Teaching content:

Do the contents on pages 50 and 5 1 of the textbook, and practice questions 4-6 of the eleventh question.

Teaching objectives:

1, master the basic properties of the ratio, and simplify the ratio according to the basic properties of the ratio.

2. The invariable nature of the connection quotient and the basic nature of the fraction are transferred to the basic nature of the ratio.

Teaching focus:

Basic properties of comprehension rate.

Teaching difficulties:

The basic properties of ratio can be applied to simplify the ratio.

Teaching process:

First, exciting calibration.

1、20÷5=(20× 10)÷( × )=( )

2、

Think about it: what is the unchanging law of business? What are the basic properties of fractions?

3. We studied the invariable law of quotient, the basic properties of fraction, and the relationship between connection ratio and division and fraction. Think about it: what kind of laws are there in the proportion? We will study this problem in this class.

Second, self-study interaction, timely inspiration

Basic properties of activity ratio

Learning style: group cooperation, report and exchange.

learning tasks

1, inspired and induced, found the problem: 6: 8 and 12: 16 are different, but their ratio is the same. What is the law? .

6:8=6÷8=6/8=3/4 12: 16= 12÷ 16= 12/ 16=3/4

2. Observe and compare, and find the law.

(1) Use the relationship between ratio and division to study the law of ratio. (Law of Constant Quotient)

(2) Using the relationship between ratio and score to study the law of ratio.

3. Summarize the law of induction.

(1) Summary: The first term and the last term of the ratio are multiplied or divided by the same number (except 0) at the same time, and the ratio remains unchanged, which is called the basic property of the ratio.

(2) Question: Why should the "same number" here emphasize the exception of 0?

Activity-based simplified ratio

Learning style: try to train, report and communicate.

learning tasks

1, know the simplest integer ratio.

(1) Question: Who knows what kind of ratio can be called the simplest integer ratio?

(2) Induction: The simplest integer ratio must meet two conditions. One is that the front and rear terms of the ratio are integers, and the other is that the common factor of the front and rear terms of the ratio is only 1.

(3) Point out several simplest integer ratios.

2. Use nature and master the method of simplification.

(1) Write down the aspect ratio of two United Nations flags.

(2) Thinking: Are these two ratios the simplest integer ratio? Why? (There are other common factors besides 1 before and after the term. )

(3) try to simplify.

(4) Reporting communication: Just divide the front and back terms of the ratio by their common factors.

(5) think about it: these two are the same after simplification. What does this mean? The two flags are different in size and the same in shape.

(6) Show examples and organize exchanges.

① Least common multiple of denominator:1/6: 2/9 = (1/6×18): (2/9×18) = 3: 4.

(2) First, the front and back terms are converted into integers, and then simplified as: 0.75: 2 = (0.75×100): (2×100) = 75: 200 = 3: 8.

③ Calculated by fractional division:1/6÷ 2/9 =1/6× 2/9 = 3/4.

(7) Abstract: If both the front and rear terms of a ratio are fractions, then multiply the front and rear terms by the least common multiple of the denominator at the same time; If the front and back terms of a ratio are decimals, praise them first, and then simplify them.

Third, the standard evaluation

1. Complete the "doing" on page 5 1 of the textbook and make collective revision.

2. Complete questions 2, 4, 5 and 6 of exercise 1 1 on page 52 of the textbook.

Fourth, class summary.

What did we learn in this class? What did you get?

extreme

Teaching content:

Page 50 ~ 5 1 and related exercises in the sixth grade mathematics textbook of the People's Education Press.

Teaching objectives:

1. Understand and master the basic properties of the ratio, and apply the basic properties of the ratio to simplify the ratio, and initially master the method of simplifying the ratio.

2. In the process of independent exploration, communicate the relationship between ratio, division and score, and cultivate mathematical abilities such as observation, comparison, reasoning, generalization, cooperation and communication.

3. Infiltrate and transform the mathematical thought initially, so that students can know that there is an internal connection between knowledge.

Teaching focus:

Basic properties of understanding rate

Teaching difficulties:

Correctly apply the basic properties of ratio to simplify ratio.

Teaching preparation:

Courseware, answer sheet, physical projection.

Teaching process:

First, review the introduction.

1. Teacher: Students, let's recall first. How much do you know by comparison?

Presupposition: the meaning of ratio, the name of ratio part, the relationship between ratio and fraction, division, etc.

2. Can you directly tell the quotient of 700÷25?

(1) What do you think?

(2) What is the basis?

Do you remember the basic nature of music score? Give examples.

An important factor that affects students' learning is what they already know, so this link is intended to let students communicate the relationship between ratio, division and score, reproduce the invariable nature of quotient and the basic nature of score, and lay the foundation for the basic nature of analogy and deduction ratio. At the same time, there is also a mechanism that permeates the transformed mathematical thought, which makes students feel that there is a close internal connection between knowledge.

Second, explore new knowledge.

