Knowledge points at the end of the second grade mathematics in People's Education Edition
1. Knowledge points of the division in the table:
(1) Understand the meaning of average score. A simple division is calculated according to the multiplication in the table.
(2) The quotient can be obtained by multiplication formula.
(3) According to the meaning of multiplication and division, solve some simple application problems of multiplication and division.
(4) Divider Divider = quotient divisor = divisor × quotient = dividend
2. Division: It is one of the four operations. The operation of finding the other factor by knowing the product of two factors and one of them is called division.
3. The nature of division
A number divided by several numbers in succession is equal to the product of this number divided by those numbers. This is the nature of division. Sometimes simple operations can be performed according to the nature of the division. Such as: 300÷25÷4=300÷(25×4)
4. Division formula
(1) frequency divider = quotient
(2) Dividend quotient = divisor
(3) divisor × quotient = dividend
5. Dividends
A number divided by another number in a division operation, such as 24÷8=3, where 24 is the dividend.
6. Divider: In the division formula, the number after the divisor is called the divisor.
Example: 8÷2=4, then 2 is the divisor. Eight is dividends. The divisor cannot be 0, otherwise it is meaningless.
7. Quotient: In a division formula, dividend/divisor = quotient+remainder, and then it is deduced that quotient × divisor+remainder = dividend.
8. Quanshang
When the number A is divided by the number B (non-zero), its quotient is called complete quotient. For example, 9÷3=3, and 3 is the complete quotient.
9. Incomplete quotient
If the number A is divided by the number B (non-zero), the quotient obtained is incomplete. For example: 10 ÷ 3 = 3... 1, where 3 is an incomplete quotient.
The relationship between dividend and business.
Dividend is enlarged (reduced) by n times, and quotient is correspondingly enlarged (reduced) by n times.
The divisor is expanded (reduced) by n times, and the quotient is correspondingly reduced (expanded) by n times.
The multiplication formula of 1 1.2-6
2×2=4
2×3=63×3=9
2×4=83×4= 124×4= 16
2×5= 103×5= 154×5=205×5=25
2×6= 123×6= 184×6=245×6=306×6=36
12. Right angle: the definition in the original geometry: when the adjacent angles formed by a straight line and another horizontal straight line are equal, each of these angles is called a right angle, and this straight line is called perpendicular to another straight line.
A right angle is equal to 90 degrees, and the symbol is Rt∞.
13. Acute angle in geometry: an angle (right angle) greater than 0 degrees and less than 90 degrees.
The sum of the two acute angles is not necessarily greater than the right angle, but it must be less than the right angle.
14. Oblique angle: an obtuse angle greater than a right angle (90) and less than a right angle (180) is called an obtuse angle.
15. Translation: Translation means that all points on a graph move at the same distance in a certain direction in a plane. This kind of graphic movement is called graphic translation movement, which is called translation for short. Translation does not change the shape and size of the graph. Translation may not be horizontal.
16. Rotation: in a plane, the graphic transformation that rotates a graph by an angle around point O is called rotation, point O is called rotation center, and the rotation angle is called rotation angle. If point P on the graph rotates into point Pˊ, then these two points are called corresponding points of this rotation.
17. The essence of rotation
(1) The distance from the corresponding point to the rotation center is equal.
(2) The included angle of the connecting line between the corresponding point and the rotation center is equal to the rotation angle.
(3) The numbers before and after the rotation are equal.
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(1) center of rotation;
(2) direction of rotation;
(3) Rotation angle.
Note: As long as you arbitrarily change one of the three elements, the graphics will be different.
Rotational transformation is the transformation from one graphic to another. In the process of transformation, all points on the original figure change in the same direction around a fixed point and rotate at the same angle.
19. Knowledge points of the division in the table:
(1) Understand the meaning of average score. A simple division is calculated according to the multiplication in the table.
(2) The quotient can be obtained by multiplication formula.
(3) According to the meaning of multiplication and division, solve some simple application problems of multiplication and division.
