Lecture Notes of Factor and Multiplication 1 I. Textbooks
(1) The location and context of the textbook: Before learning this unit, students have already known 100, 1000, 10000, 1 10,000, 1 000 and some whole billions. But this is only a superficial understanding of logarithm, which lays a foundation for students to further learn common multiples and common factors, as well as fractional, general and four operations of fractions.
(2) Teaching objectives:
Knowledge and skills objectives:
Let students understand the meaning of multiples and factors, master the method of finding multiples and factors of a number, and find the characteristics of multiples, maximum numbers, minimum numbers and their numbers.
Emotional and value goals:
Let students initially realize that we can study the characteristics and relations of non-zero natural numbers from a new angle, cultivate students' ability of observation, analysis and abstract generalization, experience wonderful and interesting teaching content and generate curiosity about mathematics.
(3) Teaching emphasis:
Understand the meaning and methods of multiples and factors
(4) Teaching difficulties:
Master the method of finding multiples and factors of a number.
Secondly, talk about the design concept.
First of all, from the students' operation, from the shallow to the deep, using the students' existing understanding of multiplication operation and the relationship between the length, width and area of a rectangle, the concepts of multiple and factor are introduced into the operation.
Secondly, students discuss, communicate and evaluate each other, encourage students to optimize the method of finding a multiple of a number and a factor of a number, improve and consolidate the integrity and effectiveness of students' method expression, and prevent students from grasping the understanding of the method but not expressing it comprehensively and correctly.
Third, talk about the teaching process:
(1) Cooperate and communicate to reveal the theme.
Use 12 small squares with the same size to show different postures. In order to avoid simple operation, students are guided to think about how they pose by formulas. Organizational communication, formula derivation, concept identification.
(2) Teaching philosophy, positive and negative promotion
Using horizontal reading and vertical reading, a systematic concept of knowledge is formed, and the whole premise is presented in time: it is a natural number without 0, so that students can give examples, demonstrate and talk to each other. Finally, the teacher gave an example that students can't easily think of: 4×4= 16, 18÷6=3, encouraging students not only to do multiplication.
(3) Doubt, question and stimulate students' reflection.
When seeking the multiple of a number in teaching, "It is said that 12 and 18 are multiples of 3 (blackboard writing: multiples of 3). Is the multiple of 3 only two numbers? " Organizational communication: What is the multiple of 3? Students evaluate and communicate with each other, form their own learning achievements, improve the holistic teaching of knowledge, intensify exploration and improve the difficulty of thinking. "Have you finished writing in minutes?" What if you give me another half minute? Why? "
(4) The deepening of teaching content in judgment has formed the whole learning process of reflection, learning and reinforcement. After students make the correct judgment that "6 is a multiple", they don't simply change chapters, but take this as an opportunity.
"Teaching the factor of a number" is introduced by conversation, which forms the connection and difference between knowledge.
"Dialogue: To be clear about who is a multiple of who and who is a factor of who. So 6 may be a multiple of some numbers or a factor of some numbers, so let's find some factors of some numbers. Can you find all the factors of 36? "
(5) Discuss and evaluate each other and learn independently.
Let students learn to find a number of factors, from disorder to order, from self-seeking to mutual learning. Ask the students to write on the blackboard and evaluate it. Q: How do you find a numerical factor? Can you introduce it to everyone? Is there any other way? "
1×36=36
36÷ 1=36
2× 18=36
36÷2= 18
3× 12=36
36÷3= 12
4×9=363
6÷4=9
6×6=36
36÷6=6
(6) Independent guidance, mastery and summary.
Question: Why is 5 not a factor of 36? (Because 36÷5 is not divisible, there is a remainder.)
Summary: A number that is not divisible by this number is not a factor of this number.
Summary: We can find the factor of a number from multiplication formula and division formula.
Question: What did you find about two examples of numbers with factors ranging from 36 to 15?
Summary: For multiples and factors of a number, they are different, but through multiplication and division, they are interdependent and interrelated.
Fourth, blackboard writing teaching.
