The teaching contents, objectives, explanations and suggestions of the eighth volume of Primary Mathematics published by People's Education Publishing House;
1 four arithmetic operations 2 position and direction 3 arithmetic and simple calculation The significance and nature of nutritious lunch 4 decimal 5 triangle addition and subtraction 6 decimal 7 statistics 8 mathematics wide-angle housekeeper 9 general review
Unit 1 Four Operations
Teaching objectives
1. Make students master the operation sequence of two-level operation and correctly calculate the three-step problem.
2. Let students experience the process of exploring and communicating to solve practical problems, feel some strategies and methods to solve problems, and learn to solve some practical problems through two or three steps of calculation.
3. In the process of solving practical problems, make students develop study habits such as careful examination of questions and independent thinking.
Explanations and suggestions
1. This unit mainly teaches and combs the order of mixed operations. In front of the mixed operation, the students have learned to calculate the two-step problem from left to right and know the function of brackets. Here, we mainly teach the operation order including two-level operation, and sort out the order of mixed operation. The main contents include: sorting out the order of operations at the same level (example 1 mixed operation, example 2 mixed operation of multiplication and division), teaching and sorting out the order of two-level operations (example 3 mixed operation of sum (difference) of product quotient, mixed operation of sum (difference) of two quotients) and bracketed operation order (example 5 three-step operation problem with brackets), and operation about 0.
2. Solving problems and sorting out the order of elementary arithmetic are organically combined. This unit combines solving problems when sorting out the order of mixed operations. The purpose is to enable students to further master the strategies and methods of analyzing and solving problems in the process of solving practical problems, and at the same time understand the necessity of specifying the operation order, so as to systematically master the order of mixed operations.
3. organically combine the process of exploring problem-solving ideas with the understanding of operation order. This unit is to make students feel the necessity of specifying the order of mixed operations and master the order of mixed operations in the process of solving problems. Therefore, in teaching, we should make full use of the vivid situations provided by textbooks, let students think and explore independently, and form steps and methods to solve problems on the basis of cooperation and communication. What do we need first? What method is used to calculate? What else do you want? What method is used to calculate? What do you want in the end? What method is used to calculate? Combine the steps of solving problems with the order of operation. When enumerating comprehensive formulas, students should also ask about the basis and practical significance of each step of the formula, so as to promote students to correctly summarize the operation order of mixed operations.
4. Help students master the steps and strategies of solving problems step by step. The order of mixed operation in this unit is combined with problem solving, and the steps and strategies of problem solving are one of the key and difficult points. In teaching, we should pay attention to strengthening the analysis of quantity relationship, and guide students to describe problem-solving ideas through the relationship between quantity and dosage when describing problem-solving ideas. For example, students can be guided to describe their thinking like this: "First calculate how many people will be received every day, and then calculate how many people will be received in six days." Don't stop at the description of "first use 987÷3, then multiply it by 6". Students may not be used to it at first, but they should gradually cultivate this analytical method.
The position and direction of the second unit
Teaching objectives
1. By solving practical problems, let students know the application of positioning in life and the methods of positioning.
2. Enable students to determine the position of objects according to the direction and distance, and describe a simple road map.
Explanations and suggestions
1, this unit * * * arranged four examples: Example 1 Determine the position of an object according to two conditions: Example 2 Draw the position of an object on the map according to the direction and distance; Example 3 describes and draws a simple road map.
2. Students have accumulated some perceptual experience in determining the position in their daily life. Through the first phase of study, they have been able to describe the relative position of objects in eight directions: up, down, left, right, front, back, east, south, west and north, and initially realized that by determining the position of objects in the first row and the first column, the position of objects can be determined by two conditions in the plane. On this basis, this unit allows students to learn to determine the position of objects according to the two conditions of direction and distance, and draw a simple road map. Enable students to further understand things from the perspective of orientation, more comprehensively perceive and experience things around them, and develop the concept of space.
3. Let the students know the importance of determining the position according to the actual life. The textbook selects real-life materials to make students understand the role and value of what they have learned. For example, through the situation of "park orienteering", this paper introduces how to determine the position according to the direction and distance, so that students can understand the application of determining the position in life and experience the close relationship between mathematics and daily life.
4. Pay attention to creating activity situations and encourage students to explore independently and cooperate and communicate.
