sentences are lyrical.

9. "grandpa. Back garden. I described the author Xiao Hong's childhood life. Grandpa and his children are very happy together, and they have close feelings for each other. Grandpa's eyes are always smiling, and his smile is often like a child's.

10 "Paper Boat-Dedicated to Mother" was written by Bing Xin, expressing the author's thoughts about his mother and motherland.

1 1. The story of "Nine Colors Deer" tells us that good is rewarded with good, and evil with evil. To be a man, you should keep your reputation and repay kindness with kindness. Any perfidious behavior will not have a good result. The king is a man who has clear rewards and punishments, distinguishes right from wrong, punishes evil and promotes good. Jiuse deer is kind, unrequited, self-sacrificing and brave in self-defense. "That man" is an ungrateful, selfish and dishonest person.

12, Lian Po as lieutenant, Lin Xiangru as prime minister. Lin Xiangru is a political visionary who has both wisdom and courage, is not afraid of violence, puts national interests first, understands the general situation and takes care of the overall situation. Lian Po is a man who dares to admit his mistakes and correct them.

13, my favorite sentence is: if you don't let him do anything, you won't let him do anything.

14, Xiuer expressed Lu You's incomparable love for the motherland.

15, Xijiang month. Walking in the middle of Huangsha Road at night expresses the author's love for the scenery of summer night mountain village. "Like a Dream" expresses the author's good mood of being intoxicated in the depths of the lotus when he was young.

16, the birth of the Monkey King was adapted from Journey to the West. The first author was Wu Cheng'en, a novelist in the Ming Dynasty. This text describes the experience of the stone monkey from birth to becoming the monkey king. China's four classical novels are The Journey to the West in Wu Cheng'en, Water Margin by Shi Naian, Dream of Red Mansions by Cao Xueqin and Romance of the Three Kingdoms by Luo Guanzhong.

17, Potala Palace introduces the Potala Palace to us from two aspects: magnificent architecture and vast and complicated collections.

18, Huizhou in ink painting is a place with unique charm, which is in line with the spirit of China ink painting.

19, Rodin in Walking Man is called "the father of modern sculpture". He has the spirit of exploration and innovation.

20. The words that describe the character's demeanor are: cheerful and cheerful, smiling and smiling.

2 1, the words describing the four seasons are: spring is blooming, the sun is like fire,

22, sweating like a pig, spending money like water, confused, anxious.

23. The old monitor in The Golden Hook has the spirit of loyalty to the revolution and self-sacrifice.

24. The text "A promise is as good as a thousand dollars" tells us that we should keep our promises and keep our promises.

The old professor in the only audience is a sincere, selfless, educated, caring and respectful person.

26. Qiu in My Comrade Qiu is a strong-willed person who is not afraid to sacrifice himself. He has the noble quality of strict discipline.

27. Deng Jiaxian is a scientist who loves and devotes himself to the motherland and the cause of science.

28. "My Best Teacher" tells us that everyone should have the ability of independent thinking and independent judgment, and at the same time have a scientific skepticism.

