99 multiplication formula table in the first grade of primary school. Learn basic addition, subtraction, multiplication and division.
In the second grade of primary school, I perfected the multiplication table, learned division and mixing operations, and learned basic geometric figures.
In the third grade of primary school, I learned multiplication and exchange law, geometric area and perimeter, time and unit. Distance calculation, distribution law, fractional decimal.
In the fourth grade of primary school, the natural number of line angle is an integer, the prime factor is trapezoidal symmetry, and the fractional decimal is calculated.
Fractional decimal multiplication and division in the fifth grade of primary school, algebraic equation and average value, comparative size transformation, graphic area and volume.
Proportional percentage probability of sixth grade in primary school, circular fan-shaped cylinder and cone.
Grade?One
Area of triangle = base × height ÷2. The formula S= a×h÷2.
Square area = side length × side length formula S= a×a
Area of rectangle = length× width Formula S= a×b
Additive commutative law: Two numbers are added to exchange addends and keep the same position.
2. Law of additive combination: When three numbers are added, the first two numbers are added first, or the last two numbers are added first, and then the third number is added, and the sum remains unchanged.
3. Multiplication and exchange law: when two numbers are multiplied, the position of the exchange factor remains unchanged.
4. Multiplication and association law: three numbers are multiplied, that is, the first two numbers are multiplied first, or the last two numbers are multiplied first, and then the third number is multiplied.
Second grade:
Appendix+Appendix = Sum
And-one addend = another addend
Negative-negative = difference
Negative difference = negative
Difference+Minus = Minus
Factor × factor = product
Product ÷ One factor = another factor
Dividend = quotient
Dividend = divisor
Quotient × Divider = Divider
Third grade:
The first unit division
Three digits divided by one digit:
1, where to divide from the high position, and where to write the quotient;
2. Divided by 100, the quotient is three digits; If the percentile is not enough, the quotient is two digits;
3. Which bit has a remainder, it is merged with the number on the next bit, and then divided;
4. Whoever is not quotient 1 is quotient 0; The remainder of each division is less than the divisor.
Division is tested by multiplication:
If there is no remainder, quotient × divisor = dividend.
If there is a remainder, quotient × divisor+remainder = dividend.
Divide 0 by any number other than 0 to get 0.
Solve the problem of two-step division: divide first or multiply first.
Divide two numbers = divide by the product of these two numbers.
Unit 2 Year, Month and Day
There are 12 months in a year.
3 1 day is a big month with seven big months:
January, March, May, July, August, October and December.
30 days is abortion, abortion has four times:
April, June, September and November.
February is 28 days in a normal year and 29 days in a leap year.
135780 wax, 3 1 day never goes bad.
There are 365 days in a normal year and 366 days in a leap year.
There are usually three normal years and 1 leap year every four years.
The Gregorian calendar year is a multiple of 4, usually a leap year;
The Gregorian calendar year is a whole hundred, and it must be a multiple of 400 to be considered as a leap year.
There are four quarters in a year.
1, February and March are the first quarter; April, May and June are the second quarter;
July, August and September are the third quarter; 10, 1 1, 65438+ February is the fourth quarter.
The first quarter is 90 days or 9 1 day; The second quarter is 9 1 day;
The third and fourth quarters are 92 days.
1 1 Women's Day on New Year's Day
May 1 Labor Day June 1 Children's Day
July 1 Party Birthday August 1 Army Day
September 10 Teacher's Day 65438+ 10/National Day
Unit 3 Translation and Rotation
Look at the translation map: find the direction and count the squares.
Draw a translation figure: find the direction, draw an arrow, determine the number of squares, and then draw the whole figure.
Unit 4 multiplication
Two digits multiplied by two digits:
First multiply the number in the unit and write the product of the unit;
Multiply by the number on the tenth place, and the product starts from the tenth place;
Finally, add up the two products.
There are three ways to estimate multiplication: who is bigger than who; Smaller than who; With whom?
Simple quantitative relationship: unit price × quantity = total price × speed × time = distance.
Unit 5 Observing Objects
Observing the same object from different angles, the shape you see may be the same or different;
When you look at different objects from the same angle, you may see the same shape or different shapes.
Unit 6 kilometers and tons
Measure the distance or length of railways, highways and rivers, usually in kilometers. Kilometers can be represented by the symbol "km".
Measure the weight of heavy or bulk goods, usually in tons. Tons can be represented by the symbol "t".
