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Teaching plan of "the meaning of comparison" in sixth grade mathematics
The teaching plan of "The Meaning of Comparison" in sixth grade mathematics1;

Nine-year compulsory education and six-year primary school mathematics textbook Volume 11 "The Significance of Comparison".

Teaching objectives:

1. Mastering the meaning of comparison is helpful for reading and writing correctly.

Remember the names of the parts of the ratio, and you will find the ratio correctly.

3. Understand the relationship between ratio, division and fraction, make it clear that the latter term of ratio cannot be 0, and understand the relationship between things at the same time.

4. Through self-study discussion, stimulate students' interest in cooperative learning and cultivate students' ability of analysis, comparison, abstraction, generalization and self-study.

First, create situations and induce participation.

1, Teacher: What is the relationship between two cups of juice and three cups of milk? What method would you use to express their relationship? What questions can I ask and how to answer them?

Raw 1: More milk than juice 1 cup.

Health 2: Fruit juice is less than milk 1 cup.

Health 3: The number of cups of juice is equivalent to that of milk.

Health 4: The number of cups of milk is equivalent to that of juice.

Teacher: Which quantity is compared with which quantity?

Health: Compare the number of cups of juice and milk.

Teacher: What is seeking? what can I say?

Health: Compare the number of cups of milk with the number of cups of juice.

2. Teacher's statement: With the new mathematical comparison method, it can be said that the ratio of cups of juice to milk is 2 to 3. Today, in this lesson, we learn to compare two quantities in a new way. (blackboard writing: proportion)

3. Teacher: What do you want to learn in this course?

(What do you mean, who is better than who ...)

Second, self-study to explore new knowledge.

1. Explore the concept of ratio

The teacher pointed to the blackboard and asked, What do you want? Which quantity is the ratio of which quantity?

Health: What we want is the score of juice and milk, and the ratio of juice and milk.

Teacher: Yes! 2÷3 is the score of juice and milk, or it can be said that the ratio of juice and milk is 2 to 3.

(Blackboard: The ratio of juice to milk is 2: 3. Read it all. )

Teacher: In this way, milk is a fraction of juice, which can also be said to be the ratio of milk to juice.

Health: Milk is a part of fruit juice. It can also be said that the ratio of milk to juice is 3 to 2.

(blackboard writing: the ratio of milk to juice is 3 to 2)

Teacher: It's all a comparison between juice and milk. Why is one 2 to 3 and the other 3 to 2?

Health: Because 2 to 3 is the ratio of juice to milk, and 3 to 2 is the ratio of milk to juice.

Teacher: Yes, the comparison of two quantities, who is in front and who is behind, cannot be reversed.

Try it out.

Teacher: What does 1: 8 mean?

Health: 1 and 8 stand for 1 cleaning solution and 8 parts water respectively.

Teacher: How to express the relationship between the washing liquid and the amount of water in the container?

Health: Find the volume first and then compare it.

Courseware presentation: Xiaojun 15 minutes, Xiao Wei, 20 minutes, 900 meters long mountain road. Ask the students to fill in the form.

Teacher: How did Xiaojun and Xiao Wei get their speed? What does 900: 15 mean? What does 900: 20 mean?

Teacher: Talk about the significance of 900m15min.

Health: 900 meters 15 minutes is the distance and time for Xiaojun to walk.

Teacher: What is the speed ratio of the small army?

Health: The speed of a small army can be said to be the ratio of distance and time.

Teacher: What do you mean by comparison? Talk to each other at the same table and report the situation. )

Life 1: division is called ratio.

Health 2: The division of two numbers is called ratio.

The division of two numbers used to be called division, but today it is called ratio. There is another name. Do you think it is more appropriate to add a word before the word "than"?

Health 1: add "OK".

Student 2: Add the word "you".

Division of two numbers is also called the ratio of two numbers. Think about what relationship this ratio represents between two numbers.

(With the students' answers, the teacher shot a bullet under "Division" and the students read the concept of comparison together. )

2. Self-study the names of each part and inquire the proportion.

Teacher: Please teach yourself 68-69 pages. Draw the knowledge that you think is important, and after the self-study, talk to each other at the same table about "What I have taught myself".

(After talking to each other, students at the same table report and explore collectively. )

Health: I learned how to write comparisons.

The teacher points to 2: 3 and asks the students to write 2: 3 on the blackboard. )

Teacher: What is the ":"symbol in 2 and 3?