29. Li Siguang is a thoughtful and persistent person.

Unit 5, Cuboid and Cube

The knowledge of cuboids and cubes is an important content in the field of "space and graphics" in primary school mathematics. The requirements of the original outline are: the characteristics of cuboids and cubes. The surface areas of cuboids and cubes. The specific contents of Mathematics Curriculum Standard are: (1) Through observation and operation, we can know cuboids and cubes, and we can know their development diagrams; (2) According to the specific situation, explore and master the calculation method of the surface area of cuboids and cubes. Compared with the syllabus, many new contents and requirements have been added to the mathematics curriculum standard, which truly realizes that geometry teaching should pay attention to the cultivation of spatial concepts. First of all, pay attention to the cultivation of space concept. The main contents of the concept of space include "being able to imagine geometric figures from the shape of objects, imagining the shape of objects with geometric figures, and transforming geometric figures from their three views and unfolded drawings", which is a process including observation, imagination, comparison and synthesis, based on the direct perception of the surrounding environment and the understanding and grasp of the relationship between space and plane. It is not only a thinking process, but also a practical operation process. Whether making a long and cubic model or drawing a figure, it must be realized through practice and hands-on operation on the basis of mental processing and combination. Therefore, the mathematics curriculum standard emphasizes the operation and experience process, and at the same time increases the contents of cuboid and cube expansion diagrams. Secondly, in the understanding of length and cubic surface area, the mathematics curriculum standard emphasizes exploring and mastering the calculation method of surface area in combination with specific conditions, which weakens the memory and understanding of concepts and strengthens the understanding of the practical significance of measurement and the experience of measurement process. By measuring the specific surface area of concrete rectangle and cube, students can master the method and knowledge of measurement and understand the necessity of measurement, instead of taking "measurement" as a simple graphic area calculation. Third, the understanding of cuboids and cubes, as well as the calculation of their surface area and volume, are arranged in the same unit in the syllabus. Because there are many contents, the calculation is boring and complicated, and the surface area and volume calculation are mixed together. In addition, the main purpose of learning is to memorize graphic features and master calculation skills, which makes students feel difficult to learn and uninterested. This textbook divides this part into two units: this unit knows the cuboid, the cube (including the plane expansion diagram) and the surface area calculation; Learn how to calculate the volume of a long cube and a cube. This arrangement has three main purposes: first, to strengthen the understanding of the characteristics of cuboids and cubes and the plane expansion diagram, and give full play to the important role of these contents in developing students' concept of space; Secondly, students are encouraged to understand and construct the knowledge of surface area calculation independently by using the knowledge of expansion diagram. Third, reduce the complexity and mutual interference of surface area and volume calculation and reduce the burden on students.

The textbook of this unit has the following characteristics in content design and writing ideas.

First, focus on hands-on operation, so that students can learn through operation and experience. In the past, when understanding the characteristics of three-dimensional graphics, although there were operations, they were not sufficient, but only for the purpose of drawing conclusions. When designing this part of the content, this textbook further strengthens the operation activities, and takes the learning process of operation, experience and exploration as one of the goals of the activities. For example, first build cuboid and cube models with thin rods and beads, and then understand the characteristics of edges and vertices of cuboid and cube; Another example is the understanding of the expansion diagram of cuboids and cubes. In the past, the study of plane expansion diagram was only the preparation of calculating surface area, and it was only a brief introduction when talking about surface area. Now, one class arranges a plane development plan separately, and successively designs activities such as cutting a cuboid and a cube box, showing cutting plane graphics, and finding the opposite side in the plane development plan. This cognitive activity of mutual transformation between three-dimensional and plane is not only helpful to further understand the characteristics of cuboids and cubes, but also enables students to form a clear representation of the transformation from three-dimensional graphics to plane graphics in their minds. It is more conducive to the development of students' space concept to prepare for the independent exploration of the calculation method of the surface area of cuboids and cubes.

Second, let students learn knowledge in independent exploration and cultivate students' autonomous learning ability. For example, when knowing cuboids and cubes, I designed the number of faces, edges and vertices myself, summarized the characteristics of cuboids and cubes, and summarized their similarities and differences; When students know the unfolded drawings of cuboids and cubes, let them cut the cuboid cartons themselves. When learning the surface areas of cuboids and cubes, let students try first, then exchange their respective calculation methods, and finally summarize the calculation methods of surface areas themselves. This kind of writing creates a space for students to explore independently, so that students can cultivate their awareness and ability of independent exploration while learning knowledge. Turn the process of mathematics learning into the process of students constructing new knowledge independently.

The main contents of this unit include: the characteristics of cuboids and cubes, the development diagram of cuboids and cubes, the surface area calculation and simple application of cuboids and cubes. ***4 class hours. Arrange the comprehensive application activities of "packaging belt" according to the unit content.

The educational objectives of this unit are:

1. Through observation and operation, we can know cuboids, cubes and their expanded diagrams.

2. According to the specific situation, exploring and mastering the calculation method of the surface area of cuboid and cube can solve the calculation problem of surface area.

