The teaching of factors and multiples should start with attracting students' interest, from shallow to deep, and let students invest in it. It is the students who truly understand the meaning and difference between the two, and on this basis, they can make in-depth changes. If students can't devote themselves to the classroom well, it will cause great obstacles to the development of later courses.
First of all, talk about textbooks.
Before learning this unit, students have learned 100, 1000, 10000, 10000,100000,100000. 000， 100，000， 100，000， 100，000， 100，000，000， 100， 100，000， 100，000， 100，000， 100， 100,00,100,000,00,100,000,100,000, I have mastered the counting method of decimals systematically, and I have basically completed the learning of four integer operations. 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.
The teaching objectives are as follows:
(1) Knowledge and skill objectives:
1. Let students know the meaning of multiples and factors, explore and master the method of finding multiples and factors of a number, and find the multiples, the numbers in the factors, the minimum numbers and their characteristics. It can find all multiples of a number within 1 0 and all factors of a number within 100 among natural numbers from1to 100.
2. In the process of knowing multiples and factors and exploring multiples or factors of a number, students can further understand the internal relationship between mathematical knowledge and improve their mathematical thinking level.
(2) 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.
The teaching focus of this lesson is to understand the meaning and methods of multiples and factors.
The difficulty in teaching is to master the method of finding multiples and factors of a number.
Second, the analysis of students' learning situation
Most students in this class lack initiative and purpose in their usual study. Some students are afraid of difficulties, lack the habit of independent thinking, and consider problems incompletely. In the teaching of this class, it is mainly to mobilize students' learning enthusiasm, improve students' enthusiasm for participating in classroom activities, experience the fun of success, and achieve the purpose of learning knowledge and mastering what they have learned through students' personal exploration and experience. At the same time, I feel the mystery in mathematics and increase my interest in learning mathematics.
Third, the guidance of teaching methods and learning methods.
Nowadays, the development of society and people can not be separated from quality education, and the implementation of quality education must be "student-oriented". Classroom teaching should focus on cultivating students' spirit of exploration and innovation, and 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 (organization) and students' operation inquiry as the main line, starting with students' operation, from the shallow to the deep, using students' existing understanding of multiplication operation and the relationship between the length, width and area of a rectangle, the concepts of multiples and factors are introduced in the operation.
2. Group discussion. Through students' discussion, communication and mutual evaluation, students are encouraged to optimize the method of finding a multiple of a number and a factor of a number, so as to enhance and consolidate the integrity and effectiveness of students' expression of methods and avoid that students can only master the understanding of methods and cannot fully and correctly express them.
3. In the design of teaching process, according to students' interests and cognitive rules, the teaching design of replacing dynamic teaching materials with teaching materials is adopted.
Fourth, the teaching process:
(A) cooperation and exchange, to understand the multiples and factors
1, hands-on operation.
Operation requirements: make a rectangle with 12 squares of the same size. How many different spellings are there? Look at the rectangle. How many do you put in each row? How many rows are there? Use multiplication formula to express various pendulum methods.
2. Question: What is your multiplication formula? Guess what he would say?
According to the students' answers, write the multiplication formula on the blackboard and demonstrate the corresponding graphics by computer.
Blackboard:12×1=126× 2 =124× 3 =12.
(Design intent: Starting with putting small squares, put forward "How many per emission?" "How many rows?" These two questions lead students to use multiplication formula to express the pendulum method, and then let students guess what it might be. Use 12 small squares with the same size to express 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. Students fully experienced the process of "from form to number, and then from number to form", which not only accumulated materials for putting forward the concepts of multiples and factors, but also preliminarily perceived the relationship between multiples and factors, which helped to understand the concepts correctly. )
3. Say: You can use 12 identical small squares to make three different rectangles and write three different multiplication formulas. According to a multiplication formula, such as 4×3= 12, we can say
"12 is a multiple of 4 and 12 is also a multiple of 3.
3 is a factor of 12, and 4 is also a factor of 12. "(said while displayed on the screen)
Say its name. Speak like a teacher.
Read horizontally first, then vertically. you do not get it , do you?
Teacher: If I say, "4 is a factor and 12 is a multiple, ok?"
Clear: multiples and factors represent the relationship between two numbers, and we can't just say who is multiples and who is factors.
