Rigid thinking, confused mind, always feel confused for 24 hours, unclear mind, serious lack of sleep.
This is a paste. You get a headache when you think.
The more you use your brain, the more flexible it becomes. Absent-minded at work, lazy and comfortable in life, playing computer or mobile phone, the result of a little carelessness over time is that my head is seriously rigid, and I feel that I can't turn around and even have a headache if I think about something a little. Really can't.
How to resist brain rigidity? Learning mathematics starts with the most basic mathematics.
According to the Mathematics Curriculum Standard for Compulsory Education (20 1 1 Edition), mathematics is a science that studies quantitative relations and spatial forms. According to Baidu Encyclopedia, mathematics is a subject that studies concepts such as quantity, structure, change, space and information.
Mathematics is the foundation of natural science and technical science, and it is an indispensable basic tool for studying and studying modern science and technology. Through mathematics learning, you can not only improve your computing ability, but also cultivate and enhance your abstract thinking ability and logical reasoning ability.
Learn mathematics, see how much computing power has deteriorated, see how difficult calculations can be made, and see if abstract thinking and logical reasoning can be carried out.
Mathematics Curriculum Standard for Compulsory Education (20 1 1 version) divides primary school mathematics into two stages: the first stage (1~3 grades) and the second stage (4~6 grades).
According to the standard, in primary school, the content of mathematics curriculum (including all grades) can also be divided into "number and algebra", "figure and geometry" and "statistics and probability". Mathematics learning in primary schools is to acquire basic knowledge, skills, ideas, methods and activities necessary for adapting to social life and further development.
And whether there are three parts in each volume: number and algebra, graph and geometry, statistics and probability. Finally, a review of each volume is given. In addition, the "arrangement and review" of each textbook sorts out the main points of the content.
The content of the first issue of "Number and Algebra" can be divided into several parts: number cognition, number operation and common quantities. The goal is to be able to use numbers to represent some things in daily life and communicate; Be able to solve simple problems in life by using numbers and numerical operations, and explain the practical significance of the results; Can solve simple problems related to common quantities in combination with real life.
There are six sections "Number and Algebra" in the first volume of Senior One. Numbers in Life allows students to know numbers and their expressions, learn to count, recognize, read and write simple numbers, and use numbers to represent the number of objects or the order and position of things. Know the size of numbers, understand the meaning of symbols, and learn to compare the size of single digits. "Comparison" combines specific conditions to learn the comparative judgment of size, quantity, height, length and weight. "Addition and subtraction (1)" knows the plus sign and the minus sign, the addition formula and the subtraction formula, and the concept of number; Learn the addition and subtraction of a number by counting (at most two steps, and the sum is not more than 10), practice oral calculation and mental calculation by hand, and make a simple addition and subtraction table. Then learn to classify. "Position and order" learns the position and order of the front, back, up, down, left and right, and can represent the order and position of things with numbers. "Addition and subtraction (2)" knows the unit and ten digits of a number, and learns the addition and subtraction operation and comparison of two digits (within 20) by counting the counter; Through the observation and memory evolution of addition and subtraction tables, the calculation ability is strengthened. "Knowing clocks and watches" is a quantitative content. Need to know the clock, know the 24-hour timing method, and experience the length of time in combination with life experience.
There are six sections on "Number and Algebra" in the second volume of Senior One. "Addition and subtraction (1)" continues to learn the addition and subtraction of two-digit numbers (within 20), learns the calculation method of the division and subtraction of two-digit numbers (10), and makes a subtraction table of two-digit numbers to help practice oral and mental arithmetic, and can skillfully add and subtract within 20. "Numbers in Life" knows the hundredth digit. By counting the digits within 100, it learns to compare the sizes of the digits within the hundredth digit, can name the digits, and understands the meanings expressed by the digits. "Addition and subtraction (II)" knows the addition formula, the sum of addends, and the subtraction formula, the minuend, the subtraction sum and the difference; Learn the addition and subtraction of two digits (within 100); Learn to use vertical calculation (addition vertical and subtraction vertical). "Addition and subtraction (III)" Learn the addition and subtraction of two digits (within 100), understand carry and borrow, use carry and borrow for vertical calculation, and can orally calculate simple addition and subtraction within 100.
