This section focuses on a series of concepts and fractions of divisibility, the basic properties of decimals, four operations and simple operations.
1. Systematically sort out the contents of numbers, establish a concept system, and strengthen the understanding of concepts (4 class hours), including the meaning of numbers, reading and writing of numbers, rewriting of numbers, comparison of numbers, divisibility of numbers and other knowledge points.
2. Communicate the connection between the contents and promote the overall perception (2 class hours), including "the nature of fractions and decimals" and "the conceptual comparison of divisibility".
3. Comprehensive concepts and calculation methods of the four operations to improve the calculation level (6 class hours), including "the meaning and law of the four operations" and "elementary arithmetic".
4. Use algorithms to master simple operations and improve calculation efficiency (5 class hours), including "algorithms and simple operations".
5. Carefully design exercises to improve comprehensive calculation ability (3 class hours).
(2) Basic knowledge of algebra (10 class hour)
The focus of this section should be to master simple equations and distinguish ratios and proportions.
1, form systematic knowledge and strengthen contact (3 class hours), including knowledge points such as "letters represent numbers", "proportion and proportion" and "positive and negative proportion".
2. Grasp problem-solving training to improve the ability to solve equations and proportions (4 class hours), including "simple equations" and "solution ratio".
3. Differentiate concepts and deepen understanding (3 class hours), including "proportion and proportion" and "positive proportion and inverse proportion".
(3) Application problems (30 class hours)
In this section, we should focus on the analysis of application problems and cultivate problem-solving skills. The difficult content is fractional application problems.
1. Analysis and arrangement of simple application problems (3 class hours).
2. Analysis and arrangement of compound application problems (6 class hours).
3. Analysis and arrangement of solving application problems by using equations (5 class hours).
4. Analysis and arrangement of fractional application problems (10 class hour).
5. Analysis and arrangement of solving application problems with proportional knowledge (3 class hours).
6. Comprehensive training of application problems (3 class hours).
(4) Measurement of quantity
This section focuses on the rewriting of nouns and numbers and practical concepts.
1. Measurement knowledge structure of completed quantity (2 class hours), including "length, area, unit of volume" and "weight, time unit".
2. Consolidate the unit of measurement and strengthen the actual concept (4 class hours), including "rewriting names and numbers".
3. Comprehensive training and application (1 class).
(5) Basic knowledge of geometry (12 class hours)
This section focuses on the identification of features and the application of formulas.
1, strengthen concept understanding and systematization (2 class hours), including "the characteristics of plane graphics" and "the characteristics of three-dimensional graphics".
2. Accurately grasp the characteristics of graphics, strengthen comparative analysis, and reveal the connections and differences between knowledge (4 class hours), including "perimeter and area of plane graphics" and "surface area and volume of three-dimensional graphics".
3. Strengthen the application of formulas and improve the mastery of calculation methods (5 class hours). Can realize the correct calculation of perimeter, area and volume.
4. Overall perception and practical application (1 class).
(6) Simple statistics (6 class hours)
This section focuses on the knowledge and understanding of charts according to the outline requirements, and can answer some simple questions.
1, the average method (1 class).
2. Deepen the understanding of the characteristics and functions of statistical charts (3 class hours), including "statistical tables" and "statistical charts".
3. Further analyze the chart and answer questions (2 class hours), including drawing and answering questions according to the chart.
Fifth, the problems that should be paid attention to in the review.
1. The content, process and time plan of the general review of primary school mathematics graduation should be adjusted according to the actual situation in actual teaching.
2. Pay attention to the connection between primary school mathematics knowledge and middle school knowledge structure, pave the way for middle school learning and expand knowledge points appropriately.
3. Grasp the outline requirements and adjust the content, process and time of plan review according to actual needs. We should not only learn knowledge comprehensively, but also master the depth of reviewing knowledge.
If you have the patience to read one book at a time according to the regulations, you will be KO if you read the related topics again.
Review of Mathematics Classification in Grade Six (Basic Knowledge of Geometry)
Acute angle, right angle, oblique angle and fillet
.
.
0< acute angle < 90 right angle = 90 90.
Classification of angles.
Perpendicular: Two straight lines intersect at right angles, and two straight lines are perpendicular to each other.
