Let's draw a rectangle with sides 5 cm and 3 cm on a piece of checkered paper. Divide it into squares with sides 1 cm (Fig. 143). Let's count the number of cells located in the rectangle. This can be done, for example, like this.
The number of squares with a side of 1 cm is 5 * 3. Each such square consists of four cells. Therefore, the total number of cells is (5 * 3) * 4.
The same problem can be solved differently. Each of the five columns of the rectangle consists of three squares with a side of 1 cm. Therefore, one column contains 3 * 4 cells. Therefore, there will be 5 * (3 * 4) cells in total.
Counting cells in Figure 143 illustrates in two ways associative property of multiplication for numbers 5, 3 and 4. We have: (5 * 3) * 4 = 5 * (3 * 4).
To multiply the product of two numbers by a third number, you can multiply the first number by the product of the second and third numbers.
(ab)c = a(bc)
From the commutative and combinatory properties of multiplication it follows that when multiplying several numbers, the factors can be swapped and placed in parentheses, thereby determining the order of calculations.
For example, the following equalities are true:
abc = cba,
17 * 2 * 3 * 5 = (17 * 3 ) * (2 * 5 ).
In Figure 144, segment AB divides the rectangle discussed above into a rectangle and a square.
Let's count the number of squares with a side of 1 cm in two ways.
On the one hand, the resulting square contains 3 * 3 of them, and the rectangle contains 3 * 2. In total we get 3 * 3 + 3 * 2 squares. On the other hand, in each of the three lines of this rectangle there are 3 + 2 squares. Then their total number is 3 * (3 + 2).
Equal to 3 * (3 + 2 ) = 3 * 3 + 3 * 2 illustrates distributive property of multiplication relative to addition.
To multiply a number by the sum of two numbers, you can multiply this number by each addend and add the resulting products.
In literal form this property is written as follows:
a(b + c) = ab + ac
From the distributive property of multiplication relative to addition it follows that
ab + ac = a(b + c).
This equality allows the formula P = 2 a + 2 b to find the perimeter of a rectangle to be written in this form:
P = 2 (a + b).
Note that the distribution property is valid for three or more terms. For example:
a(m + n + p + q) = am + an + ap + aq.
The distributive property of multiplication relative to subtraction is also true: if b > c or b = c, then
a(b − c) = ab − ac
Example 1 . Calculate in a convenient way:
1 ) 25 * 867 * 4 ;
2 ) 329 * 75 + 329 * 246 .
1) We use the commutative and then the associative properties of multiplication:
25 * 867 * 4 = 867 * (25 * 4 ) = 867 * 100 = 86 700 .
2) We have:
329 * 754 + 329 * 246 = 329 * (754 + 246 ) = 329 * 1 000 = 329 000 .
Example 2 . Simplify the expression:
1) 4 a * 3 b;
2) 18 m − 13 m.
1) Using the commutative and associative properties of multiplication, we obtain:
4 a * 3 b = (4 * 3 ) * ab = 12 ab.
2) Using the distributive property of multiplication relative to subtraction, we obtain:
18 m − 13 m = m(18 − 13 ) = m * 5 = 5 m.
Example 3 . Write the expression 5 (2 m + 7) so that it does not contain parentheses.
According to the distributive property of multiplication relative to addition, we have:
5 (2 m + 7) = 5 * 2 m + 5 * 7 = 10 m + 35.
This transformation is called opening parentheses.
Example 4 . Calculate the value of the expression 125 * 24 * 283 in a convenient way.
Solution. We have:
125 * 24 * 283 = 125 * 8 * 3 * 283 = (125 * 8 ) * (3 * 283 ) = 1 000 * 849 = 849 000 .
Example 5 . Perform the multiplication: 3 days 18 hours * 6.
Solution. We have:
3 days 18 hours * 6 = 18 days 108 hours = 22 days 12 hours.
