Fourth grade mathematics book 1 unit 1 knowledge
1, counting unit: one (one), ten, one hundred, thousand, ten million, etc. , are counting units. The forward speed between two adjacent counting units is 10.
2. Number of digits: single digit, ten digit, hundred digit, ... billion digit, etc. , are all numbers. A numerical name is to add a "bit" after the corresponding counting unit, for example: 10000- 10000 bits.
3. Series: unit level, million level, billion level ... are all digital levels, and a digital level includes four numbers.
4. Number sequence table: A table containing several levels, numbers and corresponding counting units is called a number sequence table, as follows.
5. Digital representation: the number on a number represents several counting units of the number.
For example, 2 in 12367 is in thousands, which means "2 thousand". A number of an order of magnitude means several counting units of this order of magnitude.
For example, 3647 in 36472845 is "36.47 million" on the scale of ten thousand.
6. How to read large numbers:
(1) Read from the high digit and read step by step.
(2) Ten thousand series should be read according to the reading method of single series, and then a ten thousand word should be added at the back.
(3) No matter how many zeros are at the end of each stage, other numbers have one or several zeros in succession, and only one zero is read.
Notes on reading: "2" is pronounced as "2"; If the highest digit of a large number is ten digits, one hundred thousand digits, one billion digits ... and the highest digit is "1", this "1" will not be read. For example, 125046 is pronounced as "125046".
7. How to write big numbers:
(1) Start with advanced writing and write it down at the first level.
(2) When there is no counting unit on any bit, write 0 on that bit.
Matters needing attention in writing numbers: We must pay attention to the "four-digit level" to ensure that each level has four digits, and use 0 to make up for the deficiency.
8. Test method of reading and writing numbers: The reading and writing numbers can be checked with each other, that is, after reading, they can be written and compared with the original numbers, and then they can be read by themselves.
9. Write the numbers: write the numbers of each part separately according to the numerical sequence table, and then make up with 0.
10 comparison with large numbers:
The more digits, the bigger the number.
(2) When these two numbers are the same, we should start from the left, that is, compare them from the highest place. The higher the number at the top, the higher the number.
(3) If the number on the highest bit is the same, compare it with the next bit, and so on, until we compare the number on the same bit, which number is larger, we can conclude that this number is larger.
165438+ 0~4 means "give up", the mantissa is cleared with the exact digits unchanged, 5~9 means "enter", and the mantissa is cleared with the exact digits added 1.
For example:
125933 (accurate to tens of thousands of digits) ≈ 130000
125933 (accurate to thousands) ≈ 126000
125933 (accurate to hundreds) ≈ 125900
125933 (accurate to ten digits) ≈ 125930
Note: the result after rounding is approximate, so the symbol must be ""!
12, rewritten as numbers with different counting units:
(1) Integer: four zeros of a level are rewritten as "tens of thousands", and integer: eight zeros of a level are rewritten as "hundreds of millions".
For example,
150000 = 150000
24 billion = 24 billion = 2.4 billion
370,000 = 3.7 million
Note: the rewriting of tens of thousands and billions of integers is an exact number, so use "=" to connect them!
(2) Rewriting a non-integer into a number with the unit of "ten thousand": take the number after ten thousand digits as the mantissa, round the highest digit (thousand digits) of the mantissa, and then rewrite it into a number with the unit of "ten thousand".
Such as14,7283, because the number on thousands is 7, which belongs to the situation of "entering".
So14,7283 ≈15,000 =15,000 or directly written as14,7283 ≈15,000.
(3) Rewriting a non-integer into a number with the unit of "100 million": take the number after 100 million digits as the mantissa, round the highest digit (10 million digits) of the mantissa, and then rewrite it into a number with the unit of "100 million".
For example, 56,0384,965,438+082, because the number on the tens of millions of digits is 0, which belongs to the situation of "giving up", so 56,0384,965,438+082 ≈ 56,000,000,000 = 5.6 billion or directly written as 560,384,000.
13, number of groups required:
(1) Form the maximum and minimum numbers: "Form the maximum six digits and the minimum six digits with 2, 4, 5, 6, 0 and 9".
Maximum number: arrange the given numbers in order from largest to smallest, and get 965420.
Minimum number: arrange the given numbers in order from small to large. If the highest digit is 0, the first non-zero digit is taken as the highest digit in advance, and 024569-"204569" is obtained.
(2) Numbers that make up a specific pronunciation: "Read with 2, 4, 5, 0, 0 1 zero."
