Little knowledge of fifth grade mathematics life (little knowledge of fifth grade mathematics) 1.5 little knowledge of fifth grade mathematics.
O "Everyone despises me and thinks that I am dispensable. Sometimes I don't study, and sometimes I am crossed out in the calculation.
But you know what? I also have a lot of real meaning. 1. I said "No".
When counting objects, if there is no object to count, it must be represented by me. 2. I have a digital role.
When counting, if there is no unit in a certain place of the number, I will take it. For example, in 1080, if there is no unit of hundreds or digits, use: 0 to occupy a position.
I mean the starting point. The starting point of ruler and scale is what I express.
4. I mean the boundaries. On the thermometer, my top is called "above zero" and my bottom is called "below zero".
5. I can express different accuracy. In the approximate calculation, I can't just cross out the end of the decimal part.
For example, the accuracy of 7.00, 7.0 and 7 is different. 6. I can't tell.
It's troublesome for me to go to the branch, because it's meaningless for me to go to the branch. Later, you will learn a lot about my special nature and children. Please don't look down on me.
Why do electronic computers use binary? Because there are ten fingers in human hands, human beings invented decimal notation. However, there is no natural connection between decimal system and electronic computer, so it is difficult to be unimpeded in the theory and application of computer.
Why on earth is there no natural connection between decimal and computer? What's the most natural way to count your computer? This should start with the working principle of computers. The operation of the computer depends on the current. For circuit nodes, only two states of current flow: power-on and power-off.
Computer information storage commonly used hard disk and floppy disk. For each recording point on the disk, there are only two states: magnetized and unmagnetized. In recent years, the practice of recording information with optical discs has become more and more common. An information point on an optical disc has two physical states: concave and convex, which play the roles of focusing and astigmatism respectively.
It can be seen that all kinds of media used by computers can show two states. If you want to record a decimal number, there must be at least four recording points (there can be sixteen information states), but at this time, six information states are idle, which will inevitably lead to a great waste of resources and funds. Therefore, decimal system is not suitable as a digital carry system for computers.
So what kind of carry system should we use? People get inspiration from the invention of decimal system: since every medium has two states, the most natural decimal system is of course binary. Binary counting has only two basic symbols, namely 0 and 1.
You can use 1 for startup and 0 for shutdown; Or 1 means magnetized, and 0 means unmagnetized; Or 1 stands for pits, and 0 stands for bumps. In a word, a binary number just corresponds to an information recording point of a computer medium.
In the language of computer science, one bit of a binary system is called a bit and eight bits are called a byte. It is natural to use binary inside the computer.
But in human-computer communication, binary has a fatal weakness-the writing of numbers is particularly lengthy. For example, decimal number 100000 is written as binary number11010100000.
In order to solve this problem, two auxiliary carry systems-octal and hexadecimal are also used in the theory and application of computers. Three digits in binary are recorded as one digit in octal, so that the length of the number is only one third of that in binary, which is similar to that in decimal.
For example, 100000 in decimal is 303240 in octal. A number in hexadecimal can represent four numbers in binary, so a byte is exactly two numbers in hexadecimal.
Hexadecimal system needs to use sixteen different symbols. In addition to the ten symbols of 0 to 9, six symbols of A, B, C, D, E and F are commonly used to represent (decimal) 10,1,12, 13 and 6553 respectively. In this way, the decimal of 100000 is written in hexadecimal, which is 186A0.
The conversion between binary and hexadecimal is very simple, and the use of octal and hexadecimal avoids the inconvenience caused by lengthy numbers, so octal and hexadecimal have become common notation in human-computer communication. Why are the units of time and angle in hexadecimal? The unit of time is hours, and the unit of angle is degrees. On the surface, they are completely irrelevant.
However, why are they all divided into small units with the same names as parts and seconds? Why do they all use hexadecimal? When we study it carefully, we will know that these two quantities are closely related. It turns out that ancient people had to study astronomy and calendars because of the needs of productive labor, which involved time and angle.
For example, to study the change of day and night, it is necessary to observe the rotation of the earth, where the angle of rotation is closely related to time. Because the calendar needs high precision, the unit of time "hour" and the unit of angle "degree" are too large, so we must further study their decimals.
