§ 1 Algorithm for written subtraction of many-digit numbers
Consider an algorithm for written subtraction of many-digit numbers. For example, we need to find the difference between 397.539 and 25.128.
1. Let's read them. Decreased - 397.539, subtracted - 25.128.
2. Determine the number of digits in each number. This is a six-digit and five-digit number.
3. We write the numbers one under the other so that the units of the same digits are in the same column.
We subtract bit units, starting from the very first digit - units, ending with the last digit - tens of thousands.
9 units minus 8 is 1.
3-digit tens will decrease by 2-digit tens, there will also be 1.
Subtract hundreds of places. 5 minus 1 is 4.
In the class of thousands, from 7 units of thousand, subtract 5 units of thousand, we get 2.
Subtract tens of thousands last. Nine minus two equals seven.
Bit hundreds of thousands remain unchanged.
4. We read the answer. This six-digit number is 372.411.
§ 2 Algorithm for written subtraction of three-digit numbers
Consider an algorithm for subtracting three-digit numbers. You need to remember the bit composition of the number. For example, we need to subtract 6 from 750. Let's represent the reduced as the sum of the digit terms: 750 = 700 + 50
The rule must always be observed: actions are performed with units of the same digits, starting with the smallest one. It is impossible to subtract 6 from zero, therefore, the reduced one can be represented as the sum of the bit terms as follows:
From 5 tens we take one tens, then subtract 6 from this ten and get 4. The value of the difference is 700 + 40 + 4 = 744.
Let's try to record this subtraction action in a column. When subtracting bit units, we occupied one ten bit. In order not to forget about this, let's put a dot over the number 5 on the memory line. When subtracting the tens of digit, the dot will remind us that there are only 4 tens of digit left. Thus, a point on a line of memory is put if it is impossible to perform subtraction without units of a larger digit.
§ 3 Subtraction of multidigit numbers with the transition to the next digit
Consider the subtraction of multidigit numbers with the transition to the next digit.
Decreased - 290.380, subtracted - 37.161. This is a six-digit and five-digit number.
We write the numbers one under the other so that the units of the same digits are in the same column.
We subtract bit units, starting from the very first digit - units, and end with the last digit - tens of thousands.
It is impossible to subtract 1 from 0, we occupy one-digit ten, and in order not to forget, we put a period on the memory line above the ten-digit. Subtract 1 from 10, you get 9 digit units. The dot reminds us that there are 7 digit tens left 7 minus 6, we get 1.
Subtract hundreds of places. 3 minus 1 would be 2.
In the decreasing number of units, thousands are worth 0. This means that we need to borrow ten thousand. To remember, we put a point on the memory line and subtract 7 from 10. You get 3 thousand-bit units.
In bit tens of thousands, taking into account the dot mark, it turns out 8. 8 minus 3 will be 5. Bit hundreds of thousands remain unchanged.
We read the answer: the value of the quotient is the six-digit number 253.219.
§ 4 Brief conclusions on the topic of the lesson
Thus, the written subtraction of multidigit numbers is performed in a column according to certain rules:
Firstly, it is necessary to write the numbers one under the other so that the units of the same digits are in the same column.
Thirdly, if it is impossible to subtract bit units without using higher bit units, a dot is put on the memory line.
Lesson topic: ALGORITHM FOR SUBTRACTING A COLUMN
Target: compose an algorithm for subtracting six-digit numbers in a column; improve computing skills.
Tasks: to form the ability to compose tasks in a circular pattern, according to a brief entry in the form of a table; develop the ability to analyze and generalize.
UUD:
Personal:
The internal position of the student at the level of understanding the need for learning, expressed in the predominance of educational and cognitive motives;
Metasubject:
Regulatory:
Accept and maintain the learning task and actively engage in activities aimed at solving it in cooperation with the teacher and classmates;
2. Cognitive:
- search for the necessary information to complete educational tasks using educational literature;
Possess a general technique for solving problems;
Build logical reasoning, including the establishment of cause-and-effect relationships.