The first volume of Grade Two has seven sections "Number and Algebra". "Addition and subtraction" is a simple addition and subtraction operation within 100 by adding and subtracting two digits (within 100). "Shopping" is a common quantity in learning. In the real situation, we should know the elements, angles and points and understand the relationship between them. "Count-one-number and Multiplication" is to learn multiplication through addition, understand multiplication formula and understand the meaning of multiplier, multiplication sign and product. Learn multiplication formula in two sections: "2~5 multiplication formula" and "6~9 multiplication formula", and make multiplication tables to help you learn multiplication calculation ability. "Divide by one" learns division by dividing by one, knows the division formula, and understands the meaning of dividend, divisor, divisor and quotient. "Division" is a comprehensive study of logarithm and algebra so far, including the comprehensive application of multiplication, division and ratio of numbers.
There are four sections about "Number and Algebra" in the second volume of Grade Two. "Division" includes reviewing the previous knowledge, knowing and mastering vertical division, dividing two digits by one digit, and knowing and understanding the remainder. "Large Numbers in Life" feels the significance of large numbers in life situations, knows thousands and tens of thousands of digits, estimates and knows abacus, understands and grasps the number sequence table, and knows that abacus can represent multiple digits. "Addition and subtraction" can calculate the addition and subtraction of three digits and learn to check. "Hours, minutes and seconds" are also common quantitative contents. Know hours, minutes and seconds, and understand their relationship.
The first volume of grade three is missing, and the contents are added as follows: combined with the specific situation, I realized the significance of four integer operations; Knowing parentheses, you can perform simple integer elementary arithmetic; Know the year, month and day, and understand the relationship between them;
Number and Algebra, the second volume of Grade Three, has four sections. "Division" and "multiplication" include reviewing previous knowledge, learning new things, expanding and deepening. Division is the division of two digits and three digits divided by one digit. "Multiplication" can multiply a number by two digits and three digits, and double digits by two digits, and can orally multiply and divide a simple number by two digits. Can be combined with the specific situation, choose the right unit for simple estimation, and realize the role of estimation in life. "Kilogram, gram, ton" is the content of commonly used quantity. In real situations, if you feel and know grams, kilograms and tons, you can simply convert them into units. "Cognitive score" combines the specific situation to get a preliminary understanding of the score and know the numerator, fractional line and denominator; Can read, write and grade; You can compare the sizes of two fractions with the same denominator, and you can add and subtract fractions with the same denominator (the denominator is less than 10) and add and subtract a decimal.
The content of the first lesson "Graphics and Geometry" can be divided into several parts: graphics cognition, measurement, graphics movement, graphics and position. Can classify simple geometry and graphics;
The first volume of Senior One contains a section on "Understanding Graphics", and you can know the geometric bodies such as cuboids, cubes, cylinders and spheres through the objects and models in your life. "Position and order" describes the relative position of objects with up, down, left, right, front and back.
There are two sections about "graphics and geometry" in the second volume of Senior One. "Observing objects" requires simple objects observed from different angles, which can be identified according to specific things, photos or direct views. "Interesting graphics" requires that simple graphics such as rectangle, square, triangle, circle and parallelogram can be recognized; Learn simple puzzles.
The first volume of the second grade has two sections: "Graphics and Geometry". "Graphic change" is to understand the expansion and change of graphics and the drawing, folding and cutting of simple graphics. Combining with real life, Measurement has experienced the process of measuring the length of an object with different methods, and realized the importance of establishing a unified measurement unit. Experience and understand the length units of meters and centimeters, be able to carry out simple unit conversion and know the measuring ruler.
There are three sections about graphics in the second volume of Grade Two. "Direction and position" is the content of graphics and positions. If you learn one of the four directions of east, south, west and north, you can identify the other three directions. If you know the northeast, northwest, southeast and southwest directions, you will use these words to describe the direction of objects. "Measurement" knows the length units of decimeter, millimeter and kilometer, and can carry out simple unit conversion; The length of some objects can be estimated and measured. "Understanding Graphics" recognizes right angles, acute angles and obtuse angles from the perspective of understanding life situations; Understand the characteristics of rectangle, square and parallelogram (mainly the characteristics of edges and corners).