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Lecture Notes on "Factors and Multiplies" 2 I. Textbooks
Multiplication and factor is the content of unit 2 in the second volume of grade five, the standard experimental textbook for primary school curriculum published by People's Education Press, and one of the most important knowledge in "Number and Algebra" in primary school. The study of "factor and multiple" is to explore the nature of natural numbers on the basis of preliminary understanding, and the content involved is the basic content of elementary number theory, which is relatively abstract. The arrangement of this content is different from the previous textbook. There is no mathematical language to define "divisibility", but with the help of divisibility model Na = B, this lesson gives the concepts of factor and multiple directly by multiplication formula. From the position, this lesson is an introduction to the concepts of factor and multiple, which provides the necessary and important basis for the subsequent content of this unit, as well as the greatest common factor and the least common multiple of Unit 4. (Note: Teaching objectives, teaching emphases and difficulties are omitted)
Second, the analysis of speaking and learning.
The content of this lesson is the content of the second volume of grade five, but the students of grade four choose it in the form of borrowing lessons. Prior to this, the students had learned about integers within 100 million in segments and basically completed the study of four integer operations (just finished this semester). However, due to the differences in age and personal thinking development, students need further guidance from teachers in the abstract ability and comprehensiveness of language expression and thinking. However, due to the introduction of multiplication in this course, the complex concepts such as "divisibility" in the old textbooks are reduced, and the process of telling and memorizing is greatly simplified, which is expected to be understood and mastered by students.
Third, talk about the design concept.
In the design concept of this lesson, I summed up four characteristics, and these four characteristics are produced in the four links of my teaching:
First, cut into life, realize the combination of numbers and shapes, and complete the meaningful construction of concepts.
If we study the content of number theory from the number itself, it will be more abstract for primary school students. In this lesson, the teacher solved the problem of "12 small squares making rectangles". What are the spellings? As an introduction, students can learn mathematical concepts in the process of solving problems and avoid abstraction, which is conducive to helping students complete meaningful construction. At the same time, when solving problems, when students think about "which spellings", the teacher gives different suggestions. As you can imagine, drawing a picture in a notebook is not only in line with the thinking development of different students, but also has targeted guidance. Secondly, number and shape are organically combined, so that students' understanding of concepts is not only the understanding of numbers, but also related to operational activities and graphic description. Students have experienced the process of "form first, then number", that is, the process of knowledge abstraction.
Second, grasp the "nearest development zone" of students' thinking, and urge students to learn orderly thinking, thus forming basic skills and methods.
Enumerating the factors of a number is an important part of the skill goal of this lesson. In teaching activities, teachers firmly grasp the "nearest development zone" of students' thinking, and let students list several factors independently on the basis of their existing experience. In the process of collective communication, the teacher asked, "How did you find it?" Let students fully expose their own personalized thinking methods, and teachers point out their respective advantages in students' thinking: one-on-one search; Start with "1", search in an orderly way, and then obtain the overall recognition of students through effective analysis. This design enables students to learn to think orderly in the process of independent thinking-collective communication-mutual discussion, thus forming basic skills and methods, so as to pay attention to both process and result.
Third, make full use of the generated materials to realize effective cooperative inquiry and guide students to find * * * in comparison.
It is not difficult to accept the characteristics of a number factor by memory alone. In order to prevent students from "mechanical learning", teachers will ask "What are the characteristics of the factors of arbitrary natural numbers?" Ask students to observe the factors of 6, 1 1, 16 and 24 and think: Is the number of factors of a number limited or infinite? What is the smallest? What's the biggest? Teachers provide guidance to students in research methods, and students' thinking has a clear direction, which is convenient for discovering laws through exploration.
Fourth, pay attention to the infiltration and expansion of mathematical meaning, strive to attract students with the essence of mathematics, and promote the sustainable development of students' learning mathematics.
