Lecture Notes of Factor and Multiplier 1 I. teaching material analysis.
Multiplies and Factors is the eighth volume of Mathematics by Jiangsu Education Press. This content is based on students' comments on 100, 1000, 1000,1000,000,000,000,000,000,000,000,000,000. 000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 At the same time, they basically completed the teaching on the basis of four integer operations. This is the basis for students to further study common multiples, common factors, and the reduction, division and four operations of fractions, which plays an important role in future study.
Second, the teaching objectives, key points and difficulties.
1. Knowledge and skill goal: By integrating integer multiplication and division operations, students can understand the meaning of multiples and factors, explore ways to find multiples and factors of a number, and find multiples and factors of a number.
2. Process and Method Objective: To guide students to explore and find ways to calculate multiples and factors independently, to understand the internal relationship between mathematical knowledge, and to improve the level of mathematical thinking.
3. Emotional attitude goal: to stimulate students' interest and self-confidence in learning mathematics in learning activities.
4. Focus: Understand the meaning of factors and multiples, and know that their relationship is interdependent.
5. Difficulties: Explore and master the method of finding multiples and factors of a number.
Third, teaching design.
(A) understanding multiples and factors
When understanding multiples and factors, guide students to use the existing multiplication knowledge and the relationship between the length, width and area of a rectangle to get different multiplication formulas for the same product, and further introduce the concepts of multiples and factors. Multiply and factor refer to the relationship between two numbers, and students can't tell the multiples or factors of a certain number alone, which is often confusing. In order to make students understand that multiples and factors are interdependent, I give examples of brotherly relationship and mother-daughter relationship in life to help students understand, let students feel the connection between mathematics and life, and let students understand that solving life problems with mathematical knowledge is the real purpose of learning mathematics.
(2) Explore the method of finding the multiple of a number.
From the example 1, it is concluded that 12 is a multiple of 3, and an example of a multiple of 3 given by students is purposefully written on the blackboard to guide students to say what is a multiple of 3. The figures the students said in the example are out of order. At this time, teachers guide students to think about how to find multiples of 3 in turn from small to large, thus prompting students to pay attention to thinking methods and feel orderly thinking methods in students' discussion and communication.
On the basis of students' mastery of methods, students are required to write multiples of 2 and 5 in an orderly manner in the form of competitions. Then, on the basis of observing the multiples of 2, 3 and 5 as a whole, students discuss the characteristics of a multiple of numbers. Cultivate students' ability to observe, compare and summarize concepts.
(3) Explore the method of finding the factor of a number.
As can be seen from the example, 4, 3, 6, 2, 12 and 1 are all factors of 12, so how can we find a number factor? Let the students find the factor of 36 by themselves, and then give some examples to explain how to find it. By comparing the methods of several students, a more reasonable method is obtained. Then find out the factors of 15 and 16, and summarize the characteristics of a number factor.
(4) class summary
(5) Consolidate exercises
In order to improve students' interest in learning and consolidate what they have learned, I added two exercises:
1. The purpose of the judgment question is to strengthen students' mastery of basic knowledge.
Show me some digital cards. There is only the relationship between multiple and factor, which is much more than who chooses.
Draft handout "Factor and Multiply" 2 i. 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 unit, we should arouse students' enthusiasm for learning, improve students' participation in classroom learning and experience the fun of success. Through students' personal exploration and cooperation, we can learn knowledge and master what we have learned. At the same time feel the mystery in mathematics.
Second, teaching material analysis
Multiplication and factor is the content of the fifth unit of Hebei Education Press, and it is also one of the most important knowledge in the "Number and Algebra" section of primary schools, which occupies a very important content in the fourth grade textbooks. This unit is based on students' understanding of the number within 100 million and their mastery of the four operations of integer addition, subtraction, multiplication and division. This unit lays a foundation for students to further learn common multiples and common factors, as well as reduction, division and four operations of fractions. It can be said that this unit plays a very important role in future mathematics learning. This unit mainly includes five class hours. The first kind, natural numbers. The characteristics of the second kind of multiples, the third kind of multiples of 2.5, the fourth kind of multiples of 3, the fifth kind of cognitive factors, prime numbers and composite numbers, and the sixth kind of prime factor decomposition. The seventh class, comprehensive exercises.