(A) the basic nature of the conjecture ratio

1. Teacher: We know that ratio is closely related to division and fraction, while division is quotient invariant and fraction has the basic properties of fraction. Think about these two properties: what kind of laws or properties will proportion have?

Default: Basic attribute of ratio.

The students have guessed the basic nature of the ratio.

Default: The first and last items of the ratio are multiplied or divided by the same number at the same time (except 0), and the ratio remains unchanged.

3. According to the students' guess, the teacher wrote on the blackboard that the first and second items of the ratio are multiplied or divided by the same number at the same time (except 0), and the ratio remains unchanged.

Design intention is more suitable for cultivating students' analogical reasoning ability than basic nature learning. On the basis of mastering the basic properties of quotient invariance and score, students can naturally associate with the basic properties of ratio, which not only stimulates students' interest in learning, but also cultivates students' language expression ability.

(B) the basic nature of the verification ratio

Teacher: As everyone thinks, ratio, like division and fraction, has its own regularity. Is it the same as everyone's guess that "the front and rear items of the ratio are multiplied or divided by the same number (except 0) at the same time, and the ratio remains unchanged"? This needs us to prove through research. Next, please study in groups of four to verify whether the previous guess is correct.

1. The teacher explained the cooperation requirements.

(1) Complete independently: Write a ratio and verify it in your favorite way.

(2) Group discussion and study.

① Each student presents his own research results to the students in the group and communicates in turn (other students indicate whether they agree with the student's conclusion).

(2) If there are different opinions, give examples, and then the students in the group will discuss and study.

③ Choose a classmate to speak on behalf of the group.

2. Collective communication (ask the group spokesperson to explain with specific examples on the booth).

Preset: verify according to the relationship of ratio, division and score; Verify according to the proportion.

3. Category verification.

16:20=( 16○□):(20○□)。

4. Perfect induction and summarize the basic nature of ratio.

How to fill in the ○ in the above questions □ Can I fill in any number? Why?

(1) Students express their opinions and explain the reasons, and teachers improve the blackboard writing.

(2) The basic nature of students' reading ratio with books open, and teachers write on the blackboard. (Basic attribute of ratio)

5. Questioning discrimination and deepening understanding.

Learning with design intent based on conjecture must be verified by students' independent inquiry. Cooperative inquiry is a good learning method, but cooperative learning cannot become a mere formality. Cooperative learning should first let students think independently, let students generate their own ideas, and then cooperate and communicate, so that every student can experience the learning process of independent inquiry. In the process of communication, it not only cultivates students' reasoning and generalization ability, but also really internalizes the "basic nature of ratio" from conjecture, thus greatly improving the effectiveness of cooperative learning.

Third, the application of the basic nature of the ratio

Teacher: Students, do you still remember the basic purpose of our study scores? What is the simplest score?

The basic properties of the ratio we found today also have a very important purpose-we can simplify the ratio and then get the simplest integer ratio.

(1) Understand the meaning of the simplest integer ratio.

1. Guide students to learn the simplest integer ratio by themselves.

Default: The prime integer ratio of the former and the latter is called the simplest integer ratio.

2. Find the simplest integer ratio from the following ratios and briefly explain the reasons.

3:4; 18: 12; 19: 10; ; 0.75:2。

(2) Preliminary application.

1. Simplify the ratio of front and back terms to integers. (Courseware shows page 50 of the textbook, for example 1)

Students try independently and communicate after simplification.

( 1) 15: 10=( 15÷5):( 10÷5)=3:2;

(2) 180: 120=( 180÷□):( 120÷□)=( ):( )。

Default: common factor division, gradual common factor division, but the method of common factor division is emphasized.

2. Simplify the proportion of fractions and decimals in the preceding and following items. (Courseware demonstration)

Teacher: for the ratio of the front and back terms to integers, we just need to divide by their common factor, but like: and 0.75:2,

These two ratios are not the simplest integer ratios. Can you find a way to simplify them yourself? Discuss and study in groups of four, and try to simplify.

Students study and write down the specific process, summarize the methods, and select representatives to show and report. Teachers compare different methods and guide students to master general methods.

Default: Ratios containing fractions and decimals should be converted to integer ratios before simplification. Least common multiple of denominator with fraction; If there are decimals, they should be converted into integers before simplification.

3. Summary: Through their own efforts to explore, the students summed up the methods of converting various proportions into the simplest integer proportions. When simplifying, if the first term and the last term of the ratio are integers, they can be divided by their common factors at the same time; When encountering decimals, first convert them into integers, and then simplify them; When you encounter a score, you can multiply it by the least common multiple of the denominator at the same time.

4. Method supplement, distinguishing between simplified ratio and calculated ratio.

What other methods can simplify the scale? (find the ratio)

What's the difference between simplifying ratio and seeking ratio?

Default: the final result of simplifying the ratio is a ratio, and the final result of finding the ratio is a number.

5. Try to practice.

Turn the following ratios into the simplest integer ratios (show the textbook "Doing Problems" 5 1 page).