3. In the process of exploring the characteristics of cuboids and cubes and their expansion diagrams, students' concept of space has been further developed.

4. Explore effective methods to solve problems and try to find other methods; Can express the process of solving problems and try to explain the results.

5, can take the initiative to participate in observation, calculation, trial calculation, communication and other mathematical activities, gain successful experience and understanding of independent problem solving, and enhance confidence in mathematics learning.

Characteristics of cuboids and cubes in lesson 65438. First, the textbook selects objects that students are very familiar with, so that students can find out the objects with cuboids and cubes, and then give their own examples to enrich their intuitive understanding of cuboids and cubes. Then, knowing the characteristics of cuboids and cubes, the textbook designed two activities. Activity 1: First, observe the models of cuboids and cubes, and understand the three concepts of faces, edges and vertices of cuboids and cubes, as well as the basic characteristics of faces of cuboids and cubes. Then ask the students to observe cubes and cuboid frames made of thin rods and beads and count how many edges and vertices there are. Then, by saying, "What are the characteristics of the sides of a cube? What are the characteristics of the edges of a cuboid? " Enrich students' understanding of cuboid cubes and prepare for summarizing the characteristics of abstract cubes and cuboid edges. Activity 2: Summarize the characteristics of cuboids and cubes and understand the relationship between them. The textbook designs the activity of arranging the characteristics of cuboid cubes into tables, and presents the tables of cuboid and cube characteristics. What are the similarities between cubes and cuboids? What is the difference? "By discussing the relationship between cuboids and cubes, it is concluded that cubes are special cuboids. At the end of the textbook, the concepts of length, width, height of cuboid and side length of cube are introduced. In teaching, students should be provided with enough space for observation, thinking, communication and independent exploration. For example, when understanding the characteristics of cuboids, cubes and edges, we should first understand the characteristics of cuboids and edges through observation, counting and discussion, and then let students discover and communicate the characteristics of cubes and edges themselves. For another example, summarizing the characteristics of cuboids and cubes allows students to organize themselves on the blank list first, and then exchange summaries, so that students can summarize the similarities and differences between cuboids and cubes themselves and truly understand why cubes are special cuboids.

The second class, the plane expansion diagram of cuboids and cubes. The textbook designs two activities. Activity 1: Know the plane expansion diagram of a cuboid and design three levels of activities. 1. "Cut a rectangular box and put it on a flat surface". Let students experience the process of "three-dimensional" becoming "plane" in hands-on operation. 2. Show the cutting plan, so that students can intuitively see that a cuboid can have different shapes after being cut into a plane figure. At the same time, we know that these plane figures are all called plane expansion plans of cuboids. 3. Observe the development diagram cut by yourself, find out the opposite faces on the development diagram, and express them with different symbols. So as to understand the corresponding relationship between each part of the plan and the original three-dimensional plan, and develop the concept of space. Activity 2, know the plane expansion diagram of the cube. On the basis of understanding the expansion diagram of rectangular frame, two levels of activities are designed. 1. Ask the students to cut the cube paper box and draw the opposite sides with the same color on the unfolded picture. 2. Convey the drawn flat spread diagram and describe the spread shape in language.

The third lesson, the surface area of cuboids and cubes. The textbook selects a familiar example of pasting colored paper on a rectangular gift box, and puts forward the question of "how much colored paper is needed at least" and the requirement of "figure it out by yourself". Let the students transfer the existing knowledge of rectangular area calculation and rectangular plane expansion diagram to the calculation of rectangular surface area. Then, in the process of exchanging students' personalized algorithms, master the calculation method of cuboid surface area, and understand and understand the concept of surface area. Because the calculation of cube surface area is relatively simple, students should explore the calculation method of cube surface area independently in "try it". In teaching, teachers should first help students understand that "pasting colored paper on the surface of the gift box" means pasting colored paper on all six sides of the cuboid, and then encourage students to try their own calculations. In communication, students should be given ample opportunities to show different calculation methods, affirm their reasonable calculation methods, and make them learn simpler calculation methods through comparison. It is not required to list the comprehensive formula calculation.