(4) Divider Divider = quotient divisor = divisor × quotient = dividend
Multiplication formula of 20.7, 8 and 9
7×7=49
7×8=568×8=64
7×9=638×9=729×9=8 1
Understanding of numbers within 2 1. 10000
100 =1010 (the sum of10/0 is equal to100).
1000 =10100 (the sum of10100 is equal to1000).
22.grams
Gram is the unit of mass, and the symbol G is equal to one thousandth of a kilogram. The weight of one gram is equivalent to the weight of one cubic centimeter of water at room temperature, which is equivalent to the mass of a cross clamp.
1 ton = 1, 000,000 grams (one million grams)
1 kg (1 kg) = 1 1,000 g (1 kg)
1 kg = 500g (1 g = 0.002kg)
1 mg = 0.00 1 g (1 g = 1000 mg)
1 μ g = 0.0000 1 μ g (1 μ g = 1000000 μ g)
1 nanogram = 0.0000000 1 gram (1 gram = 10000000 nanogram)
23. kg
Kilogram: (symbol kg or) is the basic unit for measuring quality in the international system of units, and kilogram is also one of the most commonly used basic units in daily life.
Learning methods of mathematics in the second grade of human education
First, the basic links and principles of mathematics learning
Students' study at school is carried out under the guidance of teachers. Classroom learning generally includes four links: first, listening to the teacher's class, which is part of the lecture; In order to digest and master the knowledge taught in class, you need to do exercises, which are part of your homework. In order to further consolidate the knowledge learned and understand its internal relations, it is necessary to remember and summarize, which is part of the review. In order to study more actively in the next class, it is necessary to read the new lesson in advance, which is part of the preview. Each part of these four links has its independent significance and function, and each part is interrelated, influenced and restricted. These four links form a small cycle, that is, the learning cycle. The learning cycle is the trajectory of a learning wheel running for one week. People who are good at learning should find its starting point, end point and intermediate links from the printing of a wheel running for one week, form a four-link stereotyped learning cycle, form a learning system, and let each link fully play its role, so as to achieve good learning results.
The basic process of mathematics learning
When students learn new knowledge independently, they will generally go through the following five basic steps.
The first step is to develop knowledge, things or numbers.
Preliminary perception of line.
For example, examine the conditions and processes of things and their existence and evolution; Participate in the demonstration, operation, existence, change and development of the learned knowledge, and then have a preliminary feeling about the learned knowledge.
Contact and preliminary understanding of new knowledge-building perceptual knowledge
Developing new knowledge representation in associative form
Exploring the Internal Relationship between Old and New Knowledge —— Second Perception
Abstract generalization of the essential characteristics of new knowledge-the transformation to rational knowledge
New knowledge in memory-Gong Gu
Applying new knowledge-transforming knowledge into ability
Paying attention to the research on the basic process of students' learning mathematics is of great significance to improving teaching methods, strengthening the guidance of learning methods and improving teaching quality.
Principles and basic methods of mathematics learning
According to the characteristics of psychological theory and mathematics, analytical mathematics learning should follow the following principles: dynamic principle and gradual principle. The principle of independent thinking, the principle of timely feedback, and the principle of integrating theory with practice, and thus put forward the following mathematics learning methods:
1. Combination of seeking advice and self-study.
In the process of learning, we should not only strive for the guidance and help of teachers, but also rely on teachers everywhere. We must actively study, explore and acquire, and seek the help of teachers and classmates on the basis of our serious study and research.
Teaching second-year math learning skills
First, form a good habit of learning mathematics.
Establishing a good habit of learning mathematics will make you feel orderly and relaxed in your study. The good habits of high school mathematics should be: asking more questions, thinking hard, doing easily, summarizing again and paying attention to application. In the process of learning mathematics, students should translate the knowledge taught by teachers into their own unique language and keep it in their minds forever. Good habits of learning mathematics include self-study before class, paying attention to class, reviewing in time, working independently, solving problems, systematically summarizing and studying after class.
Second, the key is to attend classes efficiently.
