The first volume of grade three
Summary of knowledge points
1.MM: It is a unit of length and rainfall, abbreviated as mm in English.
1mm = 0. 1cm；
=0.0 1 decimeter;
= 0.00 1m；
=0.00000 1 km
2. centimeter: it is a unit of length measurement, equal to one hundredth of one meter. Unit of length, symbol: cm. ， 1cm = 1/ 100m。
1 cm = 10/0mm
=0. 1 decimeter
=0.0 1 m
=0.0000 1 km.
3. decimeter: it is one of the metric units of length, and 1 decimeter is equivalent to one tenth of 1 meter.
0.000 1 km = 1 decimeter
0. 1 meter (m) = 1 decimeter
10cm = 1 decimeter
100 mm = 1 decimeter
10 decimeter = 1 meter (meter)
0. 1 decimeter = 1 cm
0.0 1 decimeter = 1 millimeter (mm)
4. Kilometers: Kilometers, also called kilometers, are units of length and are usually used to measure the distance between two places. It is the international standard unit of length measurement, and the symbol is km.
1 km (km) = 1 0,000m (m) =100,000m (cm) = 1 0,000mm (mm)
5. Ton: mass unit. In the metric system, one ton is equal to 1000 kg.
6. Addition: one of the four basic operations, which refers to the calculation of combining two or more numbers and quantities into one number and quantity. The addition symbol is the plus sign (+). Connect items with a plus sign when adding. Put and after the equal sign (=). Example: If the sum of 1, 2 and 3 is 6, it is written as 1+2+3 = 6.
7. Add the name of each part.
"+"is a plus sign, the numbers before and after the plus sign are addends, "=" is an equal sign, and the numbers after the equal sign are sums.
100 (addend)+(plus sign) 300 (addend) = (equal sign) 400 (sum)
8. Additional nature
(1) additive commutative law: a+b = b+a.
(2) Additive associative law: a+b+c=a+(b+c)
9. subtraction: it is one of the four operations. The operation of subtracting one number or quantity from another is called subtraction.
Given the sum of two addends and one of them, the operation of finding the other addend is called subtraction.
10. the essence of subtraction: subtracting a number is equal to adding the reciprocal of this number.
1 1. Check calculation: After calculating the problem, do it again with inverse operations (such as subtraction, addition, subtraction, multiplication and division, multiplication) to check whether the results of the previous operations are correct.
12. The function of check calculation: check calculation can effectively detect errors in the calculation process, but it is not very useful for solving errors. By comparing the data obtained by checking calculation (using the results to derive conditions) with the original data, it is suggested whether the operation is correct.
13. quadrilateral: a closed three-dimensional figure surrounded by four line segments that are not on the same line is called quadrilateral. It consists of convex quadrilateral and concave quadrilateral.
14. Parallelogram: Two groups of parallelograms with opposite sides are called parallelograms.
15. Perimeter: The integral of the perimeter of the edge of a finite area is called perimeter, and the length of the graph is the perimeter of the graph. Therefore, the perimeter is equal to the sum of all the edges of the graph.
16. estimate: roughly infer the nature, quantity and change of things according to the situation.
17. Remainder: In the division of integers, there are only two situations: divisible and non-divisible. When it is not divisible, a remainder is generated, and the remainder operation is: 1 It refers to the undivided part of the dividend in integer division.
For example, if 27 is divided by 6, the quotient is 4 and the remainder is 3.
18. Properties of remainder: The remainder has the following important properties (A, B and C are all natural numbers):
(1) The remainder is less than the divisor.
(2) Dividend = divisor × quotient+remainder;
Divider = (dividend-remainder) ÷ quotient;
Quotient = (dividend-remainder) divider;
Remainder = dividend-divisor × quotient.
19.second: Time unit Time unit second is the basic unit of time in the international system of units, and the symbol is S.
20. Minute: Time unit, equal to 1/60 hours or 60 seconds.
2 1. multiplication: refers to a shortcut to add the same numbers. The result of the operation is called product.
22. The name of each number in the multiplication formula
"×" is a multiplication sign, the numbers before and after the multiplication sign are called factors, "=" is an equal sign, and the numbers after the equal sign are called products.
10 (factor) × (symbol) 200 (factor) = (symbol) 2000 (product)
23. Score:
Divide the unit "1" into several parts on average, and the number representing such a part or parts is called a fraction. The number representing this share is called the fractional unit.