Both time and angle require its decimal units to have the properties of 1/2, 1/3, 1/4, 1/5, 1/6, etc. Can be an integer multiple of it. The unit of 1/60 has exactly this property.
For example: 1/2 equals 30 1/60, 1/3 equals 20 1/60, 1/4 equals 15 1/60 ... Mathematics. The unit of 1/60 of1is called "second", which is represented by the symbol "1229 1". Time and angle are expressed in decimal units of minutes and seconds.
This decimal system is very convenient in representing some numbers. For example, 1/3, which is often encountered, will become an infinite decimal in decimal system, but it is an integer in this carry system.
This hexadecimal decimal notation (strictly speaking, the sixty abdication system) has been used by scientists all over the world for a long time in the astronomical calendar, so it has been used until today. One day, the brothers of the length unit got together for a meeting, and the big brother "Kilometer" presided over the meeting. It spoke first: "Our unit of length is the international family. Today is a minority in our big family, and people are very strange to us. So, let's introduce ourselves first. "
First, someone stood up from the center of the meeting and said, "My name is Yin, and I'm from China.
2. Knowledge points of mathematics in the fifth grade of primary school
Summary of the knowledge points reviewed at the end of the first volume of mathematics in the fifth grade of primary school Unit 1 Decimal multiplication 1, decimal multiplication integer (p2,3): meaning-a simple operation to find the sum of several identical addends.
For example, 1.5*3 indicates how many times 1.5 is or the sum of three 1.5. Calculation method: first expand the decimal into an integer; Calculate the product according to the law of integer multiplication; Look at a factor * * *, how many decimal places there are, and count the decimal points from the right side of the product.
2. Decimal times decimal (P4, 5): that is, what is the score of this number. For example: 1.5*0.8 is eight tenths of 1.5.
1.5* 1.8 is 1.8 times 1.5. Calculation method: first expand the decimal into an integer; Calculate the product according to the law of integer multiplication; Look at a factor * * *, how many decimal places there are, and count the decimal points from the right side of the product.
Note: In the calculation results, the 0 at the end of the decimal part should be removed to simplify the decimal; When the number of decimal places is not enough, use 0 to occupy the place. 3. Rule (1)(P9): the product of a number (except 0) multiplied by a number greater than 1 is greater than the original number; A number (except 0) is multiplied by a number less than 1, and the product is less than the original number.
4. There are generally three methods to find the divisor: (P 10) (1) rounding method; (2) into law; (3) Truncation method 5. Calculate the amount of money, and keep two decimal places, indicating that the calculation has reached the point. Keep one decimal place, indicating that the angle has been calculated.
6. The operation of (p11) four decimal places is the same as that of an integer. 7. Algorithm and nature: addition: additive commutative law: a+b=b+a addition rule: (a+b)+c=a+(b+c) subtraction: subtraction nature: a-b-c=a-(b+c) a-(b-c)=a-b+c multiplication: C. The significance of fractional division: knowing the product of two factors and one of them, and finding the operation of the other factor.
For example, 0.6÷0.3 means that the product of two known factors is 0.6, and one factor is 0.3, thus finding the other factor. 9. Calculation method of decimal divided by integer (P 16): decimal divided by integer and then divided by integer.
The decimal point of quotient should be aligned with the decimal point of dividend. The integer part is not divided enough, quotient 0, decimal point.
If there is a remainder, add 0 and divide it. 10, (P2 1) Calculation method of division with divisor as decimal: first expand the divisor and dividend by the same multiple to make the divisor an integer, and then calculate according to the rule of fractional division with divisor as integer.
Note: If there are not enough digits in the dividend, make up the dividend with 0 at the end. 1 1, (P23) In practical application, the quotient obtained by fractional division can also be rounded to a certain number of decimal places as needed to obtain the approximate value of the quotient.
Division change of 12, (p24,25): ① Quotient invariance: divisor and divisor expand or shrink by the same multiple (except 0) at the same time, and the quotient remains unchanged. (2) The divisor remains the same, the dividend expands, and the quotient expands.