1km = 1000m 1t = 1000mg
Unit 7 Axisymmetric Graphics
A figure that can completely overlap after being folded in half is an axisymmetric figure.
The crease is the axis of symmetry.
Draw an axisymmetric figure: first determine the direction according to the axis of symmetry, then find the corresponding point, and finally draw the whole figure with connecting lines.
Unit 8 Cognitive Score
Take several objects as a whole and divide them into several parts on average, each part is a fraction of it and several parts are a fraction of it.
To calculate the fraction of a number, just divide it by the denominator and multiply it by the numerator.
Unit 9 area
Area is the size of the surface of an object, or the size of a plane figure.
Methods of comparing area size: observation method, overlapping method, measurement method and counting method.
Common area units are: square centimeter cm2, square decimeter dm2 and square meter m2.
A square with a side length of 1 cm and an area of1cm 2.
A square with a side length of 1 decimeter and an area of 1 square decimeter.
A square with a side length of 1 m and an area of 1 m2.
Area of rectangle = length× width S=a×b
Area of a square = side length × side length s = a× a.
The circumference of a rectangle = length× 2+width× 2 c = a× 2+b× 2.
Circumference of a square = side length ×4 C=a×4
Length of rectangle = width of area.
Width of rectangle = area ÷ length
Side length of a square = perimeter ÷4
1 m2 = 100 square decimeter 1 square decimeter = 100 square centimeter
1 m2 = 10000 cm2
When the perimeters are equal, the more square the figure is, the larger the area is.
Unit 10 Decimals
Divide 1 into 10 parts, each part is one tenth of it, that is, 0. 1.
Unit 11 Statistics
Two methods of finding the average: shifting more and supplementing less, adding first and then dividing.
Fourth grade:
Unit 1 Understanding of Large Numbers
1, 10 is ten thousand, 10 is one hundred thousand, 10 is one million, 10 is one million.
2 2. 10/010 million is one hundred million,1010 billion is one billion,1010 billion is ten billion,10100 billion is one hundred billion.
3. One, ten, hundred, ten thousand, one hundred thousand, one million, ten million, one hundred million, one billion ... are all units of counting.
According to our country's counting habit, every four digits are counted from the right.
Numeric sequence table
How many levels ... 100 million, 10 thousand.
Numbers ... billions, billions, billions, hundreds, thousands, hundreds, dozens.
Counting unit ... 100 billion billion billion billion billion.
5. The counting method with the ratio of 10 between every two adjacent counting units is called decimal counting method.
6. Reading, just add "10,000" or "100 million" at the end of each level; The zero at the end of each level is not read, and other numbers have a zero or several zeros, all of which read only a "zero".
7. When writing numbers, 10,000-level and 100-million-level numbers are written according to the method of each level, and any digit that is not enough will be filled with 0. To rewrite numbers in units of "10,000" or "100 million", just remove the four zeros or eight zeros at the end, or add the words "10,000" or "100 million". 1. Rewrite multiple numbers into "10,000" and "100 million". The middle is connected with "=".
8. Usually we use the method of "rounding" to omit the mantissa and find the divisor of a number.
The method is as follows: look at the digit with the highest mantissa, if it is 4 or less, discard the mantissa and add a counting unit "10000" or "1 100 million" at the end of the digit; If it is 5 or more, add 1 to the previous digit, then discard the mantissa and add the counting unit "10000" or "1 100 million". Get a rough figure, with a ""in the middle.
9.1,2, 3, 4, 5, 6, 7, 8, 9,10,1,... representing the number of objects are all natural numbers. An object is not represented by 0, and 0 is also a natural number. The smallest natural number is 0. There is no maximum natural number, and the number of natural numbers is infinite.
10. The computing tool invented by China in14th century and still used today is abacus. The upper bead of the abacus represents 5, and the lower bead represents 1.
1 1. On the calculator, the ON/C key is the switch and the screen clearing key, the CE key is the clearing key, and the AC key is the reset key. +,-,× and? Keys are operation symbol keys.
Measurement of the second unit angle
1. A straight line has no endpoints and can extend to both ends indefinitely, so its length cannot be measured.
2. The light has an endpoint, which can extend to one end indefinitely, and the length cannot be measured.
3. A line segment has two endpoints, and its length can be measured.
4. Extend one end of the line indefinitely, and you will get a ray. Extend both ends of the line indefinitely and you will get a straight line. Line segments and rays are both parts of a straight line.
You can draw countless straight lines and rays in a little bit. You can only draw a straight line after two o'clock.