Students already have the foundation of understanding things from the perspective of orientation, and with the growth of age, their language expression ability, hands-on operation ability and independent exploration ability have all improved. Therefore, in teaching, we should pay full attention to students' existing knowledge base and life experience, create a large number of activity situations, provide students with space for exploration, and let students further understand things from a directional perspective through observation, analysis, independent thinking, cooperation and communication. In this grade, students have a strong thirst for knowledge and curiosity. Teachers should fully mobilize students' enthusiasm and guide them to explore and think independently. And because of students' personality differences, different students have different ways of understanding things. Teachers should encourage students to express their views boldly and cooperate and communicate with their peers. Through this process, students learn to explore and think in different ways and constantly improve their thinking level.
Unit 3 Algorithm and Simple Calculation 1
Teaching objectives
1. Guide students to explore and understand additive commutative law, associative law, multiplicative commutative law, associative law and distributive law, and make some simple calculations by using algorithms.
2. Cultivate students' awareness and ability to choose algorithms according to specific conditions, and develop the flexibility of thinking.
3. Let students feel the connection between mathematics and real life, and use what they have learned to solve simple practical problems.
Explanations and suggestions
1. The teaching contents of this unit include addition law (additive commutative law, application of addition law and addition law), multiplication law (multiplication exchange law, multiplication association law and multiplication distribution law) and simple calculation (simple calculation of continuous subtraction, flexible application of addition and subtraction, simple calculation of continuous division, flexible application of multiplication and division, flexible application of multiplication and division).
2. The five algorithms learned in this unit are not only applicable to the addition and multiplication of integers, but also to the addition and multiplication of rational numbers. With the further expansion of the range of numbers, they are still valid in the addition and multiplication of real numbers and even complex numbers. Therefore, these five algorithms have an important position and function in mathematics, and are known as "the cornerstone of the building of mathematics".
3. Concentrate the knowledge about the operation rules in one unit and organize it systematically, which is convenient for students to understand the internal relations and differences between the knowledge, and is beneficial for students to build a relatively complete knowledge structure through systematic learning.
4. Strengthen the connection between mathematics and the real world and promote the understanding and application of knowledge. One of the most obvious features of this textbook is to pay attention to the realistic background of mathematics, which embodies the desire of mathematics teaching to return to society and life. Therefore, understanding this intention of the textbook, making good use of the textbook and relying on the realistic prototype of mathematical knowledge can mobilize students' life experience, help students understand the operation rules they have learned and construct personalized knowledge meaning. Furthermore, with the understanding of the meaning of knowledge, it is also beneficial to the application of the learned operation rules.
5. The purpose is to embody the spirit of mathematics curriculum reform with diversified and personalized algorithms and cultivate students' ability to choose algorithms flexibly and reasonably. For primary school students, the application of the algorithm is more flexible and requires higher mathematical ability, which is one aspect of the problem. On the other hand, the application of the algorithm also provides an excellent opportunity to cultivate and develop the flexibility of students' thinking. In teaching, we should pay attention to let students explore and try, and let students communicate and question. Accordingly, teachers should also play a leading role. When students explore, they should observe carefully, ponder over their ideas carefully, guide them according to the situation, inspire them appropriately, and lose no time. When students communicate, listen patiently, understand students' real thoughts, and give necessary guidance to help students explain their own algorithms so that other students can understand them. 、
Unit 4 Significance and Properties of Decimals
Teaching objectives
1. Let students understand the meaning of decimals, know the counting unit of decimals, read and write decimals, and compare the sizes of decimals.
2. Make students master the nature of decimal and the law of decimal size change caused by decimal position movement.
3. Let the students rewrite decimal and decimal composite.
4. Enable students to use the "rounding method" to reserve a certain number of decimal places as required, find out the approximate number of decimal places, and rewrite the larger number into decimals with tens of thousands or hundreds of millions.
Explanations and suggestions
1, the content of this unit mainly includes the meaning (decimal meaning, reading and writing) and nature (decimal nature) of decimals, the comparison of decimal size (the comparison of decimal size, the change of decimal size caused by the movement of decimal position), the decimals in life (the reciprocal of singular and composite numbers), and finding the divisor of a decimal (finding the divisor of a number and putting a larger number). These contents are taught on the basis of "Preliminary Understanding of Fractions" and "Preliminary Understanding of Decimals" in Grade Three, which is the beginning for students to learn decimals systematically. Through this part of teaching, students can further understand the meaning and nature of decimals and lay a good foundation for learning four decimal operations in the future.
