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Mathematical dictation. ORAL COUNT 6 x 8. 7 x 4. The first factor is 9, the second is 5. Find the product. 2 will increase by 6 times. Take 9 three times. 8 times 9. The first factor is 5, the second is 10. Find the product. Find the product of the numbers 23 and 3. Increase 48 by 2 times.
Swap notebooks. Mathematical dictation. 48 28 45 12 27 72 50 69 96 ORAL ACCOUNT
1800 60 5 0 4 0: + : + 3 0 3 00 33 0 2 80 7 807 800 Who is faster?
ORAL ACCOUNT Joke tasks. 100
ORAL ACCOUNT Joke tasks. 9
ORAL ACCOUNT Joke tasks.
Distributive property Recall what we know (a + b + c) d = a d + b d + c d 274 5 = (200 + 70 + 4) 5 = 200 5 + 70 5 + 4 5 = 1000 + 350 + 20 = 1370 What mathematical properties do you know?
ALGORITHM I write single digit under the units of a three-digit number. I multiply units, write under units, and remember tens (if any). I multiply the tens and add the tens that I remember. I write in tens. I remember hundreds. Multiply hundreds. I write hundreds. I read the answer. 2 7 4 5 274 5 = 0 2 7 3 1 3 1370
Work according to the textbook p.3 We apply knowledge. We develop skills.
Thank you for your work!
On the topic: methodological developments, presentations and notes
Mathematics lesson Topic: Subtracting a single-digit number from a two-digit number with a jump through the digit.
Lesson with a presentation in the 2nd grade on the program "Harmony" Compiled by the teacher primary school Fedorova O.Yu. Khanty-Mansi Autonomous Okrug Surgut Topic: Subtraction of single...
Topic: SINGLE NUMBERS Lesson objectives: - introduce the concept of "single digits"; consolidate knowledge of the composition of the studied numbers; - improve counting skills and skills of performing addition of the form + 1, + ...
In this lesson, you will learn how to multiply three-digit and two-digit numbers in a column. First, we will recall what tricks are used to multiply three-digit numbers verbally. When multiplying by a column, we will develop an algorithm by which we can further solve examples, make calculations in tasks and various tasks. After this lesson, you will be able to apply the acquired skills in practice in real life.
What is multiplication?
This is smart addition.
After all, it’s smarter to multiply times,
Than to add up everything for an hour.
multiplication table,
We all need it in life.
And not without reason named
By multiplying it!
A. Usachev
Find the meaning of expressions.
Solution: 1. Let's decompose the number 34 into the sum of bit terms. We multiply each term by the number 2. We add the resulting products:
2. We replace the first multiplier with the sum of the bit terms and proceed similarly to the first example:
3. Each time to perform multiplication in this way is inconvenient, and sometimes difficult. In such cases, they use a written technique, namely multiplication in a column. Therefore, we solve the second example in a column. First, we write down the first factor, and under it the second. Be sure to write the corresponding digits under each other. So we write the deuce under the four in the one place. Then we sequentially multiply each number in the first factor by the second factor, starting with ones and moving up to tens and hundreds. The answer is written under the line.
Multiplications by a column should be performed in the order shown in diagram 1.
Scheme 1. The order of multiplication in a column
Solve the examples by doing column calculations.
Solution: 1. When multiplying units in the first example, we get a number greater than nine. In this case, the units value is written under the bar, and the tens value is added to the tens after the multiplication is performed.
2. We act according to the algorithm.
3. We write down the numbers correctly and multiply sequentially.
4. Solve the last example using the algorithm
Find out which is bigger and by how much: the product of the numbers 151 and 6 or the product of the numbers 161 and 5.
Solution: 1. First, find the product of the first pair of numbers:
2. Calculate the product of the second pair of numbers:
3. Find out how much more the first number is than the second.
Find the mistakes and write down the correct answers (Table 1).
Table 1. Task number 3
Solution: 1. To find out where the error is, you need to solve the examples (Table 2).
Table 2. Task number 3
Find the area of the given rectangle (Scheme 2).
Scheme 2. Rectangle
Solution: 1 way
1. This rectangle (diagram 2) is divided into three parts. In each of these rectangles, the width is the same, but the length is different. You can find the area of each rectangle, and add the results.
