1, students master the method of finding the factor and multiple of a number;

2. Students can understand that the factor of a number is limited and the multiple is infinite;

3. Be able to skillfully find out the factors and multiples of a number;

4. Cultivate students' observation ability.

Teaching focus:

Master the method of finding the factor and multiple of a number.

Teaching difficulties:

Can skillfully find the factor and multiple of a number.

Teaching process:

First, introduce new courses.

1. Show the theme map and ask the students to do a multiplication formula.

2. Teacher: See if you can read the following formula.

Display: Because 2×6= 12.

So 2 is a factor of 12, and 6 is also a factor of 12;

12 is a multiple of 2 and 12 is also a multiple of 6.

3. Teacher: Can you talk about another formula in the same way?

(Name the students)

Teacher: Do you understand the relationship between factor and multiple?

Then can you find other factors of 12?

4. Can you write a formula to test your deskmate? Students write formulas.

Teacher: Who will work out a formula to test the class?

5. Teacher: Today we are going to learn factors and multiples. (Exhibition theme: factor multiple)

Pay attention to watch p 12 together.

Second, new funding.

(A) looking for factors

1, example 1: 18 What is the factor?

From the factor of 12, we can see that there is more than one factor of a number, so let's find the factor of 18 together.

Students try to finish: report

(The factors of 18 are: 1, 2, 3, 6, 9, 18).

Teacher: Tell me how you found it. (Student: By division,18 ÷1=18 ÷ 2 = 9, 18 ÷ 3 = 6, 18 ÷ 4 = by multiplication.

Teacher: What is the minimum factor of 18? What's the biggest? When we write, we usually arrange it from small to large.

2. In this case, please look for the factor of 36 again.

The factors of Report No.36 are: 1, 2, 3, 4, 6, 9, 12, 18, 36.

Teacher: How did you find it?

Give examples of errors (1, 2, 3, 4, 6, 6, 9, 12, 18, 36).

Teacher: Is this ok? Why? No, because you only need to write one repetition factor, you don't need to write two sixes. )

Look carefully, what is the smallest and largest factor of 36?

It seems that the smallest factor of any number must be () and the largest must be ().

3. Which factor are you looking for? (18, 5, 42 ...) Please write down one of them in your exercise book and report.

4. In fact, in addition to writing a number factor in this way, it can also be expressed by a set, such as

/kloc-factor of 0/8

1、2、3、6、9、 18

Conclusion: We have found so many factors. How do you think to find them so as not to miss them easily?

Start with the smallest natural number 1, that is, start with the smallest factor and find all the way. In the process of searching, one by one, from small to uppercase.

(2) Multiply

1. We found the factor of 18 together. Can you find a multiple of 2?

Reports: 2, 4, 6, 8, 10, 16, …

Teacher: Why can't I find it?

How did you find these multiples? (Health: Just multiply 2 by 1, 2 by, 3 by, 4 by …)

So what is the minimum multiple of 2? Can you find the biggest one?

2. Ask the students to finish the questions 1 and 2: Find multiples of 3 and 5.

The multiples of Report 3 are: 3,6,9, 12.

Teacher: Is this ok? Why? How should I change it?

Rewritten as: multiples of 3 are: 3, 6, 9, 12, ...

How did you find it? (Multiply 1, 2, 3, ... by 3 respectively)

The multiple of 5 is: 5, 10,15,20, ...

Teacher: To express multiples of a number, besides this method of literal narration, it can also be expressed by sets.

Multiples of 2, multiples of 3 and multiples of 5.

2、4、6、8…… 3、6、9…… 5、 10、 15……

Teacher: We know that the number of factors of a number is limited, so what is the multiple of a number?

The number of multiples of a number is infinite, the minimum multiple is itself, and there is no maximum multiple.

Third, the class summary

Let's recall, what did we focus on in this class? What did you get?

Fourth, work independently.

Complete Exercise 2, Question 1 ~ 4.

The second teaching goal of fifth grade mathematics is "addition and subtraction of scores";

1. Understanding the meaning of factors and multiples from business activities can determine whether a number is a factor or multiple of another number.