When solving the example, the distributive property of multiplication relative to addition was used:
3 days 18 hours * 6 = (3 days + 18 hours) * 6 = 3 days * 6 + 18 hours * 6 = 18 days + 108 hours = 18 days + 96 hours + 12 hours = 18 days + 4 days + 12 hours = 22 days 12 hours.
Back Forward
Attention! Slide previews are for informational purposes only and may not represent all the features of the presentation. If you are interested in this work, please download the full version.
Target: learn to simplify an expression containing only multiplication operations.
Tasks(Slide 2):
- Introduce the associative property of multiplication.
- To form an idea of the possibility of using the studied property to rationalize calculations.
- To develop ideas about the possibility of solving “life” problems using the subject “mathematics”.
- Develop intellectual and communicative general educational skills.
- Develop organizational general educational skills, including the ability to independently evaluate the results of one’s actions, control oneself, find and correct one’s own mistakes.
Lesson type: learning new material.
Lesson plan:
1. Organizational moment.
2. Oral counting. Mathematical warm-up.
Penmanship line.
3. Report the topic and objectives of the lesson.
4. Preparation for studying new material.
5. Studying new material.
6. Physical education minute
7. Work on consolidating n. m. Solving the problem.
8. Repetition of the material covered.
9. Lesson summary.
10. Reflection
11. Homework.
Equipment: task cards, visual material (tables), presentation.
PROGRESS OF THE LESSON
I. Organizational moment
The bell rang and stopped.
The lesson begins.
You sat down quietly at your desk
Everyone looked at me.
II. Oral counting
– Let’s count orally:
1) “Funny daisies” (Slides 3-7 multiplication table)
2) Mathematical warm-up. Game “Find the odd one out” (Slide 8)
- 485 45 864 947 670 134 (classification into groups EXTRA 45 - two-digit, 670 - there is no number 4 in the number record).
- 9 45 72 90 54 81 27 22 18 (9 is single digit, 22 is not divisible by 9)
Penmanship line. Write the numbers in your notebook, alternating: 45 22 670 9
– Underline the neatest notation of the number
III. Report the topic and objectives of the lesson.(Slide 9)
–
Write down the date and topic of the lesson.
– Read the objectives of our lesson
IV. Preparing to study new material
a) Is the expression correct?
Write on the board:
(23 + 490 + 17) + (13 + 44 + 7) = 23 + 490 + 17 + 13 + 44 + 7
– Name the property of addition used. (Collaborative)
– What opportunity does the combining property provide?
The combinational property makes it possible to write expressions containing only addition, without parentheses.
43 + 17 + (45 + 65 + 91) = 91 + 65 + 45 + 43 + 17
– What properties of addition do we apply in this case?
The combinational property makes it possible to write expressions containing only addition, without parentheses. In this case, calculations can be performed in any order.
– In that case, what is another property of addition called? (Commutative)
– Does this expression cause difficulty? Why? (We don’t know how to multiply a two-digit number by a one-digit number)
V. Study of new material
1) If we perform multiplication in the order in which the expressions are written, difficulties will arise. What will help us overcome these difficulties?
(2 * 6) * 3 = 2 * 3 * 6
2) Work according to the textbook p. 70, No. 305 (Make your guess about the results that the Wolf and the Hare will get. Test yourself by performing the calculations).
3) No. 305. Check whether the values of the expressions are equal. Orally.
Write on the board:
(5 2) 3 and 5 (2 3)
(4 7) 5 and 4 (7 5)
4) Draw a conclusion. Rule.
To multiply the product of two numbers by a third number, you can multiply the first number by the product of the second and third.
– Explain the associative property of multiplication.
– Explain the associative property of multiplication with examples
5) Teamwork
On the board: (8 3) 2, (6 3) 3, 2 (4 7)
VI. Fizminutka
1) Game "Mirror". (Slide 10)
My mirror, tell me,
Tell me the whole truth.