3. Communicative:
- perform orally addition, subtraction of single, two-digit numbers in cases that can be reduced to actions within 100;
4. Regulatory:
- plan your action in accordance with the task and the conditions for its implementation, including in the internal plan;
Distinguish between the way and the result of the action; control the process and results of activities;
During the classes
I. Organizational moment.
II. Verbal counting.
1. Solve examples.
2 + 55 = 72 - 30 = 83 - 3 =
38 + 49 = 73 + 6 = 91 - 24 =
- Write an example where the first term is a three-digit number:
1) the first term;
2) the second term;
3) the amount;
4) reduced;
5) deductible;
6) the difference.
2. Read the numbers:
81, 18, 680, 806, 8 001, 800 000, 8 000 000, 808 000 008.
What does the number 8 stand for in each of these numbers?
3. Write the number in which:
a) 4 thousand 2 s. 6 days 1 unit; b) 54 thousand 3 s. 9 days 8 units;
3 thousand 9 days 8 units; 60 thousand 4 d 6 units;
7 thousand 7 units; 300 thousand 6 units
III. Work on the topic of the lesson.
- Today in the lesson we will learn how to perform subtraction in a column of six-digit numbers.
1. Exercise 218.
Students subtract these numbers using a bit table.
2. Exercise 219.
- Do long subtraction
3. Exercise 220.
- Consider a circular pattern. Draw up a task according to this scheme.
- Solve the problem.
- Perform the column calculation.
Record:
It was 4571 kg.
Sold - 2325 kg.
Left - ? kg.
Solution:
Answer:2246 kg.
4. Exercise 221.
Students formulate a column subtraction algorithm by answering the questions on the assignment.
5. Exercise 223.
- Based on this short entry, compose and solve the problem.
Task... The truck was carrying construction material. On the second day, the truck transported 50,000 tons of material, and on the first day - 1,743 tons less. How many tons of material did the machine carry on the first day?
- Do long subtraction.
Solution:
- the car transported on the first day.
Answer:48257 t.
6. Independent work.
№ 1. Write down the numbers in digits:
twenty five thousand three hundred forty six;
one hundred thousand twenty one;
five hundred and ten thousand;
nine thousand one;
forty thousand one hundred.
№ 2. Imagine numbers as a sum of bit terms:
3 829 =
8 208 =
6 035 =
90 070 =
7. Compare using the signs ">", "<», «=»:
80 005 ... 60 500 35 293 ... 35 909
981 020 … 91 009 23 978 ... 24 001
IV. Lesson summary.
- What new did you learn in the lesson?
- How to perform long multi-digit subtraction?
Homework. № 222.
To find the difference by the method " column subtraction"(In other words, how to count in a column or a column subtraction), you must follow these steps:
- put the subtracted under the decrement, write the units under the ones, tens under the tens, etc.
- subtract bit by bit.
- if you need to take a dozen of the larger category, then put a full stop above the category in which you took it. Put 10 above the rank for which you took it.
- if the bit in which we occupied is 0, then we borrow from the next bit of the decreasing one and put a dot above it. Put 9 above the rank for which you have taken, because one dozen is busy.
The examples below will show you how to subtract two-digit, three-digit and any multi-digit numbers in a column.
Subtraction of numbers in a column It helps a lot when subtracting large numbers (as well as column addition). It is best to learn from an example.
It is necessary to write the numbers one under the other in such a way that the rightmost digit of the 1st number becomes under the extreme right digit of the 2nd number. The number that is greater (decreasing) is written on top. On the left between the numbers we put the action sign, here it is "-" (subtraction).
2 - 1 = 1 ... What we get we write under the line:
10 + 3 = 13.
Subtract nine from 13.
13 - 9 = 4.
Since we borrowed ten from the four, it decreased by 1. In order not to forget about this, we have a full stop.
4 - 1 = 3.