The efficiency of class determines the basic situation of our study. Moreover, the improvement of class efficiency means that the time for after-school counseling can be saved. To improve the efficiency of attending classes, we should pay attention to the following aspects:
1, preparation before class
Preview is the review of old knowledge, especially the old knowledge that is not well mastered in preview, which can be reviewed and supplemented first; When we review now, students must read the basic knowledge first, and even if they can't do it, they must deeply understand the meaning of the questions given by the teacher, so as to ensure that they can deeply understand the teacher's thoughts when listening to the class. Students who have previewed can pay more attention to the class, and they know what should be detailed and what can be omitted, because the new knowledge and difficulties found in the preview are the focus of the class. Comparing and analyzing your understanding of new knowledge with the teacher's explanation after preview can improve your thinking level; At the same time, preview can cultivate self-study ability and improve interest in learning new lessons.
Step 2 listen to lectures
Classroom is the key link to understand and master basic knowledge, skills and methods.
Pay attention to the beginning and end of the teacher's lecture. At the beginning of a teacher's lecture, it is generally to summarize the main points of the last lesson and point out the content to be talked about in this lesson, which is a link to link old and new knowledge. The conclusion is usually a summary of the knowledge mentioned in this lesson, which has a strong generality and is an outline for review.
It is necessary to master the problem-solving process of examples carefully, understand the teacher's thinking of analyzing examples and the methods to solve such problems, and improve the ability to analyze and solve problems in combination with classroom exercises.
Grasp the key points of knowledge through classroom listening, solve knowledge doubts and improve mathematics ability. While listening to the class, record the key points, difficulties, doubts, typical examples and exercises, as well as expanded knowledge, for review after preparing lessons.
Third, review and summarize after class.
Timely review is an important part of efficient learning. The effective review method is not to read books or take notes over and over again, but to review by recalling:
You can first recall what the teacher said in class, such as: analyzing the ideas and methods of the problem, and trying to think completely. Then open your notes and books, compare what you haven't remembered clearly, make up, and finally ask yourself: what math content did I learn today? What is its way of thinking? What are the methods and steps to solve related examples and exercises?
This consolidated the content of the class that day, and the new knowledge learned changed from "meeting" to "meeting".
Fourth, practice after class
Learning mathematics must pay attention to "living", not only reading books without doing problems, but also burying oneself in doing problems without summarizing and accumulating. We must be able to learn from textbooks and find the best learning method according to our own characteristics. Methods vary from person to person, but four steps (preview, class, arrangement and homework) and one step (review and summary) are indispensable.
The purpose of doing the problem is to check and consolidate the knowledge learned and the method of solving the problem. If you have to do the problem aimlessly, it is not much different from not practicing. What matters is not the amount of questions, but the efficiency of doing them. [Source: Subject Network]
The correct practice method should be to select the necessary comprehensive basic knowledge exercises on the basis of reviewing and mastering the basic knowledge and methods.
Therefore, we should pay attention to "quality" rather than "quantity" when doing problems, and inefficient "sea of problems" can only be a waste of time.
Five, according to their own learning situation, take some concrete measures.
(1) Take math notes, especially the different aspects of concept understanding and mathematical laws, as well as the extra-curricular knowledge expanded by teachers in class. Write down the most valuable thinking methods or examples in this chapter, as well as your unsolved problems, so as to make up for them in the future.
(2) Establish a mathematical error correction book. Write down error-prone knowledge or reasoning in case it happens again. Strive to find wrong mistakes, analyze them, correct them and prevent them. Understanding: being able to deeply understand the right things from the opposite side; Can get to the root of the wrong cause from reason to reason, so as to prescribe the right medicine; Answer questions completely and reason strictly.
(3) Be sure to remember some mathematical laws and small conclusions, such as the diagonal formula of a cuboid. So that their usual computing ability can reach the proficiency of automation or semi-automation.
(4) Regularly organize the knowledge structure, form a plate structure, and implement "overall assembly", such as tabulation, to make the knowledge structure clear at a glance; Often classify exercises, from a case to a class, from a class to multiple classes, from multiple classes to unity; Several kinds of problems boil down to the same knowledge method.