Are we smarter than everyone else in the world?
Funniest and funniest of all?
Repeat after me
Funny movements of naughty physical exercises.
2) Physical exercise for the eyes “Keen Eyes”.
– Close your eyes for 7 seconds, look to the right, then left, up, down, then make 6 circles clockwise, 6 circles counterclockwise with your eyes.
VII. Consolidation of what has been learned
1) Work according to the textbook. solution to the problem. (Slide 11)
(p. 71, no. 308) Read the text. Prove that this is a task. (There is a condition, a question)
– Select a condition, a question.
– Name the numerical data. (Three, 6, three liter)
– What do they mean? (Three boxes. 6 cans, each can contains 3 liters of juice)
– What is this task in terms of structure? (Compound problem, because it is impossible to immediately answer the question of the problem or the solution requires composing an expression)
– Type of task? (Compound task for sequential actions))
– Solve the problem without a short note by composing an expression. To do this, use the following card:
Help card
– In a notebook, the solution to the problem can be written as follows: (3 6) 3
– Can we solve the problem in this order?
(3 6) 3 = (3 3) 6 = 9 6 = 54 (l).
3 (3 6) = (3 3) 6 = 9 6 = 54 (l)
Answer: 54 liters of juice in all boxes.
2) Work in pairs (using cards): (Slide 12)
– Place signs without calculating:
(15 * 2) *4 15 * (2 * 4) (–What property?)
(8 * 9) * 6 7 * (9 * 6)
(428 * 2) * 0 1 * (2 * 3)
(3 * 4) * 2 3 + 4 + 2
(2 * 3) * 4 (4 * 2) * 3
Check: (Slide 13)
(15 * 2) * 4 = 15 * (2 * 4)
(8 * 9) * 6 > 7 * (9 * 6)
(428 * 2) * 0 < 1 * (2 * 3)
(3 * 4) * 2 > 3 + 4 + 2
(2 * 3) * 4 = (4 * 2) * 3
3) Independent work (using a textbook)
(p. 71, No. 307 – according to options)
1st century (8 2) 2 = (6 2) 3 = (19 1) 0 =
2nd century (7 3) 3 = (9 2) 4 = (12 9) 0 =
Examination:
1st century (8 2) 2 = 32 (6 2) 3 = 36 (19 1) 0 = 0.
2nd century (7 3) 3 = 63 (9 2) 4 = 72 (12 9) 0 = 0
Properties of multiplication:(Slide 14).
- Commutative property
- Matching property
– Why do you need to know the properties of multiplication? (Slide 15).
- To count quickly
- Choose a rational method of counting
- Solve problems
VIII. Repetition of covered material. "Windmills".(Slide 16, 17)
- Increase the numbers 485, 583 and 681 by 38 and write down three numerical expressions (option 1)
- Reduce the numbers 583, 545 and 507 by 38 and write three numerical expressions (option 2)
485
+ 38
523583
+ 38
621681
+ 38
719583
– 38
545545
– 38
507507
– 38
469
Students complete assignments based on options (two students solve assignments on additional boards).
Peer review.
IX. Lesson Summary
– What did you learn in class today?
– What is the meaning of the associative property of multiplication?
X. Reflection
– Who thinks that they understand the meaning of the associative property of multiplication? Who is satisfied with their work in class? Why?
– Who knows what he still needs to work on?
- Guys, if you liked the lesson, if you are satisfied with your work, then put your hands on your elbows and show me your palms. And if you were upset about something, then show me the back of your palm.
XI. Homework information
– What homework would you like to receive?
Optional:
1. Learn the rule p. 70
2. Come up with and write down an expression on a new topic with a solution
We have defined addition, multiplication, subtraction and division of integers. These actions (operations) have a number of characteristic results, which are called properties. In this article we will look at the basic properties of adding and multiplying integers, from which all other properties of these actions follow, as well as the properties of subtracting and dividing integers.
