Seeking all concepts of primary school mathematics Elementary school mathematics 3 ~ 6 grade concept ～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～

Seeking all concepts of primary school mathematics Elementary school mathematics 3 ~ 6 grade concept ～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～

Primary school mathematics knowledge points
1、 Significance
1. Meaning: the collected materials are sorted out and filled in a certain format of the form, which can be used to reverse
Reflect the situation and explain the problem
Statistical table 2, type: 1, single form
(2) duplex
1. Significance: to express the quantitative relationship in statistical data with graphics, so as to make it specific and give people a good impression
impressive
Statistical chart
(1) bar chart: it's easy to see the number of various quantities: simple and compound
2. Type: 2. Broken line statistical chart: it can clearly show the change of quantity: simple and compound
(3) sector statistical chart: it can clearly show the relationship between the number of each part and the total number
2、 Number
1. Network diagram of decimals:
Pure decimal and finite decimal
Infinitely non circulant decimal
Infinite decimals with decimals pure cyclic decimals
Infinite circular decimal
Mixed cycle decimal
2. Integer:
Multiple common multiple least common multiple: the common multiple of several numbers is called the common multiple of these numbers
Multiples, the smallest of which is called these numbers
The least common multiple of integral division
Divisor common divisor greatest common divisor: the divisor of several common divisors is called the common divisor of these numbers
Divisors, the largest of which is called these numbers
The greatest common divisor of
Prime number composite coprime number
Prime factorization
Characteristics of numbers divisible by 2.3.5
3. Coprime number: concept: two numbers with only one common divisor
(1) some coprime (1, 1 and any natural number; 2) two adjacent natural numbers; 3;
Coprime numbers (3, two different prime numbers)
(2) not necessarily coprime (1. A prime number and a composite number; 2. Two different composite numbers)
Prime: a number is called a prime if it has only one and its two divisors
Composite number: a number, if there are other divisors besides 1 and itself, is called composite number
The number of divisors of a number is finite, in which the smallest divisor is 1 and the largest divisor is itself; the number of multiples of a number is infinite, in which the smallest multiple is itself. The smallest multiple of a number is equal to its largest divisor
The quotient obtained by dividing an integer a by an integer B (B ≠ 0) is exactly an integer without remainder. We say that a can be divided by B (B ≠ 0), or B (B ≠ 0) can divide A. This is the most basic concept in the knowledge of integral division
Natural number can be divided into odd number and even number according to whether it can be divided by 2
Natural number is divided into 0, 1, prime number and composite number according to the number of divisors
Natural numbers are divided by divisors. 0 has infinite divisors divided by all natural numbers except 0
rewrite
The parent is 101001000 I'll give you a fraction, and then I'll give you a fraction
Fractional fraction
Remove the numerator with denominator
Move the decimal point two places to the right and add%
Write it as a fraction and reduce it
Remove% and write decimal point first
Move two digits to the left. Write it as a percentage
percentage
For the convenience of reading and writing, a large multi digit number is often rewritten as a number with "ten thousand" or "hundred million" as the unit. Sometimes, it can be written as an approximate number by omitting the mantissa after a bit of the number
4. Comparison
Fraction: if the denominator is the same, the fraction with larger numerator will be larger; if the numerator is the same, the fraction with smaller denominator will be larger; if the numerator and denominator are not the same, the fraction will be divided before comparison
Number comparison integers: first, look at the number on a bit. If the number on a bit is larger, it will be larger. If the number on a bit is the same, the number on a bit will be larger. If the number on a bit is the same, the number on a hundred bit will be larger
Decimals: compare the size of two decimals. First, look at their integral parts. If the integral part is larger, the number will be larger, and the integer part will be smaller. If the integral part is the same, the number with the larger decimals will be larger. If the decimals are the same, the number with the larger percentiles will be larger
5. Digital
Integral part decimal point decimal part
… … One hundred million, one hundred thousand
Digital Hundreds of billions, tens of billions, billions
Ten million, one million, one hundred thousand, ten thousand
Wei Qian
A hundred
be located
One
position
．
Decile, percentile, thousandth
Counting unit thousand
Hundred million
One billion one hundred and eleven
Integers and decimals are numbers written according to the decimal counting method, among which one, ten, hundred And one tenth, one percent They are all counting units. The positions occupied by each counting unit are called digits. The digits are arranged in a certain order
Digit: when writing numbers, arrange each calculation unit in a certain position according to a certain order. The position occupied by each different counting unit is called digit
Digit: the number of digits in an integer is called digit
6. Significance
Natural number: when we count objects, 1,2,3 It's called natural number. There's no object. It's represented by 0. 0 is also natural number. Natural numbers are integers
Fraction: divide the unit "1" into several parts averagely. The number indicating such a part or parts is called fraction. The number indicating one part is the fractional unit of the fraction
If two integers are divided, their quotient can be expressed as a fraction, i.e. a △ B = A / b (B ≠ 0)
Decimal: divide the integer "1" into 10 parts, 100 parts, 1000 parts Such a portion or portions is a few tenths, a few percent, a few thousandths It can be expressed as a decimal. For example, 0.1 is a decimal
Finite decimal: the decimal part of the number of digits is limited, it is called finite decimal
Circular decimal: a decimal, from a certain place of the decimal part, a number or several numbers repeatedly appear in turn. This kind of decimal is called circular decimal. The number of digits of the decimal part is infinite, which is called infinite decimal. Circular decimal is infinite decimal