(m 2)
Municipal budgetary educational institution average comprehensive school No. 27 Penza
Mathematics lesson in grade 3 on the topic "Multiplication by a single digit by a column»
Prepared by:
primary school teacher
Medvedeva S. M.
Penza, 2017
Math lesson in 3rd grade.
Education system: Promising Primary School
Lesson topic: Multiplication by a single digit by a column
The purpose of the lesson: building a model of a new way of multiplying by a single digit.
Lesson objectives:
repeat and generalize the rules of multiplication, extending them to a wider area;
to consolidate knowledge and skills in the field of numbering of multi-digit numbers;
practice oral arithmetic skills;
develop thinking, competent mathematical speech, interest in mathematics lessons;
education of partnership, mutual assistance.
UUD:
Personal:
the internal position of the student at the level of a positive attitude towards school, orientation to the meaningful moments of school reality and acceptance of the model of a “good student”;
sustainable educational and cognitive interest in new common ways problem solving;
Regulatory:
accept and save the learning task;
take into account the guidelines for action identified by the teacher in the new educational material in collaboration with the teacher;
plan their actions in accordance with the task and the conditions for its implementation, including in the internal plan;
evaluate the correctness of the action at the level of an adequate assessment of the compliance of the results with the requirements of a given task and task area;
distinguish between the method and the result of an action;
Cognitive:
use sign-symbolic means and schemes to solve problems;
build messages in oral and written form;
establish analogies;
control and evaluate the process and results of activities;
pose, formulate and solve problems;
Communicative:
adequately use communicative, primarily speech, means to solve various communication tasks, build a monologue
take into account different opinions and strive to coordinate various positions in cooperation;
to formulate own opinion and position;
negotiate and come to a common decision in joint activities, including in situations of conflict of interest;
build statements that are understandable for the partner, taking into account what the partner knows and sees, and what is not;
to ask questions;
control the actions of the partner;
use speech to regulate their actions;
Equipment:
Slide presentation of the lesson;
Task cards;
Cards are helpers;
Algorithm - handouts;
Textbook, notebook.
| Lesson stages | Teacher activity | Student activities |
| 1. Self-determination for activity (org. moment) 2. Actualization of knowledge and fixation of difficulties in activities | Let's start our lesson with a smile. Please give smiles to me, to my desk mate, to other guys. Thank you. (Five minutes of reading) And let's start our lesson with an oral account. Why do we use oral counting in class? SLIDE 1 Exercise 1."SILENT" - marker board SLIDE 2, 3 Mathematical dictation. SLIDE 4 Checking in pairs (according to the slide). Stand up those who have no mistakes. Stand up those who made 1-2 mistakes. - What needs to be done to avoid mistakes? | Complete the task and explain your choice |
| 3. Statement of the educational task 4. Building a project to get out of a difficulty, discovering new knowledge 5. Primary consolidation in external speech 6.Reflection of activity (the result of the lesson) | SLIDE 5 Consider the expressions on the board: 7024-483 837+582 274*5 Complete tasks. Work in groups GROUP WORK SLIDE 6 (Vika and Maxim together) Presentation of results. - What difficulties did you have? What do you think, what topic will we work on today? So, the topic of the lesson: Multiplication by a single-digit number by a column. What is the task before us? So how are we going to solve such examples. Someone knows how to solve such examples. (Example of a child's decision) To correctly solve such examples, you need to know the solution algorithm. What is an algorithm? Now you can try to compose it yourself. You have cards on your desks on which the actions of the algorithm are printed. Working and discussing in pairs, you will arrange the cards in the correct order. (WORK IN PAIRS) Fizminutka. Algorithm: I write a one-digit number under the units of a three-digit number. I multiply units, write under units, and remember tens (if any). I multiply the tens and add the tens that I remember. I write in tens. I remember hundreds. Multiply hundreds. I write hundreds. I read the answer. SLIDE 7 How to multiply a multi-digit number on unambiguous in a column? What rules must be followed? Why should you be careful? SLIDE 8 We perform according to the algorithm. Textbook p. 82 No. 269 - collectively on the board RESERVE: with. 81 No. 268 - independently "column" Lesson Summary: Name the topic of the lesson What learning problem did you solve? Did you manage to solve it? How to multiply such numbers? What were the challenges and were they overcome? How and where can we apply the acquired knowledge? I'm giving you a memo with the algorithm. Evaluation ruler for self-assessment SLIDE 9
learn the algorithm; for multiplication by a "column". |
Upon acquaintance students with written multiplication it is better to take such an example of multiplying a three- or four-digit number by a single-digit number, where there would be transitions through a dozen or a hundred, i.e. where it's hard to verbally multiply .