Page navigation.
The addition of integers has several other very important properties.
One of them is related to the existence of zero. This property of addition of integers states that adding zero to any integer does not change that number. Let's write this property of addition using letters: a+0=a and 0+a=a (this equality is true due to the commutative property of addition), a is any integer. You may hear that the integer zero is called the neutral element in addition. Let's give a couple of examples. The sum of the integer −78 and zero is −78; If you add the positive integer 999 to zero, the result is 999.
Now we will give a formulation of another property of addition of integers, which is associated with the existence of an opposite number for any integer. The sum of any integer with its opposite number is zero. Let's give the literal form of writing this property: a+(−a)=0, where a and −a are opposite integers. For example, the sum 901+(−901) is zero; similarly, the sum of opposite integers −97 and 97 is zero.
Basic properties of multiplying integers
Multiplication of integers has all the properties of multiplication of natural numbers. Let us list the main of these properties.
Just as zero is a neutral integer with respect to addition, one is a neutral integer with respect to integer multiplication. That is, multiplying any integer by one does not change the number being multiplied. So 1·a=a, where a is any integer. The last equality can be rewritten as a·1=a, this allows us to make the commutative property of multiplication. Let's give two examples. The product of the integer 556 by 1 is 556; the product of one and the negative integer −78 is equal to −78.
The next property of multiplying integers is related to multiplication by zero. The result of multiplying any integer a by zero is zero, that is, a·0=0 . The equality 0·a=0 is also true due to the commutative property of multiplying integers. In the special case when a=0, the product of zero and zero is equal to zero.
For the multiplication of integers, the inverse property to the previous one is also true. It claims that the product of two integers is equal to zero if at least one of the factors is equal to zero. In literal form, this property can be written as follows: a·b=0, if either a=0, or b=0, or both a and b are equal to zero at the same time.
Distributive property of multiplication of integers relative to addition
Joint addition and multiplication of integers allows us to consider the distributive property of multiplication relative to addition, which connects the two indicated actions. Using addition and multiplication together opens up additional possibilities that we would miss if we considered addition separately from multiplication.
So, the distributive property of multiplication relative to addition states that the product of an integer a by the sum of two integers a and b is equal to the sum of the products a b and a c, that is, a·(b+c)=a·b+a·c. The same property can be written in another form: (a+b)c=ac+bc .
The distributive property of multiplying integers relative to addition, together with the combinatory property of addition, allows us to determine the multiplication of an integer by the sum of three or more integers, and then the multiplication of the sum of integers by the sum.
Also note that all other properties of addition and multiplication of integers can be obtained from the properties we have indicated, that is, they are consequences of the properties indicated above.
Properties of subtracting integers
From the resulting equality, as well as from the properties of addition and multiplication of integers, the following properties of subtraction of integers follow (a, b and c are arbitrary integers):
- Subtraction of integers in general does NOT have the commutative property: a−b≠b−a.
- The difference of equal integers is zero: a−a=0 .
- The property of subtracting the sum of two integers from a given integer: a−(b+c)=(a−b)−c .
- The property of subtracting an integer from the sum of two integers: (a+b)−c=(a−c)+b=a+(b−c) .
- Distributive property of multiplication relative to subtraction: a·(b−c)=a·b−a·c and (a−b)·c=a·c−b·c.
- And all other properties of subtracting integers.
Properties of division of integers
While discussing the meaning of dividing integers, we found out that dividing integers is the inverse action of multiplication. We gave the following definition: dividing integers is finding an unknown factor from a known product and a known factor. That is, we call the integer c the quotient of the division of the integer a by the integer b, when the product c·b is equal to a.
This definition, as well as all the properties of operations on integers discussed above, make it possible to establish the validity of the following properties of dividing integers:
- No integer can be divided by zero.
- The property of dividing zero by an arbitrary integer a other than zero: 0:a=0.
- Property of dividing equal integers: a:a=1, where a is any integer other than zero.