32: 16; 48:40; 0. 15:0.3;

The new curriculum standard of design intention puts forward that the teaching concept of "student-oriented development" should be fully embodied in teaching, and the students' main role should be given full play to make them the masters of learning. Therefore, in the teaching process of simplifying ratio by using the basic nature of ratio, students are encouraged to explore independently and find ways to simplify ratio through self-study, independent exploration and group cooperation.

Fourth, consolidate practice.

Basic exercises

1. textbook page 53, question 4.

Convert the following ratio to 100.

(1) The ratio of the number of surviving plants to the number of school plants is 49:50.

(2) Prepare the medicament, and the ratio of the mass of the medicament to the total mass of the medicament is 0. 12: 1.

(3) The ratio of the actual output value to the planned output value of the enterprise in the previous year was 2.75 million: 2.5 million.

2. Question 6 on page 53 of the textbook.

(2) Expanding exercises (PPT courseware demonstration)

The students finished their oral answers.

In the ratio of 1.2: 3, the former item should be increased by 12, and the latter item should be increased to keep the ratio unchanged.

The number of boys in Class 2.6 (1) is 1.2 times that of girls. The ratio of boys to girls is (), the ratio of boys to class is (), and the ratio of girls to class is ().

The design of design intention exercises should closely focus on the key points and difficulties of teaching, and the arrangement of exercises should reflect the hierarchy from easy to difficult. 1 is a basic exercise for the basic properties of ratio, and also lays the foundation for the following percentage learning. The second problem is to simplify the ratio of two different quantities in training units and cultivate students' ability to examine questions. Expanding exercises not only develop the flexibility of students' thinking and cultivate their creativity, but also consolidate the knowledge of this lesson. At the same time, this kind of problems is also the basic training of fractional application problems and proportional application problems, and also lays a solid foundation for the study of fractional application problems and proportional application problems in the future.

Verb (abbreviation of verb) course summary

What did you learn from this course? Is there a problem?

Tisso

First, create situations and introduce new lessons.

1, ask questions

Teacher: What is the relationship between division, fraction and ratio?

2. Do the review questions. Teacher: What is the basis of your first question? What is its content? What about the second question?

3. Import theme:

We have studied the invariance of quotient and the basic properties of fractions before, and today we learn new knowledge on the basis of these old knowledge. Next, let's learn together. (blackboard title: the basic nature of ratio)

Second, learn new lessons.

1. The basic nature of teaching example 3.

(1) students fill in the form (2) problem: the invariable nature of the connection quotient and the basic nature of the score. Think about these two properties: what are the rules to follow when comparing?

(3) The basic nature of the teacher-student ratio * * * The first and second items of the ratio are multiplied or divided by the same number at the same time (except 0), and the ratio remains unchanged.

(4) Teacher: Which word do you think is more important? Except 0. How to understand it?

2. Teaching Example 4 Simplifies the basic nature of application ratio.

We have learned the simplest fractions before. Think about it: what is the simplest score? The simplest integer ratio is that both the former term and the latter term are prime numbers. For example, 9: 8 is the simplest integer ratio.

Show: Turn the following ratio into the simplest integer ratio.

( 1) 12: 18 (2) (3) 1.8:0.09

(1) Let the students try to do the problem (1).

Teacher: How did you do it? What is the relationship between 6 and 12 and 18?

Guide students to summarize the method of simplifying integer ratio: divide the front and rear terms of the ratio by their common divisor, so that the front and rear terms of the ratio are prime numbers.

(2) Simplification (2)

Teacher: What are the terms before and after this ratio? (Fraction) We have simplified the integer ratio, so can we use the basic properties of ratio to convert the fractional ratio into the integer ratio first?

(3) Guide the students to summarize the method of simplifying the fraction ratio: (Show the demonstration courseware) Multiply the front and back items of the ratio by the least common multiple of its denominator at the same time, and then convert the fraction ratio into an integer ratio, and then simplify it into the simplest integer ratio.

(4) Simplify (3) 1.8:0.09

Teacher: Think about how to simplify the decimal ratio.

Ask the students to simplify the book independently and say its name.

Teacher: Then, what is the method to change integer ratio, fractional ratio and fractional ratio into the simplest integer ratio by applying the basic properties of ratio?

Third, consolidate the practice.

1. Practice filling in the blanks.

2. Do exercises 13, questions 5-8.

3. Supplementary exercises

choose

1. 1 km: 20km = ()

( 1) 1∶20 (2) 1000∶20 (3)5∶ 1

2. To make the same part, Party A will make 7 parts in 2 hours and Party B will make 10 parts in 3 hours. The work efficiency ratio of Party A and Party B is ().

( 1)20∶2 1 (2)2 1∶20 (3)7∶ 10

Fourth, class summary.

Teacher: What knowledge have you learned through today's study? What is the basic nature of ratio? How to apply the basic properties of ratio to turn integer ratio, fractional ratio and decimal ratio into the simplest integer ratio?