1. Make students understand and master the concepts of common factor and greatest common factor of two numbers.

2. Understand the method of finding the common factor and the greatest common factor of two numbers, and find the greatest common factor of two numbers by your favorite method.

3. Cultivate students' methodical thinking through the process of mathematics learning activities.

Emphasis and difficulty in teaching

The solution of the greatest common factor.

teaching tool

Ppt courseware

teaching process

(A), review the old knowledge, lay a good foundation for new knowledge.

1, Teacher: Before, we have learned the factor. Can you give an example to illustrate what is a factor of a number? (Students give examples. Who can give an example like that classmate just now?

2. Understand what is a factor of a number. Can you find out what the factor of 8 is? Teacher: Have all the students found it? This classmate didn't repeat it or omit it. Can you introduce your method of finding the factor? Zan: It's too clear. Let's applaud this classmate. (or: think about how to find a factor of a number to avoid repetition or omission. )

Which student can find the factor of 12 in this way?

Teacher: It seems that everyone has a solid knowledge of factors. The new knowledge to be learned today is closely related to factors.

(B), create a situation to guide hands-on operation

Do students like playing games? Next, let's learn new knowledge by playing a small game.

1, the teacher shows seven digital cards. ( 1、2、3、4、6、8、 12)

(1) Ask seven students to choose any card on the stage. Remember the numbers on your card, put your digital card on your chest and face everyone.

(2) If it is a factor of 8, please stand on the left; if it is a factor of 12, please stand on the right.

Students, have you noticed that some students are double-faced? Who are the classmates?

Please stand in the middle of these three students, and the teacher will interview you. Why are you two-faced?

(3) Students, have you found that several students are double-faced? Who are the classmates?

Please stand in the middle of these three students, and the teacher will interview you. Why are you two-faced?

(4) The teacher asked: Did you find it?

(5) Teacher: 1, 2 and 4 are all factors of 4 and 12. In a word, 1, 2,4 are the common factors of 8 and 12, and the common factors of 8 and 12 are called their common factors.

(6) The teacher asked: What is the greatest common factor of 8 and 12? (4)

(7)4 is the greatest common factor of 8 and 12, so we call 4 their greatest common factor.

(8) This is the greatest common divisor that we will learn in this class.

(9) blackboard title: the greatest common divisor.

(10) except that the common factor is expressed in the above way.

We can also use the form of set circle that we learned before.

(3) methods of cooperation, communication and exploration

1, group cooperation: find the greatest common divisor of 18 and 27.

Now that the students know what the common factor and the greatest common factor are, can you try to find out the greatest common factor of 18 and 27?

Requirements for cooperation: (Group of Four)

(1) Discuss how to find the greatest common factor of two numbers.

(2) Write down on the answer sheet how your group found the greatest common factor of these two numbers.

2. Report and exchange feedback.

Method 1: Write out the factors of 18 and 27 respectively, and then circle the common factor to find the greatest common factor. The students are really great! Other groups, are there any different methods?

Method 2: First find the factors of 18: 1, 2, 3, 6, 9, 18. Then see which of the factors of 18 are the factors of 27, and finally see which is the largest. (Or: Find the factor of 27 first: 1, 3, 9, 27; Let's look at the factor of 27, that is, the factor of 18, and finally see which is the largest. )

Method 3: Write down the factors of 18 first: 1, 2, 3, 6, 9, 18. The factor of 18 is not a factor of 27, and 9 is a factor of 27, so 9 is the greatest common factor of 18 and 27.

4. These methods are enumeration methods, and you can choose your favorite method when solving problems.

5. Observe the common factor of two numbers and its greatest common factor. What did you find? The common factor of two numbers is also the factor of their greatest common factor. )

(4) expand and extend.

The students did very well just now. Will they do better next?

The teacher believes that you will use your excellent performance to prove your Excellence!

1, find the greatest common factor of 4 and 8, 16 and 32, and think about what you find.

The teacher summed up the students' findings and showed them in the courseware: if the smaller number is a factor of the larger number, then their greatest common factor is the smaller number.