- The property of dividing an arbitrary integer a by one: a:1=a.
- In general, division of integers does NOT have the commutative property: a:b≠b:a .
- Properties of dividing the sum and difference of two integers by an integer: (a+b):c=a:c+b:c and (a−b):c=a:c−b:c, where a, b, and c are integers such that both a and b are divisible by c and c is nonzero.
- The property of dividing the product of two integers a and b by an integer c other than zero: (a·b):c=(a:c)·b, if a is divisible by c; (a·b):c=a·(b:c) , if b is divisible by c ; (a·b):c=(a:c)·b=a·(b:c) if both a and b are divisible by c .
- The property of dividing an integer a by the product of two integers b and c (the numbers a , b and c are such that dividing a by b c is possible): a:(b c)=(a:b)c=(a :c)·b .
- Any other properties of dividing integers.
Let's consider an example that confirms the validity of the commutative property of multiplying two natural numbers. Starting from the meaning of multiplying two natural numbers, let's calculate the product of numbers 2 and 6, as well as the product of numbers 6 and 2, and check the equality of the multiplication results. The product of the numbers 6 and 2 is equal to the sum 6+6, from the addition table we find 6+6=12. And the product of the numbers 2 and 6 is equal to the sum 2+2+2+2+2+2, which is equal to 12 (if necessary, see the article on the addition of three or more numbers). Therefore, 6·2=2·6.
Here is a picture illustrating the commutative property of multiplying two natural numbers.
Combinative property of multiplication of natural numbers.
Let's voice the combinatory property of multiplying natural numbers: multiplying a given number by a given product of two numbers is the same as multiplying a given number by the first factor, and multiplying the resulting result by the second factor. That is, a·(b·c)=(a·b)·c, where a , b and c can be any natural numbers (the expressions whose values are calculated first are enclosed in parentheses).
Let us give an example to confirm the associative property of multiplying natural numbers. Let's calculate the product 4·(3·2) . According to the meaning of multiplication, we have 3·2=3+3=6, then 4·(3·2)=4·6=4+4+4+4+4+4=24. Now let's multiply (4·3)·2. Since 4·3=4+4+4=12, then (4·3)·2=12·2=12+12=24. Thus, the equality 4·(3·2)=(4·3)·2 is true, confirming the validity of the property in question.
Let us show a drawing illustrating the associative property of multiplication of natural numbers.
In conclusion of this paragraph, we note that the associative property of multiplication allows us to uniquely determine the multiplication of three or more natural numbers.
Distributive property of multiplication relative to addition.
The following property connects addition and multiplication. It is formulated as follows: multiplying a given sum of two numbers by a given number is the same as adding the product of the first term and a given number with the product of the second term and a given number. This is the so-called distributive property of multiplication relative to addition.
Using letters, the distributive property of multiplication relative to addition is written as (a+b)c=ac+bc(in the expression a·c+b·c, multiplication is performed first, after which addition is performed, more details about this are written in the article), where a, b and c are arbitrary natural numbers. Note that the force of the commutative property of multiplication, the distributive property of multiplication can be written in the following form: a·(b+c)=a·b+a·c.
Let us give an example confirming the distributive property of multiplication of natural numbers. Let's check the validity of the equality (3+4)·2=3·2+4·2. We have (3+4) 2=7 2=7+7=14, and 3 2+4 2=(3+3)+(4+4)=6+8=14, hence the equality ( 3+4) 2=3 2+4 2 is correct.
Let us show a figure corresponding to the distributive property of multiplication relative to addition.
Distributive property of multiplication relative to subtraction.
If we adhere to the meaning of multiplication, then the product 0·n, where n is an arbitrary natural number greater than one, is the sum of n terms, each of which is equal to zero. Thus, 
. The properties of addition allow us to say that the final sum is zero.
Thus, for any natural number n the equality 0·n=0 holds.