Let's take an example: 418 * 3 .
First students solve it familiar them way: replace the first factor the sum of bit terms and multiply the sum by the number:
418 * 3 = (400 + 10 + 8) * 3 = 400 * 3 + 10 * 3 + 8 * 3 = 1200 + 30 + 24 = 1254
418 * 3 = (8 + 10 + 400) * 3 = 8 * 3 + 10 * 3 + 400 * 3 = 24 + 30 + 1200 = 1254
After that, the teacher introduces students to written multiplication by a single number: shows a new entry in a column With detailed explanation solutions of the same example.
It is necessary to multiply 418 by 3. We write the second factor under the units of the first factor. We draw a line, put the multiplication sign “X” on the left (it is necessary to explain to the children that multiplication is indicated not only by a dot, but also by such a sign, although a dot can also be used here).
We start written multiplication with units.
We multiply 8 units by 3, we get 24 units. These are two tens and 4 units;
We write 4 units under units, and remember 2 tens;
We multiply 1 ten by 3, we get 3 tens, and even 2 tens, we get 5 tens, we write them under the tens;
Multiply 4 hundreds by 3 to get 12 hundreds. It's 1 thousand and 2 hundreds.
We write 2 hundreds under hundreds and write 1 thousand in place of thousands.
Artwork 1254.
From a detailed explanation of the solution of examples, students, under the guidance of a teacher, proceed to a brief explanation when the name of the bit units and the transformations performed are omitted, for example:
578 must be multiplied by 4.
I multiply 8 by 4, it turns out 32. I write 2, and remember 3.
I multiply 7 by 4, it turns out 28, but 3 is only 31; 1 I write, and 3 I remember.
I multiply 5 by 4, it turns out 20, yes 3.
Total 23; write down 23.
Product 2312.
You can explain it this way: four times eight is thirty-two. I write 2, I remember 3.
Four times seven is twenty-eight, and so on.
You can also write to the line: 578 * 4 = 2312.
At the beginning of the study of the topic, the teacher himself informs the students that written multiplication by a single digit begins with ones, and later it is useful to explain why written multiplication, like addition and subtraction, begins with the lowest, and not with the highest digit. To this end, the same example is solved in two ways:
It turns out that it is inconvenient to start written multiplication by a single-digit number from units of the highest digit, because you have to cross out the previously written numbers.
Consider cases with zeros in the first factor.
Let's multiply 42,300 by 6.
The solution of such examples is written as follows:
Explanation:
I sign the second multiplier 6 under the first non-zero digit of the first multiplier, under the number 3;
42,300 contains 423 hundreds;
multiply 423 hundreds by 6, you get 2538 hundreds, or 253,800.
When solving similar examples with a detailed explanation, children should pay attention to the fact that in such cases they perform multiplication, not paying attention to the zeros written at the end of the first factor, and the resulting product is assigned to the right as many zeros as they are written at the end of the first factor. At the same time, a brief explanation is given: three times six - 18, I write eight, I remember 1, twice six ... I will add two zeros to the right, it will turn out 253,800.
At this stage, students should be offered the multiplication of single-digit numbers by multi-digit ones: 9 * 136, 4 * 2836, 7 * 1230. When solving such examples, it is used commutative property of multiplication:
136 * 9, 2836 * 4, 1230 * 7.
Students, having become familiar with written calculation techniques, often use them in cases where it is easy to perform the calculation orally. It is important to prevent this unwanted transfer. To this end, it is necessary 1) to include more appropriate cases of multiplication in oral exercises, 2) to compare the written and oral methods of multiplying by a single digit.
Following multiplication by a single-digit number of natural numbers, multiplication of quantities expressed in metric units is given, for example:
9t 438kg * 3;
7 km 438 m * 6.
These examples can be solved in different ways: immediately perform the multiplication or first replace the values expressed in units of two items with the values of the same item and perform the action:
|
9 t 438 kg * 3 = 28 t 314 kg |
||||
First way more often used in practice when multiplying values expressed in units of value
18 rub. 25 kop. * 3 = 18 rubles. * 3 + 25 kop. * 3 = 54 rubles. 75 kop.
