Summary and induction of knowledge points in the first volume of mathematics in grade three

What friends are not clear about the knowledge points of mathematics in the third grade? Come and have a look! I have carefully prepared a summary of the knowledge points in the first volume of Grade Three Mathematics for you. This article is for reference only, and you will continue to get more information by paying attention to this site!

Summary of knowledge points in the first volume of junior high school mathematics 1, absolute value

The absolute value of a number is the distance between the point representing the number and the origin, |a|≥0. When the absolute value of zero is itself, it can also be regarded as its inverse. If |a|=a, then a ≥ 0; If |a|=-a, then a≤0. Positive numbers are greater than zero, negative numbers are less than zero, positive numbers are greater than all negative numbers, and the absolute values of the two negative numbers are smaller.

(1) The absolute value of a positive real number is itself; The absolute value of a negative real number is its reciprocal; The absolute value of 0 is 0.

(2) The absolute value of real numbers is non-negative. Seen from the number axis, the absolute value of a real number is the distance from the point representing this number to the origin on the number axis.

(3) If the sum of several non-negative numbers is equal to zero, then each non-negative number is equal to zero.

Note: │a│≥0, and the symbol │ │ is a sign of "non-negative number"; There is only one absolute value of the number a; When dealing with any kind of topic, as long as "│ │" appears, the key step is to remove the "│ │" symbol.

2. Solve a quadratic equation with one variable

The basic idea of solving quadratic equations with one variable is to simplify them into two quadratic equations with one variable.

(1) Direct Kaiping Method:

The equation in the form of (x-m)2=n(n≥0) is solved by direct Kaiping method, and its solution is x = m.

Direct Kaiping method is the inverse operation of square. The result of its operation is usually represented by a root sign.

(2) Matching method

The method of obtaining the root of a quadratic equation by matching it completely flat. The solution of this unary quadratic equation is called collocation method, and the formula is based on the complete square formula.

1) transformation: transform the unary quadratic equation into the form of ax 2+bx+c = 0 (that is, the general form of the unary quadratic equation).

2) Coefficient 1: set the coefficient of quadratic term as 1.

3) Move the item: move the constant item to the right of the equal sign.

4) Formula: Add half the square of the first coefficient to the left and right sides of the equal sign.

5) Deformation: Write the algebraic expression on the left of the equal sign as a complete square.

6) Square root: simultaneous square root.

7) Solution: The root of the original equation can be obtained by sorting.

(3) Formula method

Formula method: Convert the quadratic equation of one variable into a general form, and then calculate the value of the discriminant △=b2-4ac. When b2-4ac≥0, substitute the values of the coefficients A, B and C into the formula x=(b2-4ac≥0) to get the root of the equation.

3. Essential knowledge points of circle

(1) circle

In a plane, a closed curve formed by a moving point rotating around a certain point with a certain length is called a circle. A circle has countless axes of symmetry.

(2) Related characteristics of the circle

1) diameter

The line segment connecting the center of the circle and any point on the circle is called radius, and the letter is expressed as R.

The line segment passing through the center of the circle with both ends on the circle is called the diameter, and the letter is expressed as D.

A straight line with a diameter is the symmetry axis of a circle. In the same circle, the diameter of the circle is d=2r.

2) Chords

A line segment connecting any two points on a circle is called a chord. The longest chord in the same circle is the diameter. The straight line with the diameter is the symmetry axis of the circle, so there are countless symmetry axes of the circle.

3) Arc

The part between any two points on a circle is called an arc, which is represented by "⌒".

An arc larger than a semicircle is called an optimal arc, and an arc smaller than a semicircle is called a suboptimal arc, so a semicircle is neither an optimal arc nor a suboptimal arc. The optimal arc is generally represented by three letters, and the suboptimal arc is generally represented by two letters. The optimal arc is an arc with a central angle greater than 180 degrees, and the suboptimal arc is an arc with a central angle less than 180 degrees.

In the same circle or equal circle, two arcs that can overlap each other are called equal arcs.

4) Angle

The angle of the vertex on the center of the circle is called the central angle.

The angle at which the vertex is on the circumference and both sides intersect with the circle is called the circumferential angle. The angle of a circle is equal to half the central angle of the same arc.

Expanding reading: how to prepare for math in grade three? First, return to textbooks, lay a solid foundation, and prepare well.

The basic concepts, definitions and formulas of mathematics, the internal relations between mathematical knowledge points, and the basic ideas and methods of solving mathematical problems are the most important things in review. To return to the textbook, we must first sort out the knowledge points and do every example and exercise in the textbook to ensure that the basic concepts and formulas are firmly mastered. Slow and steady, don't climb blindly, haste makes waste. There are many contents in the review class, and time is tight. In order to improve the review efficiency, we must synchronize our thoughts with the teachers'. Preview is an important way to achieve this goal. Without preview, listening to the teacher will make you feel that everything the teacher says is very important and you can't grasp the key points of the teacher's speech; After previewing, listen to the teacher's lecture. You will choose what the teacher has said in your memory and focus on what you have not mastered to improve your learning efficiency.

