Teaching plan of the basic nature of mathematical proportion in the first volume of the sixth grade of primary school by People's Education Press

Teaching content: the content of pages 50 ~ 5 1 in the sixth grade mathematics textbook of primary school published by People's Education Press and related exercises.

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 emphasis: understanding the basic nature of ratio

Difficulties in teaching: Correctly using 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.

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.

Make an accurate judgment by using the basic nature of the ratio;

( 1) ( )

(2) ( )

(3) ( )

(4) The former term of the ratio is multiplied by 3, and the latter term of the ratio should be divided by 3 to keep the ratio unchanged. ( )

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: Divide by the greatest common factor, divide by the common factor step by step, but emphasize the method of dividing by the greatest common factor.

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 greatest 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 learn and write down the specific process. Summary? Method and select a representative to display the 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 transforming 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 greatest common factor 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).