6. A figure composed of two rays drawn from a point is called an angle. This point is angular (vertex) and these two rays are angular (edge). An angle is usually represented by a symbol ("∞").
7. The size of the angle has nothing to do with the length drawn on both sides of the angle. The angle depends on the size of the forks on both sides of the angle. The bigger the fork on both sides of the angle, the bigger the angle.
8. The measurement unit of angle is "degree", which is expressed by the symbol "degree".
9. The protractor divides the semicircle into 180 equal parts, and the angle of each part is 1 degree, which is recorded as "1 degree".
10, diagonally equal.
1 1, and the sum of the three angles of the triangle is 180 degrees. The sum of the four angles of a quadrilateral is 360 degrees.
12, right angle equals 90 degrees, right angle equals 180 degrees, and fillet equals 360 degrees.
13, 1 flat angle =2 right angles. 1 fillet = 2 right angle = 4 right angle.
14, the acute angle is less than 90 degrees. Obtuse angle greater than 90 degrees and less than 180 degrees;
15, acute angle
16, turn a large grid clockwise with a right angle of 30; When the minute hand turns once, the right angle is 360.
Unit 3 Multiply three numbers by two numbers
1. When three digits are multiplied by two digits, multiply three digits by two digits first, and then multiply three digits by ten digits of two digits. Finally, add up their products.
2. Multiply with 0 at the end of the factor: when writing vertically, align the numbers before 0 and multiply only the numbers before 0; There are several zeros at the end of the * * * of two factors, and several zeros are added at the end of the product.
3. If one factor remains the same, another factor will expand (or shrink) several times, and the product will also expand (or shrink) by the same multiple.
4. If one factor is expanded or reduced by several times and another factor is expanded or reduced by the same multiple, the product remains unchanged.
For example, one factor is enlarged by 2 times, and the other factor is reduced by 2 times, unchanged.
5. When one factor is multiplied, the other factor is multiplied and the product is multiplied. For example: 5×3= 15,
(5×2)×(3×2)= 15×4
6. Speed × time = distance/time = speed/distance/speed = time
Unit price × quantity = total price ÷ total price ÷ quantity = unit price ÷ total price ÷ unit price = quantity
Unit 4 Parallelogram and Trapezoid
1. Two straight lines that do not intersect in the same plane are called parallel lines, which can also be said to be parallel to each other.
2. If two straight lines intersect at right angles in the same plane, that is to say, two straight lines are perpendicular to each other, one of which is called the perpendicular of the other, and the intersection of the two straight lines is called the vertical foot.
3. If two straight lines are parallel to the third straight line, then these two straight lines are also (parallel to each other).
If two straight lines are perpendicular to the third straight line, then the two straight lines are also (parallel to each other).
5. The shortest (vertical line segment) drawn from a point outside the straight line is called the (distance) from the point to the straight line. The distance between parallel lines (equal everywhere).
6. Rectangular: the opposite sides are equal, the four corners are right angles, and the two groups of opposite sides are parallel respectively.
7. The circumference of a rectangle = (length+width) × 2; Area of rectangle = length × width;
8. Square: Four sides are equal, four corners are right angles, and two groups of opposite sides are parallel respectively.
9, the perimeter of the square = side length × 4; Area of a square = side length × side length.
10 Two groups of parallelograms with opposite sides are called parallelograms. Its characteristics are: the opposite sides are equal and the diagonal lines are equal. Two groups of opposite sides are parallel respectively.
1 1, a quadrilateral with only one set of parallel opposite sides is called a trapezoid. It is characterized in that only one group of opposite sides is parallel, and the other group is not parallel. Two parallel sides are called the bottom of the trapezoid, and the long side is called the bottom; Non-parallel edges are called waist; The distance between the two bases is called the height of the trapezoid.
12, square is a special rectangle; Rectangular and square are special parallelograms.
13, parallelogram is easy to deform and has the characteristics of instability.
14. Draw a vertical line from one point on one side of the parallelogram to the other. The line segment between this point and the vertical foot is called the height of the parallelogram, and the side where the vertical foot is located is called the bottom of the parallelogram.
15, isosceles trapezoid is called isosceles trapezoid. The two base angles of an isosceles trapezoid are equal.
16. Two identical trapezoids can be combined into a parallelogram.
17. Two identical triangles can be combined into a parallelogram.
18. Among the figures we studied, rectangle, square, isosceles trapezoid and rhombus are symmetrical figures.
19, a point beyond the straight line can only draw a vertical line of a known straight line;
20. Points outside a straight line can only draw a parallel line of a known straight line.
2 1、
The divide of unit 5 is that division of two digits.