In the understanding of integer and natural number, there are many concepts, which are easy to be confused and difficult to understand and master. In this textbook, the understanding of the concept of integers and the arrangement of related calculations are integrated and dispersed with related knowledge, which reduces the learning difficulty and enhances the application of knowledge.
Third, the unit teaching objectives
1. Understand natural numbers, odd numbers, even numbers, prime numbers and composite numbers, and make judgments.
2. Understand the meaning of multiples. In the natural number tree of 1~ 100, multiples of all natural numbers within 10 can be found. Knowing the characteristics of multiples of 2.3.5, you will judge whether a number is a multiple of 2.3.5.
3. Understand that multipliers are also called factors. In the natural tree of 1~ 100, we can find all the factors of a natural number and decompose them into prime factors.
4. In the process of observation, exploration, conjecture and verification, you can think methodically and clearly express your thinking process and results.
5. Willing to know the information related to mathematics in social life and actively participate in mathematics learning activities; Initially develop a good quality of being willing to think and dare to explore mathematical problems.
Fourth, the key points
1, find the multiple of a number.
2. The method of finding the factor of a number.
3. Find the characteristics of multiples of 2.3.5.
4. Distinguish between multiples and factors
5. Distinguish between prime numbers and composite numbers
6. Prime factor decomposition.
Verb (abbreviation of verb) oral teaching method and learning method
1. natural numbers In the first class, there are two knowledge points, knowing natural numbers and knowing even and odd numbers. According to the characteristics of the teaching content in this section, based on the thinking of the fourth-grade primary school students, we decided to adopt the cooperative inquiry teaching method to guide students to learn new knowledge and cultivate their interest in learning mathematics through the methods of inspiration, guidance, observation and direct teaching.
2. There are two knowledge points in the second lesson "Multiplication". Understanding multiples is the foundation, and the method of finding multiples of a number is the key and difficult point. I will create scenarios to inspire students to think through the setting of open questions, and experience the mathematical methods contained in the formation of mathematical concepts in thinking, so that they can get their inner feelings.
3. The third and fourth lessons, the characteristics of multiples of 2, 3 and 5, are all about finding the law. I will learn new knowledge by inspiring and inducing students to explore in groups.
4. In the fifth class "Cognitive Factors, Prime Numbers and Composite Numbers", I will use stories to stimulate interest, set questions, lead in, show the story of "Goldbach conjecture" with multimedia, introduce the concepts of prime numbers and composite numbers, and give examples to teach the concepts of prime numbers and composite numbers, so as to deepen my understanding of learning through practice. Then let the students cooperate to explore the way to find a factor. So as to be introduced into the teaching activities of this class.
5. In the sixth class, "prime factor decomposition", we introduce new knowledge by reviewing the prime numbers and composite numbers of factors, then explore new knowledge in cooperation, exchange and discussion, and finally let students explore the methods of prime factor decomposition through group cooperation discussion.
Lecture notes on "factors and multiples" 3 i. Teaching materials
(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:
1, 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 numbers of a number.
Emotional and value goals:
2. Let students initially realize that they can study the characteristics and relations of non-zero natural numbers from a new angle, cultivate the ability of observation, analysis and abstract generalization, appreciate the 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.
"Finding some factors in teaching" is introduced through conversation, which forms the connection and difference between knowledge. "Talk: Be sure to find out who is a multiple of who and who is a factor. 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 factor, from disorder to order, from self-seeking to mutual learning. Ask the students to write on the blackboard and evaluate it. "Question: How did you find the factor of a number? 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.
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 mobilize students' learning enthusiasm, improve students' participation in classroom learning, experience the fun of success, and achieve the purpose of learning knowledge and mastering what they have learned through students' personal exploration and cooperation. 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 summarize to find commonness, find differences and get a number factor, so that students can learn to think in an orderly way, thus forming basic skills and methods, so as to pay attention to both process and result. Teachers' teaching comes naturally, while students' learning is like mountains and heavy waters, and there is no way to return to doubt, and there is another village.
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 on "factors and multiples" 5.i. Teaching materials
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", teachers give 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 discover commonness through 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?" Let the students observe the factors of 6, 1 1, 16, 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.