2. Cultivate students' ability of abstract generalization, and penetrate the dialectical materialism view that things are interrelated and interdependent.

3. Cultivate students' sense of cooperation, exploration and love for mathematics learning.

Teaching emphasis: understand the meaning of factors and multiples.

Teaching process:

First, create situations and introduce new lessons.

Teacher: Everyone has his own good friends. Can you tell me who is your good friend?

The students answered.

Teacher: Oh, the teacher knows. XXX is a good friend of XXX. If he introduces XXX as a good friend. Will that work?

Health: No, so we don't know who is whose good friend.

Teacher: Friends refer to the relationship between people. When we introduce them, we must make it clear who their friends are, so that others can understand. In mathematics, there are also concepts that describe the relationship between numbers, such as multiples and factors. Today we will learn some knowledge in this class.

Second, discuss communication and solve problems.

1, Teacher: What kinds of numbers do we all know?

Health: natural numbers, decimals, fractions.

Teacher: Now let's study the relationship between numbers in natural numbers. Please write the multiplication and division formula according to different rectangles composed of 12 small squares.

According to the students' report on the blackboard:

1× 12= 12 2×6= 12 3×4= 12

12× 1= 12 6×2= 12 4×3= 12

12÷ 1= 12 12÷2=6 12÷3=4

12÷ 12= 1 12÷6=2 12÷4=3

Teacher: What are the similarities between these three groups of multiplication and division formulas?

Health: In the first group, each formula has two numbers: 1 and 12.

Health: In the second group, each formula has three numbers: 2,6, 12.

Health: In the third group, each formula has three numbers: 3,4, 12.

Teacher: (pointing to the second group) There is another saying about the relationship between three numbers in the formula of multiplication and division. Do you want to know?

Teacher: What is the relationship between 2 and 6 and 12?

Health: 2 and 6 are factors of 12, and 12 is a multiple of 2 and also a multiple of 6.

Teacher: That is to say, the relationship between 2 and 12 and 6 is the relationship between factors and multiples. Who has the relationship between factors and multiples in these formulas?

Health: 3,4 and 12 are factors and multiples, 3 and 4 are factors of 12, and 12 is multiples of 3 and 4.

Health: I think 1 and 12 also have factors and multiples. 1 is a factor of 12, and 12 is a multiple of 1.

Health: Can we say that 12 is a factor of 12?

Health: I think so. 1 2xkloc-0/= 12,1and 12 are all factors of12.

Teacher: That's good. Judging from the above three sets of formulas,

We know that 1, 2,3,4,6 and 12 are all factors of 12.

Teacher presentation:

1. According to the following formula, tell me which number is a multiple of which number and which number is a factor of which number.

12 × 5=60 45 ÷ 3= 15

1 1 × 4=44 9 × 8= 72

2 and 8 are multiples, and 4 is a factor. …………… ( )

Emphasis: when talking about multiples (or factors), we must explain who is whose multiples (or factors). You can't just say who is a multiple (or factor).

Factor and multiple cannot exist separately.

Teacher's demonstration: 0×3 0× 10

0÷3 0÷ 10

What did you find through the calculation just now?

Health: I found that 0 multiplied by any number equals 0.

Health: 0 divided by any number equals 0.

Health: Let me add that 0 can't be divided.

Teacher: So when learning factors and multiples, the numbers we refer to generally refer to integers, excluding 0.

Teacher-student summary: What knowledge have you learned in this class? What else don't you understand?

Health: I have a question. In 2×6= 12, 2 refers to its name in the formula, and 2 refers to the relationship between 2 and 12. Are these two statements the same?

Teacher: That's a good question! Who can answer his question?

Health: It seems different to me, but I don't know why.

Health: I don't think so. In 2×6= 12, 2 is called a factor and refers to its name in the formula, while 2 is a factor of 12 and refers to the relationship between 2 and 12.

Teacher: That's good. In this lesson, we learn the relationship between factors and multiples. The mentioned factor is not the "factor" in the names of the parts in the previous multiplication formula. The two can't be confused!

2、

Try it: can you choose two numbers from them and say who is the factor of who? Who is a multiple of who?