③ The dividend is constant, the divisor decreases and the quotient expands. 13, (P28) Cyclic decimal: the decimal part of a number. Starting from a certain number, one number or several numbers appear repeatedly in turn. Such decimals are called cyclic decimals.
Circular part: the decimal part of a circular decimal, which is a number that appears repeatedly in turn. For example, the loop part of 6.3232 ... is 32. 14, and the number of digits in the decimal part is a finite decimal, which is called a finite decimal.
The number of digits in the decimal part is infinite decimal, which is called infinite decimal. Unit 3 Observing the object 15, observing the object from different angles may lead to different shapes; When observing a cuboid or cube, you can see at most three faces from a fixed position.
Unit 4 Simple Equation 16, (P45) In a formula containing letters, the multiplication sign in the middle of the letters can be written as "?" , can also be omitted. The plus sign, minus sign, division sign and multiplication sign between numbers cannot be omitted.
17, a*a can write a? A or a, a is pronounced as the square of a, and 2a stands for a+a 18. Equation: An equation with an unknown number is called an equation.
The value of the unknown that makes the left and right sides of the equation equal is called the solution of the equation. The process of solving an equation is called solving an equation.
19, principle of solving equation: balance. The equation still holds when the left and right sides of the equation add, subtract, multiply and divide the same number (except 0) at the same time.
20, 10 quantitative relationship: addition: sum = addend+addend = and-two addend subtraction: difference = minuend-Mei Mei = difference+Mei Mei = minuend-difference multiplication: product = factor * factor = product ÷ another factor division: quotient = 22, equation testing process: = ... a calculation process of solving equations.
= the right side of the equation, so X=… is the solution of the equation. Unit 5 Polygon area 23, formula: rectangle: perimeter = (length+width) * 2- length = perimeter ÷2- width; Width = perimeter ÷2- long letter formula: C=(a+b)*2 area = length * wide letter formula: S=ab square: perimeter = side length *4 letter formula: C=4a area = side length * side length letter formula: S = parallelogram area = bottom * high letter formula: S=ah triangle. Height = area *2÷ letter formula: S=ah÷2 trapezoidal area = (upper bottom+lower bottom) * height ÷2 letter formula: S =(a+b)h÷2- upper bottom = area *2÷ height-lower bottom, lower bottom. Height = area *2÷ (upper bottom+lower bottom) 24. Derivation of parallelogram area formula: shear and translation 25. Derivation of triangle area formula: rotating parallelogram can be transformed into rectangle; Two identical triangles can be combined into a parallelogram, and the length of the rectangle is equivalent to the base of the parallelogram; The base of parallelogram is equivalent to the base of triangle; The width of the rectangle is equivalent to the height of the parallelogram; The height of parallelogram is equivalent to the height of triangle; The area of a rectangle is equal to that of a parallelogram and twice that of a triangle. Because the area of a rectangle is equal to the length * width, and the area of a parallelogram is equal to the bottom * height.
Because parallelogram area = bottom * height, triangle area = bottom * height ÷ 26. Derivation of trapezoid area formula: rotation.
3. What are the knowledge points of mathematics in the fifth grade of primary school?
Mathematics concept synthesis in the first semester of grade five 1, 0 is not correct.
Positive numbers are all greater than 0, and negative numbers are all less than 0. Usually, positive numbers and negative numbers represent two quantities with opposite relations. If the profit is represented by a positive number, then the loss is represented by a negative number; If it is above sea level, it is represented by a positive number; If it is below sea level, it is represented by a negative number.
The boiling point of water is 100℃ and the freezing point of water is 0℃. 2. When calculating the area of irregular figures, those with less than one grid are regarded as semi-grids.
Count full squares first, then half squares. 3. The perimeter of the rectangle = (length+width) *2 The area of the rectangle = the perimeter of the rectangle * the square of the width = the area of the side length *4 square = the side length * the side length 4. Cut along any height of the parallelogram, and then move to form a rectangle.
The length of the rectangle is equal to the base of the parallelogram, and the width of the rectangle is equal to the height of the parallelogram. Because the area of rectangle = length * width, the area of parallelogram = bottom * height, and S=a*h is represented by letters.
