The induction of mathematics knowledge points in the first volume of the fourth grade of primary school in 2020 1
Unit 1 Understanding of Large Numbers
1. Counting unit: one, ten, one hundred, thousand, ten thousand, one hundred thousand, one million, ten million, one hundred million ... are all counting units.
2. Number of digits: single digit, ten digit, hundred digit, ... billion digit, etc. , are all numbers. A digital name is to add a "bit" after the corresponding counting unit, for example, 10 thousand? Ten thousand people.
3. Series: unit level, million level, billion level ... are all digital levels, and a digital level includes four numbers. Each level includes level 1, level 10, level 100 and level 1000; The 10,000 level includes 10,000, 100,000, 1 million and 10 million; Billion includes billion, billion, billion, billion.
4. Number sequence table: A table containing several levels, numbers and corresponding counting units is called a number sequence table.
5. The advance rate between every two adjacent counting units is "10".
10 ten thousand is one hundred thousand, 10 ten thousand is one million, 10 one million is ten million, 10 ten million is one hundred million.
6. Digital representation: the number on a number represents several counting units of this number.
For example, 2 in 12367 is in thousands, which means "2 thousand".
Numbers in an order of magnitude represent several counting units in this order of magnitude.
For example, 3647 in 36472845 is "36.47 million" on the scale of ten thousand.
7. How to read large numbers: you can score first and then read. (1) contains two levels of reading: first read ten thousand levels, and then read one level; (2) Three-level reading method: read 100 million levels first, then 10,000 levels, and finally read one level. No matter how many zeros are at the end of each level, don't read them; There is a 0 in the middle and in front of each level, or several zeros in succession, all of which are read-only.
8. How to write large numbers: You can score first and then write numbers. (1) contains two series of writing methods: write 10,000 levels first, and then write one level; (2) Three-level writing method: write 100 million levels first, then 10,000 levels, and finally write one level. Where there is no previous counting unit, write 0 on it.
9. Test method of reading and writing numbers: The reading and writing numbers can be checked with each other, that is, after reading, they can be written and compared with the original numbers, and then they can be read by themselves.
10, compare the size of numbers within 100 million: when the number of digits is different, the number with more digits is larger; When the number of digits is the same, compared with the highest digit, the number on the highest digit is large, and this number is large; If the digits on the highest bit are the same, compare the next bit until the size comparison is completed.
1 1, and the numbers are rewritten into different counting units:
(1) Integer number of ten thousand and hundreds of millions: rewrite four zeros of a level as "ten thousand" and eight zeros of a level as "hundreds of millions".
Note: The rewriting of integers of ten thousand and one billion is an exact number, and it should be connected with "=".
(2) Rewriting a non-integer into a number with the unit of "ten thousand": take the number after ten thousand digits as the mantissa, round the highest digit (thousand digits) of the mantissa, and then rewrite it into a number with the unit of "ten thousand".
(3) Rewriting a non-integer into a number with the unit of "100 million": take the number after 100 million digits as the mantissa, round the highest digit (10 million digits) of the mantissa, and then rewrite it into a number with the unit of "100 million".
12. Omitted mantissa (divisor): first grade, then look at the number in the highest ellipsis, and round or round off. When omitting the mantissa after 100 million digits, we should look at tens of millions, and when omitting the mantissa after 10 thousand digits, we should look at thousands. (indicated by "≈") 0 ~ 4 means "give up", the mantissa is cleared with the exact digits unchanged, 5~9 means "enter", and the mantissa is cleared with the exact digits plus 1. Note: the result after rounding is approximate, so the symbol must be "≈";
The difference between exact number and divisor;
(1) In practical problems, some data are exact figures that are completely in line with reality. There are 44 boys and 29 girls in Class A, Class 4 .. The "44" and "29" here are accurate figures.
(2) There are still some data, which are only approximate figures that are generally in line with the actual situation. When we measure the length and mass of an object, due to the limitation of measuring tools, errors will inevitably occur, and the results obtained are approximate. Xiao Ming is 140 cm tall and weighs 35 kg. "140" and "35" here are approximate numbers.
(3) When counting a large number, it is generally only necessary to express it by its divisor. Generally speaking, there are 500,000 people in a city, and a steel plant produced1.20,000 tons of steel last year. "500,000" and "1.20,000" here are approximate figures.
"Rounding" method: 4, 3, 2, 1, 0 is rounded; 5, 6, 7, 8, 9 are discarded and moved forward to 1.