1, division calculation rule: the divisor is the division of two digits. First, try to divide the first two digits of the dividend by the divisor. If the first two digits are not enough, try to divide the first three digits of the dividend, and the quotient will go to which place. The remainder of each divisor must be less than the divisor.
Divider is the division of two digits. Generally, the divisor is regarded as an integer close to it to try quotient. It should be reduced when the trial quotient is large, and increased when the trial quotient is small.
3. When three digits are divided by two digits, the quotient may be one digit or two digits.
4. Quotient invariance: In division, the dividend and divisor are multiplied by several (or divided by several) at the same time, and the quotient remains unchanged (except 0).
5. In division, the divisor is constant, the dividend is multiplied (or divided by several), and the quotient is also multiplied (or divided by several).
6. In division, the dividend is constant, the divisor is multiplied by several (or divided by several), and the quotient is divided by several (or multiplied by several).
7. The relationship of remainder division: dividend ÷ dividend = quotient ... remainder.
Dividend = quotient × divisor+remainder
Unit 6 Statistics
1. The meaning of the bar chart: the bar chart represents a certain amount with unit length, draws straight lines with different lengths according to the amount, and then arranges these straight lines in a certain order. The advantage of a bar chart is that it is easy to see the quantity.
2. Features of bar graph:?
(1) enables people to see the size of each data at a glance. ?
(2) Differences between data are relatively easy.
3. The statistics we have studied include horizontal statistics, vertical statistics, simple statistics and retest statistics.
4. Re-examination statistics are generally composed of drawing numbers, charts, titles and illustrations. The administrative professional ability test includes bar chart, fan chart, line chart and network chart.
Summary of knowledge points in the second volume of mathematics in the fourth grade of primary school in the new curriculum standard textbook of People's Education Press
(1) Four operations:
1, operation order: 1, in the formula without brackets, if there is only addition and subtraction or only multiplication and division, it should be calculated from left to right.
2. There are addition, subtraction, multiplication and division in the formula without brackets, so multiply and divide first, then add and subtract.
3. When there are brackets in the formula, the brackets should be calculated first.
2. Addition, subtraction, multiplication and division are called four operations.
3. Operate 0: 1, and add 0 to a number to get the original number.
2. Multiply any number by 0 to get 0.
3,0 cannot be divided. 0 divided by a nonzero number equals 0.
0÷0 can't get a fixed quotient; 5÷0 can't get the business.
(2) Location and direction:
1, according to the direction and distance to determine or draw the specific position of the object. (Drawing and measuring scale and angle)
2. Relativity between positions. The mutual positional relationship between two objects will be described. (Determination of observation points)
3. Draw a simple road map.
(3) Operation method and simple operation:
1, law of addition operation: 1, additive commutative law: two numbers are added, the addend positions are exchanged, and the sum is unchanged.
a+b=b+a
2, the law of addition and association: three numbers are added, you can add the first two numbers first, and then add the third number; Or add the last two numbers first, and then add the first number, and the sum remains the same. (a+b)+c=a+(b+c)
These two laws of addition are often used together.
For example:165+93+35 = 93+(165+35) What is the basis?
2. The essence of continuous subtraction: one number subtracts two numbers continuously, which is equal to the sum of this number MINUS those two numbers.
a-b-c=a-(b+c)
3. Law of Multiplication: 1, Law of Multiplication and Exchange: When two numbers are multiplied, the position of the exchange factor remains unchanged.
a × b = b × a
2. Multiplication and association law: When three numbers are multiplied, you can multiply the first two numbers and then the third number, or you can multiply the last two numbers and then the first number, and the product remains unchanged.
(a × b )× c = a × ( b × c)
These two multiplication laws are often used in combination.
Such as: 125×78×8.
3. Multiplication and distribution law: the sum of two numbers is multiplied by one number. You can multiply these two numbers with these two numbers first, and then add up the products. (a+b)×c=a×c+b×c
4. The nature of continuous division: one number divided by two numbers equals the product of these two numbers.
a ÷ b ÷ c = a ÷ ( b × c)
5. Simple calculation of expansion:
102×38-38×2 125×25×32 125×88 3.25+ 1.98 10.32- 1.98 37×96+37×3+37
Error-prone situation: 0.6+0.4-0.6+0.4 38×99+99.