5. Assemble two identical triangles into a parallelogram, the base of which is equal to the base of the triangle, and the height of the parallelogram is higher than that of the triangle. The area of the assembled parallelogram is twice that of each triangle, and the area of each triangle is half that of the assembled parallelogram. Because the area of parallelogram is equal to the base * height, the area of triangle is equal to the base * height ÷2.
Use letters to represent S=a*h÷2. Two triangles with equal base and equal height have the same area.
6. Draw the largest triangle in the parallelogram, and the area of this triangle is equal to half the area of this parallelogram. Nail a rectangular frame with thin wooden strips. If you pull it into a parallelogram, its perimeter remains the same and its area becomes smaller, because the bottom remains the same and its height becomes smaller. If parallelograms are drawn into rectangles, their perimeters remain unchanged and their areas become larger.
7. Assemble two identical trapezoids into a parallelogram. The base of the parallelogram is equal to the sum of the upper and lower bases of the trapezoid, and the height of the parallelogram is higher than that of the trapezoid. The area of assembled parallelogram is twice that of each trapezoid, and the area of each trapezoid is half that of assembled parallelogram. Because the area of parallelogram = bottom * height, the letter of trapezoid = (upper bottom+lower bottom) * height ÷2 represents the fraction of S=(a+b)*h÷2.8, and the denominator is 10, 100, 1000. ...
Fractions with denominator of 10 are written as decimals, indicating tenths. Fractions with denominator of 100 are written in two decimal places, indicating a few percent.
Fractions with denominator of 1000 are written in three decimal places, indicating how many thousandths. The first digit to the left of decimal point is unit, the second digit to the left of decimal point of counting unit (1) is ten, the first digit to the right of decimal point of counting unit (10) is ten, the second digit to the right of decimal point of counting unit (0. 1) is percentile, and the counting unit is one percent (0.0 1).
The propulsion rate between two adjacent counting units is 10. 9. 1 includes (10) 0. 1 (one tenth) and 0. 1 (one tenth) and10.01(one percent).
10, the nature of decimal: add "0" or remove "0" at the end of decimal, and the size of decimal remains unchanged. 1 1, with "ten thousand" as the unit: 1, and put a decimal point after ten thousand digits; 2. Add the word "ten thousand".
Use the "=" symbol. Take "hundred million" as the unit: 1, and add a decimal point after the hundred million digits; 2. Add a word "billion".
Use the "=" symbol. Note: Rewriting cannot change the size of the original number.
Omit the mantissa after ten thousand: depending on the number of "thousands", use rounding method to get an approximate value. Use "".
Mantissa after omitting 1 100 million: According to the digits of "1100 million", an approximate value is obtained by rounding. Use "".
Keep an integer, that is, accurate to one place, depending on the first place (tenth place) of the decimal part. Keep a decimal place, that is, accurate to ten places, depending on the second place (percentile) of the decimal part.
Keep two decimal places, that is, accurate to one percent, depending on the third decimal place (one thousandth). Note: When representing approximate values, the "0" at the end shall not be deleted.
For example, decimals with two decimal places are 1 and 50, and the "0" at the end cannot be removed. 1, 50 and 1.5 are equal in size, but different in accuracy. 1.50 means accurate to one hundredth, while 1.5 means accurate to one tenth, so the "0" at the end of 1.50 must not be removed when representing the divisor.
12. When calculating decimal addition and subtraction, the decimal points should be aligned, that is, the same digits should be aligned. 13, find the law: 1, find the cycle; 2. Cycle number; 3. What is the remainder?
4. To calculate the number of items in each project, it can be done in three steps: (1) each item is a group; (2) There are several in each group; Multiply the number of groups (3) by 1 * * *, and finally add the remainder, which is equal to how many there are in a * * *. 14. Problem-solving strategy: List all possible situations one by one. The skill of listing is to consider the larger numbers first (put them in the first row).
15. When calculating fractional multiplication (1), calculation: according to the law of integer multiplication; (2) Look: How many decimal places does one of the two factors have? (3) Number: Count several numbers from the end of the product; (4) Point: Point decimal point; (5) Go: Remove 0 after the decimal point. 16, a decimal is multiplied by 10, 100, 1000 ... just move the decimal to the right by one place, two places, three places ... and divide a decimal by 10, 100.