According to 6×2= 12, can you tell which number is a multiple of which number and which number is a factor of which number? According to12x1=12?
(Design intention: When introducing multiples and factors with specific multiplication formulas, let the students read them fully, so that they can initially feel that multiples and factors are interdependent, and then through the analysis of counterexamples, let the students feel it more deeply. )
This is the "factor and multiple" that we are going to learn today. For the convenience of research, usually when studying factors and multiples, the numbers mentioned refer to natural numbers that are not zero.
5. practice.
Anyone can say a formula to test who is a multiple of who and who is a factor.
If the students don't get the division formula, the teacher will give an example of the division formula. "Can you say who is a multiple of who and who is a factor of who?"
Students speak freely and have a unified understanding.
Summary: Division can be converted into multiplication. As long as the product of two natural numbers is equal to another natural number, there is a relationship between multiple and factor.
(Design intention: change the question 1 of "think and do" into the question of students themselves, and talk about who is the multiple of who and who is the factor, which not only achieves the purpose of consolidation, but also makes the materials from students themselves more authentic and more acceptable to students. At the same time, considering the influence of students' fixed thinking, the examples may be relatively simple, and teachers need to "intervene" in time to play a guiding role, so that students can deepen their understanding of the meaning of multiples and factors from the connotation. )
Second, explore independently and learn to find multiples of a number.
1, dialogue: Just now we know multiples and factors, and we know that 12 is a multiple of 3. What is the multiple of 3?
Let the students think for a moment, then try to find it by themselves, and then communicate in groups.
Class report: (students may be looking for it indiscriminately; It may also be discovered in an orderly way. )
On the basis of guiding students to evaluate each other, it is obvious that:
The product of 3 times a number is a multiple of 3, so you can multiply 3 by 1, 2, 3, 4, 5 ... to find the multiple of 3. You can also add 3 at a time to find a multiple of 3.
Question: Have you finished? What should I do if I can't finish writing? (indicated by ellipsis)
2. Can you summarize the method of finding the multiple of a number?
Can you find a multiple of 2 or 5? Choose one and look for it.
Roll call report, the teacher wrote on the blackboard: the multiple of 2 is 2,4,6,8, 10. ...
The multiple of 5 is 3,6,9, 12, 15. ...
4. What do you find by observing the above example? Discuss in groups first, then communicate.
(Design intention: On the basis of students' independent exploration, group cooperation and classroom communication, students actively interact with each other to "capture" each other's ideas, improve their understanding, and initially master the method of finding a multiple. Through communication and comparison, it is found that "the number of multiples of a number is infinite, and the smallest multiple of a number is itself, and there is no multiple". )
Third, compare and communicate, and explore ways to find a factor of a number.
1, dialogue: let's study and find a factor of numbers.
Can you find all the factors of 36? If you have difficulties, you can also discuss them in the group first.
The teacher toured, and there were various situations among the students at the destination.
(It may be the idea of multiplication, some are incomplete and some are very orderly; It is also possible to think by division, and it is also possible to have disorder and order. )
2. Compare "order" and "disorder" and guide: Is there anything to add or ask about his method? Make students realize the necessity and scientificity of orderly thinking in comparison and communication. )
Comparing the two methods of multiplication and division, what do you find?
Make use of students' existing knowledge of multiplication and division and their relationship, learn to think flexibly and establish appropriate connections between old and new knowledge. )
Looking back on the communication just now, what do you think is the secret of finding all the factors of a natural number? Look at them one by one in a certain order until the two numbers are close. )
5. Can you find the factor 15 or 16? Choose one and look for it.
The factors of AC: 15 are 1, 3,5, 15.
The factors of 16 are 1, 2,4,8 and 16.
6. Observing the above three examples, what do you find?
It is the key to effective teaching to look at problems from the students' point of view. This link fully presupposes the possible situations of students. Through two targeted comparisons, students can learn to think flexibly and orderly, and guide them to find the methods of number factors in their own language in time. Then consolidate the method by trying to do the problem. Observe three examples and find the characteristics of a factor of a number, because there is a reference to the characteristics of a multiple of a number, so that students can speak freely and summarize. )
Fourth, contact life and consolidate application.
1, do the second question "Want to do".
Let the students read the questions and fill in the form by themselves.