Parallelism: In the same plane, two lines that do not intersect are called parallel lines.
Acute triangle, right triangle, obtuse triangle
All three angles are acute, one is right and the other is obtuse.
Triangle classification: according to the size of the angle.
R is divided according to the characteristics of edges.
Arbitrary triangle isosceles triangle equilateral triangle
No edge is equal.
No angle is equal, and no two sides are equal.
Two base angles are equal and three sides are equal.
All three angles are equal, and the degree of each angle is
180 ÷3=60
The relationship between isosceles triangle and equilateral triangle. The relationship between parallelogram, rectangle and square
Isosceles triangle parallelogram
rectangle
Equilateral triangular square
Perimeter: The sum of all the sides surrounding a figure is called its perimeter.
Area: The size of an object's surface or closed plane figure is called its area.
Rectangular square parallelogram triangle trapezoid circle
Perimeter (length+width) ×2 sides × 4 sum of sides × 2πr or πd sum of sides.
Area length × width side length × side length bottom × high bottom × high ÷2 (upper bottom+lower bottom)
× Height ÷2 πr2
Surface area and volume of three-dimensional graphics
Cuboid cube cylindrical cone
Surface area (length× width+length× height+width× height )× 2 side length× side length× 6 lateral area+bottom area× 2.
Volume length x width x height (bottom area x height) side length 3 (bottom area x height) bottom area x high bottom area x height.
Sum of side lengths (length+width+height) ×4 side length×12
(full name)
1, fill in the form.
Surface area volume of named strip
This rectangle is 4 meters long, 3 meters wide and 5 meters high.
The side length of a cube is 12cm.
The bottom radius of the cylinder is 8 cm and the height is 9 cm.
The conical ground is 8 cm in diameter and 9 cm in height-
2. Find the area below. (Unit: decimeter)
three
3 7 10 4.5
8 12 14 7
( 1) (2) (3) (4)
3. Find out the perimeter and area of the picture below.
6 2.4
5.5 1.2
Draw a parallelogram with two heights.
4.( 1) is the vertical line when AB crosses point P, and it is BC.
Parallel lines. (2) Draw the height on the side of AC. . P
B.C.
5.( 1) The figure below is a right triangle. Find the degree of ∠ 1 and ∠2.
∠ 1=
2 1 1 15 ∠2=
6( 1) How much surface area is increased by cutting a cylindrical steel with a length of 10 decimeter and a bottom diameter of 6 decimeters into two sections?
(2) Cylindrical pool with radius 12m and depth of 2.5m ..
A, the area of this pool.
B, how many cubic meters of soil does it take to dig this pool?
C, in the pool made of cement, what is the area of cement?
Conceptual part of four numbers
Two digits times three digits, and the product is either four digits or five digits.
1L = 1000 ml (ml, ml)
A cubic container whose length, width and height are 1 decimeter from the inside out is exactly 1 liter. 1 litre water weight 1 kg.
The total blood volume of healthy adults is about 4000-5000 ml. Voluntary blood donors generally donate 200 ml of blood each time.
Conditions for enclosing a triangle: the sum of the lengths of two short sides must be greater than the third side.
Triangle has stability, which is used by many objects in life. Such as: herringbone beam, cable-stayed bridge, bicycle frame.
A triangle with three acute angles is an acute triangle. (The sum of the two internal angles is greater than the third internal angle. )
A triangle with right angles is a right triangle. (The sum of the two internal angles is equal to the third internal angle. The sum of the two acute angles is 90 degrees. The two right-angled sides are the bottom and the height of each other. )
A triangle with an obtuse angle is an obtuse triangle. (The sum of the two internal angles is less than the third internal angle. )
Any triangle has at least two acute angles and three heights, and the sum of the three internal angles is 180 degrees.
A triangle with two equal sides is an isosceles triangle, and its two base angles are also equal. It is an axisymmetric figure with an axis of symmetry (just coincident with the height of the base). )
Vertex of isosceles triangle = 180- base angle ×2 = 180- base angle.
The base angle of an isosceles triangle =( 180- vertex angle) ÷2
In mixed operation: multiply first and then divide, then add and subtract. There are both parentheses and square brackets. You should count what is in brackets first, and then what is in brackets.
