1, quick calculation 1: quick mental arithmetic.

Fast calculation 1: fast mental calculation-a teaching mode that is really synchronized with primary school mathematics textbooks. It is the only way to make simple calculations without any physical objects, abacus practice, wrench fingers and abacus. The arrangement and difficulty of the textbook "Fast Mental Arithmetic" is a fast calculation that closely follows the syllabus of primary school mathematics and integrates with junior high school algebra, which is simpler than the primary school textbook. Simplify written calculation and strengthen oral calculation. It is simple, easy to learn and interesting. After a short period of training, primary school students can write answers directly by adding, subtracting, multiplying and dividing, not vertically. The peculiar effect of quick mental arithmetic: I have learned the multiplication, division, addition and subtraction of any multi-digit number above grade three. In the second grade, I learned the multiplication and division of multiple digits, and in the first grade, I learned the addition and subtraction of multiple digits. I have already passed the elementary school's oral calculation in advance to learn the addition and subtraction of preschool children's multi-digits. Learning quick mental arithmetic in kindergarten is helpful for children to go to primary school in the future. Children do their homework without draft paper, and write answers directly according to calculations. Fast mental arithmetic is different from abacus mental arithmetic and palm mental arithmetic. Fast mental arithmetic invented by Xi 'an teacher Niu Hongwei. (Teacher Niu Hongwei obtained the patent certificates issued by People's Republic of China (PRC) and China National Intellectual Property Administration. Patent number; ZL200830 1 174275。 Protected by the Patent Law of People's Republic of China (PRC). ) mainly through certain rules in textbooks, children are trained to perform fast operations of addition, subtraction, multiplication and division. "Quick mental arithmetic" is helpful to improve the order, logic and sensitivity of children's thinking and behavior, and train children's eyes, hands and brain to react synchronously and quickly. The calculation method is consistent with mathematics in primary and secondary schools, so it is very popular with parents of young children. Quick heart is a teaching mode that is really synchronized with primary school mathematics textbooks: 1. Learning algorithm-written arithmetic training. At present, China's education system is exam-oriented education, and the standard for testing students is exam transcripts. Then the students' main tasks are to take exams, answer questions, write with a pen, and the training of calculating with a pen is the main line of teaching. Consistent with the mathematical calculation method in primary schools, it does not use any physical calculation, and can be used freely horizontally and vertically, even adding and subtracting. Computing with a pen is the golden key to opening an intelligent express train. 2. Clear the math-math battle. Being able to write questions with a pen not only helps children understand arithmetic, but also helps them understand it. Let children understand the calculation principle and break through the calculation of numbers in spelling. The child completes the calculation on the basis of understanding. 3. Practice speed-speed training, it is far from enough to use a pen to calculate problems. There should be a time limit for oral calculation in primary schools. It takes time to tell whether it is up to standard, that is, there are not enough calculation problems, mainly to speed up. 4. Enlightenment wisdom-intellectual gymnastics is not a simple study and calculation, but focuses on cultivating children's mathematical thinking ability, fully stimulating the potential of the left and right brains and developing the whole brain. After rapid mental arithmetic training, preschool children can deeply understand the essence of mathematics (including), the meaning of numbers (cardinal number, ordinal number, including), the operation mechanism of numbers (addition and subtraction of numbers with the same number) and the way of mathematical logic operation, so that children can master the method of dealing with complex information decomposition and develop divergent thinking and reverse thinking. The child's brain works fast.

