For more information, please follow the WeChat public account: Teacher Wang from the Primary School Resource Garden has compiled 28 key knowledge points from the first volume of mathematics for fourth grade primary schools to share with everyone. I hope this information can help

For more information, please follow the WeChat public account: Primary School Resource Garden

Teacher Wang compiled 28 key knowledge points from the first volume of mathematics for fourth grade primary school to share with everyone. I hope this information can help students review mathematics better.

1. Understanding of large numbers

One hundred thousand: 10 ten thousand;

One million: 10 one hundred thousand;

Ten million: 10 one million;

One hundred million: 10 Ten million;

2. Numerical progression

Numerical progression is a reading method to facilitate people to memorize Arabic numbers. Based on the place value system (digit sequence), the numbers are classified based on the principle of three or four digits. Read and write. Usually when writing Arabic numerals, decimal points or spaces are used as symbols for each numerical level, and the numbers are separated from right to left.

3. Numerical level classification

(1) Four-digit grading method

is a grading method that uses four digits as a numerical level. The habit of reading in our country is to read in this way.

For example: ten thousand (four zeros after the number), billion (eight zeros after the number), trillion (12 zeros after the number, this is Chinese counting)...

These levels are called one level, ten thousand level, and billion level respectively. ......

(2) Three-digit grading method

is a grading method that uses three digits as a numerical level. This Western grading method is also an internationally accepted grading method. For example: thousands, 3 0s and millions after the number, 6 0s and billions after the number, 9 0s after the number...

4. Digits

Digits refer to arranging the numbers side by side in horizontal rows when writing numbers. Each number occupies a position. These positions are called digits. Counting from the right end, the first digit is the "ones place", the second digit is the "tens place", the third digit is the "hundreds place", the fourth digit is the "thousands place", and the fifth digit is the "ten thousand place". etc. This shows that the concepts of counting units and digits are different.

5. The generation of numbers

The origin of Arabic numerals: After the ancient Indians created Arabic numerals, these numbers were spread to the Arab region around the 7th century AD. By the 13th century, the Italian mathematician Fibonacci wrote "The Book of Abacus", in which he gave a detailed introduction to Arabic numerals. Later, these numbers were transmitted from the Arab region to Europe. Europeans only knew that these numbers were introduced from the Arab region, so they called these numbers Arabic numerals. Later, these numbers spread from Europe to other countries around the world.

Arabic numerals were introduced into our country around the 13th to 14th centuries. Since there was a kind of number called "chip" in ancient my country, which was more convenient to write, Arabic numerals were not promoted and used in time in our country at that time. At the beginning of this century, with the absorption and introduction of foreign mathematical achievements in our country, Arabic numerals began to be slowly used in our country. The promotion and use of Arabic numerals in our country has a history of more than 100 years. Arabic numerals have now become the most commonly used numbers in people's study, life and communication.

6. Natural numbers

are used to measure the number of things or to represent the order of things.

is a number represented by the numbers 0, 1, 2, 3, 4,... The numbers that represent the number of objects are called natural numbers. The natural numbers start from 0 (including 0), one after another, forming an infinite group.

7. Calculation tools

abacus, calculator, computer

8. Ray

In geometry, the figure composed of a point on a straight line and the part next to it is called a ray. As shown in the figure below:

ray characteristics

(1) The ray has only one endpoint, and it extends infinitely from one endpoint to the other side.

(2) rays are not measurable.

9. Straight line

A straight line is the trajectory of a point moving in the same or opposite direction in space.

10. Line segment

A line segment is represented by letters representing its two endpoints or a lowercase letter. Sometimes these letters also represent the length of the line segment, which is recorded as line segment AB or line segment BA, line segment a. where AB represents any two points on the straight line.

11. Line segment characteristics

(1) Limited length, can be measured

(2) Two endpoints

12. Line segment properties

(1) The shortest line segment between two points.