2. Simplify the description of decimal meaning. Decimal is essentially another representation of decimal, which is based on the principle of decimal value. However, considering the students' acceptance ability, the textbook downplays the reason why decimal fraction can be expressed in decimal according to integer writing, and focuses on "Decimal is another expression of decimal fraction" to explain the meaning of decimal, so that students can make it clear that "Fractions with denominators of 10, 100, 1000 ..." can be expressed in decimal.
3. Pay attention to the understanding of decimal meaning.
Understanding the meaning of decimals involves fractions of decimals, and it is difficult for students to understand the fractional relationship of fractions without systematic knowledge of fractions. Therefore, in addition to formally teaching the meaning of decimals, the textbook also helps students understand the decimal relationship of measurement units (such as length units), and arranges many exercises according to decimal measurement units to understand the practical meaning of decimals.
4. The expressions of "magnification … times" and "reduction … times" in "the law of decimal size change caused by decimal position movement" were modified. The conventional understanding of "expanding … times" and "reducing … times" in the primary school mathematics stage is: expanding several times is multiplying several times. A few times smaller divided by a few. However, some people have different views on this. Some people think that if the number A is expanded by n times, it should be a+na times, not na. Some people think that "doubling" only applies to the expansion of numbers, not to the reduction of numbers. Considering the above problems and the connection with middle schools, we have made tentative changes to this set of teaching materials. In the rule of decimal size change caused by decimal position movement, the words "enlarge … times" and "reduce … times" are changed to "enlarge to … times" and "reduce to … one third".
5. Pay attention to the teaching of basic concepts and knowledge. Some concepts, laws and properties of this unit are very important, which is an important basis for further study. Students must master them well. For example, the nature of decimals can not only deepen students' understanding of the meaning of decimals, but also be the basis for the calculation of four decimal places. For another example, the change of decimal size caused by the movement of decimal position is not only the basis of decimal multiplication and division, but also the basis of learning how to rewrite decimal and composite. This knowledge is logical and students have some difficulties in learning. In teaching, we should pay attention to taking appropriate measures to help students understand this knowledge according to their cognitive characteristics.
Unit 5 Triangle
Teaching objectives
1. Make students know the characteristics of a triangle, and know that the sum of any two sides of the triangle is greater than the third side, and the sum of the inner angles of the triangle is 180.
2. Make students know acute triangle, right triangle, obtuse triangle, isosceles triangle and equilateral triangle, know the characteristics of these triangles, and identify and distinguish them.
3. Connecting with the reality of life, through activities such as posing and designing, let students further feel the characteristics of triangles and the connection between triangles and quadrangles, feel the transformation ideas of mathematics, feel the connection between mathematics and life, and learn to appreciate the beauty of mathematics.
4. Enable students to further develop the concept of space and improve their observation ability and hands-on operation ability in exploring the characteristics, transformation and design activities of graphics.
Explanations and suggestions
1. The main contents of this unit are: the characteristics of triangles, the sum of two sides of a triangle is greater than the third side, the classification of triangles, the sum of internal angles of triangles is 180 and the combination of figures. In the study of the first semester and the first volume of grade four, I have intuitively understood triangles and can distinguish triangles from plane figures. The content of this unit is designed on the basis of the above content. Through the teaching of this content, students' knowledge and understanding of triangles are further enriched.
2. Triangle is a common figure. In plane graphics, triangle is the simplest polygon and the most basic polygon. A polygon can be divided into several triangles. The stability of triangles is widely used in practice. Therefore, mastering this part of teaching can not only deepen students' understanding of the surrounding things and develop students' spatial concept, but also expand students' knowledge and develop students' thinking ability and ability to solve practical problems in hands-on operation, exploration experiment and mathematics application in life. At the same time, it also lays a foundation for studying the area calculation of graphics in the future.