2、3、5、9、 18、20

Teacher: When listening, the teacher found that several numbers are all factors of 18. Did you find them, too Who can calculate the factor of 18 in these six numbers in one breath?

Health: 2,3,9, 18 are all factors of 18.

Teacher: 18 Are there only these four factors?

Teacher: It seems that it is not difficult to find the factor of 18. The difficulty lies in whether you can find all the factors of 18 without repetition or omission.

The projector shows students' different assignments. The solution of ac factor.

Teacher: The factors that show 18 are: 1,18,2,9,3,6;

Do you know how this student worked out the factor of 18? Look at this answer, can you guess a little?

Health: He looks for it regularly, one by one. Write down which two integers are multiplied to get 18.

Teacher: He found it by multiplication. Do other students have anything to add? When can I find it?

Student: You can find it by division. Divide 18 by 1 to get 18, 18 and 1, which are the factors of 18. Divide 18 by 2.

Teacher: Both multiplication and division are acceptable. Which method do you think is easier?

Student: Multiplication.

The factors of blackboard writing: 18 are: 1, 2,3,6,9, 18.

The factor of 18 can also be expressed in this way. (The courseware shows the assembly diagram)

Organize communication:

Is there any way to find a digital factor through the communication just now? Is there any way to avoid repetition and omission?

Highlights: orderly (from small to large), find the right one.

(which two integers are multiplied to get this number), and then write it in order from small to large.

Try one in the way we found.

Courseware demonstration:

Fill in the blanks:

24= 1×24=2×( )=( ) ×( )=( ) ×( )

The factors of 24 are: _ _ _ _ _ _ _ _ _ _ _ _

Try another one: the factor of 16 is ()

Teacher: We all look for a number factor one by one. Why does 16 only have five factors?

Health: Because 4×4= 16, just write a 4.

Teacher: Observe all the factors of 18 and 16. Did you find anything? We can observe it from three aspects: factor number, minimum factor and maximum factor.

18 has six factors, the smallest is 1 and the largest is 18.

16 has five factors, the smallest is 1 and the largest is 16.

Teacher: Who can sum up the students' findings in mathematical language?

Write on the blackboard when communicating:

Factors: minimum quantity and maximum quantity

Finite 1 itself

Teacher: Just now, through independent exploration and cooperative communication, students not only mastered the method of finding the factor of a number, but also discovered the characteristics of the factor of a number. So how do you find the multiple of a number? Find a smaller one, a multiple of 2, and please write it on paper.

Teacher: Stop, are you finished? Can you write down all multiples of 2? then what

Health: You can't write it all down. You can use ellipsis to indicate what you haven't finished yet.

Teacher: You write so fast. Do you have any suggestions?

Health: multiply this number by 1, 2, 3, 4, ...

Write 2 first, and then add 2 one by one.

Blackboard writing: multiples of 2: 2, 4, 6, 8, 10 ...

A multiple of 2 can also be expressed in this way. (Displays multiples of 2 represented by the set circle)

Find the multiple of 3: 3,6,9, 12, 15. ...

Look at multiples of 2 and 3, what will you find:

Blackboard writing: multiples: minimum number and maximum number

Infinity itself does not.

Teacher: Find the multiple of 5 within 30:

Health: 5, 10, 15, 20, 25, 30.

Teacher: What did you find this time? Why not add ellipsis?

Courseware demonstration: a set chart of multiples of 5 within 30.

Guide students to abstract what is the minimum factor and maximum factor of a number, and draw the conclusion that the number of factors of a number is limited.

The thinking method of abstract induction from individual to whole, from concrete to general.

Third, consolidate the application and improve the internalization.

1. In each set of numbers below, who is a multiple of who and who is a factor of who.

16 and 2 4 and 24 72 and 8 20 and 5

2. Is the following statement correct? Tell me why.

(1)48 is a multiple of 6.

(2) 13÷4 = 3... 1, 13 is a multiple of 4.

(3) Because 3×6= 18, 18 is a multiple, and 3 and 6 are factors.