(2) The length of the line segment connecting two points is called the distance between the two points.

(3) Two points on a straight line and the part between them are called line segments, and these two points are called the endpoints of the line segment.

Straight lines have no distance. Rays have no distance either. Because straight lines have no endpoints, rays have only one endpoint and can be extended indefinitely.

13. Angle

(1) Static definition of angle

A figure composed of two non-overlapping rays with common endpoints is called an angle. This common endpoint is called the vertex of the angle, and the two rays are called the two sides of the angle.

(2) Dynamic definition of angle

The shape formed by a ray rotating from one position to another around its endpoint is called an angle. The endpoint of the rotated ray is called the vertex of the angle, the ray at the starting position is called the starting side of the angle, and the ray at the ending position is called the terminal side of the angle

14. The symbol of the angle

The symbol of the angle: ∠

15. Types of angles

The size of the angle is related to The length of the sides does not matter; the size of the angle is determined by the degree to which the two sides of the angle are spread out. The greater the spread, the larger the angle. On the contrary, the smaller the spread, the smaller the angle. In dynamic definition, it depends on the direction and angle of rotation. Angle can be divided into 10 types: acute angle, right angle, obtuse angle, straight angle, circumferential angle, negative angle, positive angle, superior angle, inferior angle and zero angle. The system of measuring angles in degrees, minutes, and seconds is called the angle system. In addition, there are also metric systems, radian systems, etc.

(1) Acute angle: An angle greater than 0° and less than 90° is called an acute angle.

(2) Right angle: An angle equal to 90° is called a right angle.

(3) Obtuse angle: An angle greater than 90° and less than 180° is called an obtuse angle.

16. Multiplication

Multiplication refers to how many times a number or quantity is increased. For example, 4 multiplied by 5 means that 4 is multiplied by 5 times. It can also be said that 5 4s are added in a row.

17. The name of each number in the multiplication formula

"×" is the multiplication sign, the numbers before and after the multiplication sign are called factors, "=" is the equal sign, and the number after the equal sign is called the product.

10 (factor) When they have a common point, they are said to be parallel. As shown in the figure, straight line AB is parallel to straight line CD, denoted as AB∥CD. Parallel lines never intersect.

19. Perpendicular to each other

Two perpendicular straight lines or two planes intersect, or a straight line intersects a plane. If the intersection angles are at right angles, they are called mutually perpendicular.

20. Parallelogram

A quadrilateral with two sets of opposite sides being parallel in the same plane is called a parallelogram.

21.Trapezoid

Trapezoid refers to a quadrilateral in which one set of opposite sides is parallel and the other set of opposite sides is not parallel. The two parallel sides are called the bottom of the trapezoid, the long side is called the lower bottom, and the short side is called the upper bottom; you can also simply think that the upper one is called the upper bottom, and the lower one is called the lower bottom. The non-parallel sides are called the waist; the vertical segment sandwiched between the two bases is called the height of the trapezoid.

22. division

division rule: first look at the first few digits of the dividend, if the first few digits of the dividend are not enough to divide, look at one more digit. Whichever digit you divide to, the quotient will be written on that digit. If the quotient is not enough, one, 0 Placeholder.

The remainder is smaller than the divisor. If the quotient is a decimal, the decimal point of the quotient must be aligned with the decimal point of the dividend; if the divisor is a decimal, it must be divided into an integer and then calculated.

extended information

1

"Number", "number of digits", and "counting unit" are concepts with different meanings.

"Digit" refers to the position occupied by each digit of a number. Counting from the right end of the numerical sequence table, the first digit is the "ones digit", the second digit is the "tens digit", the third digit is the "hundreds digit", the fourth digit is the "thousands digit", and the fifth digit is the "ten thousand digit". bit", etc. The same number represents different values ​​due to different digits.For example, when using Arabic numerals to express numbers, the same '6' is placed in the tens place to represent 6 tens, placed in the hundreds place to represent 6 hundreds, placed in the billion place to represent 6 hundred million, and so on.