The second method is used in solving problems, as well as in the future when multiplying values by any two-digit and three-digit number.
Methodology for studying the written multiplication algorithm (stage 2).
II stage. Multiplication by bit numbers .
After students have firmly mastered the multiplication by a single number, the methods of multiplying by 10, 100, 1000, and then by 40, 400, 4000 are considered.
When multiplying by two-digit-four-digit bit numbers, use multiplication property of a number, for example:
14 * 60 = 14 * (6 * 10) = 14 * 6 * 10 = 840.
To get acquainted with this property, students are invited to calculate the value of the expression 16 * (5 * 2) in different ways. Under the guidance of a teacher, they find the meaning of the expression in such ways;
16 * (5 * 2) = 16 * 10 = 160
16 * (5 * 2) = (16 * 5) * 2 = 80 * 2 = 160
16 * (5 * 2) = (16 * 2) * 5 = 32 * 5 = 160
Students notice that
in the first case, they multiplied the number 16 by the product of the numbers 5 and 2;
in the second - the number 16 was multiplied by the first factor 5 and the resulting product was multiplied by the second factor 2;
in the third - the number was multiplied by the second factor 2 and the resulting product was multiplied by the first factor 5;
expression values are the same.
After completing several of these exercises, students formulate the property: “To multiply a number by a product, you can find the product and multiply the number by the result, or you can multiply the number by one of the factors and multiply the result by another factor”.
The property of multiplying a number by a product is used when performing various exercises:
solving examples and problems in various ways, for example:
in a convenient way, for example: 25 * (2 * 7) = (25 * 2) * 7 = 350;
comparison of expressions, for example. 24*5*10 and 24*50 etc.
This property is then used to disclosing the computational trick of multiplication into two-digit - four-digit bit numbers.
Preparatory exercises are introduced to replace bit numbers with the product of a single-digit number and 10 (100, 1000), for example: 70 = 7 * 10, 600 = 6 * 100.
Next, oral methods of multiplication by bit numbers are considered. For example, you need to multiply 15 by 30; let's represent the number 30 as a product of convenient factors 3 and 10, we get an example: multiply 15 by the product of numbers 3 and 10; here it is more convenient to multiply the number 15 by the first factor - by 3 and multiply the result 45 by the second factor - by 10, you get 450. Recording:
15 * 30 = 15 * (3 * 10) = (15 * 3) * 10 = 450
Students sometimes mix the property of multiplying a number by a product with the property of multiplying a number by a sum.
For example, an error like 15 * 12 = 300 indicates such a confusion: the student multiplies 15 by 2 and the result is multiplied by 10, i.e. he replaced the number 12 with the sum of the bit terms 10 and 2, and then multiplied as the product of these numbers, i.e. to the number 20.
A similar error also occurs when performing expression comparison exercises, for example:
27 * 7 * 10 = 27 * 7 + 27 * 10
To prevent such errors, it is useful to offer exercises for comparing the corresponding methods of calculation. For example, students solve the following examples with commentary and detailed recording:
6 * 50 = 6 * (5 * 10) = 6 * 5 * 10 = 300
6 * 15 = 6 * (10 + 5) = 6 * 10 + 6 * 5 = 90
Then it turns out that in both examples the first factors are the same, but the second ones are different; when solving the examples, the second factor (50) was replaced by the product of convenient factors (5 and 10) and the property of multiplying a number by a product was used: the number 6 was multiplied by the first factor and the resulting product was multiplied by the second factor. In the second example, the factor 15 was replaced by the sum of the bit terms 10 and 5 and the property of multiplying a number by the sum was used; multiply the number 6 by the first term, then multiply the same number 6 by the second term and add the results.
It is useful to offer children exercises for comparing expressions (put the sign “>”, “<» или « = »):
36 * 10 * 4 □ 36 * 14 17 * 5 * 10 □ 17 * 50
45 * 6 + 45 * 10 □ 45 * 60 16 * 10 □ 16 * 3 +16 * 10
21 * 4 + 21 * 3 □ 21 * 12 18 * 9 + 18 * 10 □ 18 * 19
In order to prevent errors in mixing the properties of arithmetic operations studied in elementary grades, it is necessary to perform exercises in their comparison more often.
After studying the methods of oral multiplication by bit numbers, the methods of written multiplication are introduced. It is proposed to solve the example 546 * 30.
