Mathematics knowledge points of the new semester in the third grade of the catalogue
Induction of knowledge points in the first volume of mathematics in grade three
Five methods of reviewing mathematics in grade three.
Mathematics knowledge points in the new semester of grade three 1. Definition of circle
1, a graph composed of points with a fixed point as the center and a fixed length as the radius.
2. A graph composed of points with the same distance to a fixed point on the same plane.
Second, the elements of a circle
1, radius: the line connecting a point on a circle with the center of the circle.
2. Diameter: Two points on the connecting circle have a line segment passing through the center of the circle.
3. Chord: a line segment connecting two points on a circle (the diameter is also a chord).
4. Arc: The curve between two points on a circle. A semicircle is also an arc.
(1) Bad arc: the arc is less than half a circle.
(2) Optimal arc: an arc larger than half a circle.
5. Central angle: an edge with the center of the circle as the vertex and the radius as the angle.
6. Circumferential angle: the vertex is on the circumference, and the two sides of the circumferential angle are chords.
7. Chord center distance: the length from the center of the chord to the vertical section of the chord.
Third, the basic properties of the circle
1, symmetry of circle
(1) A circle is a figure, and its symmetry axis is the straight line where the diameter lies.
(2) A circle is a figure with a symmetrical center, and its symmetrical center is the center of the circle.
(3) The circle is a symmetrical figure.
2. Vertical diameter theorem.
(1) bisects the chord perpendicular to its diameter and bisects the two arcs opposite the chord.
(2) Inference:
Bisect the diameter (non-diameter) of a chord, perpendicular to the chord and bisecting the two arcs opposite the chord.
Bisect the diameter of the arc and bisect the chord of the arc vertically.
3. The degree of the central angle is equal to the degree of the arc it faces. The degree of the circle angle is equal to half the radian it subtends.
(1) The circumferential angles of the same arc are equal.
(2) The circumferential angle of the diameter is a right angle; The angle of a circle is a right angle, and the chord it subtends is a diameter.
4. In the same circle or equal circle, as long as one of the five pairs of quantities, namely two chords, two arcs, two circumferential angles, two central angles and the distance between the centers of two chords, is equal, the other four pairs are also equal.
5. The two arcs sandwiched between parallel lines are equal.
6. Let the radius of ⊙O be r and op = d. ..
Summary of knowledge points in the first volume of junior high school mathematics 1. Digital classification and concept number system table;
Note: Classification principle: 1) Proportionality (no weight, no leakage) 2) Standard.
2. Non-negative number: the collective name of positive real number and zero. (Form: x0)
Property: If the sum of several non-negative numbers is 0, then each non-negative number is 0.
3. Countdown:
① Definition and representation
② attribute: a.a1/a (a1); 1/a，aC.0
4. The opposite number:
① Definition and representation
② Property: the position of aB.a and -a on the number axis when A.a0; The sum of c is 0 and the quotient is-1.
5. Number axis:
① Definition (three elements)
② Function: a. Visually compare real numbers; B. clearly reflect the absolute value; C. establish a one-to-one correspondence between points and real numbers.
6. Odd numbers, even numbers, prime numbers and composite numbers (positive integer natural numbers)
Definition and expression:
Odd number: 2n- 1
Even number: 2n(n is a natural number)
7. Absolute value:
(1) definition (2):
Algebraic definition:
Geometric definition: the geometric meaning of the absolute value top of the number A is the distance from the point corresponding to the real number A on the number axis to the origin.
②│a│0, and the symbol │ │ is a sign of non-negative numbers;
③ There is only one absolute value of number A;
(4) To deal with any kind of topic, as long as there is a │ │ in it, the key step is to remove this │ │ symbol.
Five methods of math review in grade three: 1. 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, 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 in turn 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.
Third, 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, remind students that on the one hand, we should improve our 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"
Fourth, 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. Notes are not records, but simple and concise records of the main points and thinking methods in the above lectures for review, digestion and thinking.
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.
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