Edit paragraph 2. Quick calculation 2: swallow gold in the sleeve

Quick calculation 2: In the CCTV hit drama "Going West", tofu flower praised Ching Tien Association for its quick calculation of "swallowing gold in the sleeve" many times. (that is, you don't need an abacus for calculation)! So what is the speed algorithm of swallowing gold in the sleeve? Swallowing gold in the sleeve is a quick calculation method and a numerical calculation method invented by ancient businessmen in China. The sleeves of ancient clothes were hypertrophy, and only two hands were in the sleeves when calculating, which was called swallowing gold in the sleeves. There used to be a ballad about this calculation method; "Swallowing gold on the sleeve is as wonderful as a fairy, and the number of fingers is moving. You learn priceless treasures, but your bosom friends don't pass them on." The algorithm of swallowing gold in the sleeve is a folk palm calculation method. Businessmen in China do math, and Shanxi businessmen do accounts while walking. Ten fingers are an abacus, so Shanxi people always swallow a pair of hands in their sleeves for fear of revealing his economic secrets. In the past, in order to make a living, people would not easily spread the secret of this algorithm, and a fast calculation method called "swallowing gold in the sleeve", which has been circulating in China for at least 400 years, is also on the verge of extinction. According to relevant data, in A.D. 1573, a scholar named Xu Xinlu wrote a book "The Pearl Plate Algorithm", which first described the rapid calculation of swallowing gold into the sleeve; In A.D. 1592, a mathematician named Cheng Dawei published a book, Algorithm Planning, which described the swallowing of gold in the sleeve in detail for the first time. Later, merchants, especially Shanxi merchants, popularized this ancient quick calculation method. The algorithm of "swallowing gold in the sleeve" is a stunt of Shanxi's bank secrecy, and some big merchants and shopkeepers in xi 'an know this fast algorithm. The method of quickly calculating numbers by swallowing gold into the sleeve is to use five fingers of the left hand as the digital dial, each finger represents a number, and five fingers can represent five numbers: one, ten, hundred, thousand and ten thousand. The upper, middle and lower segments of each finger respectively represent the number 1-9. Arrange three numbers on each section, and the arrangement rules are divided into three columns: left, middle and right. Fingers are arranged upside down on the left (from bottom to top), 1, 2, 3; Fingers are arranged upside down (from top to bottom) in the middle, 4, 5, 6; Fingers are arranged upside down, 7, 8, 9. The calculation method of swallowing gold in the sleeve is a method of using mental arithmetic to reproduce the calculation process with the image of the brain and get the result. It regards the left hand as a virtual abacus with five gears, and clicks the virtual abacus with the right hand to calculate. When counting, point the fingers of your left hand with the fingers of your right hand. Its clear division of labor is: right thumb/left thumb, right index finger, left middle finger, right ring finger, left ring finger and right little finger. The corresponding professional division of labor does not interfere with each other. Which finger is clicked, which finger is extended, and which finger is not clicked, bending, indicating 0. It doesn't need any calculation tools, and it doesn't list arithmetic programs. It only needs to close two hands gently to know the answer number, and can perform four operations of addition, subtraction, multiplication and division on any number within100000 digits. Swallowing gold in the sleeve, its operation speed (after a certain period of practice, of course) can be comparable to that of an electronic computer, multiplication and division are faster than abacus calculation, and square calculation is much faster than pen calculation. Although for beginners, using' swallowing gold in the sleeve' to calculate simple data is not as fast as a calculator, after mastering this skill, the calculation speed is even faster than a calculator. Someone once calculated the speed of the' swallowing gold in the sleeve' algorithm. A person skilled in this skill will get a 3-to 4-digit multiplication result, which takes about 2 seconds. The result is 5 to 7 digits, about 7 seconds; Although the algorithm of swallowing gold into the sleeve is born out of abacus, compared with abacus, it does not need any tools, only uses one pair of hands. Because it has the characteristics of "swallowing gold in the sleeve" without tools and eyes, it is very suitable for field work and can also be used in the dark, especially for the blind, and some problems can be solved through this algorithm. "As the saying goes,' ten fingers are connected to one heart', training calculation skills with fingers can exercise bones and muscles, and clever thinking can promote the mind and improve brain power." Nowadays, businessmen don't have to swallow gold into their sleeves to settle accounts. However, some educators have applied this method to the field of early childhood education. Teacher Niu Hongwei of Xi 'an has been engaged in education for many years, which has improved the swallowing of gold in his sleeve. Make learning easier, more convenient and faster. He has taught thousands of children to learn the improved "swallowing gold in the sleeve". It has a good effect in inspiring children's intelligence. Swallowing gold in the sleeve-developing the child's whole brain. Swallowing gold in the sleeve is not a special function, but a scientific teaching method. More magical than abacus mental arithmetic. It uses hands and brains to complete the fast calculation of addition, subtraction, multiplication and division with amazing speed and high precision. It effectively develops students' brains and stimulates their potential. Innovative fast calculation of swallowing gold in sleeve —— whole brain palmprint calculation —— Niu Hongwei obtained the patent certificate issued by People's Republic of China (PRC) and China National Intellectual Property Administration on May 6th, 2009. Patent number; ZL200830 1 164377。 . Protected by the Patent Law of People's Republic of China (PRC). The speed algorithm of swallowing gold in the sleeve reduces the complicated calculation process of the pen calculation formula, saves time and effort, and improves the calculation speed of students. You can calculate the addition, subtraction, multiplication and division of any number within100000 digits by hand and brain, and use it to quickly complete the calculation of addition, subtraction, multiplication and division with high accuracy. After two or three months' study, with calculations like 64983+68496 and 78×63, junior children can blurt out the answers with their hands folded. Innovate the algorithm of swallowing gold in the sleeve-the whole brain palm is a way for children to remember it in their hands and work it out in their minds. Without any calculation tools, they will know the answer with their hands folded. This method is to count the knuckles of the left hand by simulating the bead counting gear on the abacus, and use the left hand as a "five-gear abacus" and use the right hand to draw beads, thus making the human hand a perfect calculator. Students can calculate the result of 100 thousand digits in the calculation process, which is easy to understand and learn. It can really exercise children's brain, heart and hands, and improve their computing ability, memory and self-confidence.