In order for the commutative property of multiplication to remain valid, we also accept the validity of the equality n·0=0 for any natural number n.
So, the product of zero and a natural number is zero, that is 0 n=0 And n·0=0, where n is an arbitrary natural number. The last statement is a formulation of the property of multiplication of a natural number and zero.
In conclusion, we give a couple of examples related to the property of multiplication discussed in this paragraph. The product of the numbers 45 and 0 is equal to zero. If we multiply 0 by 45,970, we also get zero.
Now you can safely begin studying the rules by which multiplication of natural numbers is carried out.
References.
- Mathematics. Any textbooks for 1st, 2nd, 3rd, 4th grades of general education institutions.
- Mathematics. Any textbooks for 5th grade of general education institutions.
Combinative property of multiplication
Goals: introduce students to the associative property of multiplication; teach to use the associative property of multiplication when analyzing numerical expressions; repeat the properties of addition and the commutative property of multiplication; improve computing skills; develop the ability to analyze and reason.
Subject results:
get acquainted with the associative property of multiplication, form ideas about the possibility of using the studied property to rationalize calculations.
Meta-subject results:
Regulatory: plan your action in accordance with the task, accept and save the learning task.
Cognitive: use sign-symbolic means, models and diagrams to solve problems, focus on a variety of ways to solve problems; establish analogies.
Communication: construct speech statements in oral and written form, form your own opinion, ask and answer questions, proving the correctness of your opinion.
Personal: develop the ability for self-esteem, promote success in mastering the material.
Lesson type: learning new material.
Equipment: task cards, visual material (tables), presentation.
PROGRESS OF THE LESSON
I . Organizational moment(emotional mood)
The long-awaited call is given
The lesson begins.
Did you all have time to rest?
And now - go ahead, get to work!
Guys, let's wish each other to be attentive, collected, and diligent in class. Let's greet each other with smiles and start the lesson.
II. Updating of basic knowledge + Goal setting
There is an incomplete record of the topic on the board ______________________ the property of multiplication
Looking at the incomplete recording, think about what we will do in class and what the topic of today's lesson is. (Children's reasoning)
Today we will get acquainted with a new property of multiplication, the name of which we will learn by completing the tasks of mental calculation and tasks included in your sheets - lesson cards, we will learn to use the new property of multiplication when analyzing numerical expressions; Let us repeat the properties of addition and the commutative property of multiplication;; We will develop computational skills, the ability to analyze and reason.
We will work together and creatively, in pairs and independently, to complete tasks and draw conclusions.
In your cards, after each task you will have to evaluate your work. If you completed the task without errors, you will give yourself a +, if you failed, then -
Why do we need this?
Where can we apply the acquired knowledge?
Proverb
To teach mathematics is to sharpen the mind
How do you understand the meaning of this proverb?
“Mathematics must be taught later because it puts the mind in order”
M. Lomonosov
III. Oral counting
1. Game “Truth is a lie.” Children show + or - sign
The sum of numbers 6 and 5 is 12
The difference between the numbers 16 and 6 is 9
9 increased by 5 equals 14
100 is the largest three-digit number
A cube is a three-dimensional figure
A rectangle is a flat figure
The letter C opens on the board
2.Ingenuity task
Add the number of colors of the rainbow to the student's favorite grade.
Add the number of days in a week to the number of months in a year.
The letter 0 opens on the board
3.Logic task
There were 2 birch trees, 4 apple trees, 5 cherries growing in the garden. How many fruit trees were there in the garden? The letter H opens on the board
4.What groups can the following figures be divided into?
