Lecture Notes on the Application of Comparison 1 I. Talking about Teaching Materials
I said that the content of the course is the application of example 2 and example 3-proportion in unit 2, page 52 of the nine-year compulsory education and six-year primary school mathematics volume 1 1 published by People's Education Press, which are mainly distributed in this textbook.
The reason why Example 2 and Example 3 are put in one class is mainly to form the hierarchy and gradualism of knowledge, and to help students firmly perceive the results of knowledge through the comparison of knowledge points.
Proportional allocation is to allocate a quantity according to a certain proportion, which is an extension of students' learning of "average score" and "fractional application problem". The textbook is to turn the proportion into fractions and answer them with the knowledge of fractions that students have learned before. This arrangement is easy for students to accept, which not only deepens the understanding of fractional application problems, but also helps to strengthen the connection between knowledge and lay the foundation for learning positive and negative proportions in the future.
Second, students.
Grade six students have certain ability to analyze problems and comprehensively apply knowledge, while most students in my class are active in thinking, can analyze problems and learn new knowledge by combining existing knowledge, and have certain self-study ability and practical operation ability.
Third, talk about teaching objectives.
1, to make students clear that proportional distribution is the application of ratio and the development of "average score", and to make clear the significance and function of proportional distribution.
2. It has always been a difficult problem for students to master the characteristics and solutions of proportional distribution application problems and apply them.
3. Cultivate students' abilities of observation, analysis, hands-on operation and self-study, and promote the development of their abilities.
Today, with the vigorous reform of basic education curriculum, how to face all students and make them develop fully, freely, harmoniously and comprehensively is the leading idea in setting classroom teaching objectives. Therefore, according to the mathematics curriculum standards, I have formulated the above three teaching objectives of this course.
Fourth, stress the difficulties.
Key points: the characteristics and solutions of proportional distribution application problems
Difficulty: let students know "what quantity should be allocated according to what proportion"
The proportional distribution of application problems has typical characteristics. If we understand and master this feature, we can correctly use this knowledge to solve practical problems.
However, it is often difficult for a large number of students to allocate what quantity according to what proportion, so it is a difficult point. Mainly adopt the method of "self-study-comparison-application", highlight key points and break through difficulties.
Verb (abbreviation of verb) oral teaching method and learning method
This course mainly adopts teaching methods such as operation exercises, review and introduction, guiding self-study, analysis and comparison, and practical application.
The main channel to promote quality education is classroom teaching. How to change students' listening into active participation lies in breaking the traditional indoctrination teaching mode. Therefore, it is necessary to establish the concept of respecting students, trusting students and letting students learn actively. In view of this teaching concept, we should pay attention to the following problems in the teaching of this course:
First, we should create a happy, harmonious and democratic classroom atmosphere.
Teachers should convey a kind, encouraging and trusting emotional consciousness to students with language, actions and expressions, and form a harmonious classroom atmosphere, so as to effectively guide students to learn actively and reflect their dominant position in learning.
Secondly, we should mobilize students' initiative in learning and stimulate their interest in learning. The main means adopted is to let students operate and feel initially. Arrange hands-on operation, encourage students to participate in various senses, and further perceive the concept of "proportional distribution" on the basis of "average score"
The third is to guide self-study and cultivate self-study ability.
Let the students learn by themselves and think with the questions given by the teacher, so as to achieve the purpose of thinking and learning. In this way, students can learn and cultivate their own abilities.
Fourth, pay attention to application. As the saying goes, "apply what you have learned" can not only test students' learning situation, but also consolidate what students have learned in this class, killing two birds with one stone.
Teaching procedure of intransitive verbs
The teaching process of this lesson is divided into two parts:
The first part mainly solves what is proportional distribution, and adopts the practical operation method of dividing stones to let students feel it through hands-on operation and deepen their understanding of proportional distribution; The second part mainly solves the problem of how to distribute in proportion.
In order for students to master the characteristics and solutions of the proportional distribution of application problems and apply them to solving problems in real life, we should first make students understand what "proportional distribution" is, and adopt the practical operation method of dividing stones, that is, combining with the reality of rural students, let students feel through hands-on operation, which not only implements the new curriculum concept, but also embodies the main position of students' learning, and is more for achieving teaching objectives, highlighting key points and breaking through difficulties.
first part
What is "proportional distribution"
Operation perception, leading into new lessons.
Understanding Proportional Distribution in Practical Situations 《 Mathematics Curriculum Standard 》 2 1 page
Divide one point by the same party.
This will help to cultivate students' cooperative learning ability.
(1). Divide 8 stones into two parts according to 1: 1
(2) Divide eight stones into two parts according to 2: 1.
Through hands-on operation, students feel that the first situation is "average score", while the second situation is not "average score". Explain that in our daily life and industrial and agricultural production, in addition to the "average score", we often have to allocate a quantity according to a certain proportion. In addition to the first case, there is a second case, which leads to a new lesson, "proportional distribution."
This arrangement is conducive to the development, change and extension of students' knowledge, thus stimulating students' interest in learning.
the second part
How to allocate in proportion
(1) review
(1), number a is 8, number b is 10, then number a is () of number b, and the ratio of number a to number b is (): ().
(2) A review question is put forward on page 52: A farm plans to sow 60 hectares of wheat and 40 hectares of corn on 100 hectares of land; How much of this land is sown by wheat and corn? What is the planting area ratio of wheat and corn?
The purpose of this arrangement is to seize the old and new knowledge and connection points and play a positive role in dispersing difficulties.