Health: This is a comparative number. (blackboard writing: comparison number)

Teacher: When writing comparison numbers, the upper and lower points should be aligned and placed in the middle. Let the students at the same table look at each other to see if the comparison figures are correct, and then report. )

Health: I know that the number before the comparison symbol is called the first item of comparison, and the number after the comparison symbol is called the last item of comparison.

The teacher (pointing to 2: 3) asked: What is the entry after the first paragraph? (Students answer and then report. )

Health: I know how to pronounce Bibi.

(The teacher points to 2: 3 and calls the students to try to read 2: 3, and then the students read 2: 3 together. )

Teacher: We already know the pronunciation, writing and the names of the parts. Think about it. What else did you learn?

The sixth grade mathematics teaching plan 2 "the meaning of comparison" teaching goal;

1, understand the meaning of ratio, learn the reading and writing methods of ratio, master the names of each part of ratio and the methods of finding ratio.

2. Make clear the relationship between ratio and division and fraction, make clear that the latter term of ratio cannot be 0, and understand that things are interrelated.

3. Stimulate the sense of cooperation, cultivate the ability of comparison, analysis, abstraction, generalization and autonomous learning, and cultivate patriotic feelings through active discovery and discussion.

Teaching focus:

The meaning of ratio

Teaching preparation:

Multimedia courseware, three red chalks and five pens.

Teaching process:

First, create a situation and understand its meaning.

1, Teacher: Students, we just finished the National Day. Do you know how big the motherland was on June 10 this year? On June 10 and 1 56 years ago, the five-star red flag was first raised in the square of Ran Ran, which made people all over China proud. But do you know that there are many interesting math problems hidden in our national flag?

Show me a national flag:

3. Judgment: Xiao Qiang's height 1 m, his father's height 173 cm, and the ratio of Xiao Qiang to his father's height is 1: 173.

Clear: the quantity of the same kind should be the same as the unit name.

Fourth, the whole class summarizes and unfolds.

1, last year's Olympic Games, the China women's volleyball team beat the United States 3-0 in the first game, playing the role of China women's volleyball team. What does 3: 0 mean here? Is it the same as what we learned today? Why?

Emphasis: 3∶0 here refers to how many games each team won, not the division relationship. The ratio learned today refers to the division relationship between two numbers.

2. What did you gain from today's study?

3. Do you know? In the 4th century AD, the Greek mathematician eudoxus used line segments to find the most beautiful geometric proportion in the world-the golden section. The ratio is about 0.6 18, and the ratio is about 2∶3.

Introduction: The golden section is widely used. The aspect ratio of the national flag is 2 to 3, which is close to the golden section. Now you know why the five-star red flag looks so good!

There are many places in life where the golden section is used:

Choosing a model on the runway also requires that the ratio of the length of the model to the length of the leg conforms to the golden section.

Barbers also apply the golden section to hairstyle design.

Students can also investigate after class.

The teaching plan of "The Significance of Comparison" in the sixth grade of primary school 3 I. Analysis of teaching materials and students;

"The meaning of comparison" is one of the teaching focuses of the eleventh textbook of the sixth grade in primary school. It plays an important role in teaching materials. Through the teaching of this part, students can not only sublimate the existing knowledge about the comparison of two numbers, but also lay a solid foundation for students to further learn the nature, application and proportion of comparison. The knowledge of "the meaning of comparison" is complicated, and students lack the original perception and experience, so it is difficult to understand and master it. According to the characteristics of knowledge content and students' cognitive law, in the teaching process, I adopt the teaching method of organizing students' autonomy, exploring, cooperating, communicating, analyzing, summarizing, comparing and inducing the problem of "ratio", highlighting the traditional teaching mode and realizing students' autonomous learning. In the teaching process, cultivate students' innovative spirit.

2. Teaching objectives:

Determine the following goals from three dimensions: knowledge and skills, process and method, emotional attitude and values.

(1) Understand and master the meaning of comparison, and read and write correctly. Remember the names of the parts of the ratio and find the ratio correctly.

(2) Through the discussion and study of active discovery, stimulate the sense of cooperation, understand and correctly grasp the relationship between ratio, division and score, and make it clear that the latter term of ratio cannot be zero. At the same time, I understand that things are interrelated.

(3) Cultivate students' abilities of comparison, analysis, abstraction, generalization and autonomous learning. Cultivate their awareness of finding mathematical problems and asking questions in their lives.

3. Emphasis and difficulty in teaching:

Understand the significance of mastering ratio and the relationship between ratio and fraction and division.

Second, the design of teaching methods

1. Create situational method to stimulate students' research interest in comparative knowledge.

2, from daily life, cultivate students to find math problems.

3. Change students' learning style, so that students can improve their problem-solving ability in independent inquiry and cooperative communication.

