Multi digit computing power
Publish: 2021-04-13 16:44:11
1. 1 / 6 first of all, it is clear that the knowledge system
multiplication of multiple digits by one digit is based on children's learning and mastering multiplication in the table (i.e. multiplication formula) and addition and subtraction within 100. Therefore, mastering these two knowledge points is the premise of learning how to multiply multiple digits by one digit< The first level is oral multiplication. First, learn how to multiply the whole ten, the whole hundred, the whole thousand by one digit and the two digit by one digit
3 / 6
the second level is to multiply multiple digits by one digit. From carry to carry to multiply with 0 in the middle and at the end of the multiplier. Understand the meaning of each step in the vertical calculation
4 / 6
the third level is: solving problems (solving practical problems). It is divided into solving problems by estimation and solving problems by multiplication and division
5 / 6
finally, understand the calculation principle and make clear the practice
multiply multiple digits by one digit: multiply each digit of another multiplier with one digit, and then add the proct
6 / 6
in addition, mastering how to multiply multiple digits by one digit requires proper practice. Besides, we should connect with life more and improve our ability to solve problems.
multiplication of multiple digits by one digit is based on children's learning and mastering multiplication in the table (i.e. multiplication formula) and addition and subtraction within 100. Therefore, mastering these two knowledge points is the premise of learning how to multiply multiple digits by one digit< The first level is oral multiplication. First, learn how to multiply the whole ten, the whole hundred, the whole thousand by one digit and the two digit by one digit
3 / 6
the second level is to multiply multiple digits by one digit. From carry to carry to multiply with 0 in the middle and at the end of the multiplier. Understand the meaning of each step in the vertical calculation
4 / 6
the third level is: solving problems (solving practical problems). It is divided into solving problems by estimation and solving problems by multiplication and division
5 / 6
finally, understand the calculation principle and make clear the practice
multiply multiple digits by one digit: multiply each digit of another multiplier with one digit, and then add the proct
6 / 6
in addition, mastering how to multiply multiple digits by one digit requires proper practice. Besides, we should connect with life more and improve our ability to solve problems.
2.
example: 21 × 41=
solution: 2 × 4=8
2+4=6
1 × 1=1
21 × 41 = 861
example: 13 × 326=< The 13 bits are 3
3 × 3+2=11
3 × 2+6=12
3 × 6=18
13 × 326 = 4238
note: one must be added to the sum of ten
The fast calculation method of multi digit multiplication is as follows:
1, more than ten times more than ten: Formula: head by head, tail by tail, tail by tail
example: 12 × 14=
solution: 1 × 1=1
2＋4＝6
2 × 4＝8
12 × 14 = 168
note: if the number of indivial digits is multiplied by each other, if it is less than two digits, 0 should be used
2. The head is the same and the tail is complementary (the sum of the tails is equal to 10): Formula: after a head plus 1, the head multiplies the head and the tail multiplies the tail
example: 23 × 27=
solution: 2 + 1 = 3
2 × 3＝6
3 × 7＝21
23 × 27 = 621
note: if the number of digits is multiplied by one, if it is less than two digits, 0 should be used
3. The first multiplier complements each other, and the other multiplier has the same number: the formula: after a head plus 1, the head multiplies the head, and the tail multiplies the tail
example: 37 × 44=
solution: 3 + 1 = 4
4 × 4=16
7 × 4=28
37 × 44 = 1628
note: if the number of digits is multiplied by one, if it is less than two digits, 0 should be used
example: 21 × 41=
solution: 2 × 4=8
2+4=6
1 × 1=1
21 × 41 = 861
5, 11 times any number: pithy formula: head and tail do not move down, the sum of the middle pull down
example: 11 × 23125=
solution: 2 + 3 = 5
3 + 1 = 4
1 + 2 = 3
2 + 5 = 7
2 and 5 are at the head and tail
11, respectively × 23125 = 254375
note: when he is ten, he must enter one
example: 13 × 326=< The 13 bits are 3
3 × 3+2=11
3 × 2+6=12
3 × 6=18
13 × 326 = 4238
note: one must be added to the sum of ten
3. For example, 79 * 13 = 80 * 13-13
for another example, 63 * 25 = 63 * 4 * 25 / 4
3, more vertical operation, practice makes perfect
4, there is a strange line multiplication, such as 12 * 15
vertical drawing |||||||||||||||
let them intersect
oblique view, there are three rows of intersection points, the first row is ||||||||||||||||, The second row is the intersection of |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
for another example, 63 * 25 = 63 * 4 * 25 / 4
3, more vertical operation, practice makes perfect
4, there is a strange line multiplication, such as 12 * 15
vertical drawing |||||||||||||||
let them intersect
oblique view, there are three rows of intersection points, the first row is ||||||||||||||||, The second row is the intersection of |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
4. Let's start with the high order of division, such as 3276 ÷ 24, the divisor is 24, which is a two digit number. Then, we can see that the highest two digits of the divisor are 32, which can be up to 1, and there are 8 and 8 left in the hundreds. We can also find the 7 of the ten digits, that is, 87 divided by 24, which can be up to 3, and the remaining 15, which can be down to the low level if it is not enough.
generally speaking, it is not difficult to divide the multi digit number into several two digit numbers, starting from the high level, The remainder is the highest of the next two digits. If the divisor is a 3-digit number, it can be divided into several 3-digit numbers, and so on.
generally speaking, it is not difficult to divide the multi digit number into several two digit numbers, starting from the high level, The remainder is the highest of the next two digits. If the divisor is a 3-digit number, it can be divided into several 3-digit numbers, and so on.