Mathematics teaching should establish the consciousness of serving students' continuous learning and lifelong development, and should not pay attention to short-term effects and quick success. In the design of this class, the teacher noticed the students' learning stamina. For example, at the beginning of preparing lessons, teachers repeatedly consider whether to introduce the choice of perfect numbers: due to the limited time in a class, in order to express the overall relationship between factors and multiples, many teachers include all the methods of finding factors and multiples in a class. But in the end, I chose to give up the multiple and put it in the later class, and integrate the introduction of perfect numbers and short stories into the teaching of this class. Although these contents have little to do with the current learning tasks, they are what students need to continue learning mathematics, because only with the breath of culture can mathematics become the soul, make students feel the massiness and charm of mathematics, and make students feel positively about mathematics through boredom, thus enhancing the durability of learning mathematics.
Fourth, talk about the teaching effect.
After class, some teachers think that some students have not mastered the knowledge and skills in the teaching objectives and have not mastered effective methods. Students' thinking level and expressive ability are limited, so it is not suitable to use this content in grade four. First of all, I think the teachers in this class have insufficient guidance and the teaching objectives have not been well implemented. I have also seen a large number of famous teachers find students in grade four or even grade three to take this class. In theory, as long as students can basically complete the study of integer multiplication and division, they can do this part of the study. Of course, the effect of each grade should be different. Similarly, the fourth-grade students in this class also have their own level of thinking. Due to the limited level of students' thinking development, it is very reasonable to have some thinking disorders. As a teacher, don't pay too much attention to short-term effects, and don't be too eager for quick success. However, whether to put it in the fourth grade, if so, how to grasp the degree of teaching methods and learning methods, I just made an immature attempt, I only hope that teachers can give more opinions as a meaningful talk.
"Factor and Multiply" Lecture Note 3 Dear judges and teachers,
? Good Morning, everyone! I am the No.8 candidate who interviewed a primary school math teacher. Today, I said that the theme of our class is multiplication and factorization. I will talk about teaching materials, learning situation, teaching methods, teaching process, blackboard writing design and so on. Let's begin my speech.
First of all, talk about teaching materials.
Multiplication and factor are the contents of lesson 1 in chapter 3 of the first volume of the fifth grade of primary school mathematics published by Beijing Normal University. This paper mainly talks about the meanings of multiples and factors and their interdependence. The teaching content is based on students' mastery of multiplication and division. This will lay a foundation for further study on the characteristics of multiples of 2, 3 and 5 and the composite number of prime numbers in the future, so it has the function of connecting the preceding with the following.
Through the analysis of teaching materials, according to the requirements of the new curriculum standards, I have established the following three-dimensional goals:
1. Knowledge and skill goal: Students will judge who is whose factor and who is whose multiple, and understand that multiple and factor are interdependent.
2. Process and Method Objective: Students cultivate their cooperative ability and innovative consciousness through hands-on operation, cooperative inquiry and other learning processes.
? 3. Emotional attitude and values goal: in the process of exploring the relationship between multiples and factors, we feel interdependence and cultivate students' emotional quality of being willing to explore and communicate.
Through the analysis of teaching materials and teaching objectives, I think the teaching focus of this course is to understand and master the meaning of multiples and factors. The difficulty in teaching lies in understanding that multiples and factors are interdependent and finding multiples of 7.
Second, talk about learning.
Ausubel said: "The most important factor affecting learning is what learners already know. We should find this and teach accordingly. " Therefore, at the beginning of teaching, it is very important to pay attention to the basic situation of students. The thinking of the fifth-grade students has begun to transition from concrete image thinking to abstract thinking, but the reasoning ability needs to be improved, so I will closely follow the students' existing knowledge and experience and create a situation conducive to students' independent learning and cooperative communication.
Third, preach the law.
Based on the analysis of teaching content, learning situation and the requirements of the new curriculum reform, I mainly adopt the teaching method, supplemented by heuristic teaching method, discussion and exchange method, practice method and so on, so as to achieve the purpose of cultivating ability and forming good habits. Scientific learning method is very important, it is the "golden key" to open the treasure house of knowledge and the "bridge" to success. In this class, I use independent exploration and group discussion to cultivate their cooperative communication ability and the ability to independently summarize mathematical laws.
Fourth, talk about the teaching process
The teaching process is the core of this lecture, so I will focus on the teaching process.