4. Consolidate in class, practice feedback in class and practice in various forms, so that students can understand the significance of comparison from various learning activities.

5. Encourage students to compare and think more, be good at exploration and cooperation, and adopt various effective methods such as encouragement and evaluation to cultivate students' good habits of learning mathematics.

Three. Activities and arrangements in the teaching process

(A) the creation of situations, the introduction of new courses

Using a piece of news to arouse students' interest in comparative knowledge learning, students can not only gain emotional experience through ideological education, but also find the application of comparison in life, thus cultivating students' awareness of discovering mathematical problems and asking questions in life.

Independent research, cooperation and exchange

1, "the meaning of comparison" teaching.

The first step is to give two conditions: the number of boys and the number of girls in the class, so that students can ask questions in parallel. According to the division formula in the column of students, we can clearly see that boys and girls are comparing, which inspires students' thinking. In addition to comparing two quantities with the division knowledge learned before, we can also compare them in a new way. Then, the teaching activity of "the meaning of comparison" is launched, and the ratio of the number of boys to the number of girls is said. The second step is to look at the formula and speak with new knowledge. (Description: Extract mathematical problems from the quantities around students, thus leading to new knowledge. Inheriting old knowledge is relaxing and enjoyable. The third step is to show the form (fill in the form) so that students can initially know that the relationship between two different categories of quantities can also be expressed by ratio. On the basis of the above two examples, let the students summarize the significance of comparison.

2. Reading and writing the ratio, the names of each part, and the teaching of the method of finding the ratio.

Teachers guide students to master the reading and writing methods of ratio, and explore the names of each part of ratio and the methods of finding ratio independently in group cooperative learning. Then organize students to report their learning results and guide them to introduce the method of finding the ratio. After knowing it, instruct students to use the method, write several examples of ratios, calculate the ratios and consolidate their knowledge. In the process of reporting, look for the law of the ratio, which can be a fraction, an integer or a decimal.

3. The relationship between ratio, division and score. Why can't the latter term of the ratio be zero?

Cooperation and communication can guide students to read on the blackboard, compare the relationships among "ratio", "division" and "score", fill in the form, and then clarify their differences through understanding the word "equivalent".

(3) Summarize and induce students to talk about learning feelings.

What knowledge did the students learn through this class? Can you tell us what you have gained? In the student report, you can consolidate the knowledge points of this lesson.

(4) Multi-level practice to consolidate new knowledge.

Various forms of exercises not only consolidate the knowledge of this class, but also increase the interest, especially cultivate the habit of independent thinking of students.

The significance of the fourth ratio in the math teaching plan for the sixth grade of primary school lies in starting classes. It is the knowledge core of this unit and has a far-reaching influence on future study. The teaching content of this lesson is pages 47-48 of Volume 12 of the Six-year Program Outline, which is the beginning of this unit. Teaching this lesson well can affect a large area and let teachers take the initiative in teaching from the beginning. The meaning of ratio is developed from division, which is related to and different from division and fraction. In view of this, the teaching objectives of this lesson are determined as follows:

Understand and master the meaning of comparison, learn the reading and writing methods of comparison, and compare the names of various parts; Will find the proportion; Can understand the relationship between ratio, division and score; Infiltrate and transform ideas into students.

Teaching emphasis: mastering the meaning of comparison.

Teaching difficulty: make up the ratio of two quantities and calculate the ratio on this basis.

The key to teaching: understanding the relationship between ratio and division. In view of the above teaching objectives, the teaching materials can be treated as follows:

First, the migration of the elderly leads the topic to the migration of the elderly.

Mainly to grasp the best connection point between old and new knowledge. That is to review the application problems of division calculation and transfer knowledge. Significance of bridging slope to learning ratio. Then the division is transformed into another method to compare the two quantities, which naturally leads to the positioning of the topic and puts forward the teaching objectives of this lesson. The specific approach is:

1. Answer:

What is the relationship between (1) fraction and division?

(2) Can the divisor be zero? Can the denominator of a fraction be zero?

2. Column solution: (oral English, teacher board)

(1) A red flag, 3 cm long and 2 cm wide. How many times the length is the width? What is the width?

(2) A car travels for 2 hours100km. How many kilometers per hour?