The letter E opens on the board
The letter T opens on the board
The letter A opens on the board
7. Can we say that the area of these figures is the same?
The letter T opens on the board
8. Work in pairs: Divide the numbers into two groups.
Write down each group in ascending order (Sign of teamwork) e
499 75 345 24 521 86
The letter E opens on the board
9. Independent work
Fill out the card
The letter L opens on the board
10. Select the desired sign (+ or )
Increase by 6
Increase 3 times
The letter b opens on the board
11. ,
2 6 … 6 + 6 + 6
5 6 … 6 4
8 6 … 6 8
The letter H opens on the board
12. Which numerical expression is redundant? Why?
(2 +7) 0 365 0
(9 2) 1 (94-26) 0
The letter O opens on the board
13.Front work
Fill in the missing numbers:
– What properties of addition and multiplication helped you complete the task? (Commutative and associative properties of addition; commutative property of multiplication.)The letter E opens on the board
The topic opens on the boardConjunctive property of multiplication
Fizminutka
To begin with we With you
To begin with, you and I
We only turn our heads.
(Rotate your head.)
We also rotate the body.
Of course we can do this.
(Turns right and left.)
Finally we reached out
Up and to the sides.
We caved in.
(Stretching up and to the sides.)
III. Posting new material
1. Statement of the educational problem
Can we say that the meanings of the expressions in this column are the same?
(For expressions 1 and 2, the combinatory property of addition is applicable - 2 adjacent terms can be replaced by a sum and the meanings of the expressions will be the same;
3 and 1 expression - applied the commutative property of addition
4 and 2 expression is a commutative property.)
-What properties are applicable for calculating data?
expressions?
(Commutative and associative property)
- Is it possible to say that the meanings of the expressions in this column are the same?
This is the question we have to answer.
Today we will find out Is it possible to use the combining property when multiplying?)
2.Primary assimilation of new knowledge
Count the number of all small squares in different ways and write it down as an expression.
1 way:(6*4)*2 = 24*2=48
(There are 6 squares in one rectangle, multiplying 6 by 4, we find out how many squares are in one row. By multiplying the result by 2, we find out how many squares are in two rows).
Method 2: 6*(4*2)= 6*8=48
(First, we perform the action in brackets - 4 * 2, that is, we find out how many rectangles there are in two rows. There are 6 squares in one rectangle. By multiplying 6 by the result obtained, we answer the question posed.)
Conclusion: Thus, both expressions indicate how many small squares there are in the picture.
This means: (6*4)*2=6*(4*2) - the associative property of multiplication
Familiarity with the formulation of the associative property of multiplication and its comparison with the formulation of the associative property of addition.
IV. Initial check of understanding
Open your textbook to page 50 and find No. 160
Explain what the numerical equalities under each picture mean?
(4*3)*2= 4*(3*2)
(4 snowflakes were placed in 3 squares and 2 rows were taken, or 4 snowflakes were placed in 3 squares of 2 rows each.)
(6 squares took 5 rows and placed in 2 large squares or 6 squares took 5 rows in two large squares)
Let's read the rule:
Primary consolidationWork at the board
Find number 161 (1 column)
Reading the task: ( Write each expression as a product of three single-digit numbers)
Find number 162 (1 column)
Reading the task : Is it true that the values of the expressions in each column are the same?
We work independently in rows (we check at the board), using the combining property: To multiply the product of two numbers by a third, you can multiply the first number by the product of the second and third numbers.
Summing up the lesson.
Assessment
Let's return to the numerical expressions that we met at the beginning of the lesson. Tell me, is it possible to say that the meanings of the expressions in this column are the same?
What discovery did you make in class today? Where can it be used?
(We got acquainted with the new property of multiplication) To multiply the product of two numbers by a third, you can multiply the first number by the product of the second and third numbers.
Homework: rule p.50, no. 163 *Find proverbs or sayings of famous people about mathematics
Grading.
“5” marks are given to those guys who have no minuses in the card.
Anyone with 1-2 minuses gets a “4”
3-5 minuses – “3”
More than 5 minuses – “2”
Reflection
Finish the sentence
Today in class I.....
The most difficult thing for me was…..
Today I realized...
Today I learned...
Decide for yourself