5. Add: first add from one digit, every decimal one, in to ten, hundred, and so on to get the final result
subtraction: start with the subtraction of indivial digits, and if it is not enough to borrow from ten digits, one will be subtracted, and ten digits will be subtracted by one; From the first to the tenth, and so on
subtraction: start with the subtraction of indivial digits, and if it is not enough to borrow from ten digits, one will be subtracted, and ten digits will be subtracted by one; From the first to the tenth, and so on
6. Multi digit number refers to the number composed of three or more digits, which is called multi digit number.
7. There are two kinds of division: division by return and division by quotient.
division is calculated by pithy formula, including nine return pithy formula, withdrawal pithy formula and nine quotient pithy formula.
nine return pithy formula has 61 sentences:
one return (divided by 1): every one enters one, every two enters two, every three enters three, every four enters four, every five enters five, every six enters six, every seven enters seven, every eight enters eight, Every nine into nine.
two returns (divide by 2): every two into one, every four into two, every six into three, every eight into four, 21 into five.
three returns (divide by 3): every three into one, every six into two, every nine into three, 31 into three, 32 into three, 32 into two.
four returns (divide by 4): every four into one, every eight into two, 42 into five, 41 into two, Four three seven more than two.
five GUI (divide by five): every five into one, five one times make two, five two times make four, five three times make six, five four times make eight.
six GUI (divide by six): every six into one, every twelve into two, six three add five, six one add four, six two three more than two, six four six more than four, six five eight more than two.
seven GUI (divide by seven): every seven into one, every fourteen into two, Seven one adds three, seven two adds six, seven three four more than two, seven four five more than five, seven five seven more than one, seven six eight more than four.
eight GUI (divide by eight): every eight enters one, eight four adds five, eight one adds two, eight two adds four, eight three adds six, eight five six more than two, eight six seven more than four, eight seven seven more than four, eight seven eight more than six.
nine GUI (divide by nine): every nine enters one, nine one adds one, There are nine sentences in the formula of quitting business:
one without quitting business, two without quitting business, three without quitting business,
four without quitting business, five without quitting business, five without quitting business, six without quitting business,
seven without quitting business, The formula of Shang Jiu consists of nine sentences:
see one nothing except for ninety-one, see two nothing except for ninety-two, see three nothing except for ninety-three,
see four nothing except for ninety-four, see five nothing except for ninety-five, see six nothing except for ninety-six,
see seven nothing except for ninety-seven, see eight nothing except for ninety-eight, see nine nothing except for ninety-nine
division is calculated by pithy formula, including nine return pithy formula, withdrawal pithy formula and nine quotient pithy formula.
nine return pithy formula has 61 sentences:
one return (divided by 1): every one enters one, every two enters two, every three enters three, every four enters four, every five enters five, every six enters six, every seven enters seven, every eight enters eight, Every nine into nine.
two returns (divide by 2): every two into one, every four into two, every six into three, every eight into four, 21 into five.
three returns (divide by 3): every three into one, every six into two, every nine into three, 31 into three, 32 into three, 32 into two.
four returns (divide by 4): every four into one, every eight into two, 42 into five, 41 into two, Four three seven more than two.
five GUI (divide by five): every five into one, five one times make two, five two times make four, five three times make six, five four times make eight.
six GUI (divide by six): every six into one, every twelve into two, six three add five, six one add four, six two three more than two, six four six more than four, six five eight more than two.
seven GUI (divide by seven): every seven into one, every fourteen into two, Seven one adds three, seven two adds six, seven three four more than two, seven four five more than five, seven five seven more than one, seven six eight more than four.
eight GUI (divide by eight): every eight enters one, eight four adds five, eight one adds two, eight two adds four, eight three adds six, eight five six more than two, eight six seven more than four, eight seven seven more than four, eight seven eight more than six.