(2) Self-study
1. Ask questions and let students study by themselves purposefully.
First show the self-study requirements: what is the homework for this problem? According to what distribution? The ratio of sown area of wheat to corn is 3: 2, that is to say, what is the ratio of sown area of wheat to total sown area? What is the percentage of wheat sown area to the total sown area? What is the ratio of corn area to total sown area? What percentage of the total sown area is corn?
The teacher guided the students to try and let them teach themselves textbooks. Its purpose is to let students find solutions to problems in textbooks.
2. Students study by themselves in groups, and teachers give guidance.
Group autonomous learning is an important form of cooperative learning, which is conducive to cultivating students' sense of cooperation, which is also one of the requirements of the new curriculum for cultivating students' ability and quality.
3, students report, teachers and students * * * with problems to solve.
Check the self-study first. Teachers and students use simple solution 2.
Then let the students report: who should be allocated according to what proportion?
4. Self-study Example 3
Let students naturally transition to Example 3 on the basis of learning and understanding Example 2, and use the skills of Example 2 to solve Example 3, so that students can realize the transfer and comprehensive application of knowledge and skills.
5. Comparative Examples 2 and 3
Example 2 is to allocate the total area 100 hectare according to 3: 2, and example 3 is to allocate the total number of trees according to the proportion of three types of people.
The purpose of this is to let students know that the proportional distribution can be two or three or more proportions through comparison.
(3) Practice
Multi-level training to consolidate new knowledge and form skills.
Practice is an important part of mathematics classroom teaching. Practice strives to change from easy to difficult, from shallow to deep, with distinct levels, gradual progress, harmony between old and new knowledge, formation of skills, development of thinking and development of ability, so as to achieve the expected purpose of practice.
1, basic exercise
The ratio of boys to girls in a class is 9: 4, with boys accounting for () and girls accounting for () the whole class.
This exercise dispersed the difficulties and promoted the internalization of the knowledge structure.
2. Practice accordingly.
62-page "Do it" question 1
Consolidate what you have learned by combining teaching with practice, so that students can be consolidated immediately after learning new knowledge.
3. Comprehensive exercises.
(1) The average of A and B is 50, and the ratio of A and B is 7: 3. What are the numbers of A and B respectively?
(2) The perimeter of the rectangular plot is 120m, and the length-width ratio is 3: 1. What is its length and width?
This kind of exercise aims at strengthening contrast and improving students' ability to analyze and comprehensively apply knowledge.
(4) Use
The ratio of concrete, stone, sand and cement is 3: 2: 5. There are 20 tons of cement now. How much stone and sand does it take to produce this qualified concrete?
Having basic knowledge does not mean having skills. Only by mastering the basic knowledge and methods can teachers provide time and space for application, so that students can independently use "double basics" to solve practical problems, and students can form skills and apply knowledge and methods to solve new and unfamiliar practical problems, which is very important for cultivating innovative ability and spirit.
(5) class summary
What knowledge have you learned? What methods have you mastered?
This not only tests the effect, but also reflects the integrity of classroom teaching, thus cultivating students' ability of generalization and oral expression.
Application of Comparative Method: Lecture 2: Teaching Materials
The application of the proportion in the first volume of the sixth grade of primary school mathematics is taught on the basis that students understand the meaning of positive and negative proportion and learn from solution ratio. It mainly includes positive and negative proportion application questions, which is a comprehensive application of proportion and proportion knowledge. The textbook explains the solution of positive and negative proportion application problems through two examples, so that students can master the characteristics and solving steps of positive and negative proportion application problems.
To solve the application problem of positive-negative ratio, we must first analyze the quantitative relationship according to the meaning of the problem and find two related quantities from the problem. The ratio (or product) of the corresponding two numbers in these two quantities is determined, so as to judge whether these two quantities are in positive (or negative) proportion, and then set the unknown X to solve the problem in proportion. The judgment process is also the practical application process of positive and negative proportional meaning.
Say the goal
I. Knowledge objectives
1, let students correctly judge the proportion of the amount involved in the application problem.
2. Use the meaning of positive and negative proportions to enable students to answer application questions correctly.
Second, the ability goal
1, cultivate students' judgment and reasoning ability.
2. Cultivate students' analytical ability.
Third, emotional goals.
Guide students to use existing knowledge, explore and solve practical problems by themselves, and cultivate students' exploration spirit.
Teaching emphases and difficulties
Correctly judge the proportion of quantity in the problem and list the relationship according to the equation relationship.
teaching method
Guide inquiry and cooperative learning.
On the Teaching Process
First, check the import.
The teaching content of this lesson is the application of positive and negative proportions. Therefore, through the teaching of this section, students can deepen their understanding of the meaning of positive and negative ratio and correctly judge the positive and negative ratio.
Second, explore new knowledge.
Examples of positive and negative proportional learning in application problems. Among the four application problems that students have learned, in fact, only the induction method is touched. Therefore, in teaching, students should first use the methods they have learned to solve them. Then, we should guide them to teach with new knowledge with the transformation of analogy, so that the new knowledge is not new and the old knowledge is not old, and stimulate students' interest in learning.
Let the students solve the problem in the previous way first, and then ask: What are the two quantities in this problem? What's the ratio? Why? Guide students to judge the proportional relationship between two quantities, and then list the equation solutions according to the meaning of proportion, which deepens the understanding of proportion and reveals the connection with old knowledge.
Third, the new lesson summary
Through the explanation of examples, students sum up the key to solving application problems in proportion.
Fourth, practice is improved.
1, basic exercise
2, judgment reasoning does not answer
Step 3 become an exercise
Verb (abbreviation of verb) summary of this lesson
Effect prediction of intransitive verbs
In this lesson, we learn to find two related quantities and judge whether these two quantities are directly proportional or inversely proportional. In the process of solving practical problems, students can actively participate and give full play to their dominant position.