The numerator is above the denominator, which can also be regarded as division. The numerator is divided by the denominator, and the opposite multiplication can also be expressed as a fraction.
24. Fraction line, numerator and denominator
The horizontal line in the middle of the score is called fractional line, the number above the fractional line is called numerator, and the number below the fractional line is called denominator. Read it as a score.
Fractions can be expressed by the division formula: for example, half equals 1 divided by 2. Where 1 numerator is equal to dividend,-fractional line is equal to divisor, denominator of 2 is equal to divisor, and 0.5 fractional value is equal to quotient.
25. Source of scores
Fractions have a long history in China, and the original forms of fractions are different from the present ones. Later, India appeared a score representative similar to China's. Later, the Arabs invented the fractional line, and the expression of the score became like this.
More than 200 years ago, the Swiss mathematician Euler said in his book General Arithmetic that it is impossible to divide a 7-meter-long rope into three equal parts because there is no suitable number to represent it. If we divide it into three equal parts, each part is 7/3 meters. Like 7/3 is a new number, which we call a fraction.
26. Possibility: Possibility refers to the probability of things happening, which is a quantitative indicator contained in things and indicates the development trend of things.
The second volume of grade three
Summary of knowledge points
1. location: the place where it is located or occupied.
2. Direction: refers to the east, west, south, north and other directions.
3. Division: The operation of finding another factor by knowing the product of two factors and one of them is called division.
If ab=c(b≠0), the operation of finding another factor A by multiplying the product C and the factor B is division, written as c/b, and read as C divided by B (or B divided by C). Among them, c is called dividend, b is called divisor, and the result of a operation is called quotient.
4. Division rule: How many digits is the divisor? Look at the first few digits of the divisor first. If the first few digits are not divided enough, look at another one. The quotient is written except one, which is not enough to quotient one and zero. The remainder is less than the divisor. If the quotient is decimal, the decimal point of the quotient should be aligned with that of the dividend. If the divisor is a decimal, it must be divided into integers and then calculated.
5. Quotient invariance: The divisor and divisor are multiplied or divided by a non-zero natural number at the same time, and the quotient remains unchanged.
6. The essence of division: a number divided by several numbers equals the product of this number divided by those numbers, which is the essence of division. Sometimes simple operations can be performed according to the nature of the division. Such as: 300÷25÷4=300÷(25×4).
7. The relationship between dividend, divisor and quotient:
Dividend is enlarged (reduced) by n times, and quotient is correspondingly enlarged (reduced) by n times.
The divisor is expanded (reduced) by n times, and the quotient is correspondingly reduced (expanded) by n times.
8. Pen division: First, according to the law of integer division, the decimal point of quotient should be aligned with the decimal point of dividend; If there is a remainder at the end of the dividend, add "0" after the remainder to continue the division.
9. Division calculation rules with divisor as decimal: first move the decimal point of divisor to make it an integer, then move the decimal point of divisor to the right by a few digits (add "0" if there are not enough digits), and then calculate according to the division rules with divisor as integer.
10. Mixed operation without brackets:
Operations at the same level are operated from left to right in turn; Two-stage operation calculates multiplication and division first, and then addition and subtraction.
1 1. First-level operation: addition and subtraction are called first-level operations.
12. Secondary operations: multiplication and division are called secondary operations.
13. Data: Data, also known as observed values, is the result of experiments, measurements, observations and investigations. , and often given in quantitative form.
14. data analysis: data analysis is a process in which an organization collects and analyzes data purposefully and makes it into information.
15. Steps and application of data analysis:
Data analysis is widely used. Typical data analysis may include the following three steps:
(1) Exploratory data analysis. When the data is first obtained, it may be chaotic and irregular. By means of drawing, tabulating, fitting various equations and calculating some characteristic quantities, the possible forms of regularity are explored, that is, from what direction and how to discover and reveal the regularity implied in the data.
(2) Model selection analysis, which puts forward one or several possible models on the basis of exploratory analysis, and then selects a certain model from them through further analysis.
(3) Inference analysis, usually using mathematical statistics to infer the reliability and accuracy of a given model or estimate.
16. Average
The average value refers to the sum of all data in a set of data divided by the number of data. The average value is a quantity representing the trend of a set of data sets and an index reflecting the trend of data sets.