1 hectare is the area of a square with a side length of 100 m, which is equal to 10000 m2. 1 km2 = 100 hectare.
1 ha = 100 ha = 10000 m2 18, and the operation rules of integer addition, subtraction, multiplication and division are also applicable to decimals. Additive commutative law: a+b=b+a additive associative law: (a+b)+c= a +(b+c) multiplicative commutative law: a*b=b*a additive associative law: (a*b)*c= a *(b*c) The nature of subtraction: A-B-C = A.
4. Five mathematical knowledge in life
In people's daily life, mathematics is everywhere, and the correct use of mathematical knowledge can improve life.
Although mathematics is a great contributor to us humans, if we humans can't use it, it is still "not good for the world". Therefore, we must use our clever brains to make our life more convenient. Magical mathematics is actually around us. Let's start with every little thing around us, and you will find that this magical mathematics affects us all the time and helps us. Mathematical knowledge and ideas exist in industrial and agricultural production and people's daily life. For example, after shopping, people should keep an account for year-end statistical inquiry; Go to the bank to handle savings business; Check the water and electricity charges of each household. These facilitate the use of knowledge of arithmetic and statistics.
In addition, the "push-pull automatic telescopic door" at the entrance of the community and government compound; Smooth connection between straight runway and curved runway in sports field; Calculation of the height of the building whose bottom cannot be closed: determination of the starting point of two-way operation of the tunnel; The design of folding fan and golden section is the property of straight line in plane geometry, and it is about the application of solving Rt triangle knowledge. Mathematics is also widely used in sociology, especially statistics.
It can even be used to avoid epidemics or reduce their effects. When we can't immunize the whole population, mathematics can help us determine who must be vaccinated to reduce the risk.
In the field of art, mathematics is still everywhere. Music, painting, sculpture ... all kinds of arts are helped by mathematics in one way or another.
Japanese sculptor Chao Huisan likes to create his own works with geometry and topology, and carve granite by mathematical calculation. Chao Huisan said: "Mathematics is the language of the universe."
"Mathematics is an intangible culture of our time", which affects our way of life and work in many fields to varying degrees. Of course, ordinary people and scientists understand mathematics from different angles and at different levels. Ordinary people generally only understand the connection between mathematics and one aspect of life, but can't understand its connection with all aspects of life.
People always think that mathematics is abstract and has no direct help to practical work, so it is unnecessary to study and study mathematics in depth. In fact, mathematics, like other sciences, is closely related to our lives.
Mr. Hua, a famous mathematician, once said: "The universe is big, the particles are tiny, the speed of rockets, the cleverness of chemical engineering, the change of the earth and the complexity of daily use require mathematics everywhere." This is a brilliant description of the relationship between mathematics and life by wise scientists.
Contemporary mathematics is far more than arithmetic and geometry, but a colorful subject, which is a creative combination of calculation and deduction. It is rooted in data, presented in abstract form, and helps people to understand and know the world around them by revealing the hidden patterns in phenomena. It involves scientific data, measurement and observation data, reasoning, deduction and proof, mathematical model of natural phenomena, human behavior and social system, numbers, opportunities, shapes, algorithms and changes.
Let me give you an example to show you the application of mathematics in real life. During the Second World War, we faced a series of difficult problems in military, production and transportation: how to detect submarine activities by aircraft, how to deploy limited forces, how to organize production more reasonably, and so on.
In the middle of World War II, Nazi Germany ruled by Hitler was rampant and submarine activities were frequent. At the suggestion of some mathematicians, the plan of aircraft system patrol was adopted.
According to this plan, a certain range of waters can be controlled with as few planes as possible. After the implementation of this plan, the possibility of German submarines being discovered has greatly increased.
1943 In February, the US military learned that a Japanese fleet was assembled on New Britain Island in the South Pacific, intending to cross the Bismarck Sea for New Guinea. The US Southwest Pacific Air Force was ordered to intercept and sink the Japanese fleet.
There are two routes from New Britain to New Guinea, north and south, with a three-day voyage. The weather forecast obtained by the US military shows that the northern line will continue to be rainy in the next three days, and the weather in the southern line will be better.