The difference between "=" and "material":
7580000 = 75808000 ≈ 75 10000
90000000000 = 9 billion 9420000000 ≈ 9.4 billion
12, natural number: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,1,... The number of objects is a natural number. There is no object, which is 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.
13, decimal counting method: the rate of advance between every two adjacent counting units is ten, which is called decimal counting method.
14, Understanding of Computing Tools:
In ancient times, it was counted by "physical objects", "knotting ropes" and "carving roads".
(1) abacus:14th century, China invented the abacus. The abacus has an upper gear and a lower gear, each bead in the upper gear represents 5, each bead in the lower gear represents 1, and each rod is equivalent to a number, for example, "a bead on the 10,000 bit" represents "five tens of thousands".
(2) Calculator: CE or AC is the "clear key" and ON/C is the "switch and clear screen key". Close is the close key.
15, can use a calculator to calculate and explore the law.
2020 Elementary School Grade Four Volume I Mathematical Knowledge Points Induction II
Unit 2 hectares and square kilometers
When surveying a large area of land, "hectare" and "square kilometer (km2)" are often used as units.
1 ha = 1 0000m2 1 km2 =100ha1km2 =100000m2.
Measurement of the third unit angle
1. line segment: a part of a straight line with two endpoints, whose length can be measured and cannot be extended.
2. Ray: It is a part of a straight line with only 1 endpoints, which can extend to one end indefinitely and cannot be measured.
3. Straight line: there is no end point (or "there are zero end points"), which can extend to both ends indefinitely and cannot be measured.
4. Angle: A figure composed of two rays drawn from a point is called an angle. This point is called the "vertex" of the angle, and the two rays are called the two "edges" of the angle. The sign of the angle is "∞".
5. Number of straight lines drawn by points:
A little bit can draw countless rays and countless straight lines.
Because "two points can determine a straight line", you can only draw a straight line after two points.
6. Angle measurement: The tool is a protractor.
The unit of measurement of an angle is "degree", which is represented by the symbol "degree". Divide the semicircle into 180 equal parts, and the angle of each part is 1 degree, and record it as 1 degree.
Step: (1) The center point of the protractor coincides with the vertex of the angle.
(2) The 0-degree scale line (one of protractors) coincides with one side (of the angle)
(3) The scale on the protractor corresponding to the other side of the angle is the degree of this angle.
7. Comparison of angle size: The angle size has nothing to do with the length of both sides of the angle. The size of the angle depends on the size of both sides. The bigger the opening, the bigger the angle.
8. Find the complementary angle, complementary angle and antipodal angle of the known angle:
As shown on the right, if ∠ 3 = 25, ∠ 4 = 90-25 = 65.
If ∠ 1 = 25, ∠ 2 = 180-25 = 155.
If ∠1= 25, ∠ 3 = ∠1= 25 (the top angles are equal).
9. Classification of angles:
(1) acute angle
(2) 1 right angle =2 right angles; 1 fillet =2 right angles =4 right angles.
10, clock face time problem (find the angle between the hour hand and the minute hand): Because the fillet is 360, and there are 12 hour scales on the clock face, the angle between every two hour scales is 360 ÷12 = 30.
1 1. Method of drawing corners:
A, draw an angle with a protractor (for example, draw an angle of 65).
(1) Draw a ray as the vertex and edge of the angle.
(2) Make the center of the protractor coincide with the endpoint of the ray, and the zero scale line coincides with the ray.
(3) Point a point on the 65-degree scale line of the protractor (in the same circle as the 0-degree scale line).
(4) Take the endpoint of the drawn ray as the endpoint and draw another ray through the point just drawn (because "two points determine a straight line", the endpoint and the point just drawn are used to determine the position of the other side)
(5) Draw a small arc and mark it.
B draw an angle with a triangle (for example, draw an angle of 75).
The method of drawing an angle is the same as using a protractor, but the marking method is different. You need to mark which angles on the triangle are combined (added or subtracted).
All angles that are multiples of 15 can be drawn by a triangle, such as 75, 105, 120, 135, 150, 165.
The angles of 75, 105, 120, 135 and 150 can be "spelled" with "one set (two sets) of triangles".
2020 Elementary School Grade Four Volume I Mathematical Knowledge Points Induction 3
Unit 4 Multiply three numbers by two numbers
1 and two digits multiplied by one digit: (for example, 16×3) Divide 16 into 10 and 6, first calculate 10×3=30, and then calculate 6× 3 =/kloc-0.