The key to solve the problem of average application is to determine the "total amount" and the total number of copies corresponding to the total amount.
In statistical work, mean and standard deviation are the two most important measures to describe the trend and deviation of data sets.
17. 24-hour timing method
(1) Time division method (12 point method): A day starts at midnight 12, and the 24 hours of 1 day are divided into two sections, each of which is 12 hours. From 12 midnight to 12 noon is called the morning, and from 12 noon to 12 midnight is called the afternoon. This timing method is often used in life.
(2) 24-hour timing method: This is the 0-24-hour timing method adopted by radio stations, stations, post offices and other departments. According to this timing method, 1 pm is 13: 00, 2 pm is 14: 00... 12 pm is 24: 00.
18. Number names in the multiplication formula
"×" is a multiplication sign, the numbers before and after the multiplication sign are called factors, "=" is an equal sign, and the numbers after the equal sign are called products.
10 (factor) × (symbol) 200 (factor) = (symbol) 2000 (product)
19. Multiplication algorithm
Integer multiplication meets the following requirements: exchange law, association law, distribution law and elimination law.
With the development of mathematics, the object of operation has developed from integer to more general group.
Intra-group multiplication is no longer needed to satisfy the commutative law. The most famous noncommutative example is the quaternion group discovered by Hamilton. But the law of association is still satisfied.
(1) Multiplication commutation law: a× b = b× a.
(2) multiplicative associative law: (a×b)×c=a×(b×c)
(3) Multiplicative distribution law: (a+b) × c = a× c+b× c.
20. multiplication table
2 1. area: the size of the surface shape of objects is called their area.
22. The common units of area are square centimeter, square decimeter and square meter.
(1) A square with a side length of 1 cm and an area of1cm 2.
(2) A square with a side length of 1 decimeter and an area of 1 square decimeter.
(3) A square with a side length of 1m and an area of 1m2.
23. Large areas are generally measured in hectares and square kilometers.
(1) Square with side length 1 00m and area1hectare.
(2) Square with side length 1km and area 1km2.
24. Area calculation method
Rectangular: S=ab{ rectangular area = length × width}
Square: S=a2{ square area = side length × side length}
Parallelogram: S=ab{ parallelogram area = base × height}
Triangle: S=ab÷2{ triangle area = base × height ÷2}
Trapezoid: S=(a+b)×h÷2{ Trapezoid area = (upper bottom+lower bottom) × height ÷2}
Circle (perfect circle): S=πr2{ area of circle (perfect circle) = pi × radius}
25. Area measurement unit and ratio:
1 square kilometer = 100 hectare 1 square kilometer =10 million square meters.
1 ha = 1 0000m21m2 = 100 square decimeter (dm2)
1 square decimeter = 100 square centimeter (cm2).
26. hectare: the unit symbol of hectare is "hm2", where H stands for 1 00m, and hm2 stands for the square of100m, i.e.10000m2, i.e.1hectare.
27. Decimal: Decimal consists of integer part, decimal part and decimal point. When measuring an object, it is often not an integer, so the ancients invented decimals to supplement integer decimals, which is a special form of fractional fractions. Fractions with denominators of 10, 100, 1000 ... can be expressed in decimals. All fractions can be expressed as decimals, except infinite acyclic decimals, all decimals can express the number of components.
28. Basic properties of decimals: Add or remove 0 at the end of decimals, the size of decimals remains unchanged, but the counting unit has changed. Moreover, if the decimal point is moved one, two or three places to the left, the original number will be reduced by 10 times, 100 times and 1000 times; if the decimal point is moved one, two or three places to the right, the original number will be expanded by 10 times and 100 times.
29. Decimal writing: the integer part is written before the decimal point, the decimal part is written after the decimal point, and the middle is separated by the decimal point.
30. Decimal reading:
(1) Read by fraction. Read with integers with decimals. The fractional part is read by the fraction.
For example, 0.38 is pronounced as 38%, and 14.56 is pronounced as 14 and 56%.
(2) The integer part is still read as an integer, the decimal point is read as a "dot", and the decimal part reads the numbers on each digit in sequence. If there are several zeros repeated, you should not read only one zero.
For example: 0.45 is read as 0.45; 56.032 is read as 56.032; 1.0005 is pronounced one point zero five.