Lesson summary "grouping terms". Grouping terms Calculate using the grouping technique

	4th grade
	I half of the year
	MATHEMATICS
	Technological map No. 3



Topic of study	Rational calculation techniques (17 hours)

	Create a view about the methods of rational calculation.


	Groupings of terms;
	Rounding terms;
	Multiplying numbers by 10 and 100;
	Algorithms:
	Rounding numbers when adding;
	Definitions of the arithmetic mean;
	Oral/written multiplication of two-digit numbers by round tens;
	Written multiplication of a two-digit number by a two-digit number.
	Teach to use acquired knowledge and skills in practical activities.

	Studying techniques for grouping and rounding terms, multiplying numbers by 10 and 100,
	method of multiplying a number by a product, an algorithm for determining the arithmetic mean of a number
	la, algorithm for multiplying a two-digit number by round tens, algorithm for multiplying two-digits
	th number by a two-digit number (written calculation).
Terms and concepts	Grouping terms, rounding terms, arithmetic average, multiplication
	two-digit number by two-digit number, multiplying a two-digit number by round tens.
	Planned result
	Planned result

Personal skills		Meta-subject skills	Subject Skills

Manifest:		Cognitive skills:	Fulfill:
Interest in studying the topic;		Expand the meaning of the concepts “grouping of terms”, “district”	Calculation,	using
Wish	determine	division of terms", "arithmetic average", "multiplication	grouping technique
GPA	values	two-digit number by round tens", "multiplying a two-digit number	guerrillas and the district algorithm
educational and extracurricular dos		numbers by a two-digit number" and use them in the active dictionary;	number division during addition
		Determine the method of grouping terms and the order of rounding
Awareness	own	numbers when adding and justify your opinion;	Multiplying a number by 10,
achievements in mastering		Determine ways to multiply a number by a product and justify it
educational topic.		express your opinion;	Orally/written
		Determine the most convenient way to multiply a number by its product	wearing a two-digit number
		conduct and justify your opinion;	la for round tens;
		Determine the order of oral/written multiplication in two digits	In writing	multiplication
		the number of round tens and justify your opinion;	two-digit number by two
		Determine the order of written multiplication of a two-digit number
		to be ambiguous and justify your opinion;	Calculate
		Use the acquired knowledge to determine the average	arithmetic
		th score of the value of academic and extracurricular achievements.	to determine the average
		Regulatory skills:	educational scores
		Correlate the educational action using a well-known technique, algo	and extracurricular achievements

		Carry out self-examination, mutual examination and adjustment of studies
		task and provide the necessary mutual support in cooperation

		Carry out self-assessment and mutual assessment of the educational task;
		Correlate the result obtained with the goal.
		Communication skills:
		Use speech to regulate your actions;
		Comment on the educational task as part of the educational dialogue;
		Comment on the actions of oral/written multiplication by two
		digit number by round tens and written multiplication by two
		digit number to two digit number as part of an educational dialogue, using

mathematical terms;

Adequately use speech means to represent

results.

Organization of educational space

Interdisciplinary connections		Forms of work

Technology	Information material:	Frontal;
Topic: Product marking.	Textbook "Mathematics", 4th grade, part 1; Workbook No. 1, methods	individual -
Topic: Product marking.		individual -

	technical manual for teachers.
	Demo material:
	Demo material:	group -
	Tables: “Arithmetic mean”, “Written multiplication by two”
	a digit number by a two-digit number", "Multiplying a two-digit number by
	round tens."
	Interactive material:
	Cards with educational tasks.

TECHNOLOGY FOR STUDYING THE TOPIC

	Stage I. Self-determination for activity

Activity goals	Situational task	Planned result

Motivate	The school received vouchers for the best students to travel to the Zehr camp	Personal skills:
understanding of the topic.	cal". It was necessary to select the most worthy students of the school.	Show interest in learning
Stimulate	Among the fourth grade students there were 10 excellent students, and to go to	understanding of the topic.
ability to determine the average	Only two elementary school students could “Mirror.” Then it was	Show desire
educational value score	it was decided to award vouchers to those schoolchildren who	divide the average score
and extracurricular achievements	tinge* have the highest scores in academic and extracurricular achievements.	academic and extracurricular activities
	Students were asked to determine their grade point average	new achievements.
	meta and average score based on the results of various subject Olympiads. At
	In completing this task, they made mistakes, and therefore arose
	difficulties in identifying applicants for the trip.

Guys, why didn’t the excellent students cope with this task?

The students offered different versions, but their statements showed that they do not yet have certain knowledge and skills to convincingly present their position.

Do you have a desire to learn how to determine the GPA value in academic and extracurricular achievements?