2. Oral calculation of three digits (with zeros at the end) multiplied by one digit: (for example, 160×3) Take the last part of zero as 16×3, and make oral calculation 48, then add all removed zeros at the end of the obtained number, with 1 zeros at the end.
3, pen multiplication:
First, multiply the three digits by the number on the two digits, and the last digit of the number is aligned with the single digit of the two digits; Then multiply the three digits by the number on the ten digits of the two digits, and the last digit of the number is aligned with the ten digits of the two digits; Finally, add the products of the two multiplications.
Such as145×12 =17404, with 0 at the end:
(1) Align the numbers before 0 and multiply them first.
(2) Look at how many zeros are at the end of the factor, and add a few zeros at the end of the product.
Such as 160×30=4800.
5. Multiply with the 0 in the middle of the factor: Note that when three digits are multiplied with two digits, the 0 in the middle of the three digits should also be multiplied. Don't forget to add the numbers that appear.
Such as 105×30=3 150.
6. Law of product change and law of product invariance:
Multiply two numbers, one of which is a constant, the other is multiplied (or divided) by several (except 0), and the product is also multiplied (or divided) by several.
Multiply two numbers, where one factor is multiplied by several (except 0) and the other factor is divided by several (except 0), and the product remains unchanged.
7. Multiplication estimation:
First of all, we should pay attention to conform to the actual situation and approach the accurate value. 2 15×58≈ 12000
The second is to "round" one or two factors into similar integers of 10 and 100 to simplify the calculation.
8, multiplication calculation method:
Multiply the position of the exchange factor again to see if the multiplied product is the same as the original product.
9. Common quantitative relations:
Unit price × quantity = total price; Total price ÷ quantity = unit price; Total price/unit price = quantity
Unit price unit: yuan/quantity unit (compound unit)
Each 28 yuan is represented as 28 yuan/Ben, and each 5 yuan is represented as 5 yuan/Ben.
Speed × time = distance; Distance ÷ time = speed; Distance/speed = time;
Speed unit: distance unit/time unit (compound unit)
For example, 80 km/h is expressed as 80 km/h and read as 80 km/h.
Work efficiency × working hours = total workload.
Total workload ÷ working time = working efficiency
Total amount of work ÷ work efficiency = working hours
2020 Elementary School Grade Four Volume One Mathematical Knowledge Point Induction 4
Unit 5 Parallelogram and Trapezoid
1. The positional relationship between two straight lines in the same plane: intersection and non-intersection.
2. Parallelism: Two straight lines that do not intersect on the same plane are called parallel lines, or they are parallel to each other.
3. Verticality: If two straight lines intersect at right angles, they are said to be perpendicular to each other, one of which is called the perpendicular of the other, and the intersection of these two straight lines is called vertical foot.
4. Methods of drawing vertical lines: overlapping edges, converting into points and drawing line labels.
5. Distance from point to straight line: The vertical line drawn from a point outside the straight line is the shortest, and its length is called the distance from the point to the straight line. The length of the vertical line segment is called the distance.
6. Drawing method of parallel lines: one stick, two moves and four paintings.
7. Nature of parallel lines: The distance between two parallel lines is equal everywhere.
This property can be used to prove that the opposite sides of a rectangle are equal and parallel.
8. Key points when drawing rectangles and squares: draw vertically and parallelly, and pay attention to marking: a rectangle should mark the length (length and width) of a group of adjacent sides, and a square should mark the length of two sides, or write "rectangle" and "square" beside it.
9. The concept of parallelogram and trapezoid: two groups of parallelograms with parallel opposite sides are called parallelograms;
A quadrilateral with only one set of parallel sides is called a trapezoid.
10, quadrilateral feature:
Quadrilateral has the characteristics of "easy deformation" and "instability". Application: sliding door
Draw a rectangle into a parallelogram with the same perimeter and smaller area.
1 1, base and height of parallelogram: draw a vertical line from a point on one side of parallelogram to the opposite side, the line segment between this point and the vertical foot is called the height of parallelogram, and the side where the vertical foot is located is called the base of parallelogram. Parallelogram has countless heights, but only one height can be drawn from one vertex to the opposite. Draw the height with a dotted line. Make a footprint
12 bottom, height and waist of trapezoid: draw a vertical line from a point on the upper bottom of trapezoid to the lower bottom. The line segment between this point and the vertical foot is called the height of trapezoid, and there are countless kinds of heights of trapezoid. But only one height can be drawn from one vertex at the bottom to the other.