(4) The meaning and nature of decimals:
Fractions with denominators of 1, 10, 100, 1000 ... can be expressed in decimals.
Decimal is another form of decimal.
3. Decimals are counted in tenths, hundredths and thousandths ... Write 0. 1, 0.0 1, 0.00 1 ...
4. The propulsion rate between every two adjacent counting units is 10.
5. Decimal reading and writing method: reading method: read the integer part according to the integer reading method, and the decimal part should read each number in order.
Writing: the integer part is written as an integer, and the integer part is 0, so write 0, and the decimal part writes each number in turn.
6. Properties of decimals: Add "0" or remove "0" at the end of decimals, and the size of decimals remains unchanged. Note: the "0" in the middle of the decimal cannot be removed, and some "0" at the end cannot be removed when approximating. Functions can be reduced to decimals, etc.
7. Decimal size comparison: compare the integer part first, the integer part is the same as the decimal part, and the decimal part is the same as the percentile. ...
8. Decimal size change law caused by decimal position movement:
Decimal point to the right: move one place, and the decimal point will be expanded to 10 times the original number;
Move two places, and the decimal will be expanded to 100 times of the original number;
Move three places, and the decimal will be expanded to 1000 times of the original number;
……
Decimal point moves to the left: move one place, and the decimal point is reduced by 10 times (the decimal point is reduced to the original number);
If you move two places, the decimal number will be reduced by 100 times.
If you move three digits, the decimal number will be reduced by 1000 times (the decimal number will be reduced to the original number);
……
9. Rewrite the name number: 1 ton, 30kg+800g = () ton.
Unit of length: kilometer ————————————————— decimeter ———————— centimeter.
Area unit: square kilometer-hectare-square meter-square decimeter-square centimeter.
Mass unit: ton-kilogram-gram
10, find the approximate number of decimal places (rounding): (Keep the expression with two decimal places, with the accuracy of 1%)
Keep an integer, indicating accuracy to one place, one decimal place, indicating accuracy to ten places, and two decimal places, indicating accuracy to one hundred places. When taking an approximation, the 0 after the decimal point cannot be removed.
Rewriting large numbers. Rewrite first, then find the approximate number. Note: bring your unit.
(5) Triangle:
1. Definition of triangle: A figure surrounded by three line segments (the endpoints of every two adjacent line segments are connected or overlapped) is called a triangle.
Draw a vertical line from the vertex of the triangle to its opposite side. The line segment between the vertex and the vertical foot is called the height of the triangle, and the opposite side is called the bottom of the triangle. Key point: the drawing method of triangle height.
3. Characteristics of triangle: 1. Physical characteristics: stable. Such as: tripod for bicycles, tripod on telephone poles.
2. Characteristics of sides: the sum of any two sides is greater than the third side.
4, the classification of triangle:
By angle: acute triangle, right triangle, obtuse triangle.
Divided by side length: triangle with unequal sides and isosceles triangle (equilateral triangle or regular triangle is a special isosceles triangle).
The three sides of an equilateral triangle are equal and each angle is 60 degrees. (The concepts of top angle, bottom angle, waist and bottom)
5. The sum of the internal angles of the triangle is equal to 180 degrees. Calculation and format of degree.
6. Combination of graphics: Two identical triangles can definitely be combined into a parallelogram.
7. Dense shop: The patterns that can be densely laid are rectangle, square, triangle and regular hexagon.
(6) Addition and subtraction of decimals:
1, calculation rule: align with the same digit (decimal point alignment). According to the integer calculation method, the decimal point of the obtained number should be aligned with the decimal point on the horizontal line. The result is that decimals should be simplified according to the nature of decimals.
2. Vertical calculation and check calculation. Pay attention to the horizontal answer, not the result of checking calculation.
3. The four operation sequences and algorithms of integers are also applicable to decimals. (Simplified calculation)
(7) Statistics:
Broken line statistical chart: a unit length is used to represent a certain quantity, points are drawn according to this quantity, and then the points are connected in turn by line segments.
Advantages: You can not only see the quantity, but also see the change of quantity, predict the future trend and provide guidance and help for future production and life.
(8) Mathematical wide angle: planting trees.
Number of intervals = total length ÷ interval length
Situation classification: 1, planting at both ends: number of plants = number of intervals+1.
2. Planting one head and not planting the other: number of plants = number of intervals.
3. No planting at both ends: number of plants = number of intervals-1.
4. Close: number of trees = number of intervals.