We will calculate in writing, write an example like this:
The number 546 is first multiplied by 3, and the result is multiplied by 10. Multiply 546 by 3:
three times six - 18; write eight, remember 1;
three times four - 12, yes 1, it will turn out 13, we write three, remember 1;
three times five - 15, yes 1, it turns out 16, we write down 16, we get 1638.
We multiply 1638 by 10, for this we attribute one zero to the resulting number on the right.
Product 16 380.
Note that here, when multiplying by a single-digit number (546 * 3), we use a brief explanation. Similarly, one should proceed in the future, when in new, more complex cases of multiplication, an integral part is multiplication by a single-digit number.
Multiplication by three-digit and four-digit bit numbers is the same as multiplication by two-digit bit numbers.
Particularly noteworthy are those cases in which both factors end in zero, for example: 20 30, 400 50, 800 70, 4000 60, etc.
First, when solving such examples, students reason as follows: to multiply 300 by 50, you need to multiply 3 hundreds by 5, and then multiply the resulting number by 10, it will be 150 hundreds, or 15,000.
Such examples are written in a line and solved orally.
Students argue in a similar way with written multiplication in the case when both factors end in zero.
It is more convenient to write such examples in a column as follows:
Observing the multiplication of numbers ending in zeros, the students come to the conclusion that first in these cases it is necessary to multiply the numbers that will be obtained if these zeros are discarded, and then to the resulting product, add as many zeros to the right as they are written at the end of both factors together. In the future, when multiplying numbers ending in zero, students are guided by this conclusion.
Methodology for studying the written multiplication algorithm (stage 3).
Multiplication by a single digit by a column
You can multiply a multi-digit number by a one-digit number using the rule for multiplying a sum by a number, while decomposing a multi-digit number into bit terms. But this method is not always convenient.
When multiplying a multi-digit number by a single-digit number, you can record in a column, as with addition and subtraction. This method is very helpful when multiplying multi-digit numbers. In this lesson, we will learn how to find the value of the product of multi-digit and single-digit numbers by writing in a column.
Find the value of the product: 32 ∙ 2.
Let's write the work in a column.
The first multiplier 32 has two digits: 3 tens, 2 units.
The second multiplier 2 has one bit - 2 units.
When writing in a column, we write the multipliers bit by bit: units under units.
When multiplying by a column, we write the multiplication sign with a cross "x".
Instead of an equal sign, we draw a line under the second factor.
Note that when multiplying a multi-digit number by a single-digit number, we multiply the number of each digit of the first multiplier by the second multiplier.
We start multiplying with units: 2 times 2 is equal to 4.
4 units are written under the units.
Then we multiply the tens of the first factor, 3 tens times 2 - equal to 6 tens.
We write 6 under tens.
We read the result 64.
Similarly, you can multiply any multi-digit number by a single-digit number.
For example, 4211 times 2.
We start with units:
1 multiplied by 2 is equal to 2, 2 units are written under the units.
1 ten multiplied by 2 is equal to 2 tens, 2 is written under the tens.
2 hundreds multiplied by 2 is equal to 4 hundreds, 4 is written under hundreds.
4 units of thousands multiplied by 2 is equal to 8 units of thousands, 8 is written under the units of thousands.
We read the result: 8422.
Now consider the products in which, when multiplying the numbers of digits, a two-digit number is obtained.
For example, 547 times 4.
We start multiplying from units:
7 times 4 equals 28.
28 is a two-digit number, it has 2 tens and 8 ones.
We write 8 units under the units, remember 2 tens and add to the tens.
We multiply 4 tens of the first factor by 4 - equal to 16, add 2 tens obtained by multiplying units, we get 18 tens.
We write 8 under tens, and remember 1 and add to hundreds.
Multiply 5 hundreds by 4 - equal to 20 hundreds, add 1 hundred by multiplying tens, you get 21.
1 is written under hundreds, 2 are units of thousands.
We read the result: 2 188.
Let's summarize.
1. When multiplying by a column, we write the factors under each other bit by bit: we write units under units.
2. We start multiplying from the units digit.
3. If, when multiplying a single-digit number by the value of the digit of a multi-digit number, a two-digit number is obtained, the number of units of this two-digit number is written to the digit that was multiplied, and the number of tens is added to the result of multiplying the single-digit number by the value of the next digit of the multi-digit number.