2. Find the greatest common factor of 2 and 7, 8 and 9, and think about what you find.

It is found that if two numbers only have the common factor of 1, then their greatest common factor is 1.

3. Teacher's summary: Through the study just now, we know that there are three situations where we can find the greatest common divisor.

(3 kinds: multiple kinds; The common factor is only1; General situation. )

When the relationship between two numbers is multiple and the common factor is only 1, the greatest common factor can be directly judged. Generally speaking, the greatest common factor is obtained by enumeration. )

(5) consolidate and improve.

Just now, everyone not only showed their math ability, but also highlighted their exploration ability. Then, I believe these problems brought by teachers are more obvious to students.

1.

The common factor of (1) 10 and 15 is _ _ _ _ _ _ _.

(2) The common factor of14 and 49 is _ _ _ _ _ _ _.

2. Choose the number of the correct answer and fill it in the horizontal line.

The greatest common factor of (1) 9 and 16 is _ _ _ _.

A. 1 B. 3 C. 4 D. 9

(2) The greatest common factor of16 and 48 is _ _ _ _ _.

A.4 B. 6 C. 8 D. 16

(3) The number A is a multiple of the number B, and the greatest common factor of the numbers A and B is _ _ _ _ _.

A. 1 b. A number C. B number product of d. A and b.

3. Write the greatest common factor of the numerator and denominator of the following fractions.

( 1) (4) ( 18) (3)

Verb (abbreviation for verb) class summary.

Teacher: Class, this class is coming to an end. Can you tell me something about your harvest?

The students gained a lot. In addition to using the enumeration method learned in this lesson to find the greatest common factor of two numbers, the teacher has two simpler methods to find the greatest common factor, which I want to share with you.

One is: the method of solving the greatest common factor by decomposing prime factors, which is demonstrated by courseware.

The other is: short division

We only know about these two methods, so we won't study them in detail here. Interested students can learn this part of the knowledge on page 6 1 by themselves after class.

The teaching plan "Conversion and the greatest common denominator" (2) Teaching objectives

1, through teaching, let students understand the meaning of approximate score and simplest score.

2, master the method of approximate score, and can approximate score correctly and skillfully.

3. Infiltrate the idea of identity transformation into students by learning, and cultivate students' observation ability, comparison ability and generalization ability.

Emphasis and difficulty in teaching

Key points:

1. Let students understand the meaning of approximate score and simplest score.

2. Master deductive method, and be able to perform deductive method skillfully.

3. Cultivate students' thinking ability of observation, comparison and induction.

Difficulties:

We can quickly see the common factor of numerator and denominator, and accurately judge whether the result of simplification is simplest fraction.

teaching tool

Ppt courseware

teaching process

1. Review the introduction and introduce the concept.

Teacher: Students, we have learned the basic properties of common factor, greatest common factor and score. Let the teacher test you first!

Courseware demonstration:

Teacher: Can you answer according to what we have learned?

Answer by name

Follow-up: What are the numerator denominators of 2 and 3 here? (Common factors)

Teacher: Can you tell us what we have learned to solve this problem?

Health: the basic properties of fractions

What is the basic nature of the roll call answer score?

Let's recite the basic nature of scores together!

Teacher: Let's think about how to directly convert 18/24 into 3/4 to equal it. (Courseware demonstration)

Student: Both numerator and denominator are divided by 6.

Teacher: What is the denominator of 6 here? (greatest common divisor)

Teacher: Let's have a look. What happened to the numerator and denominator of the fraction after we changed 18/24 to 9/ 12 and 3/4?

Health: It's getting smaller.

Teacher: Has the size of the score changed?

Health: No change.

Introduce the concept: like this, changing a fraction into a fraction equal to it, but the numerator and denominator are smaller, which is called approximate fraction. (blackboard writing topic)

Please read the concept of approximate fraction together.

Read all the students.

Teacher: What do you think is the most important sentence in the concept of reduction?

Report: the size of the score remains unchanged.

Fractions have smaller numerator and denominator.

(These two sentences on the blackboard)

Today, we will learn about contracts!

? Explore the method of reduction

1. courseware gives example 4.