Edit this paragraph 3, quick calculation 3: Montessori quick calculation

Quick calculation 3: Montessori quick calculation is the development and innovation on the basis of Montessori mathematics, which is relatively young, and "Montessori quick calculation" is aimed at preschool children. The biggest advantage is that children are well connected, which is consistent with the calculation method of primary school mathematics. Suitable for kindergarten middle school children and primary school students. Montessori's fast calculation can make children deeply understand the basic principle of digital calculation in play. In this way, it is easy to break through children's mathematical calculations. The calculation of numbers includes abstract thinking such as inclusion, classification, decomposition and merger, induction and symmetrical logical reasoning. However, preschool children can only think in images and cannot understand and reason, so it is very difficult for preschool children to learn calculation. The birth of the Montessori Fast Calculation Card enables the principles of mathematical calculation to be presented to children in the form of images. When children understand arithmetic, natural calculation will be simple. The spelling of the numbers 5 and 6 not only shows the answer, but also shows why you should carry it. This is the latest invention patent of Mr. Xi An Niu Hongwei, Montessori Quick Calculation (patent number: ZL200830 1 164396). Its card contains four information: the writing method of number, the shape of number, the amount (base) of number and number. Thereby easily leading children into the interesting digital kingdom. Montessori quick calculation-the calculation principle is simple, which fully conforms to the national nine-year compulsory education curriculum standard, so that 4.5-year-old children can learn addition and subtraction within 10 thousand in one semester. Montessori's quick calculation starts with the most basic concept of number, which is consistent with the mathematical calculation method in primary schools. But the teaching method is simple, and students are easy to learn and accept. The relaxed and pleasant Montessori quick calculation teaching uses digital images such as cartoons and objects to visualize abstract and boring mathematical concepts and simplify complex problems. Montessori fast calculation is a new method to connect the best math courses for children and improve their math quality.