The bottom of the trapezoid is fixed with two sides-an upper bottom and a lower bottom (a group of mutually parallel opposite sides are respectively called the upper bottom and the lower bottom of the trapezoid); A set of non-parallel opposite sides is called trapezoidal waist.
Special trapezoid: isosceles trapezoid is called isosceles trapezoid, and right-angled trapezoid is called right-angled trapezoid. An isosceles trapezoid cannot be a right-angled trapezoid, nor can a right-angled trapezoid be an isosceles trapezoid.
12. Set graph: use set graph to represent the relationship between quadrangles.
Quadrilateral includes parallelogram and trapezoid. Rectangular and square are special parallelograms. Because they have the characteristics of parallelogram. A square is a special rectangle.
14, sum of quadrilateral internal angles: sum of quadrilateral internal angles is 360.
15, graphic cutting:
(1) parallelogram: A parallelogram can be cut into two equal triangles, parallelograms or trapeziums.
Methods: First, determine the center point, the intersection of two diagonal lines is the center point, and then draw a dotted line through the center point, so that the parallelogram is divided into two identical figures on average.
(2) Trapezoids: Trapezoids can be cut into two trapezoids, a parallelogram, a triangle and two triangles.
16, graphic assembly (please draw it yourself):
(1) Two identical triangles can be combined into a parallelogram.
(2) Two identical parallelograms can be combined into a parallelogram.
(3) Two identical rectangles can be combined into one rectangle.
(4) Two identical squares can form a rectangle.
(5) Two identical trapezoids can be combined into a parallelogram.
(6) Two identical right-angled trapezoids can be combined into a rectangle or parallelogram.
17, axis of symmetry:
A rectangle has two symmetry axes, a square has four symmetry axes, and an isosceles trapezoid has only 1 symmetry axis. Parallelogram has no symmetry axis.
2020 Elementary School Grade Four Volume I Mathematical Knowledge Points Induction 5
Unit 6 divisor is the division of two digits
1, the meaning of division: know the product of two factors and one of them, and find the operation of the other factor.
2. The following four situations require division:
(1) How many units are there in total? How many units in 180 are 30: 180÷30?
(2) Know how many times a number is and find this number. Three times a number is 270. Find this number? : 270÷3
(3) Find how many times one number is another. How many times if 160 is 40: 160÷40.
(4) Divide the total into several parts. If 240 is divided into six parts, how much is each part: 240÷6?
3. The relationship between numbers in division (division with remainder):
Dividend/Dividend = quotient ... remainder Divided = quotient × divider+remainder (check method)
Divider = (dividend-remainder) ÷ quotient = (dividend-remainder) ÷ divisor
Remainder = dividend divided by quotient
4. Oral calculation and division: Oral calculation uses an integer of ten divided by an integer of ten or several hundred dozen, which can be divided by multiplication, or the dividend and zeros with the same number at the end of the divisor can be removed before calculation. (For example, 160÷20=)① It is considered that: 20×8= 160, so 168.
② Remove a 0 at the end of 160 and 20, which is equivalent to 16÷2=8, so 160÷20=8. For the reason, see "Law of Quotient Invariance".
5. The difference between "fen" and "fen": the pronunciation and meaning are different, and it is often used as a test center.
Example: 120 divided by 30, the formula is:120 ÷ 30 = 4 divided by 130, and the formula is: 130 ÷ 20 = 6... 10.
6. Division estimation method: According to the characteristics of dividend and divisor, first treat a number that is not a dozen or hundreds of integers as a dozen or hundreds of integers close to it, and then calculate it.
7. The pen division of divisor is an integer with five steps: at first glance, determine the position of quotient; Second, try to determine the first quotient; Multiply the quotient and divisor three times, and then subtract the product from the divisor; The size of four ratios, divisor and remainder, and the remainder must be less than the divisor; Five falls, reducing the dividend yield.
8. For the division where the divisor is close to the integer ten, the divisor is generally regarded as the integer ten close to it according to the "rounding" method to try the quotient. Using the four-shed method to measure the quotient, the quotient is easy to be too large and should be adjusted downwards; Using the five methods to test the quotient, the quotient is easy to be small, and it is necessary to adjust the quotient.
9. For the division where the divisor is not close to the integer ten, you can try the quotient by rounding, or you can try the quotient by treating the divisor as a few tenths of it.
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