Turn 24/30 into a fraction with smaller numerator and denominator and the same fraction size.

Teacher: Students, think about it first. According to the requirements of the topic, what about 24/30? Why?

Report: Make 24/30 a fraction, because the topic requires that this fraction be converted into a fraction with smaller numerator and denominator and the same fraction size. It's called a score.

(Encouragement, it seems that you have a deep understanding of the concept of reduction)

Teacher: Now, please try to mark 24/30 by yourself and write down the marking process in your exercise books.

Division patrol guidance.

Report and tell the method of approximate score.

The courseware shows four methods.

Teacher: There are too many ways for students to agree to the main points! Who can tell me what the numbers 2, 3 and 6 are here? 24 and 30? (Common factors)

Teacher: that is to say, when we divide, what number should we use to divide the numerator and denominator?

Student: Divide by the common factor of numerator and denominator.

Teacher: This is the way to divide.

Courseware demonstration: (The common factor of numerator and denominator can be used for division)

Teacher: Let's look at the first two methods of reducing points. Can you continue to score 12/ 15 and 8/ 10 after the score is lowered?

How much is it after continuing the reservation?

Health: It will be 4/5 after the deduction continues.

Follow-up: Can 4/5 continue to score?

Student: No, because now the denominator is only the common factor of 1, and it can't be smaller.

Great answer, please give him applause!

Teacher: That is to say, can you divide the numerator and denominator by the common factor 1? (can't)

In this case, do you need to supplement the reduction method (you can divide it by the common factor of the numerator and denominator)?

Health: Except 1. (Courseware demonstration)

Teacher: Like 4/5, the denominator of the numerator is only the fraction of the common factor 1, which is called the simplest fraction. (blackboard writing)

Important: We usually quote the simplest score when dating.

Teacher: Can you give some examples of the simplest grades?

Report after thinking and tell why it is the simplest score.

Teacher: Now let's look at these two methods, which are equal to 4/5 of the simplest score. How many times did the third method get 4/5? (twice)

What about the fourth method? (once)

Which method do you prefer? Can you tell me your reasons?

Health: I prefer the fourth one, because it can make the simplest score at one time.

Teacher: Can you tell us who divided the numerator and denominator here at the same time?

Health: the greatest common denominator of numerator and denominator

What you said is great! Please give her applause!

Teacher: If you can see the greatest common factor of numerator and denominator quickly, you can divide it by the greatest common factor, so that the simplest fraction can be simplified at one time.

2. We have a simpler way to write these two methods about 4/5. Please teach yourself this simple method by combining problems. Then try to write it in the exercise book.

Report by name

The teacher synchronized the blackboard writing.

? Consolidation exercise

1. Through the study just now, we already know the simplest fraction and how to break it down into the simplest fraction. The teacher has a set of scores here (show me page 65 of the textbook? Do it. Question 1), can you find out which are the simplest scores with a critical eye?

Answer by name and modify collectively.

Emphasize what is the simplest score.

Can you use the simple method you just learned to write the remaining scores into the simplest ones? Please finish it in the textbook.

Answer by name, which leads to that the numerator and denominator are divided by the greatest common factor at the same time.

2. Teacher, there are two lines of scores here. Can we continue to turn those who are not simplest fraction into simplest fraction? Would you please finish? Do it. Second question, make an appointment before connecting.

Report by name and modify collectively.

Let's use today's knowledge to solve the problems in life!

Read the questions by name.

Done independently.

Report.

Emphasize the simplest score as needed.

2. In the third grade, we learned the method of comparing scores with denominators. The following are two groups of scores, (courseware presentation)

Q: Do they have the same denominator? Can you solve it with what you learned today?

Think independently.

Answer by roll call.

Emphasize the method of reduction. I also appreciate the method of increasing numerator and denominator.

Four. Class summary

It's almost time for class. What did you gain from today's study?

Health report.

Teacher: The students have gained a lot today! In the sea of fractions in Wang Yang, the simplest fractions are like gold grains. Turning a score into the simplest score by conversion method can often get twice the result with half the effort, and students will have a deeper understanding in their later study!