Link 1, introduction of heart-to-heart, stimulating curiosity
At the beginning of school, I will broadcast the video of the military parade on the xx anniversary of the National Day, so that students can celebrate their mother's birthday again, feel the strength of the motherland and wish her prosperity. Then the screen is enlarged to the two squares of the military parade. Ask the students to calculate how many people there are in each square. It is not difficult for students to give the formulas of 94=36 (person) and 57=35 (person), and then ask the relationship between the numbers in the formulas, which leads to a new lesson.
Through the introduction of video, on the one hand, the enthusiasm of students to participate in the classroom is increased, on the other hand, the students' strong thirst for knowledge is stimulated, and the teaching of this class is better completed.
Link 2: Enlighten and discover new knowledge.
In this session, I designed the following two learning activities.
Activity 1: Analyze the relationship between multiples and factors.
First, let students observe the formula 94=36 by introducing questions, and explain that 36 here is a multiple of 9 and 4, and 9 and 4 are factors of 36. Then let the students think about "which number is a multiple of which number and which number is a factor of which number" according to 57=35. Students use 35 as a multiple and 5 and 7 as factors. Some students will question whose multiples of 35 are and whose factors of 5 and 7 are. Furthermore, teachers and students explored and found the correct expression: 35 is a multiple of 5 and 7, and 5 and 7 are factors of 35. Homeopathy emphasizes that we can't say who is a multiple and who is a factor, and points out that we only study multiples and factors (except 0) within the range of natural numbers. Affirm the students' findings throughout the process and give positive comments.
Secondly, guide students to talk about which number is a multiple of which number and which number is a factor of which number according to the formulas 253=75, 205= 100 in the big screen. Students will accurately answer that 75 is a multiple of 25 and 3, and 25 and 3 are factors of 75. 100 is a multiple of 20 and 5, and 20 and 5 are factors of 100. Teachers and students must pay attention to the relationship between multiples and factors, because factors and multiples are interdependent, so it is necessary to say who is whose multiple and who is whose factor. Let students actively participate in the classroom, seriously think about problems, and put more praise language into students.
Activity 2: Find a multiple of 7.
First, after students can successfully express the relationship between multiples and factors according to the given formula, let students think about "which numbers on the screen are multiples of 7", and then discuss in groups of four. The results of the group report will be: 7=7 1, 14=72, 77=7 1 1, so 7, 14 and 77 are multiples of 7, which shows that this is to solve the problem by using the relationship between multiples and factors in this lesson. There are also answers such as 14÷7=2, 14 is twice that of 7, 17 ÷ 7 = 2 ... 3, and 17 is not a multiple of 7. It is pointed out that this is solved by division, and all divisible multiples are multiples of 7. Use the situation to guide students to sum up. In the relationship between multiples and factors, if the quotient is an integer and there is no remainder, we can also say that the dividend is a multiple of the divisor and quotient, and the divisor and quotient are factors of the dividend.
In these activities, students are placed in the main position of learning, and students are encouraged and guided to cultivate their autonomous learning ability, cooperative exploration spirit and innovative consciousness.
Third, practice and consolidate new knowledge.
I designed an after-class exercise to consolidate what I have learned, aiming at cultivating students to further clarify the meaning of multiples and factors, and then further understand and master the interdependence of multiples and factors.
Step 4: Start reflection, the whole class.
Let the students review new knowledge, talk about their own gains, give them a chance to communicate again, remind each other and further highlight the main points of this lesson. Teachers and students complete classroom evaluation together.
Step 5: Assign homework and improve after class.
According to the individual differences of students, in order to better reflect the principle of teaching students in accordance with their aptitude, I divide my homework into two parts: compulsory and elective, and the compulsory is after-school exercise; Choosing a topic is to find applications in life.
Design of blackboard writing system of verb (abbreviation of verb)
What is presented on the blackboard is my blackboard design, and my design is mainly based on the outline blackboard book, so that the whole course content can be displayed intuitively, clearly and clearly, which is convenient for students to understand and master what they have learned.
That's all I said. Thank you for your patience. Now, can I erase my blackboard writing?
Lecture Notes of Factor and Multiplication 4 Dear leaders and teachers,
Good Morning, everyone! Our team teaches factors and multiplication.