3. The basic knowledge of geometry, whether it is the characteristics of lines, surfaces and bodies, or the characteristics and properties of graphics, is abstract for primary school students. To solve the contradiction between the abstraction of mathematics and the thinking characteristics of primary school students, we must make full use of the intuition of mathematics in teaching. "Let students do science with their hands, not listen to science with their ears", let students start with their hands, use their mouths and brains, mobilize all kinds of senses to participate in mathematics learning activities, and gain knowledge in the activities.
4. In this unit, the combination of figures is added, so that students can feel the characteristics of triangles and the connections and differences between triangles and quadrangles again, so as to understand the internal connection between mathematical knowledge and further develop students' spatial concept and hands-on operation and exploration ability.
5. The teaching goal of triangle understanding in this book is different from the first issue of "getting the intuitive experience of simple plane graphics". Students should gradually understand triangles through observation, operation and reasoning. Therefore, in the teaching of this unit, the implementation of specific objectives such as "knowing that the sum of any two sides of a triangle is greater than the third side" and "the sum of the internal angles of a triangle is 180" not only requires students to actively participate in various forms of practical activities, but also actively guides students to judge, analyze, reason and abstract the results of activities, thus improving their ability in the process of learning knowledge.
Unit 6 Addition and Subtraction of Decimals
Teaching objectives
1. Let students explore the calculation method of decimal addition and subtraction independently, understand the calculation principle, and correctly add, subtract and mix operations.
2. Make students understand that the rules of integer operation are also applicable to decimals, and use these rules to simply calculate some decimals, thus further developing students' sense of numbers.
3. Make students realize the wide application of decimal addition and subtraction in life and study, and improve their understanding of decimal addition and subtraction ability.
Explanations and suggestions
1. The main contents of this unit are: addition, subtraction, mixed operation of decimals and the generalization of integer operation rules to decimals.
2. The calculation methods of decimal addition and subtraction are basically the same; The emphasis and difficulty of calculation are concentrated on the treatment of decimal point; The result of calculation should consider whether to use the basic properties of decimal to make it the simplest. For the above reasons, the addition and subtraction of decimals are taught in the same example (for example 1). This not only highlights the organic connection between knowledge, but also saves teaching time, so that students can form a good cognitive structure of decimal addition and subtraction at a faster speed.
3. Number addition and subtraction and integer addition and subtraction are connected mathematically. For decimal addition and subtraction, students feel deja vu. The textbook firmly grasps this cognitive feature of students, deliberately does not give the calculation process of decimal addition and subtraction, and does not summarize the laws of decimal addition and subtraction, but deliberately guides students to use the old knowledge of integer addition and subtraction to migrate to the new situation of decimal addition and subtraction. For example, in example 1 and example 2, let students explore the vertical writing method of decimal addition and subtraction independently, and go through the whole process of calculation. At the same time, through cooperation and communication, * * * understands that "number alignment" is "decimal alignment". When knowing that there is a zero at the end of the calculation result, according to the basic nature of decimal, 0 should be omitted to make the result form the simplest.
4. Decimal addition and subtraction and integer addition and subtraction have constant connections and similarities. The calculation method of integer addition and subtraction has been mastered by the students in the first phase of Grade Three. Therefore, it is an important strategy for students to make full use of old knowledge to learn the addition and subtraction of decimals independently. In teaching, teachers' duties are: to help students activate the existing knowledge and experience of integer addition and subtraction, and try to use it to calculate decimal addition and subtraction; Let students know clearly how to align numbers when they are in vertical position, and understand the reasons. Learn to express the process and result of independent attempt in your own language. It is an important way for students to learn new knowledge by learning this unit independently and applying what they have learned.
Unit 7 Statistics
Teaching objectives
1. Through the simple analysis of the data, students can further understand the significance and role of statistics in life.
2. Let students know the simple broken-line statistical chart, read the broken-line statistical chart, and answer simple questions according to the statistical chart to find mathematical problems from the statistical chart.
3. Through the statistics of all kinds of information in real life, stimulate students' interest in learning mathematics, guide students to pay attention to mathematical problems in life, and use the knowledge they have to solve simple mathematical problems in life.
Explanations and suggestions
1, this unit includes an example 1 Understanding the statistical chart of broken lines, understanding its characteristics, answering simple questions according to the statistical chart of broken lines, and understanding the role of statistics according to the change of data. Example 2 Complete the broken line statistical chart, solve the problem according to the statistical chart, and make reasonable speculation according to the change of data.