Edit paragraph 4. Fast Calculation 4: Fast Calculation of Special Numbers

Fast calculation 4: Fast calculation of conditional special numbers. The fast calculation principle of two-digit multiplication: let two digits be 10A+B and 10C+D respectively, and the product is s, According to the polynomial expansion: s = (10a+b )× (10c+d) =10a×10c+b×10c+/kloc-0. Please don't forget that the first product is the first two digits, the second product is the last two digits and the middle product is the middle two digits. A: Multiplication is very fast. The first few are the same: 1. 1. That is, A = C = 1, B+D = 10, s = (10+b+d) ×10+a× b method: the hundred digits are two, the digits are multiplied, the digits are the last product, and the first ten digits are full. Example:13×1713+7 = 2-("-"is used as a mnemonic when you are not proficient. You can stop using it after you are proficient) 3× 7 = 2 1-22 1 means13×17 = 2216538. B+D ≠ 10, s = (10+b+d) ×10+a× b method: the digits of the multiplier are added to the multiplicand, and the number is the front product. When the digits of two numbers are multiplied, the number is the back product and the first ten digits are full. Example:15×1715+7 = 22-("-"is used as a mnemonic when you are not proficient, and you can stop using it after you are proficient) 5× 7 = 35-255 means15×/kloc-0. S = a × (a+1) ×/kloc-0+a× b method: add1to the ten digits, and multiply the sum by the ten digits. The digits are the previous product and the single digits are multiplied. For example, the product is 56× 54 (5+1)× 5 = 30-6× 4 = 24-30241.4. Ten digits are the same. S=A×(A+ 1)× 10+A×B method: the first two are multiplied by the first one, and the number is the front product and the number is the back product. Multiply the first of several multipliers by 10 according to whether the multiplier is greater than or less than 10. And vice versa: 67× 64 (6+1)× 6 = 427× 4 = 28 7+4 =1-10 =14228+. 2. Multiply the first two digits (that is, find the square of the first digit), and the number obtained is the front product. When the sum of the two mantissas is multiplied with the first digit, the number obtained is the middle product. When the two mantissas are multiplied, the number obtained is the back product. For example: 67× 64 6× 6 = 36-(4+7 )× 6 = 66-4× 7 = 28-4288. If the last number is the same, it is 2.65438+. A+c =10s =10a×10c+10/method: multiply ten digits to get the product, and then add1kloc-0/. -8× 2 = 1 6-1017012.2.<'s not very simple > the unit is1,and the ten digits are not complementary, that is, b = d = For example: 71× 9170× 90 = 63-70+90 =16-1-646655. A+C =10s =10a×10c+25 Method: the product of ten digits, plus the sum of ten digits as the front product, plus 25. Example: 35× 75 3× 7+5 = 26-25-2625 2.4 digits are 5, and the ten digits are not complementary, that is, b = d = 5, a+c ≠10s =10a×10c+522. For example: 86× 26 8× 2+6 = 22-36-2236 2.6. The digits are the same, but they are not complementary: the digits are multiplied by the digits, and the digits are the front product. And vice versa: 73× 43 7× 4+3 = 3197+4 =113109+30 = 3139-. Ten-bit non-complementary speed algorithm method 2: the first multiplication by the head, the square of the tail, plus the result of the head and the tail, and the tail multiplication 10 example: 73× 437× 4 = 289 2809+(7+4 )× 3×10 = 2809+1kloc. Methods: Add 1 to the first digit of complement, multiply the sum by the first digit of multiplicand, the number is the front product, the two mantissas are multiplied, the number is the back product, and there is no ten digits to complement 0. Example: 66× 37 (3+1)× 6 = 24-6× 7 = 42-2442 3.2, the number of a factor is the same from beginning to end, and the ten digits of a factor are not complementary to the single digits. Methods: Add 1 to the first digit of the random number, and multiply the sum by the first digit of the multiplicand. The number is the front product, and the two mantissas are multiplied, and the number is the back product. If there are no ten digits, add 0. Then see how much the sum of non-complementary factors is larger or smaller than 10, and multiply several numbers with the same number by ten. And vice versa: 38× 44 (3+1) * 4 =128 * 4 = 321632 3+8 =1-kloc-0/0 =/kloc. Then see how many different factor tails are bigger or smaller than the first one, and multiply the first of several remainders by ten. And vice versa: 46× 75 (4+1) * 7 = 356 * 5 = 305-7 =-22 * 4 = 8 3530-80 = 3450-. Method: Add 1 to the first place of 9, and then multiply it by the first place's complement, and the number obtained is the front product. Multiply the complement of the mantissa of the first digit less than the mantissa by the number of 9 and add 1 to the back product. No ten digits complement 0. Example: 56× 3610-6 = 43+1= 45 * 4 = 204 * 4 =16-20163.5, two factors. Method: Determine multiplier and multiplicand, and vice versa. Multiply the multiplier head by one, the number is the front product, the tail is multiplied by the tail, and the number is the back product. Let's see how much the head of the multiplicand is bigger or smaller than the head of the multiplier. If it is larger, multiply the tails of several multipliers by ten. And vice versa: 74× 56 (7+1) * 5 = 404 * 6 = 247-5 = 22 * 6 =12 */kloc-0 =120 4024+/kloc-0. The difference between the two factors is one, and the mantissa is 23 * 3-1= 862 = 36 100-36 = 64-864 3.7, near100. Algorithm method: Determine the multiplier and multiplicand, and vice versa. The multiplicand subtracts the multiplier's complement to get the front product, and then multiplies the two numbers' complements to get the back product (if it is less than 10, for example: 93× 9100-91= 9 93-9 = 84100-) Find the square of 1 1 ~ 19, which is the same as that of 1.2. When the digits of the multiplier are added to the multiplicand, the number is the front product, and when the digits of the two numbers are multiplied, the number is the back product. An example before the tenth birthday:17×1717+7 = 24-7× 7 = 49-289. The square of two digits with the unit of 5 is the same as above 1.3, ten. Example: 35× 35 (3+1)× 3 =12-25-1225 The square of two digits with four or ten digits is the same as above. Example: When 53× 53 25+3 = 28-3× 3 = 9-2809 IV, 2 1 ~ 50 is used for the square of two digits between 25 and 50, 1 ~19 refers to the first/kloc-0. Remember the following four data: 21= 44122 = 48423× 23 for example: 37× 37 37-25 =12-(50-37) 2 =169-. For example, 10 minus 9 equals 1, then the complement of 9 is 1, and vice versa. Application of Complement: Complement is often used in fast calculation. For example, find the multiplication or division of two numbers close to 100, and turn the seemingly complicated subtraction operation into a simple addition operation. D, division speed 1. When a number is divided by 5,25, 125, dividend ÷ 5 = dividend ÷ (10 ÷ 2) = dividend ÷ 10 × 2 = dividend. Dividend ÷ 25 = dividend × 4 ÷ 100 = dividend × 2 ÷ 100 3, dividend ÷ 125 = dividend × 8 ÷ 1000. Because of my limited level, the above algorithm is not necessarily the best heart algorithm.