"Digits" refers to the number of digits contained in a natural number. A number like 458 consists of three digits, and each number occupies a digit. We call it a three-digit number. 198023456 consists of 9 digits, then it is a nine-digit number. "Digits" and "digits" should not be confused.

counting units: one (one), ten, one hundred, thousand, ten thousand, one hundred thousand, one million, ten million, billion, one billion, ten billion, one hundred billion..., they are all counting units. The counting unit in the "ones place" is "one (one)", the counting unit in the "tens place" is "ten", the counting unit in the "hundreds place" is "hundred", and the counting unit in the "thousands place" is The counting unit for "thousands" and "ten thousand" is "ten thousand", etc. So when reading, read the number first and then the counting unit.

2

Natural Number Knowledge Extension

The natural number set has addition and multiplication operations, and the addition of two natural numbers is or The result of multiplication is still a natural number, and subtraction or division can also be performed, but the results of subtraction and division are not necessarily all natural numbers, so the subtraction and division operations are not always valid in the set of natural numbers.

Natural numbers are all that people know. The most basic category of numbers. In order to give the number system a strict logical foundation, mathematicians in the 19th century established two equivalent theories of natural numbers: the ordinal theory of natural numbers and the cardinal number theory, which made the concepts, operations and operations of natural numbers possible. The relevant properties are strictly discussed. It must be an integer, a number used to measure the number of things or the order of things. That is, the number represented by the numbers 0, 1, 2, 3, 4, etc. It is called a natural number. The natural numbers start from 0 (including 0), one after another, forming an infinite group.

3

Other classifications of angles

Straight angles: angles equal to 180° are called straight angles

Excellent angles: greater than 180° and less than 360° are called excellent angles. Angle.

Minor angles: greater than 0° and less than 180° are called minor angles. Acute angles, right angles and obtuse angles are minor angles.

Circumferential angles: Angles equal to 360° are called minor angles.

Negative angles: rotated in a clockwise direction. The angle is called a negative angle.

Positive angle: An angle that rotates counterclockwise is a positive angle.

Supplementary angle and Supplementary angle : If the sum of two angles is 90°, the two angles are complementary to each other. Angle, if the sum of two angles is 180°, the two angles are supplementary angles. The supplementary angles of equal angles are equal, and the supplementary angles of equal angles are equal.

Vertex angles : The intersection of two straight lines has only one common vertex. The two sides of an angle are opposite extensions of each other. Such two angles are called opposite vertex angles. Two straight lines intersect to form two pairs of opposite vertex angles.

There are many other angles. The relationship between various angles, such as internal misaligned angles , homotopic angles , homologous internal angles (among three lines and eight angles, mainly used to judge parallelism)

4

Properties of parallel lines

(1) Two straight lines are parallel and homologous internal angles complementary.

(2) Two straight lines are parallel and their internal offset angles are equal.

(3) Two straight lines are parallel and have equal angles.

5

Judgment of parallel lines (in the same plane)

(1) The interior angles on the same side are complementary, and the two straight lines are parallel.

(2) The internal offset angles are equal and the two straight lines are parallel.

(3) The parallel angles are equal and the two straight lines are parallel.

(4) If two straight lines are parallel to a third straight line at the same time, then the two straight lines are parallel to each other.

(5) If two straight lines are perpendicular to a third straight line at the same time, then the two straight lines are parallel to each other.

6

Properties of vertical lines

(1) In the same plane, there is only one straight line perpendicular to the known straight line passing through a point.

(2) Among all the line segments connecting a point outside the straight line and each point on the straight line, the perpendicular line segment is the shortest. Simply put: the vertical line segment is the shortest.

(3) Distance from point to straight line: The length from a point outside the straight line to the perpendicular segment of this straight line is called the distance from point to straight line.