Summary of basic knowledge points of mathematics unit in the first volume of grade four
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: look at the number in the highest digit of mantissa, if it is 4 or less, discard mantissa and add a counting unit "10000" or "1 100 million" at the end of the number; 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, the product change rule:
(1) If one factor remains unchanged, another factor will be expanded (or reduced) several times, and the product will be expanded (or reduced) by the same multiple.
For example, 1: It is known that A×B=2 15, then A×B×2= ().
This is to expand B by 2 times, and the product will also be expanded by 2 times. That is, 2 15×2=430, so A×B×2=(430).
For example, 2: known: 2×A×B=200, then A×B= ().
In this way, a is reduced by 2 times and the product is also reduced by 2 times. That is 200÷2= 100, so A×B=( 100).
(2) One factor is expanded or reduced by several times, and the other factor is reduced or expanded by the same multiple, and the product remains unchanged.
For example, A×B=5 10 is known. If A is enlarged by 5 times and B is reduced by 5 times, the product is (5 10).
(3) If one factor is expanded m times and the other factor is expanded n times, the product is expanded m×n times.
④ If one factor is reduced by m times and the other factor is reduced by n times, the product will be reduced by m×n times.
④ One factor is expanded by m times, and the other factor is reduced by n times. If m > n, the product is expanded by (m÷n) times. If m < n, the product is reduced by (n÷m) times.
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. Until the remainder is less than the divisor.
3. When three digits are divided by two digits, the quotient may be one digit or two digits.
4. Invariance of quotient:
(1) in division, the dividend and divisor are multiplied (or divided) several times at the same time (except 0), and the quotient remains unchanged.
(2) In division, the divisor is constant, the dividend is multiplied (or divided) by several (except 0), and the quotient is also multiplied (or divided) by several.
(3) In division, the dividend is a constant. If the divisor is multiplied by (or divided by) several, the quotient is divided by (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.