Edit this paragraph 5. Quick calculation 5: Quick calculation of historical gains

Quick calculation 5: the quick calculation of historical harvest is a quick calculation method invented by the quick calculation master Shi Fengshou after 10 years of research. It is a method of direct calculation by the brain, also known as fast mental arithmetic, fast mental arithmetic. This method breaks the traditional method of counting from the low position for thousands of years, and summarizes 26 formulas by using the carry rule. Counting from the high position and counting with the help of fingers can speed up the calculation, which can instantly calculate the correct results, help human beings develop their brain power and strengthen their ability to think, analyze, judge and solve problems. It is a great pioneering work of contemporary applied mathematics. This set of calculation method, officially named "Fast Algorithm of Historical Harvest" by the state in 1990, has been incorporated into the mathematics textbook of modern primary schools in China's nine-year compulsory education. UNESCO praised it as a miracle in the history of educational science and should be popularized all over the world. The main features of the historical harvest speed algorithm are as follows: ⊙ Starting from a high position, from left to right ⊙ No calculation tools ⊙ No calculation program ⊙ Directly reporting the correct answer when you see the formula ⊙ It can be applied to the addition, subtraction, multiplication and division of multi-bit data, as well as examples of practical fast calculation in mathematical operations such as power, root, trigonometric function and logarithm ○ The fast algorithm of historical harvest is simple and easy to learn. The algorithm starts with high digits, and remembers 26 formulas summarized by the professor of history (these formulas don't need to be memorized, but they conform to scientific laws and are interrelated) to express the carry law of multiplying one digit by multiple digits. If you master these formulas and some specific rules, you can add, subtract, multiply and divide quickly. In this paper, an example of multiplication shows that the zero-speed algorithm, like the traditional multiplication, needs to deal with each bit of the multiplier bit by bit. We call the number being processed in the multiplicand "standard", and the number from the first digit to the last digit on the right side of the standard is called "last digit". After the standard is multiplied, only the single digit of the product is taken as "this bit", and the number to be carried after the standard is multiplied by the multiplier is "the last bit". ○ Every bit of the product is a single digit of the sum of "Ben plus Backward", that is, the single digit of the sum of-□ standard product = (Ben plus Backward) ○ Then when we calculate, we must find out Ben and Backward one by one from left to right, and then add them to get its single digits. Now, let's give a correct example to illustrate the thinking activity in calculus. (Example) The first digit of the multiplicand is supplemented by 0, and the formula is as follows: 7536×2= 15072. The carry rule of the multiplier of 2 is "2 all quintiles 1", 7× 2 is a 4, the last digit is 5, and 4+1 is a 5× 2. 6+ 1 gets 7 6×2, without postposition, gets 2. Here we only give the simplest examples for readers' reference. As for multiplication 3, 4 ... to multiplication 9, there are certain carry rules, which cannot be listed one by one due to space constraints. Based on these carry rules, a "historical harvest fast algorithm" is gradually developed. As long as it is skillfully used, the purpose of calculating four multi-digit operations quickly and accurately can be achieved. & gt& gt Exercise Example 2 □ Mastering the knack The algorithm of human brain winning computer history is not complicated, and it is easier to learn, faster and more accurate than the traditional calculation method. Professor Shi Fengshou said that ordinary people can master the tricks as long as they study hard for one month. For accountants, businessmen and scientists, fast algorithms can improve the calculation speed and work efficiency; For students, it can develop their intelligence, use their brains flexibly, and help improve their math and physics abilities.