First, the law of addition:
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?
3. 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)
Second, the law of multiplication:
1, multiplication method of substitution: When two numbers are multiplied, the exchange factor position 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 by this number first, and then add up the products.
(a+b)×c=a×c+b×c (a—b)×c=a×c—b×c
Knowledge points of mathematical concepts
Integer part:
Decimal counting method; One (a), ten, one hundred, one thousand, ten thousand ... are all called counting units. Where "one" is the basic unit of counting. 10 1 Yes 10, 10 Yes 100 ... The forward speed between every two adjacent counting units is 10. This counting method is called decimal counting method.
How to read integers: read from the previous level, read the name of the level (100 million, 10 thousand), and don't read the zero at the end of each level. One or more zeros in other numbers read only one "zero".
How to write integers: write from the previous level, and write 0 if there is no unit.
Rounding method: Find the divisor and see what the digit with the highest mantissa is. If it is less than 5, it is rounded; If it is 5 or above, it will be rounded and the mantissa will be forward 1. This method of finding approximate value is called rounding.
Comparison of integer sizes: the number with more digits is larger, the number with the same digit is larger, and the number with the same digit is larger than the number with the second digit, and so on.
Decimal part:
Divide the integer 1 into 10, 100, 1000 ... such parts are one tenth, percentage, one thousandth ... These fractions can be expressed in decimals. For example, the record of110 is 0. 1, and the record of 7/ 100 is 0.07.
The first digit to the right of the decimal point is called the tenth digit, and the counting unit is one tenth (0. 1); The second digit is called percentile, and the counting unit is one percent (0. 0 1) ... The largest counting unit of the decimal part is one tenth, and there is no smallest counting unit. There are several figures in the decimal part, which are called several decimals. Such as 0. 36 is two decimal places, 3. 066 is a three-digit decimal.
Decimal reading: integer reading, decimal reading, sequential decimal reading.
Decimal writing: the decimal point is written in the lower right corner of the unit.
The essence of decimals: Add 0 at the end of decimals, and the size of 0 remains unchanged. simplify
The movement of decimal point position causes the change of size: it moves to the right and expands to the left, which is1.1230,000 times.
Decimal size comparison: if the integer part is big, it will be big; If the integers are the same, ten digits will be big; And so on.
Summary of Mathematical Geometry Formulas in Primary Schools
1, the perimeter of the rectangle = (length+width) × 2: c = (a+b) × 2.
2. The circumference of a square = side length × 4: c = 4a.
3. Area of rectangle = length × width: S=ab.
4. area of square = side length × side length: s = a.
5. Area of triangle = base × height ÷ 2: s = ah ÷ 2.
6. Area of parallelogram = base × height: S=ah.
7. Trapezoidal area = (upper bottom+lower bottom) × height ÷ 2: s = (a+b) h ÷ 2.
8. Diameter = radius × 2: d = 2r; Radius = diameter ÷ 2: r = d ÷ 2.
9. The circumference of a circle = pi× diameter = pi× radius× 2: c = π d = 2π r.
10, area of circle = pi × radius× radius: s=πr2.
Jiangsu education printing plate fourth grade second volume mathematics unit 7 knowledge points
1 and 1 in the statistical chart represent different units, so it is necessary to judge how many units 1 represents according to the specific situation. The amount of data is large, and each 1 grid represents more units, while the amount of data is small, and each 1 grid represents fewer units.
2. Understand the meaning of the data on the bar chart.
3. Make clear the characteristics of the bar graph: intuitive, convenient and easy to check.
4. Bar chart making method: determine the horizontal direction and mark the items; Determine the number represented by the vertical direction (the number represented by one grid); Draw straight lines with different lengths according to the size of the data; Write the title.
5. Get to know the composite bar chart, get information from it and answer the corresponding questions.
Broken line statistical chart
1, broken-line statistical chart: you can get the information of data changes and make simple predictions.
2. The method of broken-line statistical chart: on the grid paper, mark the points according to the given data, and then connect the points with lines in order.
3. Be able to see the information provided by the dotted statistical chart and answer related questions.
supplement
1. The difference between a bar chart and a line chart: a bar chart indicates the quantity with a straight line, and a line chart indicates the change of quantity with a broken line.
2. Have a preliminary understanding of the statistical chart of compound broken lines, and get the corresponding information from it to answer the questions raised.
What is the primary school mathematics cycle festival?
1, Introduction to Loop Section
After the decimal point of an infinite decimal point, a period of numbers that starts from a certain bit to the right and ends at a certain bit appears circularly, which is called cyclic decimal, and this period of numbers is called cyclic segment.
13÷99=0。 13 13…, this quotient is a cyclic decimal, and its cyclic segment is 13. In the second method, the cyclic part of the cyclic decimal can be determined by looking at the remainder, for example, 1 1÷9= 1. ..... 2, we can see through longitudinal calculation that the number 2 appears repeatedly and the quotient appears repeatedly, so the cycle segment is the quotient 2 obtained by the first appearance of the remainder 2, so we can determine the cycle segment by looking at the remainder.
2, the judgment of the cycle section
To judge whether a decimal is a cyclic decimal, the key is to judge whether the decimal is infinite first, and then to see if there are duplicates in the decimal part of the decimal. However, how to correctly judge the number of repetitions in the decimal part can be judged according to the following points.
Method 1: Determine according to the meaning of cyclic decimal. That is, according to "an infinite decimal, if its decimal part starts somewhere and is repeated by one or several numbers in turn, such a decimal is called a cyclic decimal." This meaning is used to determine the cyclic part of the cyclic decimal.
Method 2: By looking at the remainder, you can determine the cyclic part of the cyclic decimal. For example: 1 1÷9= 1. ……2。 Through longitudinal calculation, it can be seen that if the remainder "2" appears repeatedly, the quotient will also appear repeatedly, so the cyclic node is the quotient "2" obtained when the remainder "2" first appears.
Knowledge points in primary school mathematics field
(1) area and area unit:
1, find out the connection and difference between length unit and area unit;
2. Carefully examine the questions, and explicitly ask for it again.
(2) Calculation of rectangular and square areas:
1, squared: (a) perimeter = side length ×4- Use length units.
(b) Area = side length × side length-use area units.
2. Rectangle: (a) Perimeter = (length+width) × 2-Use the unit of length.
(b) Area = length× width-use area units.
(3) the forward speed between regional units
1, length unit: meter, decimeter, centimeter-forward speed is10; 1 m = 10 decimeter =100 cm =1000 mm.
2. Area unit: square centimeter, square decimeter and square meter-the propulsion rate is100;
1 m2 = 100 cm2, 1 cm2 = 1 0000 cm2,1m2 = 10000 cm2;
3. "hectares" (measuring the area of vegetable fields and orchards) and "square kilometers" (measuring the area of urban land) are larger units for measuring land;
4. Mass units: grams (g), kilograms (kg, also called kilograms) and tons (t). 1000g = 1 kg,1000kg = 1 ton.
5. When measuring distance or measuring relatively long objects such as railways and rivers, it is generally in kilometers, also called kilometers.
(4) The characteristics of each figure: the characteristics of a rectangle: the opposite sides are equal, and the four corners are right angles; The characteristics of a square: four sides are equal and four corners are right angles; Characteristics of parallelogram: two groups of opposite sides are parallel and equal.