Second, improve the efficiency of classroom lectures, use more brains and work hard.

There are only two forms of class in grade three: review class and class evaluation. By the third day, all classes have entered the review stage. Through review, students should know which knowledge points they have mastered better and which knowledge points need to be improved. Therefore, they must have their own thinking before reviewing the class, so that the purpose of the class is clear. Now students will have some review materials in their hands. They should do the example again before the teacher gives a lecture. The difficulty found in doing the problem is the focus of the lecture. For the old knowledge that is not well mastered in the preview, we can check and fill in the gaps, thus reducing the difficulties in the course of listening to lectures. By comparing and analyzing what you understand with the teacher's explanation, you can improve your mathematical thinking. Experience the thinking of analyzing problems and the thinking method of solving problems. If you persist, you will be able to draw inferences and get twice the result with half the effort. In addition, it is very important to take notes on the difficulties of teachers' lectures. Taking notes is not a record, but a simple and concise record of the main points and thinking methods in the above lectures for review, digestion and thinking.

Third, the establishment of wrong account, leak detection.

In the third grade review, dozens or even hundreds of sets of various test questions should be done. Special-grade teachers of People's Education and Learning Network remind students to set up a wrong problem book, sort out the problems they usually make, write comments and reasons for doing mistakes on it, and take out the "wrong problem book" every once in a while. When reading reference books, you can also target the key or wrong questions, and then focus on this book in the future. The process of checking and filling gaps is the process of reflection. In addition to understanding different problems, we should also learn to "draw inferences from others" and summarize them in time. Every time you revise a test paper or homework, write down the reasons for doing it wrong next to the wrong questions.

Fourth, grasp the key points, highlight the key points, and don't talk about heroes by the amount of questions.

It takes a lot of problems to learn math well, but doing a lot of problems is not necessarily good at math. "Don't talk about heroes by the amount of questions", the tactics of asking questions about the sea sometimes get twice the result with half the effort, and it is necessary to improve the efficiency of solving problems. The purpose of doing the problem is to check whether you have mastered the knowledge and methods well. If you are not accurate or even biased, the result of doing so many questions will consolidate your shortcomings. It is necessary to do a certain amount of exercises on the basis of accurately mastering the basic knowledge and methods, but you should do the questions in a targeted manner, highlight the key points and grasp the key points. In review, the so-called highlighting the key points mainly refers to highlighting the key knowledge in the textbook, highlighting the knowledge that is difficult to understand or has not been deeply understood, and highlighting mathematical ideas and problem-solving methods. Mathematical thoughts and methods are the essence of mathematics and the link of all kinds of knowledge in mathematics. It is necessary to grasp the key contents in the textbook, master the analytical methods, think about the problem from multiple angles, and explore the methods of solving multiple problems, changing problems and using multiple problems. Cultivate the correct transformation from everyday language to algebraic and geometric language. And gradually master the mathematical language skills of listening, speaking, reading, writing and translation.

Fifth, we should develop good problem-solving habits.

For example, some students (especially those with good brains) look at the questions carefully, see the figures clearly, standardize the problem-solving format, and feel very good about themselves. Usually, I just write an answer when I do the problem, and I don't pay attention to the problem-solving process, so my writing is not standardized. Even if the answer is correct in the formal exam, they will be deducted more points because of the incomplete process. Some students usually lack self-confidence in the learning process, so it is inevitable to check each other's answers when doing homework, and they have not carefully found out the reasons for the mistakes and corrected them. These students often make psychological mistakes when they arrive at the examination room, which leads to "meeting without being right", or in order to ensure the correct rate, they repeatedly check and calculate, wasting a lot of time and affecting the overall performance. These problems are difficult to solve in a short time and must be corrected in peacetime. "Meeting without being right" is a taboo in math learning in grade three. There are common mistakes in exams and calculations, which are usually considered to be carelessness. In fact, this is a bad study habit, which must be gradually overcome in the first round of review. Otherwise, there will be endless trouble.

Sixth, improve the review interest and overcome the "plateau phenomenon".

Plateau phenomenon is very obvious in mathematics review stage. Usually give new lessons, fresh and interesting; When reviewing, you should repeat what you have learned. Some students will feel monotonous and will slow down or even lower their grades. In view of this situation, the teacher of People's Education Learning Network reminded the students that on the one hand, they should improve their understanding of review ideologically and take the initiative to review; On the other hand, use novelty to improve the enthusiasm of review. For example, make a new review plan; Adopt flexible review methods; Grasp the novel and interesting content and exercises, connect the knowledge in series, and make the book "from thick to thin"

What major is better in technical school? 1, kindergarten teacher

Kindergarten teachers' major is now a major that the country attaches great importance to. With the rapid development of preschool education in China, the demand for kindergarten teachers and managers has increased sharply, and the demand for kindergarten teachers is in short supply. The main reasons why people are more optimistic about kindergarten teachers' major are: stable employment, high employment rate and decent work.