(3) The introduction of these two questions (fingerboard playing) just reviewed in the new lesson, both of which are the comparison of two quantities, both of which are the calculation of division, and the students have mastered it very well. However, in daily life and production, there is another way to compare these two quantities. This is what we are going to learn today. In this lesson, we should understand the meaning of comparison and find the ratio. (The meaning of blackboard-to-book ratio)

Second, explore and discover, sum up the law

Exploration and discovery refers to giving full play to students' main role under the guidance of teachers, changing emphasis on speaking and neglecting practice into a combination of speaking and practice, allowing students to practice and use their brains to participate in the activities of learning mathematics knowledge with various senses, and realizing two leaps: first, from sensibility to rationality; A leap from rationality to practice. For example, the meaning of teaching ratio should be divided into the following three levels:

1. The meaning of teaching ratio, its reading and writing methods, and the names of its parts.

The meaning of (1) ratio The students accurately answered the question 1 in review question 2, and found out how many times the length is the width with 32, which means that the relationship between length and width is expressed by division. 32 can also be written as 3 to 2 (3 to 2 on the blackboard), indicating the aspect ratio. Q: Who is 3 to 2? The aspect ratio is 3 to 2. 32 can represent 3 to 2, and 23 can represent several to several. (2 to 3), which means who is competing with whom? (indicating the aspect ratio). Combined with the second question, how much can 1002 be expressed?

Who is competing with whom? (100 to 2, indicating the ratio of the distance traveled by the car to the time. Pay attention to these two examples. Who can compare? According to the students' answers, the teacher summed up that the division of two numbers is also called the ratio of two numbers. (blackboard writing) The significance of the ratio of roll call reading to chorus reading.

(2) Reading and writing method of ratio The operation symbol of division is the division symbol. What is the symbol for the ratio? Is a comparison number, written as (blackboard writing) and pronounced as comparison. 3 to 2 can be written as. 3 to 2 (blackboard writing) can be read as 3 to 2. Q: 2 to 3, 100 to 2, can students write? Let one student write on the blackboard and the other students write on the table.

(3) The name of each part of the ratio is the ratio symbol, which is read as the ratio. The number before the comparison symbol is called the first item of comparison, and the number after the comparison symbol is called the last item of comparison. The quotient obtained by dividing the former term of the ratio by the latter term of the ratio is called the ratio. (Write the following on the blackboard) 3 ... The first item: ... The comparison number is 2 ... The last item = 32 = 1 ... The ratio is 12.

(4) Practice (watch the slide screen)

(1) Tell the ratio of the former, the latter and the ratio. 4 ∶ 7 = 47 = 479 ∶ 5 = 95 =14513 ∶ 9 =139 =14915 ∶ 29 =1529. The ratio of the number of books to the number of classes is (). The school held a sports meeting. In a class of six years, there are 10 people running and 7 people taking part in the high jump. The ratio of the number of people who take part in the race and the high jump in this class is (). (5) Through the practice of the above two questions, do you know what to pay attention to in writing comparison? Summary: When writing a comparison, you should pay attention to who compares who, who is the first item of comparison and who is the last item of comparison, and the order cannot be reversed.

2. The teaching method of ratio.

(1) Q: What is the ratio? The definition of (abbreviated) ratio has been mastered, so how should we compare it? (Divide the first term of the ratio by the second term of the ratio). Students all know how to calculate the proportion. Let's practice the proportion.

(2) Find the ratio and explain the arithmetic. 32: 85: 2512:150.8: 37 (3) summary: the ratio is a number, which can be expressed by integers, decimals and fractions.

3. The relationship between teaching ratio and division and score.

The visible ratio of (1) 3 ∶ 2 = 32 is closely related to division. What are the parts where ratio is equivalent to division? (Omitted) (2) The relationship between score and division was answered accurately in the review. From the relationship between fraction and division, what is the relationship between ratio and fraction? (Omitted) Combine the relationship between the ratio, division and score mentioned by the students to form the relationship table of ratio, division and score.

(3) According to the relationship between the ratio and the score, the ratio can also be written as a score. 3: 2 can be written as 32, but it can still be read as 3: 2, not as trisection.

2∶3, 100∶2 Let the students write.

(4) Q: Can the latter term of the ratio be zero? Why?

Third, feedback error correction, perseverance.

Refers to the process that information output from a certain part of the system returns to the input part. This process is not only a process of sending information to teachers to check the teaching effect, but also a process of students' self-adjustment.

Then, feedback correction, implemented from beginning to end, this lesson refers to the comprehensive practice after the practice. The content of comprehensive exercises should be from shallow to deep. Practice writing proportion first, and then practice judging questions. By comparing right and wrong, let students know the difference between ratio, division and score. Finally, arrange expansion exercises, write comparisons and seek comparisons. It is required to write not only two direct quantities, but also the ratio of two indirect quantities, such as the ratio of speed. Through this practice, not only the whole class can eat well, but also the top students can eat well.