First, the introduction of new courses.
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.
Comments: An important factor affecting students' study is what they already know. Therefore, this session is intended for students to communicate the relationship between ratio, division and score through review and recall, and to reproduce the invariable nature of quotient and the basic nature of score, thus paving the way for the basic nature of analogy. 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, the new lesson learning
(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.
Comments: The study of the basic nature of comparison is very suitable for cultivating students' analogical reasoning ability. On the basis of mastering the invariable nature of quotient and the basic nature of score, students can naturally associate with the basic nature of comparison, which not only stimulates students' interest in learning, but also cultivates their 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.
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) 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. ( )
Comments: Learning based on conjecture must be verified by students' independent inquiry. Cooperative inquiry is a good way of learning, 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.
(C) the basic nature of the ratio application
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.
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。
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.
2. Simplify the proportion of fractions and decimals in the preceding and following items. (Courseware demonstration)
3. Summary: Through their own efforts to explore, the students summed up the methods of converting various proportions into the simplest integer proportions.
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.
Third, the conclusion summary
Fourth, classroom exercises.
Verb (abbreviation for verb) assignment
Sixth, blackboard design
Basic properties of ratio
The two items before and after the ratio are multiplied or divided by the same number at the same time (except 0), and the ratio remains unchanged.
Comments on the lecture:
Understand and master the basic properties of the ratio, and can simplify the ratio by applying the basic properties of the ratio, and initially master the method of simplifying the ratio. In the process of independent exploration, communicate the relationship between ratio, division and division, and cultivate mathematical abilities such as observation, comparison, reasoning, generalization, cooperation and communication. It mainly permeates the transformed mathematical ideas, so that students can realize that there is an internal connection between knowledge.