Induction of mathematics knowledge points in grade three
Space and graphics
Understanding of graphics:
1, point, line, surface
Points, lines and faces:
① Graphics are composed of points, lines and surfaces.
(2) The line where the surface intersects and the point where the line intersects.
(3) Points become lines, lines become surfaces, and surfaces become bodies.
Expand and collapse:
(1) In a prism, the intersection of any two adjacent faces is called an edge, and a side is the intersection of two adjacent edges. All sides of the prism have the same length, the upper and lower bottom surfaces of the prism have the same shape, and the side surfaces are cuboids.
(2) N prism is a prism with N faces on its bottom.
Cutting a geometric figure: cutting a figure with a plane, and the cutting surface is called a section.
Views: main view, left view and top view.
Polygon: It is a closed figure composed of some line segments that are not on the same straight line.
Arc, sector:
(1) A graph consisting of an arc and two radii passing through the end of the arc is called a sector.
② The circle can be divided into several sectors.
corner
Line:
① A line segment has two endpoints.
(2) The line segment extends infinitely in one direction to form a ray. A ray has only one endpoint.
③ A straight line is formed by the infinite extension of both ends of a line segment. A straight line has no end.
Only one straight line passes through two points.
Comparison length:
① Of all the connecting lines between two points, the line segment is the shortest.
② The length of the line segment between two points is called the distance between these two points.
Measurement and representation of angles;
The (1) angle consists of two rays with a common endpoint, and the common endpoint of the two rays is the vertex of the angle.
② One degree of 1/60 is one minute, and one minute of1/60 is one second.
Angle comparison:
The angle (1) can also be regarded as a light rotating around its endpoint.
(2) The ray rotates around its endpoint. When the ending edge and the starting edge are on a straight line, the angle formed is called a right angle. The starting edge continues to rotate, and when it coincides with the starting edge again, the angle formed is called fillet.
(3) The ray from the vertex of an angle divides the angle into two equal angles, and this ray is called the bisector of the angle.
Parallel:
(1) In the same plane, two disjoint straight lines are called parallel lines.
② One and only one straight line is parallel to this straight line after passing through a point outside the straight line.
If both lines are parallel to the third line, then the two lines are parallel to each other.
The induction of mathematics knowledge points in the second volume of the ninth grade
1. Proportional Theorem of Parallel Lines and Its Inference:
Theorem: Three parallel lines cut two straight lines, and the corresponding line segments are proportional.
2. Inference: A straight line parallel to one side of a triangle is directly proportional to the corresponding line segment obtained by cutting the other two sides (or extension lines of both sides).
3. Inference inverse theorem: If the corresponding line segment obtained by cutting two sides of a triangle (or the extension lines of two sides) is proportional, then this line segment is parallel to the third side of the triangle.
Second, the similar preparation theorem:
A straight line parallel to one side of a triangle and intersecting with the other two sides, the three sides of the cut triangle are directly proportional to the three sides of the original triangle.
Third, similar triangles:
1. Definition: A triangle with equal corresponding angles and proportional corresponding sides is called similar triangles.
2. Properties: (1) The angles corresponding to similar triangles are equal;
(2) The line segments corresponding to similar triangles (side, height, midline and angular bisector) are proportional;
(3) The perimeter ratio of similar triangles is equal to the similarity ratio, and the area ratio is equal to the square of the similarity ratio.
Description: ① The area ratio of equal-height triangle is equal to the ratio of bottom, and the area ratio of equal-bottom triangle is equal to the ratio of height; ② Pay attention to the correspondence between two graphic elements.
3. Decision theorem:
(1) Two angles are equal and two triangles are similar;
(2) The two sides are correspondingly proportional, the included angle is equal, and the two triangles are similar;
(3) Three sides are proportional and two triangles are similar;
(4) Two right-angled triangles are similar if the hypotenuse and one right-angled side of one right-angled triangle are directly proportional to the hypotenuse and one right-angled side of another right-angled triangle.
Mathematics learning methods in grade three
First, don't think you understand what you should remember and recite.
Some students think that mathematics is not like English, history and geography. Words, dates, and place names are required. Mathematics depends on wisdom, skill and reasoning. I said you were only half right. Mathematics is also inseparable from memory. Imagine, elementary school addition, subtraction, multiplication and division and Divison, can you operate smoothly without memorizing the multiplication table? Although you understand that multiplication is the operation of the sum of the same addend, when you do 9.9, you add 9 9s to get 8 1, which is too uneconomical. It is much more convenient to use "998 1". Similarly, it is also made with the rules that everyone knows by heart. At the same time, there are many laws in mathematics that need to be memorized, such as law (a≠0) and so on. So, I think mathematics is more like a game. It has many rules of the game (that is, definitions, rules, formulas, theorems, etc. Whoever remembers these rules of the game will be able to play the game smoothly. Whoever violates these rules of the game will be judged wrong and sent off. Therefore, mathematical definitions, rules, formulas, theorems, etc. Must recite, some can recite, catchy. For example, the familiar "Three Formulas of Algebraic Multiplication", I think some of you here can recite it, while others can't. Here, I want to remind the students who can't recite these three formulas. If they can't recite it, it will cause great trouble for future study, because these three formulas will be widely used in future study, especially the factorization of senior two, in which three very important factorization formulas are all derived from these three multiplication formulas, and they are deformations in opposite directions.
Remember the definitions, rules, formulas and theorems of mathematics, and remember those that you don't understand for the time being, and deepen your understanding on the basis of memory and application to solve problems. For example, mathematical definitions, rules, formulas and theorems are just like axes, saws, Mo Dou and planers in the hands of carpenters. Without these tools, carpenters can't make furniture. With these tools, coupled with skilled craftsmanship and wisdom, you can make all kinds of exquisite furniture. Similarly, if you can't remember the definition, rules, formulas and theorems of mathematics, it is difficult to solve mathematical problems. And remember these, plus certain methods, skills and agile thinking, you can be handy in solving mathematical problems, even solving mathematical problems.
Second, several important mathematical ideas
1, the idea of "equation"
Mathematics studies the spatial form and quantitative relationship of things. The most important quantitative relationship in junior high school is equality, followed by inequality. The most common equivalence relation is "equation". For example, uniform motion, distance, speed and time are equivalent, and a related equation can be established: speed and time = distance. In this equation, there are generally known quantities and unknown quantities. An equation containing unknown quantities like this is an "equation", and the process of finding the unknown quantities through the known quantities in the equation is to solve the equation. We were exposed to simple equations in primary school, but in the first year of junior high school, we systematically studied the solution of one-dimensional linear equations and summarized five steps of solving one-dimensional linear equations. If you learn and master these five steps, any one-dimensional linear equation can be solved smoothly. In the second and third day of junior high school, you will also learn to solve one-dimensional quadratic equations, binary quadratic equations and simple triangular equations. In high school, we will also learn exponential equation, logarithmic equation, linear equation, parametric equation, polar coordinate equation and so on. The solution ideas of these equations are almost the same, and they are all transformed into the form of linear equations or quadratic equations in one variable by certain methods, and then solved by the familiar five steps to solve linear equations in one variable or the root formula to solve quadratic equations in one variable. Energy conservation in physics, chemical equilibrium formula in chemistry, and a large number of practical applications in reality all need to establish equations and get results by solving them. Therefore, students must learn how to solve one-dimensional linear equations and two-dimensional linear equations, and then learn other forms of equations.
The so-called "equation" idea means that for mathematical problems, especially the complex relationship between unknown quantities and known quantities encountered in reality, we are good at constructing relevant equations from the viewpoint of "equation" and then solving them.
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