The fifth grade mathematics knowledge of Beijing Normal University Edition (Volume I)

The first unit 1, when a factor is decimal, can be calculated by integer multiplication, and finally the decimal point is calculated.

2. Calculate decimal multiplication, which can be converted into integer multiplication for operation.

3. The * * of two factors has several decimals, and the product has several decimals.

If the product number is not enough, please add 0 before the number.

5. When calculating decimal multiplication, you can use integer multiplication to calculate first, and then determine the decimal places of the product according to the decimal places of the factors.

6. The operation law of integer multiplication is also applicable to decimal multiplication (multiplication and division first, then addition and subtraction).

Unit 2 1. If the symmetrical figure is folded in half from the middle, the two sides will completely overlap.

2. Fold the graph in half along a straight line. If the parts on both sides of a straight line can completely overlap, such a graph is called an axisymmetric graph.

3. The straight line where the crease is located is called its symmetry axis.

4. A figure can be translated or rotated to form a larger figure.

Unit 3: 1. When calculating fractional division, turn a blind eye to the decimal point and use integer division to calculate. Calculate the number, if there is a remainder, add zero after the remainder, then divide by the divisor, if there is a remainder, add zero, and finally put the decimal point on the quotient, which should be above the quotient of the zero of the first remainder.

2. When calculating the divisor with decimals, first move the decimal point of the divisor to the right as an integer, then move the divisor to the right by several digits, and the dividend will also move to the right by several digits. If there are not enough digits in the dividend, add zero after the dividend.

Generally speaking, the approximate value of quotient is obtained by rounding.

4. The decimal part starts from a certain place, and one number or several numbers appear repeatedly in turn. Such numbers are called cyclic decimals.

5. The number of digits in the decimal part is limited, which is called finite decimal, and the number of digits is infinite decimal.

6. The decimal part of the cyclic decimal, that is, the number that appears repeatedly in turn, is called the cyclic segment of this cyclic decimal. When writing cyclic decimals, you can only write the first cyclic segment, and write a point at the first and last position of this cyclic segment.

7. In an equation, if there are parentheses and parentheses, count the parentheses first and then the parentheses.

8. Multiplication and division of decimals are converted into multiplication and division of integers to calculate.

Unit 4: Equation: An equation with equal left and right sides is called an equation.

Equations with unknowns, such as 1, x+300 = 400, 10x = 1600, 3x+ 100 = 1000 ... are called equations.

2. The left and right sides of the equation add, subtract, multiply or divide the same number at the same time, and the left and right sides of the equation remain unchanged.

3. Making the unknowns on the left and right sides of the equation get values is called the solution of the equation. The process of solving an equation is called solving an equation.

Unit 5: Area of Polygon

4. Parallelogram: Two groups of parallelograms with opposite sides are called parallelograms. The vertical line segment from a point on one side of a parallelogram to its opposite side is the height of the parallelogram, and this opposite side is the bottom of the parallelogram. Convert the parallelogram into a rectangle with the same area as the original parallelogram. The length of a rectangle is equal to the base of the parallelogram, and the width is equal to the height of the parallelogram. The area of parallelogram is equal to the base x height. Expressed in letters: S=ah

5. Triangle: Two identical right triangles can form a parallelogram. The area of the triangle = base × height ÷2, expressed in letters: S=ah÷2.

6. Trapezoid: characterized by four corners and quadrangles, only one group of opposite sides is parallel. A quadrilateral with only one set of parallel sides is called a trapezoid. An isosceles trapezoid is called an isosceles trapezoid. A group of mutually parallel opposite sides are the upper bottom and the lower bottom of the trapezoid, and a group of non-parallel opposite sides are the waist of the trapezoid. The vertical line segment from a point on the upper bottom edge to the lower bottom edge is the height of the trapezoid. Trapezoids can be divided into triangles and parallelograms Two identical trapezoids form a parallelogram. Trapezoidal area = (upper bottom+lower bottom) × height ÷2, expressed in letters: S=(a+b)×h÷2.

7. Review: (Unit 5)

trait

Surface product

Rectangular shape

There are four sides, the opposite sides are equal; All four corners are right angles.

S=ab

Regular square

There are four sides, the opposite sides are equal; All four corners are right angles.

S=2a

Hirayuki

Edge shape

There are four sides, and the opposite sides are parallel and equal to each other; The four angles are equal.

S = ah

triangle

There are three sides, which are fixed objects; Internal angle and 180.

S=ah÷2

Step shape

There are four sides, and only one group is parallel to each other; Angle has nothing to do with angle.

S=(ab)×h÷2

8. I found that the area formulas of parallelogram, triangle and trapezoid are all derived by transformation method.

Unit 6: 1, I found that the characteristics of multiples of 2 are 0, 2, 4, 6, 8.

2. I found that multiples of 5 are represented by 0 and 5 in units.

I found that the sum of digits of a number is a multiple of 3, and this number is a multiple of 3.

4. Among natural numbers, numbers that are multiples of 2 are called even numbers, and numbers that are not multiples of 2 are called odd numbers.

5. A tree with only 1 and its own two factors like 2, 3, 5,,,, is called a prime number; Like 4, 6, 8,,,

In this way, besides 1 and itself, there are other factors called composite numbers; 1 has only one factor, which is neither prime nor composite.

6. Multiplying a composite number by a prime factor is called prime factor decomposition.

Unit 7

1, use a unit length to represent a certain quantity, track all points according to the size of the data, and then connect all points in turn with line segments. The statistical chart obtained is called broken line statistical chart.

2. If you only need to express the size of the quantity, it is more appropriate to use a bar chart. If you need to reflect the increase or decrease of quantity, you need to use a line chart.

3. Note: 1, title, 2, time, 3, arrow, 4, unit, 5, scale (starting from zero), 6, drawing, 7, data.