Teacher: There are two different views on question (3). Please explain the reasons of the students who disagree.

Health: No, because I didn't say whose multiple 18 is.

Teacher: What do you think is right?

I think it should be said that 18 is a multiple of 3 and 6, and 3 and 6 are factors of 18.

Teacher: When talking about multiples (or factors), be sure to explain who is whose multiples (or factors). You can't say who is a multiple (or factor) alone, that is to say, factors and multiples can't exist alone.

3.36, 4, 9, 12, 3, 0, who has a factor and multiple relationship with whom.

4. games. Please write a natural number within 60 (except 0) at will. Listen to the teacher's request Please raise your hand if the quantity meets the requirements, and check with each other at the same table.

① () is a multiple of 4.

() is a factor of 60.

() is a multiple of 5.

() is a factor of 36.

Let a student imitate the teacher's request just now and continue to practice.

Think about it, what requirements should be put forward to make the class raise their hands?

Health: () is a multiple of 1

Teacher: The whole class raised their hands. Who can sum up what they just said?

Health: Any natural number excluding 0 is a multiple of 1.

Fourth, review, reflect and improve.

What did you gain from today's study?

Homework after class: Make a turntable with the knowledge of factors and multiples by yourself or in cooperation with classmates after class.

Reflection after teaching:

Forty minutes passed quickly, and the relaxed and happy classroom atmosphere made the students' learning mood unprecedentedly high. The enthusiasm of students and the improvement of mathematical thinking in the process of learning have made me feel endless surprises in this short time.

Classroom lead-in, cordial and effective, allows students to leave the impression of "relationship" in their minds first. Students can learn who is whose factor and who is whose multiple through their own reading, and then try to practice, especially (8 is multiple and 4 is factor. You can't just say who is a multiple (or factor).

Factor and multiple cannot exist separately.

By finding the factor of a number and the multiple of a number, let the students find the law through multiple examples.

The third teaching goal of the fifth grade mathematics "factor and multiple" teaching plan;

Knowledge and skills: through hands-on operation, with the help of geometric intuition, we can know and understand factors and multiples, and understand the interdependence between multiples and factors of a number.

Problem solving and mathematical thinking: through the process of "active construction" and "independent exploration", we can discover and master the methods and characteristics of finding the factors and multiples of a number, develop students' sense of number and cultivate the order of their thinking.

Emotion, attitude and values: experience the wonder and interest of mathematics and generate curiosity about mathematics.

Important and difficult

Key points: 1. Understand the meaning of factors and multiples and their interdependence.

2. Master the method of finding the factor and multiple of a number.

Difficulties: Understanding the meaning and interdependence of factors and multiples.

Instructional design:

First, cognitive factors and multiples

1, classification perception.

Example 1.

12÷2=6 8÷3=2? 2 30÷6=5

19÷7=2? 5 9÷5= 1.8 26÷8=3.25

20÷ 10=2 2 1÷2 1= 1 63÷9=7

Teacher: Who will read these formulas? If you were asked to classify these formulas, how would you divide them?

Health 1: There are two categories. The first category: 8÷3=2? 2 19÷7=2? 5 Their quotient has a remainder; The second category:12 ÷ 2 = 630 ÷ 6 = 59 ÷ 5 =1.826 ÷ 8 = 3.2520 ÷10 = 22122. .

Health 2: divided into two categories: the first category12 ÷ 2 = 6 30 ÷ 6 = 5 20 ÷10 = 2 21=163. The second category: 8÷3=2? 2 19÷7=2? 5 9÷5= 1.8 26÷8=3.25 The quotient is decimal or has a remainder.

……….

Teacher: Different classification standards have different classification methods. Today, we will study on the basis of the second classification. In integer division, if the quotient is an integer without remainder, we say that the dividend is a multiple of the divisor, and the divisor is a factor of the dividend. For example, 12÷2=6, we say that 12 is a multiple of 2, and 2 is a factor of 12.

Teacher: Tell me about each formula in the first category. Who is who? Who is a multiple of who?

Try to talk about it.

Teacher: In 12÷2=6, it can be simply said that 12 is a multiple and 2 is a factor?