Let's talk about textbooks first:
"Factor and multiplication" is the content of the second unit of the fifth-grade experimental textbook of the curriculum standard of primary school People's Education Edition, and it is also one of the most important knowledge in the "number and algebra" part of primary school. The study of factors and multiples is to explore the nature of natural numbers on the basis of preliminary understanding. The content involved is the basic content of elementary number theory, which is abstract. The arrangement of this content is different from the previous textbook. There is no mathematical language to define "divisibility", but this lesson directly gives the concepts of factors and numbers with the help of divisibility mode Na = B. This lesson is an introduction to the concepts of factors and multiples, which provides the necessary and important basis for the last content of this unit and the greatest common factor and the least common multiple of Unit 4.
According to the status and background of the textbook, the following objectives have been determined:
Knowledge and skills objectives:
Master the concept of factor multiple, understand the meaning of factor and multiple, and master the method of finding factor and multiple of a number.
Emotion, value goal:
Cultivate students' ability of cooperation, observation, analysis and abstract generalization, experience wonderful and interesting teaching content, and generate curiosity and thirst for knowledge about mathematics.
Teaching emphases and difficulties:
Understand the meaning of multiple and factor, and master the method of finding the factor and multiple of a number.
Second, the analysis of learning situation:
Students lack initiative in their usual study, some of them are afraid of difficulties, lack the habit of independent thinking, and consider problems comprehensively. In the teaching of this class, it is mainly to arouse students' learning enthusiasm, improve students' participation in classroom learning and experience the fun of success. Through students' personal exploration and cooperation, they can learn knowledge and master what they have learned. At the same time feel the mystery in mathematics.
Third, the guidance of teaching methods and learning methods.
In today's society, human language is inseparable from quality education. The implementation of quality education must be a "student-oriented" classroom teaching, and we should pay attention to cultivating students' spirit of exploration and innovation, so as to lay a certain foundation for comprehensively improving students' comprehensive quality. This course designs teaching strategies and methods according to students' cognitive ability and psychological characteristics.
1, following the idea of taking students as the main body, teachers as the leading factor, independent inquiry and cooperative communication as the main line, and using students' multiplication operation to understand the concept.
2. Group discussion. Discuss, communicate and evaluate with students, and encourage students to optimize and improve the method of finding factors and multiples of a number. Consolidate the integrity and effectiveness of students' method expression, and avoid students only mastering the understanding of the method without expressing it comprehensively and correctly.
Fourth, the teaching process
1, revealing the theme
The teacher directly reveals the theme and boldly innovates, breaking the traditional teaching mode of importing for importing. It provides an open space for students to study independently and cooperatively.
2. Cooperate and communicate, and understand the concepts and significance of factors and multiples.
Teachers show their homework, communicate in groups, report their learning results, give timely guidance, and truly return the classroom to students, which also fully reflects the leading role of teachers and the dominant position of students. Students can cultivate the awareness of cooperative learning in communication, have a preliminary understanding of the concepts of factors and multiples, and have a better understanding of their relationship.
3. Learn how to find the factor and multiple of a number.
The factors and multiples of numbers are an important part of the skill objectives of this lesson. Let the students list the factors of a number independently on the basis of their existing experience, and let them get them in group cooperation and communication. Find the factor and multiple of a number. Really give the initiative to students, teachers can help students deepen their understanding and resolve difficulties through guidance.
4. Guide students to analyze, compare and find out the differences, and get a number factor, so that students can learn to think in an orderly way, thus forming basic skills and methods, and paying equal attention to both process and result. Teachers teach naturally, while students learn at the end of their tether.
5. Guide students to ask questions, communicate collectively and solve problems, so that students can better digest and understand what they have learned in this lesson.
Verb (abbreviation of verb) practice
These exercises are designed in different forms with gradients. Paying attention to both foundation and improvement has truly realized the effectiveness of classroom teaching.