According to the reading rules, first determine the position of 0. If you read only 1 zero, then this zero can't be at the end of each level, and it is known that this number is five digits, so the number of digits that a single zero can appear is ten, hundred and thousand, and the positions where two consecutive zeros can appear are thousand, hundred, hundred and ten. Finally, fill in non-zero numbers. Get 24050, 20450, 20045, 24005.
(3) Maximum and minimum number of specific pronunciations: First, take care of pronunciations, and arrange the position of 0, and arrange other numbers according to the maximum or minimum requirements.
14, carry system: the counting method of using the same number to represent different sizes in different digits is the carry system. Simply put, "all decimal one" is "decimal". All decimals are decimals (counting method), and * * * has 10 digits (0~9).
15, natural number: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,1,... The number of objects is a natural number. There is no object, which is represented by 0, and 0 is also a natural number. The smallest natural number is 0. There is no maximum natural number, and the number of natural numbers is infinite.
16, Understanding of Computing Tools:
(1) abacus: China invented the abacus. The abacus has an upper gear and a lower gear, each bead in the upper gear represents 5, each bead in the lower gear represents 1, and each rod is equivalent to a number, for example, "a bead on the 10,000 bit" represents "five tens of thousands".
(2) Calculator: CE is the "clear key" and ON/C is the "switch and clear screen key".
Skills and methods of learning primary school mathematics quickly
1. Preview
Before class, browse the unit content that the teacher will teach, and pay attention to the part that you don't understand.
2. Pay attention to the class
(1) There are many new definitions of terms or new ideas at the beginning of the new curriculum. The teacher's explanation must be clearer than the students' own reading. Be sure to listen attentively, don't be smart and make mistakes.
If the teacher says what you didn't understand in the preview, you should pay special attention.
Some students think that the teacher's explanation is simple, and then they are distracted to do other things, but they miss the most wonderful and important words, which may be the key to getting the wrong answer in the future exam.
(2) While listening to the lecture, recite the key points. Definitions, theorems, formulas and other key points should be memorized in class so that teachers can understand the essence of teachers when giving examples.
After returning home, it only takes a short time to review the lessons learned today. Get twice the result with half the effort. Unfortunately, most students enjoy the teacher's performance as easily as watching a movie in class, and they don't remember anything after class. It's a pity to waste a class in vain.
homework
(1) finishing points
In the evening of math class, we should sort out the contents taught that day, and memorize definitions, theorems and formulas. Some students think that mathematics focuses on reasoning and does not need to recite anything. This concept is incorrect. Generally speaking, the so-called immortal rote learning refers to the immortal rote learning method, but the basic definitions, theorems and formulas are our tools to solve problems. If we don't remember these things, we can't use them flexibly when solving problems, just as a doctor can't save people in the first place if he doesn't memorize all medical knowledge and medication knowledge. Many students didn't do well in the math exam, that is, they didn't understand the definition clearly, and some important theorems and formulas were not completely memorized.
(2) Proper exercise
After you finish the key points, you should practice properly. In class, do the examples explained by the teacher first, then do the textbook exercises, spare no effort, and then do the reference books or supplementary questions issued by the teacher. If you can't solve it for a while, you can skip it first to avoid wasting time, and then challenge it in your spare time. If you still can't solve it, discuss it with your classmates or teachers.
(3) When practicing, you must do calculus by yourself. Many students often can't go on when they solve problems in the middle of the exam. The reason is that he watches while doing exercises, and many key steps are ignored.
test
(1) Before the exam, it is necessary to sort out the key points within the scope of the exam, and pay attention to the important questions specially prompted by the teacher.
(2) When taking an exam, you must do the right questions. Students who often make calculation mistakes should try to slow down the calculation speed, carefully move items and add, subtract, multiply and divide, and use less "mental arithmetic".
(3) During the exam, our purpose is to get high marks, not to do academic research. So if you encounter a difficult topic, skip it first, and then use the rest of the time to challenge the problem, so as to fully show your strength and achieve the most perfect performance.
(4) There are two possible reasons for nervous students during the exam:
A. insufficient preparation leads to lack of confidence. Such people should strengthen their preparation before the exam.
B.the expectation of the score is too high. If you encounter several difficult problems and can't solve them, you won't be able to concentrate, resulting in a lower score. Such people must adjust their mentality. Don't expect too much.
5. Error correction and reinforcement
After the exam, regardless of the score, you should correct the wrong questions again. We must find out the mistakes and correct our thinking, so that we can learn the unit better.
Think back
After learning a unit, students should recall the key contents of the whole chapter from beginning to end, paying special attention to the title. Generally speaking, the title of each section is the theme of the section and the most important. Only by focusing on the theme can we fully understand what we are learning.
Nine elements for primary school students to learn mathematics well
First, we must lay a good foundation.
