The need of mathematical business calculation, understanding the system between numbers, measuring land area and predicting astronomical concepts. The following is a summary of the knowledge points of fourth-grade mathematics in Hebei Education Edition. Welcome to refer to!

The first unit multiplication

One or three digits multiplied by two digits.

1, the calculation rule of multiplying three digits by two digits: the digits of two digits are multiplied by each digit of three digits, and the product is aligned with the digits, then the digits of two digits are multiplied by each digit of three digits, and the product is aligned with the ten digits, and finally the product of the two multiplications is added.

2. Multiply three digits by two digits, and the product is either four digits or five digits.

2. Multiply by 0 at the end of the multiplier

1, the multiplication method ending in 0: multiply the non-zero parts of two multipliers first, then see how many zeros are at the end of a * * * of two multipliers, and add a few zeros at the end of the product.

2. The zero at the end of the product is not determined by the zero at the end of the multiplier. Multiplication sometimes produces zero at the end of the calculation process. Attachment: Common quantitative relations

Area of a square = side length? Side length = perimeter of a square with side length? four

Area of rectangle = length? The perimeter of a wide rectangle = (length+width)? 2

① Total price = unit price? Quantity unit price = total price? Quantity quantity = total price? unit price

② Distance = speed? Time speed = distance? Time = distance? speed

Unit 2 liters and milliliters

First, the understanding of ability

1. Capacity is how much liquid an object can hold.

Second, the ratio between liters and milliliters.

1, 1 l (L)= 1000 mL (ml, ml)

2. When measuring liquids such as water, oil and drinks, liters or milliliters are usually used as units.

3. 1 ml is approximately equal to 23 drops of water.

The third unit triangle

Definition: A closed figure surrounded by three line segments is called a triangle.

Second, the characteristics and classification of triangles

1, the sum of any two sides of a triangle is greater than the third side.

2. The vertical line segment from a vertex of a triangle to the opposite side is the height of the triangle, and this opposite side is the bottom of the triangle.

3. The triangle is very stable. Such as: herringbone beam, bicycle frame.

4. A triangle with three acute angles is an acute triangle.

5. A triangle with right angles is a right triangle.

6. A triangle with an obtuse angle is an obtuse triangle.

7. Any triangle has at least two acute angles and three heights, and the sum of the internal angles of the triangle is 180 degrees.

Three, isosceles triangle, equilateral triangle

1. A triangle with two equal sides is an isosceles triangle. Two equal sides are called waist and the other side is called bottom. The included angle between two waists is called vertex angle, and the included angle between two bottoms and waists is called bottom angle. Its two base angles are equal, and it is an axisymmetric figure with an axis of symmetry.

2. A triangle with three equal sides is an equilateral triangle, and all three angles are equal (each angle is 60? . )

An isosceles triangle with a right angle is called an isosceles right triangle, and its base angle is equal to 45? , the vertex angle is equal to 90? .

4. Vertex of isosceles triangle = 180? -Bottom corner? 2 or 180 -Bottom corner. -Bottom angle

5. The base angle of isosceles triangle =( 180? -Vertex angle)? 2

Unit 4 Mixing Operation

First, the mixed operation without brackets

1. If brackets are not included in the four arithmetic operations, multiply first, then divide, and then add and subtract.

Second, mixed operation with brackets.

1, you must first count what is in parentheses.

Third, mixed operation with brackets.

1. There are both parentheses. You should count the brackets first, then the brackets.

Unit 5 Parallelogram and Trapezoid

I. Understanding parallelogram

1, two groups of parallelograms whose opposite sides are parallel are called parallelograms, and their opposite sides are parallel and diagonal are equal.

There can be two different heights from one vertex to the opposite. Bottom and height must correspond. A parallelogram has countless heights.

2. Two identical triangular rulers can be used to form a parallelogram.

3. The parallelogram is easily deformed (unstable). Xu in life

Many objects take advantage of this feature. Such as: (electric retractable door, iron sliding door,

Extend and lower the machine

4. Draw the parallelogram into a rectangle with constant perimeter and area.

Second, understand the trapezoid

1, only a set of quadrilaterals with parallel opposite sides is called trapezoid. flat

A set of rows with shorter opposite sides is called trapezoidal upper bottom, and the longer one is called trapezoidal upper bottom.

It is called the base of a trapezoid, and a group of non-parallel opposite sides is called a trapezoid.