The first volume of the third grade is missing, and the contents are added as follows: for example, know the perimeter, measure the perimeter of simple figures, and explore and master the perimeter formulas of rectangles and squares. ;
There are two sections about graphics in the second volume of Grade Three. The Movement of Graphics, with examples, feels the phenomena of translation, rotation and axial symmetry, understands the concept of axial symmetry, and preliminarily understands axial symmetry graphics through observation and operation. Be able to recognize translated simple graphics; Can use grid paper to translate graphics. "Area" combines examples to understand the area (concept), understand and understand the area units of square centimeters, square decimeters and square meters, and can carry out simple unit conversion. Mastering the area formulas of rectangles and squares will estimate the area of a given simple figure.
The content of "Statistics and Probability" in the first learning period is a preliminary understanding of statistics and probability, and the data can be analyzed simply.
The "Classification" section of the content of "Statistics and Probability" in the first volume of Senior One can be summarized as the initial understanding of "Statistics", which can classify things or data according to given standards or standards chosen by oneself, and feel the relationship between classification and classification standards; Can classify simple geometry and graphics.
There is a section "Investigation and Record" in the second volume of Senior Two, which is the content of "Statistics and Probability". After a simple process of data collection and arrangement, I understand simple data collection methods such as investigation and measurement, and can present the results of data collection in my own way (words, pictures, tables, etc.). ).
The second volume of grade three contains statistics and probability. After a simple process of data collection and arrangement, I understand simple data collection methods such as investigation and measurement, and can present the results of data collection in my own way (words, pictures, tables, etc.). ).
The content of the second issue of "Numbers and Algebra" can be divided into several parts: the understanding of numbers, the operation of numbers, formulas and equations, and proportional and inverse proportions. In the process of concrete operation and solving simple practical problems, we should be able to understand the reciprocal relationship of addition, subtraction, multiplication and division.
The first volume of grade four has five sections "Numbers and Algebra". "Know a bigger number" Under certain circumstances, if you know a number above 10000 and know the counting method of decimals, you will use 10000 and1000000 as units to represent large numbers; Understand the meaning of the symbol ≈ (about equal to sign, pronounced about equal to), understand the divisor (corresponding to the exact number), and master the rounding method; Know natural numbers. "Multiplication" calculates three digits multiplied by two digits; Know calculation tools and some interesting formulas. "Algorithm" understands parentheses and the operational priority of parentheses and parentheses; Able to perform simple integer elementary arithmetic (mainly divided into two steps, no more than three steps); Explore and understand the algorithm (the exchange law and association law of addition, the exchange law and association law of multiplication, and the distribution law of multiplication to addition), and use the algorithm to do some simple operations. "Division" studies the division of three digits divided by two digits; Master the invariable law of quotient; In specific cases, I can understand the common quantitative relationship: distance = speed × time, total price = unit price × quantity, and can solve simple practical problems. "Negative Numbers in Life" In familiar life situations, if you understand the meaning of negative numbers and positive numbers, you will use negative numbers to represent some quantities in daily life. Know the coding, know the coding method of ID card and bank card; Will use numbers to describe some characteristics of things and further understand the role of numbers in daily life.
There are three sections about "Number and Algebra" in the second volume of Grade Four. The meaning and addition and subtraction of decimals understands the meaning of decimals in combination with specific situations, and will convert decimals and fractions (excluding the conversion of cyclic decimals into component numbers); Know the decimal, percentile and thousandth after the decimal point, know the counting unit of the decimal part, and compare the sizes of decimals; Can perform simple decimal addition and subtraction mixed operation (mainly divided into two steps, no more than three steps). Decimal Multiplication can learn decimal multiplication by shifting, learn the multiplication of one decimal place and two decimal places, and can perform simple decimal multiplication operation. "Cognitive equation" can represent numbers with letters in specific situations; Combined with the simple actual situation, understand the equivalence relationship and express it in letters; Master the concept of equation (equation with unknown number), and use equation to express the equivalence relation in simple cases (such as 3x+2 = 5, 2x-x = 3) to understand the function of equation; Knowing the properties of equality, we can use the properties of equality to solve simple equations.