Mathematics is a highly systematic subject, and its contents are closely related. As far as the content taught by school teachers is concerned, the previous content is often the necessary basis for later learning. If you don't learn well in the front, it will definitely affect the learning of knowledge in the back. If you can't even count four integers, how can you count decimals? If you can't solve the application problem in one step, how to solve the comprehensive application problem in two or more steps? ..... So learning mathematics must follow the principle of starting from the basics, step by step, and gradually expanding. If the previous mathematics has not laid a good foundation, it is very necessary to make up for the missing knowledge. Just like building a tall building, only by laying a good foundation can one, two or three floors be built on it. Of course, it is not easy to make up for the lack of basic knowledge. Basic calculation (such as oral calculation and written calculation), basic concepts, basic quantitative relations, basic graphic knowledge, as well as the most basic mathematical ideas and basic methods to solve mathematical problems are the foundation. We must first find out what is missing. Then we can make targeted remedies.
Second, learn to listen.
Mathematics is an abstract knowledge with strong thinking and logic, which requires students to use their brains and study hard. So don't drive in class, especially when the teacher is explaining the analysis. When students answer questions, you should eliminate all interference, listen attentively, think, discover and expand with the teacher's explanation. Only by understanding the words of teachers and classmates can you analyze and judge whether others' words are correct and learn how teachers and other classmates analyze problems. For example, analyzing the quantitative relationship and seeking solutions to problems are just like the police solving a case, pressing step by step and interlocking. Every step explained by the teacher is the basis of the next analysis. If the previous step is not clear, it will affect the following analysis and understanding. This shows how important it is to listen carefully. In addition, learning to listen is also a courtesy, a respect and a learning spirit.
Third, we should pay attention to the methods and processes of solving problems.
To learn mathematics knowledge, we should not only pay attention to the results of doing problems, but also pay attention to the methods and processes of solving problems. Paying attention to results will only lead to imitation, rote memorization and mechanical copying. When you encounter strange problems, you are often at a loss. Only students who pay attention to the process and method of solving problems can get real training in thinking and become smarter and smarter. In fact, some students only pay attention to what is the result of a certain topic, and don't want to find out why. For example, some graphic calculation formulas, we should not only remember them, but also understand how these formulas are derived and how to push them down. Only in this way can we use it flexibly and achieve mastery. Even if we forget the formula, we can deduce the formula and summarize it. Our analytical and reasoning abilities can be improved.
Fourth, we should do proper exercise.
Learning mathematics is inseparable from doing problems. Confucius said: "learn from the times" and "review the old and learn the new". It means: Only by reviewing the knowledge learned in the past from time to time, sorting out and finding out the clues and consolidating them can we constantly absorb and understand new things. Without proper practice, there is no way to consolidate what you have learned. For example, we have learned the calculation of circular area, and we understand the process of formula derivation, but we have not practiced it in time, so the calculation method we have learned may soon be forgotten. Therefore, in order to better master old knowledge and acquire new knowledge, it is necessary to do appropriate exercises.
Fifth, we should dare to ask questions and our own opinions.
Regardless of the knowledge in the textbook or what the teacher said, we should boldly put forward different viewpoints and questions. What the teacher says is not necessarily the best way. We should dare to challenge teachers and textbooks. Of course, people who do not think about peacekeeping and are not good at thinking can't do this. For example, when learning to use comparative knowledge to solve practical problems, you can also think about whether you can use other knowledge to solve them. Then you will find that this problem can be solved by using the knowledge of integer division or converting it into fractional knowledge. So you must be proud of the way you solved the problem.
Sixth, we should be good at discovering laws, summarizing and transferring analogies.
Mathematics is a discipline with strong regularity. Learning mathematics must be good at discovering and summarizing mathematical laws. We should be able to draw inferences from others, organically combine old and new knowledge, systematize it and organize it into a framework. As the saying goes, if you master the system of mathematical knowledge, you will have the ability to solve comprehensive problems.
Seven, we must persevere.
Interest is the best teacher. To generate and maintain interest in mathematics, the most important thing is persistence. As long as you persist for a long time, you will be interested in mathematics and keep it. No effort, no gain. The process of learning mathematics may be hard, but when we solve difficult problems, only we can best understand the feeling of pride and success. If you persist in this way, you will be interested in mathematics. Many times, many students are afraid of giving up halfway and can't appreciate the fun of learning mathematics.
Eight, try to preview before class.
The effect of preview is different. Because if you preview, you will have a general understanding of what you are going to learn today, which not only exercises your self-study ability, but also helps you to have a clear aim when listening to lectures and improve the efficiency of listening to lectures.
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