Lesson four, solving problems. The textbook selects the practical problem of painting the walls of the classroom around students, gives the relevant data of the length, width and height of the classroom and the area of doors, windows and blackboards in the form of words and situational dialogues, and asks "How many square meters do you need to paint?" And the requirement of "try to do it yourself". Let students use the knowledge of cuboid surface area flexibly to solve problems. Then, in the process of exchanging students' personalized algorithms, I realized that when calculating the area of painting classroom walls, we should subtract the area of floor, doors and windows and the area of blackboard, so that we can learn to use the formula for calculating the surface area of cuboid flexibly to solve practical problems. In the "try it", the practical problem of calculating and making a cuboid iron ladle without cover is designed, and the material for students to flexibly use the method of calculating the surface area of cuboid to solve practical problems is created again.

Comprehensive application-packing tapes and arranging 1 class hour.

The textbook * * * designed two exploration activities. Activity 1: Pack 6 tapes. First of all, the textbook asks "How to put six tapes together?" Ask students to play tapes in groups, and then exchange different placement methods. Then two questions are designed. (1) Estimate which packaging method saves more wrapping paper. (2) Actually measure which packaging method uses less paper. Three typical tape placement methods are selected in the textbook, so that students can actually measure their length, width and height respectively, and calculate their surface area, that is, the area of wrapping paper. And fill in the relevant data in the form. Through actual measurement and calculation, it is proved by data which packaging method uses the least paper. Activity 2: Pack 8 tapes. The textbook puts forward, "Which way to save wrapping paper is to pack 8 tapes?" First, let the students think about several packaging methods, and then compare which one saves wrapping paper. Through two activities, students realized that the larger the surface and the more overlapping it is, the smaller its surface area and the more wrapping paper it saves. In practical activities, students may have other ways to put them, and teachers should pay attention to them. You can also ask students to actually measure it.

Unit 6 Fractional Division

Fractional division, like fractional multiplication, is an important mathematical content in primary schools. Judging from the previous teaching practice, this part of knowledge has always been a difficult point for students to learn mathematics. The requirements of the original outline are: understanding the meaning of fractional division; Master the calculation rules of fractional division; Can calculate fractional division; Able to calculate simple fractional division; Can grade elementary arithmetic (no more than three steps); Can solve the problem of score application (no more than two). The specific standard of fractional division in Mathematics Curriculum Standard is that it can be divided into fractional division and mixed operation (mainly divided into two steps, no more than three steps). Will solve simple practical problems about fractions. Compared with the original syllabus, the requirements of the mathematics curriculum standard for fractional division calculation have not changed much, but the number of steps of mixed operation in the syllabus has been changed from "no more than three steps" to "two-step-based, no more than three steps". Like fractional multiplication, the reform still downplays the significance of fractional division and emphasizes the calculation of fractional division to solve simple practical problems. Compared with the traditional textbooks, the textbook of this unit has changed greatly in terms of writing ideas, content arrangement and teaching methods, and has the following characteristics:

First, understand the significance of fractional division in combination with specific conditions, and strengthen the mastery and application of calculation methods.