In this case, will the Japanese fleet go north or south? This is something that the US military must analyze and judge. Because to complete the bombing mission, we must first send a small number of planes to conduct reconnaissance and search, demanding that the Japanese fleet be discovered as soon as possible, and then send a large number of planes to bomb.
The air force commander considered the strategy of sending several planes to search in two ways. There are the following types: first, the search focuses on the north road, and Japanese ships also take the north road. At this time, although the weather is very bad and the visibility is very low, due to the concentrated search power, it is expected that the Japanese ship will be found within one day, so there will be two days of bombing.
Second, the telegram was concentrated in the north road, but the Japanese ship took the south road. At this time, although the weather in the south road is good, it will take another day to find the Japanese ship because the search force is concentrated in the north road and there are only a few planes in the south road.
So the bombing time is only two days. Third, the search focused on the south road, but the Japanese ship went north.
At this time, there are only a few planes on the North Road, and the weather is very bad. It took two days to find the Japanese ship, and there was only one day left for bombing. Fourth, the search focuses on the south road, and Japanese ships also take the south road.
There are many planes searching at this time, and the weather is fine. It can be expected that Japanese ships will be discovered soon. The bombing time is basically three days from the standpoint of Americans. Of course, the fourth situation is the most favorable. However, fighting cannot be "wishful thinking".
From the standpoint of the Japanese, of course, it is much more advantageous to take the north road. So the possibility of the second and fourth cases is very small.
Therefore, the air force commander decisively decided to focus on the North Road. As expected, the Japanese army did choose this route, and the naval battle basically took place in the place expected by the US. As a result, the Japanese army was defeated.
Some people say that mathematics is the queen of science. I think the position of mathematics is very similar to that of philosophy.
Throughout the ages, philosophers have attached great importance to mathematics. Plato, a great philosopher, once wrote a sentence at his door: "People who don't know mathematics are not allowed to enter." This shows the importance of mathematics in the minds of philosophers.
Mathematics, like philosophy, comes from and serves life, seemingly abstract.
5. All the knowledge points of fifth grade mathematics
Grade 5 Mathematics Book 10 Final Examination Paper Result: 1. Fill in the blanks: 20% 1. 2.5 hours = () hours () minutes 5060 square decimeters = () square meters. Divider of 2. 24 is (), and the prime factor of decomposition 24 is (). 3. The decimal unit is the maximum value of 1/8.
4. The numerator of the simplest fraction is the smallest prime number, the denominator is the composite number, and the maximum fraction is (). If you add decimal units like (), you will get 1. 5. Cut a cuboid whose length, width and height are 5 decimeters, 3 decimeters and 2 decimeters respectively into two small cuboids, and the maximum sum of the surface areas of these two small cuboids is () square decimeters.
6. With a 52 cm long wire, you can weld it into a rectangular frame. The frame is 6 cm long, 4 cm wide and () cm high.
7.A = 2 * 3 * 5, B = 3 * 5 * 5, the greatest common divisor of A and B is (), and the smallest common multiple is (). 8. When the side length of a cube is enlarged by 3 times, its surface area is enlarged by () times and its volume is enlarged by () times.
9. Compared with 5/ 1 1, () has a larger decimal unit and a larger fractional value. 10. The greatest common divisor of two numbers is 8 and the least common multiple is 48, where one number is 16 and the other number is ().
Second, multiple-choice questions (fill in the serial number of the correct answer in brackets): 20% 1. In the following formula, the divisible formula is ()14÷ 8 = 0.5239÷ 3 =1335.2÷ 2.6 = 22. Fractions that can be converted into finite decimals are ()13,22,31. 3. The product of the multiplication of two prime numbers must be () 1 addend 2, even number 3 and composite number 4. A = 5b (both A and B are non-zero natural numbers) The following statement is incorrect: ()1The greatest common divisor of A and B is the least common multiple of A2A and B, and A3A is divisible by B, and A contains about 5 5. Add 10g salt into 10g water, and the salt accounts for () ①1/9②110③116. Given A&B, compare 2/a with 2/b () ① 2/a >; 2/b ②2/a .