Result:
Subtraction in a column from numbers containing zeros.
Again, let's take an example:
We write down the numbers in a column. Which is more - on top. We start subtracting from right to left one digit at a time. 9 - 3 = 6.
It will not work to subtract 2 from zero, then again we borrow from the digit on the left. This is zero. We put a point over the zero. And again, you won't be able to borrow from zero, then we move on to the next figure. We borrow from one. We put a point over it.
Note: when there is a dot in column subtraction above 0, zero becomes a nine.
There is a dot above our zero, which means that it has become a nine. Subtract 4 from it. 9 - 4 = 5 ... There is a point above the unit, that is, it decreases by 1. 1 - 1 = 0. The resulting zero does not need to be written down.
Theoretical provisions underlying the subtraction of multidigit numbers:
Number representation in decimal notation;
Rules for subtracting a number from a sum and an amount from a number;
Table cases for adding single-digit numbers;
Distributive Holy Island multiplication relative to subtraction.
1) We write down the subtracted under the strictly reduced digit under the digit.
2) We start the subtraction from the ones place. If the number of units in the category of units to be reduced is greater than or equal to the number of units in the category of units to be subtracted, then we subtract and write the res-at in the category of units of the difference and proceed to subtraction in the next. discharge.
3) If the number of units in the category of units of the reduced is less than the number of units in the category of units of the subtracted, then we reduce the number of units in the category of tens of the reduced (in the event that there is not zero in the category of tens) by 1, simultaneously increasing the number of units in the category of units to be reduced by 10, after which we perform the subtraction. We write down the obtained result in the category of the unit of the difference.
4) If the number of units in the digit of tens of the reduced is equal to zero, then we find the first of the digits in the reduced, in the cat. the number of units is not equal to zero and we decrease the number of units in it by 1, while increasing the number of units in those categories in the cat. is zero by 9, and the number of units in the digit of units is reduced by 10. We subtract, write down the answer in the corresponding digit of the difference and proceed to subtraction in the next digit.
5) In the next digit, # 2, 3 or 4 is repeated.
6) The process of subtraction is considered complete when the subtraction is made from the most significant digit of the decreasing one.
Methodology for studying the algorithm.
Of course, junior schoolchildren cannot master written subtraction algorithms in general. But the teacher needs to know them.
This will allow him to:
When acquainting students with the algorithm, organize the preparatory work correctly;
Manage the activities of schoolchildren aimed at mastering the algorithm;
In exercises to consolidate the algorithm, take into account all the possibilities of its use.
Descriptions of algorithms are given to primary school students in a simplified form, where only the main points are recorded:
1) the subtracted must be written under the decreasing so that the corresponding digits are under each other;
2) subtraction should start from the lowest digit, i.e. subtract units first.
Other operations included in the algorithm are either explained to younger students using specific examples, or they become aware of them in the process of performing specials. selected exercises.
Traditional program: acquaintance with the methods of letters. addition / subtraction in the topic "Thousand"; addition / subtraction "in a column" of two-digit numbers according to the pattern of actions: Explain the solution of example 43 - 29 "in a column": I write units under units, tens - under tens. Subtract units. I occupy 1 dozen. 13-9 = 4. I write under units 4.
Subtract tens. We took one dozen, so there are 3 dozen left in the decreasing one. 3-2 = 1. I write 1 under tens. I read the answer: the difference is 14.
Various cases of subtraction of three-digit numbers are considered sequentially.
Istomina's program: children become familiar with writing algorithms for addition and subtraction after they master the numbering of numbers within a million.
Starting to study algorithms for written addition and subtraction, students complete the task:
How much can you reduce 308282 so that the digits in the ones and tens digits change, and the digits of the other digits remain the same?
(Analysis of the course of action for subtraction in a column). Explain how numbers are subtracted. Guess why you need to start subtracting multi-digit numbers "in a column" with the ones place? (Focusing on the performance of the "column" recording, discussion of correct and incorrect entries).