Step 2: Care

Nursing has always been one of the occupations with high status and high salary in the world. Of course, nursing talents are also in short supply in China. In China, every doctor must be equipped with three nurses, but at present, nurses in China are far from meeting this standard. Major hospitals are often short of nursing staff, and there are very few professional nursing talents. It is undoubtedly a good choice to learn nursing. The professional name of nursing after graduation is: nurse. In all our impressions, when it comes to nurses, we all have the image of angels in white. A qualified nurse sincerely treats patients in pain, pursues technical perfection and pursues wholehearted service. Is a respected noble profession!

Step 3 travel

Learn to be a tour guide, travel around the world, enjoy the scenery all over the country and feel different cultural life! The longer you work, the more you can improve your self-cultivation and become an intellectual woman. Of course, there are still many people who think that tour guides eat young food. In fact, many tour guide students become talents in their posts and become tour managers after promotion. Some students also transferred to the second-line departments as they grew older. Or the ability has been improved and transferred to other industries, doing very well.

4. Railways and high-speed rail

With the rapid development of high-speed railway and urban rail transit, it provides students with good employment information and development opportunities. Students who graduated from junior high school choose to study railways and high-speed rail, which has become the pursuit of many students. After graduation, some students become high-speed train attendants, train conductors, rail car drivers, urban light rail drivers, subway drivers, railway electricians, railway maintenance workers, passengers, ticket sellers, signalmen and security inspectors, and some outstanding graduates hold leadership positions in railway sections! Junior high school graduates can choose secondary school majors: urban rail transit power supply, electrified railway power supply, railway transportation management, urban rail transit operation management, diesel locomotive operation and maintenance, etc. After that, I will be employed in the railway and urban rail industries, engaged in: subway/light rail maintenance electrician, railway maintenance electrician, high-speed rail passenger transport, light rail/subway security inspector, diesel locomotive driver, etc.

5. Chef

Many girls like boys who wear tall white hats and cook delicious food for their beloved girls. In a special festival, you will feel extremely happy. In addition to learning to be a chef, the development of the industry itself is also an important factor for students to choose. The catering industry has maintained a strong growth momentum for many years, which has also led to an increase in the salary level of the catering industry. Chef's salary is among the best, and he is known as one of the top ten golden occupations. Chef has the advantages of high salary, low pressure and stable work, and has become a profession that everyone is scrambling to choose.

6. Computer information technology

Computers have become an indispensable part of our daily life. What should we learn in a technical school? What can be used in employment is good. And computers have this feature. No matter where you go, you can't leave the computer. However, many students may think that it is necessary for me to go to a technical school to learn computers from primary school computers. Of course it is necessary. What I learned from primary school is nothing more than some simple computer use and internet access functions. If you want to go deep into the computer industry, there are many categories, such as graphic design, interior decoration design, network marketing, software development, UI design, big data, VR technology, e-sports and other majors all belong to the computer category. Computer, a major closely related to the flavor of the times, has also become a profession with relatively hot employment in recent years.

7, numerical control

The major of numerical control is more suitable for boys because it weighs students' practical ability. The employment scope of this major is very wide, involving many fields: (1) machinery manufacturing technology; (2) Information processing, processing and transmission technology; (3) Servo drive technology; (4) automatic control technology; (5) sensor technology; (6) Software technology, etc. This means that after learning CNC technology well, there will be more choices for employment! Most of the employment units are large and medium-sized enterprises, and the employment salary is higher than other majors.

8. Accounting

As we all know, with the growth of age, accounting is becoming more and more popular, and it is a profession that can be developed for a long time. Generally, the accounting work of a company is in the hands of one's cronies. The accounting profession is serious and principled. Suitable for students with delicate mind and serious study.

9. Marketing

At the major job fairs, we can easily see that there are many occupations that recruit market talents. Because the core competitiveness of many enterprises lies in marketing talents. The average employment rate of this major over the years is around 97%. Marketing is also a challenging and passionate industry, which needs hard work. Students who like adventure, dare to challenge, are willing to pay, and want to engage in management and marketing can choose this major.

10, automobile maintenance

Automobile maintenance is to meet the needs of social development. With the development of China society, the increase in the number of automobiles and the lack of automobile maintenance personnel, a group of professional and high-quality maintenance personnel are needed. Automobile maintenance, as one of the key points of the skill shortage talent training project implemented by the Ministry of Education, requires more than 300,000 talents nationwide. The major of automobile maintenance is to adapt to the development of modern automobile industry, master the basic knowledge of automobile, such as automobile structure and principle, the use of automobile electrical equipment, automobile inspection equipment, automobile fault diagnosis, etc., master the use of various automobile inspection equipment and the inspection process of the whole vehicle, have a high level of professional operation skills and technical guidance technicians of automobile inspection, and have advanced management knowledge and skills of automobile maintenance enterprises.