From the traditional teaching materials of fractional division, there are three main points. First, the significance of fractional division; Second, the law of fractional division. That is, a number divided by a fraction is equal to the number multiplied by the reciprocal of the fraction. Third, use equations or arithmetic to solve the problem of fractional division. From the perspective of knowledge construction, students are very familiar with division as "average score" when learning integer division, but in real life, it is difficult to find specific examples to illustrate the practical significance of "dividing a number by a fraction". Therefore, in traditional textbooks, we choose "knowing the operation of the product of two factors and one of them to find the other factor" to illustrate the significance of fractional division. This reciprocal relationship of multiplication and division is an important mathematical conclusion, which should be understood by students under the knowledge background of multiplication and division calculation. But it is really difficult for students to understand the meaning expression of fractional division with this relationship now. In addition, the boring practice of reading the meaning of formulas makes students confused at the beginning when they are exposed to fractional division. In addition, the significance of this fractional division has nothing to do with the core knowledge of fractional division, that is, "a number divided by a fraction is equal to the number multiplied by the reciprocal of the fraction". Therefore, it not only increases the learning difficulty of students, but also is not conducive to students' mastery of knowledge. Based on the principle of "reducing the difficulty and highlighting the key points", this set of teaching materials does not arrange the content of fractional division at the beginning. Instead, we should make use of students' existing knowledge about the meaning of integer division and learn division calculation through practical and understandable concrete examples. Do you understand why division is used? Why do you count like this? For example, in order to understand the core knowledge point of fractional division, "a number divided by a fraction is equal to this number multiplied by the reciprocal of this fraction". First of all, three groups of oral arithmetic exercises corresponding to integer division and fractional multiplication are arranged in the textbook. By observing the calculation results and the characteristics of the formula, students can find the law of "A number ÷ B number = reciprocal of A number ×B number". Then choose the practical problems in students' life. My mother bought 1/2 cakes and divided them into three pieces on average. How much is each cake? To solve this problem, students' own knowledge and experience is to divide half a cake into three parts on average, and the formula is ÷3. A number ÷ B number = the reciprocal of A number ×B number and the reciprocal of 3 are. In the process of solving problems, with the help of intuition, students' existing knowledge and experience are integrated to generate new mathematical knowledge. Analysis divided by a number (except 0) is equal to the score multiplied by the reciprocal of this number. In this way, the study of the law of fractional division is designed. First of all, the process of deducing the calculation method that is difficult for students to understand is omitted. In addition, the migration from the law of integer division and fractional multiplication to fractional division is a process of verifying the calculation method and also a process of forming and consolidating the calculation method. What is deleted here is the secondary and excessive requirements, and what is strengthened is the most basic and valuable content for students to calculate the fractional division in a down-to-earth manner. At the same time, cultivate students' ability to construct knowledge independently.

2. Infiltrate the idea of mathematical modeling, strengthen the application of equations and solve the problem of fractional division.

Judging from the past experience, the characteristic of the application problem of fractional division is "knowing the part and the corresponding fraction, seeking the whole". Practically speaking, this kind of application problems are all things that have happened, and they are artificially "processed" and "fabricated" application problems. Although such problem solving is rarely used in real life, it has always been the focus of teaching materials and teaching evaluation topics in traditional teaching materials and teaching. As we all know, for a long time, the problem of fractional division needs two methods: arithmetic method and equation method. However, it is impossible to solve the problem situation that students can understand and explain the quantitative relationship by arithmetic. Therefore, people use the problem-solving routine of "knowing the sum of parts, knowing the corresponding fraction, seeking the whole and seeking division" to solve problems. This kind of learning is not conducive to students' understanding of the quantitative relationship in the problem. There is no systematic training of thinking, only rote memorization and mechanical imitation training. The problem of fractional division in this textbook is only solved by column equation. The idea of this design has the following points: first, it is beneficial for students to apply existing knowledge to solve problems. That is, the unit "1" is regarded as χ, and the equivalence relation in the problem is found according to "what is the fraction of a number". Multiply. " Secondly, it permeates the idea of mathematical modeling. Equation is an effective mathematical model for practical operation. Combined with solving the problem of fractional division, through some typical examples, let students go through the process of analyzing the problem (finding the equivalence relationship)-listing the expression of the equation-solving the equation. This is the concrete embodiment of the mathematical modeling thought advocated by the mathematical curriculum standard.

Thirdly, analyze the quantitative relationship with the help of line segment diagram, and play its instrumental role.