2. Through the previous study, students have mastered the basic methods of collecting, sorting, describing and analyzing data, can use statistical tables (single and composite) and histogram (single and composite) to express statistical results, and can solve simple practical problems according to statistical charts; Understand the significance and function of statistics in real life and establish the concept of statistics. On this basis, this unit learned a new statistical chart-broken line statistical chart. Help students understand the characteristics of statistical charts of broken lines and simply analyze the data according to the ups and downs of broken lines.
3. Rational use of migration laws, according to students' existing knowledge and experience, to guide students to master new knowledge. Because the broken-line statistical chart is similar to the bar statistical chart, it only draws points instead of straight lines according to the size of the data, and then connects them with line segments in turn. Therefore, the histogram with changeable data is selected in the textbook, which leads to another expression and naturally transitions to a line chart. For example, case 1, based on the statistics of the number of primary and secondary school students visiting the science and technology exhibition in a city in recent six years, deduces the broken-line statistical chart, and then guides students to observe the characteristics of the statistical chart, making it clear that the broken-line statistical chart can not only reflect the number of people, but also reflect the increase and decrease of the number of people, so as to further understand the characteristics of the broken-line statistical chart.
4. Statistics are closely related to life, and the broken-line statistical chart can more clearly reflect the increase and decrease of data. In teaching, we should make full use of its characteristics, let students feel this characteristic, think from it, understand the guiding significance of broken-line statistical chart to life, and learn to make correct predictions according to the changes of data.
5. Like the previous teaching requirements, we don't ask students to draw a complete statistical chart of broken lines, as long as they can supplement the statistical chart according to the data and describe and analyze the data. Students with ability can try to draw, but there is no uniform requirement for this.
Unit 8 Mathematics Wide Angle
Teaching objectives
1. Give students a preliminary understanding of the thinking method to solve the problem of planting trees through examples in life.
2. Initially cultivate students' ability to explore laws from practical problems and find effective methods to solve problems.
3. Let students feel the extensive application of mathematics in daily life, try to solve simple problems in real life with mathematical methods, and cultivate students' application consciousness and ability to solve practical problems.
Explanations and suggestions
1. This book mainly permeates some ideas and methods about tree planting. Through some common practical problems in real life, students can find some laws, extract their mathematical models, and then use the found laws to solve some simple practical problems in life.
2. The thinking method to solve the problem of planting trees is a mathematical thinking method widely used in real life. The problem of planting trees usually refers to planting trees along a certain route. The total length of this route is divided into several sections (intervals) by the tree on average. Due to different routes and different tree planting requirements, the relationship between the number of road sections (intervals) divided by routes and the number of trees planted is also different. In real life, there are many similar problems, such as installing street lamps on both sides of the expressway, arranging flowers in flower beds and queuing squares. , all hide the relationship between the total number and the interval number, so we collectively refer to this kind of problem as tree planting problem.
3. In the problem of planting trees, the route of "planting trees" can be a line segment or a closed curve, such as a square, a rectangle or a circle. Even regarding the planting of a line segment, there may be different situations, such as planting at both ends, planting at one end only, or planting at both ends. Through some examples in life, this unit allows students to sum up laws according to different situations and use these laws to solve similar practical problems.
4. The arrangement of mathematics wide-angle units in this textbook is mainly to infiltrate some important mathematical thinking methods through simple examples, or introduce some famous mathematical problems, so that students can actively try to use the knowledge and methods they have learned, find strategies to solve problems from a mathematical point of view, and cultivate students' practical experience and ability to solve practical problems. The most important purpose is to let students experience the process of mathematical exploration such as guessing, experiment and reasoning by contacting these important mathematical thinking methods, to stimulate students' curiosity and thirst for knowledge, and to improve students' interest in learning mathematics.
5. This unit is to let students experience the thinking method of solving the problem of planting trees and its application in solving practical problems through simple examples in life. In teaching, we should start with practical problems, guide students to discover the laws hidden in different situations, experience the process of extracting mathematical models and experience the application of mathematical thinking methods in solving practical problems. However, we should also be careful not to make too many changes to the examples, which will increase the difficulty of the problems and cause too high teaching requirements.