The first volume of the fifth grade has three sections: "Number and Algebra". "Decimal Division" learns decimal division through unit conversion, and can perform simple decimal Divison; Know cyclic decimals. Multiples and Factors grasps the concepts of multiples, factors, odd numbers, even numbers, prime numbers and composite numbers; Know the characteristics of multiples of 2, 3 and 5. "The meaning of the score" is to know the score, understand the meaning of the score according to the specific situation, and master the concepts of score unit, true score and false score; Understand the relationship between fraction and division and the basic properties of fraction; Master the concepts of approximate score, simplest fraction and general score, and learn to calculate approximate score and general score. Understand the common multiple and the least common multiple; From the natural numbers from 1 to 100, you can find the multiples of all natural numbers within 10, and you can find the common multiple and the least common multiple of two natural numbers within 10. Understand the common factor and the greatest common factor; From the natural numbers from 1 to 100, all the factors of a natural number can be found, and the common factor and the greatest common factor of two natural numbers can be found.
There are four sections about "Number and Algebra" in the second volume of Grade Five. "Fraction addition and subtraction" can be used for simple addition and subtraction of fractions (excluding fractions). "Fraction Multiplication" can be used for simple multiplication of fractions (excluding fractions) (positive number multiplied by fraction, fraction multiplied by fraction); Master the concept of reciprocal. "Fraction Division" can perform a simple Divison on fractions (excluding fractions) (fractions divided by positive numbers). "Solving problems with equations" can use equations to express the equivalence relation in simple cases, and can use the properties of equations to solve simple equations. Learn to use equations to solve classic encounter problems.
The first volume of the sixth grade has four sections of "Number and Algebra". "Fraction mixed operation" can be used for simple addition, subtraction, multiplication and division of fractions (mainly divided into two steps, no more than three steps), and equations with fractions can express equality and solve equations. "Percent" combined with the specific situation, understand the meaning of percentage, and know percentage sign, percentage and percentage; Can perform simple mixed operation of percentage addition, subtraction, multiplication and division; Decimals, fractions and percentages will be converted (excluding the conversion of circular decimals into fractions); Can solve the simple practical problem of percentage. "Understanding of comparison" understands the meaning of comparison in the actual situation, grasps the concept of comparison, remembers the concepts of front, back and comparison, and learns to simplify comparison. The application of percentage can solve the simple practical problem of percentage.
There are two sections on "Number and Algebra" in the second volume of Grade Six. "Proportion" understands proportion (equality formula) and the concepts of internal and external terms; Understand the concept of mastering scales; Under certain circumstances, the distance on the map will be converted into the actual distance according to the given ratio; You can use grid paper to enlarge or reduce simple graphics in a certain proportion. "Positive proportion and inverse proportion" understands the quantity in positive proportion and the quantity in inverse proportion through specific situations, and grasps the concepts of positive proportion and inverse proportion; Will be drawn on the grid paper according to the given proportional data, and will estimate the value of another quantity according to the value of one quantity; You can use grid paper to enlarge or reduce simple graphics according to a certain proportion; Be able to find examples of positive and negative proportional relations in life and communicate with them.
The content of "Graphics and Geometry" in the second period can be divided into several parts: graphics cognition, measurement, graphics movement, graphics and position.
The first volume of the fourth grade has two sections: "Graphics and Geometry". "Line and angle" combines examples to understand line segments, rays and straight lines; Find the shortest line segment among all the connecting lines between two points and know the distance between them; Understand the intersection and vertical, translation and parallel relations of two straight lines on the plane; Understand the relationship between rotation and angle of a straight line, right angle and fillet, and the relationship between fillet, right angle, obtuse angle, right angle and acute angle; Can use a protractor to measure the degree of a specified angle, can draw an angle of a specified degree, and can draw angles of 30, 45, 60 and 90 with a triangular ruler. "Direction and Location" will convert the distance on the map into the actual distance according to a given proportion under certain circumstances; Can use number pairs (limited to positive integers) to represent the position on the grid paper, and know the corresponding relationship between number pairs and points on the grid paper; The position of an object can be determined according to its direction and distance from a reference point; A simple road map will be described.
There are two sections on "Graphics and Geometry" in the second volume of Grade Four. "Know triangles and quadrangles" know isosceles triangles, equilateral triangles, right triangles, acute triangles and obtuse triangles; Through observation and operation, it is known that the sum of two sides of the triangle is greater than the third side, and the sum of the inner angles of the triangle is180; Know parallelogram and trapezoid. Observing an object can identify the shape diagram of the object seen from different directions (front, side and top).