(5) Review in time, strengthen the understanding and memory of the basic concept knowledge system, and make appropriate repeated consolidation, so as to learn without forgetting.
(6) Whether it's homework or exams, we should put accuracy in the first place and law in the first place, instead of blindly pursuing speed or skills. This is an important problem to learn mathematics well.
Pre-examination guidance
What is the content of the exam? Simply put, it is four words, three basics and five abilities. The so-called three basics are basic knowledge, basic skills and basic thinking methods. These five abilities are imagination, abstract generalization, reasoning and proof, operational solution and data processing. Among them, basic knowledge and skills are the key points, and the ability to prove and solve problems by reasoning is the key point. Finally, sprint review, we must pay attention to strategies and overcome blind problem solving. You might as well try the following, maybe your grades will improve.
First, how to return the particles to the warehouse, and do the right questions. You should do it during training; 1. I'd rather slow down and do the next question when I'm sure it's right. 2. The problem-solving method is better and the meaning of the problem is clearer. Study it carefully. Choose the best way to solve the problem. 3. Standardize the calculation steps. The mistake often lies in "miscalculation". When calculating, we should also write down the steps in our draft and confirm them before going down. 4. consider the problem comprehensively and beware of the trap. Pay attention to the omission, and investigate from the aspects of concept, formula, law and graph, especially whether there are special cases and whether the conclusion meets the meaning of the question. If all the questions that can be done correctly are done correctly, the results will not be bad and there will be no regrets.
Second, correcting mistakes Finally, it is not enough to just stop at correcting mistakes. Mistakes are often repetitive and stubborn, and you may still make mistakes next time you encounter the same problem. It is precisely because the wrong questions reflect your weak knowledge in some aspects or the defects in your thinking methods that we should firmly grasp the wrong questions and finally correct them. A more effective way to correct mistakes is to find out the root causes of mistakes, make in-depth analysis and consolidate several problems of the same type, which will be more effective than doing new problems.
Third, returning to textbooks In the sprint stage, I don't advocate reading textbooks through, but on the premise of correcting mistakes, I return to textbooks with my own shortcomings, find out my original vague concepts, understand the relevant formulas and laws of memory, and do some examples and exercises in textbooks. Some college entrance examination questions come from textbooks or variations of textbook questions. When returning to textbooks, we should also pay attention to the relationship between knowledge points and systematically master basic knowledge and methods.
Fourth, practice the questions skillfully, be correct but not quick, be precise but not much, and understand but not finish the homework. We practiced a lot, took a lot of exams and came up with many new questions. It is better to do some old ones selectively, for example, do many questions that we are not sure about in the mock exam again and do them well according to the standard writing format. For example, if we can't get the solid geometry test, we can choose ten questions to do by comparison. We will find the similarities and differences of these problems, analyze the methods and skills of solving problems, and summarize the laws.
Fifth, adjust the mentality and treat the exam correctly. First of all, we should focus on basic knowledge, basic skills and basic methods, because most of the exams are basic topics. For those difficult and comprehensive topics, we should seriously think about them, try our best to sort them out, and then summarize them after finishing the questions. Adjust your mentality, let yourself calm down at any time, think in an orderly way, and overcome impetuous emotions. In particular, we should have confidence in ourselves and always encourage ourselves. No one can beat me except yourself. If you don't beat yourself, no one can beat my pride.
Be prepared before the exam, practice routine questions, spread your own ideas, and avoid improving the speed of solving problems on the premise of ensuring the correct rate before the exam. For some easy basic questions, you should have a 12 grasp and get full marks; For some difficult questions, you should also try to score, learn to score hard in the exam, and make your level normal or even extraordinary. Students, Tengzhou No.1 Middle School has a beautiful learning environment and a group of enthusiastic teachers who are willing to do business. All the teachers are experienced and willing to make paving stones for you until you walk into the gate of colleges and universities. All the teachers in our math group will make you succeed in math study.
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