Two groups of parallelograms with parallel opposite sides are called parallelograms. Their opposite sides are equal and their diagonal angles are equal. There can be two different heights from one vertex to the opposite. Bottom and height must correspond.
Parallelogram is easy to deform. Many objects in life take advantage of this feature. Such as: (electric retractable doors, iron sliding doors, elevators) draw a parallelogram into a rectangle, with the perimeter unchanged and the area changed. Parallelogram is not an axisymmetric figure.
A quadrilateral with only one set of parallel sides is called a trapezoid. A trapezoid with two equal waists is called an isosceles trapezoid, and its two bottom angles are equal, which is a symmetrical figure with an axis of symmetry.
Multiplicative commutative law: a×b=b×a
Law of multiplicative association: (a×b)×c=a×(b×c)
Multiplication and distribution law: (a+b)×c=a×c+b×c
Graphic translation, first translate the key points to the designated places, and then connect the points.
Rotation of the figure, first rotate the key edge to the specified place, and then connect the lines. (No matter translation or rotation, the basic graphics cannot be changed. )
4×3= 12, or 12÷3=4. Then 12 is a multiple of 3 and 4, and 3 and 4 are factors of 12.
The minimum factor of a number is 1, the maximum factor is itself, and the number of factors of a number is limited. For example, the factors of 18 are: 1, 2,3,6,9, 18.
The minimum multiple of a number is itself, and there is no maximum multiple. The multiple of a number is infinite. For example, the multiple of 18 is: 18, 36, 54, 72, 90. ...
The largest factor of a number is equal to the smallest multiple of this number.
Numbers that are multiples of 2 are called even numbers. (Units are numbers 0, 2, 4, 6 and 8)
Numbers that are not multiples of 2 are called odd numbers. (The unit number is 1, 3, 5, 7, 9)
The sum of the digits of a number is a multiple of 3, and this number is a multiple of 3. (For example, the sum of the digits of 453 is 4+3+5= 12. Because 12 is a multiple of 3, 453 is also a multiple of 3. )
Since it is a multiple of 2 and 5, the number in the unit must be 0. (For example: 10, 20, 30, 40 ...)
A number with only 1 and its own two factors is called a prime number. (or prime numbers) such as 2, 3, 5, 7, 1 1, 13, 17, 19...2 are unique even prime numbers.
A number has other factors besides 1 and itself, which is called a composite number. Such as: 4, 6, 8, 9, 10 ...
1 is neither prime nor composite, because the factor of 1 is only 1: 1.
Goldbach conjecture: Any even number greater than 2 is the sum of two prime numbers. 20=3+ 17、40= 1 1+29
The changing law of product: ① One factor is reduced by several times, and the other factor is expanded by the same multiple, and the product remains unchanged.
(2) If one factor shrinks (or expands several times) and the other factor remains unchanged, the product will also shrink (or expand) several times.
The changing law of quotient: ① Dividend and divisor expand (or shrink) by the same multiple at the same time, and the quotient remains unchanged except 0.
(2) The divisor is expanded (or reduced) several times, and the quotient is also expanded (or reduced) several times under the condition that the divisor is unchanged.
(3) The dividend is constant, the divisor is reduced several times (except 0), but the quotient is expanded several times.
The broken-line statistical chart can not only see the quantity, but also clearly see the increase and decrease of the quantity. The production steps of broken-line statistical chart: ① fixed point ② writing data ③ connecting line ④ writing date.
Commonly used quantitative relations:
Area of a square = side length × side length (S=a×a=a)
Circumference of a square = side length ×4 (C=a×4=4a)
Area of rectangle = length× width (S=a×b=ab)
The circumference of a rectangle = (length+width) × 2c = (a+b) × 2.
Total price = unit price × quantity unit price = total price/quantity = total price/unit price.
Distance = speed × time speed = distance/time = distance/speed
Federation of trade unions = work efficiency × time efficiency = time of Federation of trade unions = time of Federation of trade unions.
Room area = area per block × number of blocks = room area/area per block
Meeting distance = (speed A+ speed B) × meeting time = speed A × time+speed B × time.
Distance = (speed A- speed B) × time = speed A × time-speed B × time.