Lecture Notes of Factor and Multiplication 5 I. Textbooks
1, unit analysis
The chapter of "factors and multiples" includes: factors and multiples; Multiplication characteristics of 2, 5 and 3; Prime number and composite number are the basic contents of elementary number theory, which is based on students' understanding of integers. First, the concepts of factor and multiple are given directly by the multiplication formula in the textbook, so that students can clearly understand the interdependence between factor and multiple. On this basis, let students explore the multiple characteristics of 2, 3 and 5 according to their existing life experience, in which the concepts of even number and odd number are arranged on the basis of mastering the multiple characteristics of 2; Then further explore the law of factors and multiples to understand prime numbers and composite numbers. The knowledge content of this unit is abstract and there are many concepts. Appropriate use of life cases or specific situations in teaching materials can cultivate students' inquiry consciousness and abstract thinking ability. Through this review, a systematic knowledge network is formed in students' minds.
2. Teaching objectives
Knowledge goal:
Summarize the related concepts of "factor and multiple", understand and master the internal relationship between concepts, and form a cognitive structure.
Skill objectives:
Experience the arrangement process of mathematical knowledge and cultivate students' logical thinking ability such as observation, analysis, comparison, generalization and judgment.
Emotional goals:
In the process of sorting out and reviewing, cultivate students' awareness of cooperation and exchange, and infiltrate the dialectical thought that things are interrelated and interdependent.
3. Teaching focus
The connection and development between concepts, using the knowledge learned to solve problems.
4. Teaching difficulties
Summarize and sort out the knowledge points, and build a knowledge network of "factors and multiples" in combing.
Goals should be clear and concise:
(1) Form a knowledge network
(2) check the missing and fill the leak
(3) Comprehensive application of knowledge
(4) Solving practical problems
Second, the analysis of speaking and learning.
1, students have mastered the relevant knowledge of integers and have some knowledge as the basis;
2. As a fifth-grade student, my abstract ability has been further developed, and I have a certain thinking foundation, and I can explore, discover and summarize new knowledge in my activities.
3. For the understanding of concepts, students should be guided to master knowledge from the perspective of connection, instead of memorizing concepts and conclusions mechanically.
Third, talk about teaching methods and learning methods.
1, strengthen the connection between concepts, guide students to understand and master knowledge in essence from the perspective of connection, and avoid rote learning.
2. Teachers should make proper use of life examples or specific situations, make full use of intuitive means to communicate the connection between knowledge, and let students think and analyze in an orderly and well-founded way.
3. Review in groups according to students' cognitive characteristics, so that students can master knowledge and cultivate abstract thinking ability in exchange and exploration.
Fourth, talk about design concepts and teaching strategies.
Concept teaching is abstract and boring for students, and it is difficult for students to master this part of knowledge. Therefore, we should be prepared before class and carefully design exercises. In the design, I first let students sort out the concepts of this unit by creating situational review, and cultivate students' ability to summarize knowledge, and then practice in practice to clarify concepts, deepen understanding and emphasize important and difficult points.
V. Express design ideas
1. Teacher's teaching link: building a knowledge network-consolidating problem-solving methods-emphasizing important and difficult points.
2. Students' learning links: organizing knowledge points in groups-clarifying key points and difficulties-consolidating knowledge points.
Sixth, talk about the teaching process.
Link 1: Create a situation to stimulate the introduction of interest.
Ask the students to describe 4 and 5 with the knowledge in the chapter on factors and multiples. This design aims to let students review these concepts in this unit.
Link 2: Sort out the concept and form a structure diagram.
In this link, the teacher guides students to organize these scattered concepts and knowledge into a relatively systematic knowledge network diagram according to these concepts about numbers and their relationships. This is my blackboard design. (Design intention: Looking at the network diagram will make the messy knowledge in students' minds clear at a glance, help students understand these concepts, clarify the relationship between them, and cultivate students' ability to organize knowledge. )
Link 3: Comprehensive application and knowledge internalization.
By filling in the blanks, judging and deciphering the mobile phone number, students can internalize the knowledge of this unit and improve their comprehensive application ability.
Link 4: Improve the evaluation and classroom summary.
(Design intention: Pay attention to students' emotional experience, and make students learn to evaluate their learning behavior and attitude objectively and fairly through self-evaluation, so as to obtain positive emotional experience. )