Waist, the distance between two parallel lines is called the height of trapezoid.

(countless articles).

2. Two trapezoid with equal waist are called isosceles trapezoid. Its two base angles are equal, and it is an axisymmetric figure with an axis of symmetry. A right-angled trapezoid has only two right angles.

3. Two identical trapezoids can be combined into a parallelogram.

4. Square and rectangle are special parallelogram.

Unit 6 Looking for the Law

1, collocation law: the number of two things is multiplied. (for example, the matching of hat and clothes)

2, arrangement: mom and dad I arrange photos, there are several arrangements: 2? 3。 Is that n? (n- 1) 1

Unit 7 Algorithm

1, multiplicative commutative law: a? b=b？ A 2, the law of multiplicative association: (a? b)？ c=a？ (b？ c)

3. Multiplicative distribution law: (a+b)? c=a？ c+b？ C (Multiplication equals multiplication separately)

4. Derivation of the law of multiplication and distribution: (a-b)? c=a？ c-b？ c

Unit 8 Symmetry, Translation and Rotation

A, axisymmetric graphics

If a figure is folded in half, the parts on both sides of the crease can completely overlap, then the figure is axisymmetric. The straight line where the crease lies is called the symmetry axis of the graph.

Second, the number of symmetry axes.

1, a regular triangle (equilateral triangle) has three symmetry axes, a regular quadrilateral (square) has four symmetry axes, a regular pentagon has five symmetry axes, and a regular n deformation has n symmetry axes.

Third, translation and rotation.

1, the translation of the graph, first draw the translation direction, then translate the key points to the designated place, and finally connect them into a graph.

2, the rotation of graphics, first find a point, and then rotate the key edge to the specified place, (pay attention to the direction and angle) and then connect.

Unit 9 Multiplication and Factor

1、4? 3= 12 or 12? 3=4。 Then 12 is a multiple of 3 and 4, and 3 and 4 are factors of 12. (Multiplies and factors exist mutually. It cannot be said that 12 is a multiple or 3 is a factor. We can only say who is a multiple of who and who is a factor of who. )

2. The minimum factor of a number is 1, and the maximum factor is itself. The number of factors of a number is limited.

The minimum multiple of a number is itself, and there is no maximum multiple. The multiple of a number is infinite.

The biggest factor of a number is equal to the smallest multiple of this number (both are themselves).

5. Numbers that are multiples of 2 are called even numbers. (Units are numbers 0, 2, 4, 6 and 8)

6. Numbers that are not multiples of 2 are called odd numbers. (The unit number is 1, 3, 5, 7, 9)

7. Numbers with units of 2, 4, 6, 8 and 0 are multiples of 2, and numbers with units of 0 or 5 are multiples of 5.

8. It is both a multiple of 2 and a multiple of 5, and each bit must be 0. (e.g. 10, 20, 30, 40)

9. The sum of digits of a number is a multiple of 3, and this number is a multiple of 3. 10, a number with only 1 and its own two factors is called a prime number (or prime number).

10 and 2 are the only even numbers in prime numbers. (So? All prime numbers are odd numbers? This statement is wrong. )

1 1, a number with other factors besides 1, is itself called a composite number. Such as: 4, 6, 8, 9, 10.

12 and 1 are neither prime numbers nor composite numbers. Prime numbers have only two factors, and composite numbers have at least three factors.

13, Goldbach conjecture: Any even number greater than 4 can be expressed as the sum of two odd prime numbers. Such as 8=3+5, 10=5+5, 12=5+7 and so on.

Prime numbers within 14 and 100: 2, 3, 5, 7, 1 1 3, 17, 19, 23, 29. (***25)

Unit 10 Exploring Laws with Calculator

The changing law of the product of 1 sum;

(1) A constant factor, another factor is multiplied or divided by several (except 0), and the product is also multiplied or divided by several (except 0).

(2) If one factor is enlarged several times and the other factor is reduced by the same multiple, then the product remains unchanged.

2. The changing law of quotient: ① The dividend and divisor are multiplied (or divided) by the same number (except 0) at the same time, and the quotient remains unchanged. Note: the change of dividend will bring about the change of remainder.

(2) The dividend is multiplied by (or divided by) a number, and the quotient is multiplied by (or divided by) a few under the condition that the divisor is unchanged.

;