As a tool for combining numbers and shapes and analyzing quantitative relations in primary school, line drawing has always been an important content of primary school mathematics. In traditional textbooks and teaching, people pay attention to describing the quantitative relationship intuitively with line segments, and at the same time, it is also a common requirement to express the quantitative relationship with line segments. That is, drawing a line segment to represent the quantitative relationship in the problem as a learning requirement increases the difficulty of learning. This set of teaching materials only plays an instrumental role in line drawing. That is to say, it is not a learning requirement to analyze the quantitative relationship with the help of line segment diagram and draw line segment diagram to express the quantitative relationship. In this paper, the mathematical information and quantitative relationship in the problem are analyzed by line segment diagram, so as to find out the implicit equivalence relationship in the problem. Let students experience the advantages and tools of drawing, analyzing and solving problems in solving problems independently.

This unit * * * arranges 5 class hours. The main contents include: fraction divided by integer; Divide a number by a fraction; Simple application problems; Mixed operation.

The educational objectives of this unit are:

1, can carry out simple fractional division and fractional elementary arithmetic, and can solve simple practical problems about fractional division with equations.

2. Being able to analyze the quantitative relationship with the help of the line segment diagram, thinking methodically in the process of solving simple fractional division application problems with equations, and convincingly explaining the rationality of the conclusion.

3. Be able to express the process of solving the practical problems of simple fractional division and try to explain the results.

4. Experience the intuitiveness of line segment analysis and the order of thinking when solving problems with equations, and realize that many problems of fractional division can be solved with equations.

● Fractional division, 4 class hours.

1 class, fraction divided by integer. The textbook first designs three groups of related oral arithmetic questions. Such as: 20÷5, 20×. By calculating 20÷5=4 and 20× =4, we find that their results are the same, and then we get the following conclusion: A number ÷ B number = the reciprocal of A number × B number. Then, the design is "divide the pie into three parts on average. How much is this pie for each part?" Discuss the calculation method of dividing fraction by integer. The textbook presents the process of students' calculation and verification in the form of student communication. One is to deduce ÷ 3 = = by using graphs and existing fractional knowledge, and the other is to directly obtain ÷ 3 =× = by using the law of discovery. Get: A fraction divided by a number equals a fraction multiplied by the reciprocal of this number. Then, in the "try it", three questions are designed to divide the score into integers, so that students can try to calculate by the above methods. In teaching, students should be given enough time to calculate orally and discuss the rules. Then inspire students to use the meaning of division, reciprocal knowledge and fractional multiplication knowledge they have learned before to solve problems, and explain the correctness of the results. The learning process of divisible fraction by integer calculation method becomes the process of knowledge expansion and method verification.

In the second class, a number is divided by a fraction. The textbook implements the design idea of learning while calculating in solving problems, selects a typical example of packaging disinfectant in a small bottle that can be lifted, and designs two problems. (1) How many bottles does it take to put 2 liters of disinfectant into a small bottle that can hold each liter? Learn the division of integer divided by fraction; (2) How many bottles of disinfectant do you need to hold in a small bottle that can be lifted? Learn the calculation method of dividing the score by the score. Two methods are proposed for these two problems: arithmetic and equation solving. The content and calculation method of this lesson is a further expansion of the last lesson, and the calculation formula and equation according to the meaning of the question are the key points. In teaching, we should first help students understand the meaning of the question, and understand how many bottles are needed to pour 2 liters of disinfectant into a small bottle that can hold 2 liters, that is, how many liters are there in 2 liters? Then encourage students to try to answer in their own way. χ = 2 and χ =, in addition to solving equations according to their basic properties, we can also use the knowledge of reciprocal, that is, the reciprocal of direct multiplication of two sides. If students only use the method of dividing both sides of the equation at the same time, the teacher will ask Dr. Rabbit the question "How can I solve χ = 2?" Enlighten students to solve the reciprocal knowledge sequence equation χ× = 2×. In Try, there are three kinds of questions with divisor as score, so students should be given enough time to try and communicate and focus on what they think. Teachers can also guide students to discuss the similarity between fractions divisible by integers and fractions divisible by fractions, and further consolidate the calculation method of fractional divisibility.