Supplement (1) four operations: in an expression without brackets, if it contains the same level of operation, it should be calculated from left to right; if it contains two levels of operation, it should first do the second level operation, and then do the first level operation. If in an expression with brackets, it should first calculate the operation in the small bracket, and then calculate the operation in the bracket
Note: when calculating, we should carefully examine the topic, see the characteristics of operation symbols and numbers, and flexibly choose reasonable calculation methods
3、 Four operations
(1) Four operations
Range of numbers
Operational significance
Name integer decimal fraction letter representation
Addition (first level operation) the operation of combining two numbers into one. It has the same meaning as integer addition. It has the same meaning as integer addition. A + B = C
Subtraction (first order operation) the operation of finding the sum of two numbers and one of the addends. It has the same meaning as the subtraction of integers. It has the same meaning as the subtraction of integers. C-B = a
Multiplication (secondary operation) is a simple operation for finding the sum of several identical addends. Multiplying a number by a decimal can be regarded as finding the number of tenths, percentages The multiplication of a number by a fraction can be regarded as finding the fraction of the number. A × B = C
Division (two-level operation) the product of two numbers and one of the factors are known. The operation of finding the other factor has the same meaning as integer division and integer division. C △ B = a
Subtraction is the inverse operation of addition; division is the inverse operation of multiplication; multiplication is the simple operation of addition with the same number; division is the simple operation of subtraction with the same number
It can be divided into four kinds: ①, the same level ②, two levels ③, with brackets ④, simple calculation
(2) Operation law and simple algorithm
Additive commutative law: a + B = B + a additive associative law: a + B + C = a + (B + C)
Quick calculation of addition and subtraction: A-B = a-c-d, a + B = a + C + D
The nature of subtraction: a-b-c = a - (B + C) commutative law of multiplication: a × B = B × a
Multiplication combination law: a × B × C = a × (B × C) multiplication distribution law: (a + b) × C = a × C + B × C
The property of product invariance: ab = (a × C) × (B △ C) the property of division: a △ B △ C = a △ B × C
The properties of quotient invariance: a △ B = (a △ C) / (B △ C), a △ B = (a × C) / (B × C)
4、 Equation
Equation: an equation containing unknowns is called an equation
Algebra: 1. Using letters to express numbers can concisely express quantity relations, operation laws and calculation formulas
2. Multiply the number by the letter, omit the multiplication sign, and write the number before the letter. (e.g. 1A = a × 1)
3. When a letter is multiplied by a letter, the multiplication sign can be omitted, or it can be abbreviated as multiplication sign (e.g. a × B = AB = A.B)
4. The multiplication sign cannot be omitted for numbers and numbers
The solution of the equation is the value of the number of knowledge which makes the left and right sides of the equation equal
The process of solving an equation is called solving an equation. It's just a process
When n is any natural number, 2n is even because it can be divided by 2. 2n + 1 is odd
The equation is not proportion, proportion is equation
5、 Practical questions
1. Simple application questions
The basic applied problems in primary school mathematics are simple applied problems, and all kinds of applied problems are synthesized on the basis of simple applied problems
2. Compound problem
General application problem solving steps (as follows)
(1) (2) analysis of quantitative relationship (key) (3) formula calculation (key)
(4) Checking calculation (guarantee of correctness) (5) write answers (complete must)
There are four types of simple application questions: 1. The relationship between total number and part number. 2. The relationship between large number, decimal number and difference number. 3. The relationship between one multiple, several multiples and multiple. 4. The relationship between total number, number of copies and each number. 11 kinds of simple application questions: 1. The relationship between total number and part number. 2. The relationship between large number, decimal number and difference number. 3. The relationship between multiple number and multiple number (9) a number is several times of another number. (10) find out how many times a number is. (11) know the fraction of a number and another number, and find the number
6、 The relation of ratio, fraction and division
Antecedent -- numerator -- divisor ratio sign -- fraction line -- division sign
Last term denominator divisor ratio fractional value quotient
Ratio is the multiple relationship between two numbers. Fraction is a number. Division is an operation
7、 Ratio, proportion
The division of two numbers is also called the ratio of two numbers. The formula of equal ratio is called proportion
The basic properties of ratio: the first and second terms of ratio are multiplied by or divided by the same number (except 0), and the ratio remains unchanged
The basic property of proportion: in proportion, the product of two inner terms equals the product of two outer terms
The difference between calculating ratio and reducing ratio: calculating ratio is a quotient; reducing ratio is a ratio, the former and the latter are integers
Positive proportion: two related quantities, one of which changes, and the other changes with it. If the ratio (quotient) of the two numbers corresponding to the two quantities is fixed, the two quantities are called positive proportion quantities, and their relationship is called positive proportion relations. Y / x = K (fixed)
Inverse proportion: two related quantities, one of which changes, and the other changes with it. If the product of the two numbers corresponding to the two quantities is fixed, the two quantities are called inverse proportion quantities, and their relationship is called inverse proportion relations. X × y = K (fixed)
The same point of positive and negative proportion: there are three kinds of quantity, two of which are related quantity, and the other is a certain quantity. One quantity changes, and the other changes with it
8、 The difference between equation solution and arithmetic solution
The solution of equation is forward thinking, which regards the quantity of knowledge as its own quantity. The arithmetic solution is backward thinking
1. Score application questions
Comparative quantity / standard quantity =? /? Or?% (percentage)
The quantity of "1" x the corresponding fraction of the quantity sought = the quantity sought
Known quantity of equation