The first volume of the fifth grade, Graphics and Geometry, consists of three sections. "Axisymmetry and translation" can further understand the axisymmetric figure and its axis of symmetry, and can draw the axis of symmetry of axisymmetric figure on grid paper; Can complete simple axisymmetric graphics on grid paper; Knowing the translation and rotation of the graphics on the grid paper, we can translate the simple graphics horizontally or vertically on the grid paper and rotate the simple graphics 90 degrees on the grid paper. "Polygon area" learns to compare the area of plane graphics by cutting and filling method and counting grid method; Understand the base and height, explore and master the area formulas of parallelogram, triangle and trapezoid, and solve simple practical problems. "Combination map area" calculates the area by combination and division, and knows the area unit: square kilometers and hectares.
The second volume of the fifth grade, Graphics and Geometry, consists of three sections. Through observation and operation, "cuboid 1" can understand cuboid and cube (including length, width, height, edge, fixed point and so on. ), understand the development diagram and surface area of cuboids, cubes and cylinders, explore and master the calculation method (formula) of the sum of edges and surface areas of cuboids and cubes, and solve simple practical problems. "Cuboid II" understands the concepts of cuboid volume and volume, and explores and grasps the calculation methods (formulas) of cuboid and cube volume in combination with specific situations, which can solve simple practical problems. Determining the position can determine the position of the object according to its direction and distance from the reference point.
There are two sections about "graphics and geometry" in the first volume of grade six. Through observation and operation, "circle" understands the circle, grasps the concepts of center, radius R, diameter D and their relationships, and draws the circle with compasses; Understand the ratio of the circumference to the diameter of a circle as a fixed value, understand the pi and master the formula of the circumference of a circle; Understand the sector, explore and master the area formula of the circle, and solve simple practical problems. "Observing objects" can identify the shape diagrams of objects seen from different directions (front, side and top); Master a measurement method by observing objects.
The second volume of the sixth grade, Graphics and Geometry, has two sections. Cylinders and cones Through observation and operation, we can know cylinders and cones, and know the development diagram of cylinders. Combined with the specific situation, explore and master the calculation method (formula) of surface area and volume of cylinder and volume of cone to solve simple practical problems. The Movement of Graphics understands the translation and rotation of graphics on grid paper through observation and operation. It can translate simple graphics horizontally or vertically on the grid paper, and rotate simple graphics 90 on the grid paper. We can appreciate the patterns in life from the perspectives of translation, rotation and axial symmetry, and use them to design simple patterns on grid paper.
The second issue of "Statistics and Probability" can be divided into two parts: the simple statistical process of data and the possibility of random phenomena.
The content of "statistics and probability" in the first volume of grade four has a section of "possibility" In specific situations, we can feel simple random phenomena through examples; Can list all possible results in simple random phenomena; Through experiments, games and other activities, feel the possibility of random phenomena, qualitatively describe the possibility of some simple random phenomena, and communicate with each other.
The second volume of the fourth grade contains the section of "data representation and analysis" about "statistics and probability", and you can know bar charts and line charts; Can use bar charts and line charts to represent data intuitively and effectively; Understand the concept of average, understand the function of average, calculate average, and explain its practical significance in your own language.
The content of "Statistics and Probability" in the first volume of the fifth grade has a section of "Possibility" to further understand the possibility probability.
The second volume of Grade Five contains the section of "Representation and Analysis of Data". You can know compound bar graphs and compound line graphs and use them to represent data intuitively and effectively. Recognize the average again, understand its function, calculate the average and explain its practical significance in your own language.
The first volume of the sixth grade, Statistics and Probability, includes a section on "data processing" to understand the fan-shaped statistical chart; Data can be represented intuitively and effectively by histogram, fan chart and line chart. Go through a simple process of collecting, sorting, describing and analyzing data; Can design simple questionnaires according to practical problems, and can choose appropriate methods (such as investigation, experiment and measurement) to collect data; Able to read simple statistical charts; Be able to interpret statistical results, make simple judgments and predictions based on the results, and communicate.
A quick glance is superficial after all.
If you can't do it in depth and detail, it is also a good thing to open the book.
If you can organize the knowledge points with tables, trees and mind maps, you will certainly be able to better answer the gains from reading.
Elementary school mathematics is a simple foundation, but it also contains multi-branch contents and the cultivation of various abilities.
Common doubts and the simplest knowledge are often unspeakable; The application of the simplest knowledge, skills and thinking methods is often unknown.
When reading, I feel that my brain is still thinking, which is the greatest reward.