Health: You can't say that. Let's talk about whose multiple 12 is and whose factor 2 is, because in this formula, 12 is a multiple. If 24÷2= 12, 12 becomes a factor. Therefore, whether it is a factor or a multiple, it is a relatively different number.

2. Practice

Tell me who are the factors in the following four groups of numbers? Who is a multiple of who?

Teacher: It should be noted that, for convenience, when learning factors and multiples, the number we are talking about refers to a non-zero natural number.

Second, find the factors.

1, Teacher: We know the factors just now. What is the factor of 18? Can you find them? Try to find it in the exercise book yourself.

Students try to do it independently, and teachers patrol and guide them.

2. Teacher: Who can tell me what you think?

Health 1: I want to divide 18 by a few to get an integer, 18 by 1 to get an integer, 1 is a factor of 18, 18 by 9 to get an integer, and so does 9.

Health 2: I think we should look for them one by one. 18 is divided by 1 equal to 18, so 1 and 18 are both factors of 18. 18 divided by 2 equals 9, so both 2 and 9 are factors of 18, and 18 divided by 3 equals 6, so both 3 and 6 are factors of 18.

Teacher: Did he find them all? How did he find it? Who can comment?

Health: He looks for orders, and he won't miss them or repeat them.

Teacher: That's a good point. When we look for factors again, we should look for them in an orderly way.

What are the factors of 3 and 30? What about 36?

Teacher: Observe the factors of several numbers and see what is the same.

Health 1: 1 is a factor of all natural numbers.

Health 2: The smallest factor of a number is 1, and the largest factor of a number is itself.

Third, find multiples.

1, Teacher: When finding the factor of a number, if you want to divide the calculation formula in an orderly way, how to find the multiple of a number? Try to find a multiple of 2.

Look in the exercise book.

2. Teacher: Who can tell me what numbers you are looking for and what are you thinking?

Health 1: I want to divide by 2 to get an integer, 2÷2= 1, 4÷2=2, 6 ÷ 2 = 3 ..................... These numbers are multiples of 2.

Teacher: He thinks from the perspective of division. Do you have any different ideas?

Health 2: I was thinking of multiplication: 2× 1=2, 2×2=4, 2×3=6, 2×4=8 ... so 2, 4, 6, 8 ... are all multiples of 2.

Teacher: They found multiples of 2 from different angles. Have they all found it?

Student: The number of multiples is infinite. You can't find them all.

Teacher: What are the characteristics of the minimum multiple?

Student: The smallest multiple is the number itself.

3. Find 5 multiples of 3 and 5 respectively.

Fourth, consolidate and improve.

1. Fill the middle qualified number in the corresponding oval box.

1 2 3 4 5 6 7 8 9

10 12 15 16 18 20

24 30 36 60

36 times and 60 times.

Teacher: How can I find them all?

Design intention: to cultivate students' habit of orderly thinking.

2.( 1) Write the factors of the following numbers. (Each person writes 5)

10 17 28 32 48

(2) Write multiples of the following numbers.

4 7 10 6 9

Design intention: consolidate the method of finding factors and multiples.

3. Is the following statement correct? Please tick () to select the correct answer. If it is wrong, please press "x".

(1) 1 is the factor ............ () of 1, 2,3.

(2) The multiples of 8 are only 16, 24, 32, 40, 48. ( )

(3)36÷9=4, so 36 is a multiple of 9. ( )

5.7 is a multiple of 3. ( )

Verb (abbreviation of verb) course summary

What did you learn from this course? Are the factors and multiples we learned today the same as before?

Teacher: In this lesson, we learned the factors and multiples with the help of the division formula, and also learned how to find the factors and multiples of a prime number. What needs to be clear is that the factors and multiples we study today are different from those in the multiplication formula, representing multiples, but interdependent.

blackboard-writing design

Factor and multiple

When 12÷2=6, we say that 12 is a multiple of 2 and 6, and 2 and 6 are factors of 12.

The smallest factor of a number is 1, and the largest factor is itself.

The number of multiples of a number is infinite, the smallest is itself, and there is no maximum multiple.