nine GUI (divide by nine): every nine enters one, nine one adds one, There are nine sentences in the formula of quitting business:
one without quitting business, two without quitting business, three without quitting business,
four without quitting business, five without quitting business, five without quitting business, six without quitting business,
seven without quitting business, The formula of Shang Jiu consists of nine sentences:
see one nothing except for ninety-one, see two nothing except for ninety-two, see three nothing except for ninety-three,
see four nothing except for ninety-four, see five nothing except for ninety-five, see six nothing except for ninety-six,
see seven nothing except for ninety-seven, see eight nothing except for ninety-eight, see nine nothing except for ninety-nine
8. Generally, in the book of decimal addition and subtraction, the last few decimal places can form an integer (the number of decimal places is usually two) or only one decimal place, but the decimal place is five, and irregular ones are generally one decimal place addition and subtraction
add the decimal places first, and remember the part that can form an integer first, then add the integral part, and finally add the previously recorded part
or you can bring it in directly, but don't forget to add it more than once It is suggested to check the calculation after calculation. You can check the calculation if you want, but I don't think it's very useful. Most people don't check the calculation seriously after calculating it once It depends on the indivial. If you can't take it seriously, don't forget it. It's a waste of time. Those who are very serious can continue to keep) come on! I wish you learn decimals well.
add the decimal places first, and remember the part that can form an integer first, then add the integral part, and finally add the previously recorded part
or you can bring it in directly, but don't forget to add it more than once It is suggested to check the calculation after calculation. You can check the calculation if you want, but I don't think it's very useful. Most people don't check the calculation seriously after calculating it once It depends on the indivial. If you can't take it seriously, don't forget it. It's a waste of time. Those who are very serious can continue to keep) come on! I wish you learn decimals well.
9. 1. In the creation of the situation, starting from the actual life of students. Contact them to hold the winter long-distance race, show the problem situation, put forward, what do you understand, make them feel that "problems" exist in life, around them, every moment will proce, and solving problems is our need, shorten the distance between mathematical problems and students' emotion
2. Let the students ask questions freely. After creating a situation, ask: according to the information in the picture, who can ask a mathematical question? Not many students raised their hands in the class, and then I asked: what else do you want to know? At this time, more students raised their hands in the class. From the mouth of the students burst out a question, of which there are six valuable. These two different ways of asking questions make me feel that there is a sense of question among students. The key is that teachers' language should be close to students' life, consider from their point of view, and create space, so that students can create more space for themselves
3. In solving problems, we should explore independently. Students ask six valuable questions. When the students asked questions, I wrote on the blackboard: ① how far is Dasheng's home from the stadium than Xiaohua's? ② How many meters are Dasheng's and Xiaohua's away from the stadium How many meters is Xiaohua's stadium? How many meters is Dasheng's home from the stadium ③ How many meters does Dasheng travel more than Xiaohua per minute? ④ How many meters did Xiao Hua Run? ⑤ How many meters is the distance between his two families? ⑥ Which of them got to the stadium first? The third problem is old knowledge, which they have the ability to solve. After the sixth question was put forward, the students answered immediately, because they all arrived in 4 minutes, so they arrived at the same time. Then, according to the teaching task of this lesson, let the students do it by themselves and use their brains to explore and communicate the two hidden problems in the second question. The calculation method of multiplying three digits by one digit is the focus of this lesson. Let the students have a bold try and explore the calculation method independently. For the first and fifth questions, I wanted to stay after class. But when the bell rang, the students proposed that it could be solved immediately, so I respected the students' wishes and answered. This treatment leaves students a lot of thinking space, many problems for students to find and solve. It's good for the cultivation of students' problem awareness, because the students' performance in class gives me a more positive response. At the same time, the larger space also provides students with free choice space, which reflects different students' different ideas of learning mathematics.
2. Let the students ask questions freely. After creating a situation, ask: according to the information in the picture, who can ask a mathematical question? Not many students raised their hands in the class, and then I asked: what else do you want to know? At this time, more students raised their hands in the class. From the mouth of the students burst out a question, of which there are six valuable. These two different ways of asking questions make me feel that there is a sense of question among students. The key is that teachers' language should be close to students' life, consider from their point of view, and create space, so that students can create more space for themselves
3. In solving problems, we should explore independently. Students ask six valuable questions. When the students asked questions, I wrote on the blackboard: ① how far is Dasheng's home from the stadium than Xiaohua's? ② How many meters are Dasheng's and Xiaohua's away from the stadium How many meters is Xiaohua's stadium? How many meters is Dasheng's home from the stadium ③ How many meters does Dasheng travel more than Xiaohua per minute? ④ How many meters did Xiao Hua Run? ⑤ How many meters is the distance between his two families? ⑥ Which of them got to the stadium first? The third problem is old knowledge, which they have the ability to solve. After the sixth question was put forward, the students answered immediately, because they all arrived in 4 minutes, so they arrived at the same time. Then, according to the teaching task of this lesson, let the students do it by themselves and use their brains to explore and communicate the two hidden problems in the second question. The calculation method of multiplying three digits by one digit is the focus of this lesson. Let the students have a bold try and explore the calculation method independently. For the first and fifth questions, I wanted to stay after class. But when the bell rang, the students proposed that it could be solved immediately, so I respected the students' wishes and answered. This treatment leaves students a lot of thinking space, many problems for students to find and solve. It's good for the cultivation of students' problem awareness, because the students' performance in class gives me a more positive response. At the same time, the larger space also provides students with free choice space, which reflects different students' different ideas of learning mathematics.
10. First look at the size of the highest digit. If the highest digit is the same, push it down one by one
Hot content