In the third class, we simply know what the score of a number is, and find a simple problem of this number. The teaching material selects the venue layout for the students' get-together, and presents a map of the venue layout, as well as text information such as "Total red balloons are used", "There are 28 red balloons" and "One * * *, how many balloons are used". problem Through Dr. Rabbit's words, he put forward the requirement of "taking the total number of balloons as the unit'1'and drawing a line chart for analysis" and put forward a line chart. In teaching, after students know the mathematical information and the problems to be solved, teachers and students draw a line diagram together, analyze the quantitative relationship, find out the equivalent relationship, and then encourage students to try to solve it themselves and test the calculation results. When communicating, let the students talk about their own ideas, how to answer them, and explain the correctness of the calculation results in their own way. In "Try it", we arranged a question that how much part of a number is the sum of two numbers, and encouraged students to draw line segments and answer them.

The fourth class "How many fractions are known in a number and how to find this number" is a slightly complicated problem. The textbook first selects an example of bumper cars planned by a toy factory, and presents the completed 190 cars and "How many bumper cars are there in this batch?" problem Through Dr. Rabbit's words, he suggested drawing a line graph to analyze the quantitative relationship and present a complete line graph. This is a practical problem that requires two-step fractional division. We can find two sets of equivalence relations and list the solutions of two equations. (1) number of planned vehicles-number of vehicles produced = number of vehicles to be produced, and the equation is: χ-χ = 190. (2) The number of planned vehicles × remaining fraction (1-) = the number of vehicles to be produced, and the equation is: χ (1-) = 190. In teaching, we should make full use of line graphs to guide and help students to analyze the mathematical information and quantitative relationship in the problem, find the equivalent relationship given in the problem, and then encourage students to solve it by the method of sequential equations.

● Mixed operation, 1 class hour.

The order of fractional mixing operation is the same as that of integer. The mixed operation in this lesson is mainly based on the characteristics of fractional division to solve the method problems in the operation process. The textbook designs three problems of fractional mixed operation. The problem (1) is a mixed operation of division and addition. In the operation, division should be calculated first, and the division should be turned into the reciprocal of multiplication and division. (2) The problem is the mixed operation of multiplication and division. In operation, there are different reduction methods after the division is converted into the reciprocal of multiplication and division. First, cut directly on the three scores; Second, multiply three fractions to get the formula of numerator multiplied by numerator and denominator multiplied by denominator, and then simplify the fractions. (3) It is a mixed operation of division and subtraction with brackets. In teaching, students are very familiar with the order of two-step mixed operation, so let students talk about the order of operation and calculate by themselves. While exchanging students' calculation methods and results, master the two-step mixed operation method of fractions.

Unit 4, fractional multiplication

Fractional multiplication and division is an important content of mathematics calculation teaching in primary schools, and it is also an important basis for studying mathematics in the future. The requirements of "Mathematics Curriculum Standard" for multiplication and division of primary school scores are: multiplication, division and mixed operation of scores (excluding scores) (mainly in two steps, not more than three steps); Will solve simple practical problems about fractions. Compared with the requirements of the original syllabus, the significance of fractional multiplication and division is weakened, and the connection between knowledge is emphasized, so that students can understand the significance of four fractional operations in specific situations and learn calculation methods. The purpose of this change is, first of all, to change the phenomenon that teachers refine the meaning of formulas according to textbooks and students memorize them. For example, in traditional textbooks, the meaning of integer multiplied by fraction and fraction multiplied by integer is different. Multiplying a fraction by an integer, just like multiplying an integer by an integer, is to find the sum of several identical addends (the same addend is a fraction), while multiplying an integer by a fraction means "what is the fraction of a number". It is difficult for teachers to teach and students to understand fractional multiplication. In addition, some questions with the meanings of ×3 and × 6 often appear in the examination, which not only increases the learning burden of students, but also is not conducive to the formation of computing skills. In addition, by using integer multiplication and the meaning of three fives, we can write existing knowledge such as 3×5 or 5×3, so that students can understand why multiplication is used in specific situations, which is conducive to reducing students' burden and forming a systematic knowledge structure.

The arrangement of the teaching materials in this unit has the following characteristics:

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