* Rating is a numerical or ordinal indicator that reflects the importance or significance of a certain object or phenomenon.

Stage II. Educational<познавательная деятельность

Activity goals				Training assignments
Activity goals				to “knowledge” (K), “understanding” (P), “skill” (U)
				to “knowledge” (K), “understanding” (P), “skill” (U)

				Block A. Reception of grouping and rounding of terms

				Task 1 (W)
Update:				Read the expression 70 + 50 + 30 and name ways to calculate it
		move
telny property				Name each value of the sum of this numerical expression.
				Name the most convenient method of calculation.
		fulfill		Explain the rule about the commutative property of addition. (From pe
educational mutual examination				Changing the places of the terms does not change the value of the sum.)
tasks and provide				Teacher's message
cooperation				Many methods of rational calculations in mathematics are based
mutual assistance.				on the properties of arithmetic operations and the rules for their implementation.
				For example, the commutative property of addition underlies
Concepts		"grouped		method of grouping terms. The meaning of this technique is
ka terms", "district				in changing the order of terms in a numerical expression
addition of terms";				nii, which allows you to calculate faster. In this case, the change in order
	factions			actions are usually shown with		For example:
terms			algorithm	73 + 138 + 107 + 50 + 42. Note,	what's the first thing	terms,
rounding				and the second and fifth terms add up to round numbers. Is
addition				Using the grouping of these terms, we get:

Planned result

Diagnostic tasks:

1. Textbook, p. 35, no. 2.

Calculate the chi word expression using the method of grouping terms.

2. Calculate the value of a numeric expression using the well-known rounding algorithm

numbers.

587 + 375 + 498

699 + 787 + 496 + 274

547 + 469 + 828 + 277 + 159

Cognitive skills:

Expand the meaning of the concepts “grouping of terms”,

(73 + 107) + (138 + 42) + 50 = 180 + 180 + 50 = 410.

"rounding of terms" and using

Teach:

Answer: 410.

use them in the active layer

Define

Task 2 (W)

factions

terms

Tell us about the technique of grouping terms using numbers.

Define the groupie technique

and justify

expression: 276 + 13 + 44 + 200 + 57 + 500.

alignment of terms and justification

Task 3 (P)

express your opinion;

Define

Is it true that using the order of actions does not affect the meaning

Determine the order of the district

rounding

amounts? Justify your opinion.

number division when adding and

addition

justification

Task 4 (U) Textbook, p. 33, No. 1, with mutual verification.

justify your opinion.

express your opinion;

Regulatory skills:

Fulfill

groupings of terms.

Perform training activities

groupings of terms;

Task 5 (U) Workbook, p. 24, No. 1, with mutual checking.

vie, using an algorithm;

Calculate

Calculate a numeric expression using the technique

Perform cross-check

using lime

grouping of terms based on the sample.

educational assignment and provide

algorithm

Teacher's message

in cooperation

necessary

numbers when adding

To quickly evaluate an expression, use the rounding technique

mutual assistance.

numbers.

Communication skills:

Algorithm for rounding numbers when adding

Use speech to regu

using

In order to calculate the sum of the numbers 697 and 145, using the technique

lations of their action.

algorithm

rounding, you need:

Subject Skills:

number learning;

1) add the first term to a round number: 697 + 3 = 700;

Perform a groupie move

Use speech to

2) add the second to the result obtained

term:

adjustments of terms;

regulation of one's actions

700 + 145 = 845;

Evaluate expression using

3) subtract the “added” units from the received

result:

taking advantage of the famous

algorithm

845 – 3 = 842;

rounding numbers when adding

4) formalize the addition of numbers using rounding:

697 + 145 = (700 + 145) – 3 = 845 – 3 = 842.

Solve a problem,

using

The technique of rounding numbers can be used when necessary

when calculating the algorithm is ok

calculate the sum of more than two terms.

cursing numbers.

For example: 286 + 175 + 394.

Let's round each term of the sum so as to get a round number

Therefore, 286 is rounded to 300. In order to complete 286

- multiply a number by 10, by 100;

- perform multiplication of a number by a product in three ways;

- compare numeric expressions using comparison signs (>,<, =);

- solve the problem using a known rule in the calculation;

- perform a learning action using a rule;

9 × 100 = 900, 45 × 100 = 4500.

Task 1 (W)

Explain the rule for calculating a numerical expression: 74 × 10 and 62 × 100.

Task 2 (P)

Is the expression 50 × 100 calculated correctly if its value is 500? Justify your opinion.

Task 3 (U) Textbook, p. 40, No. 4, with mutual assessment.

Calculate an expression using the technique of multiplying a number by 10.

Task 4 (U) Textbook, p. 41, No. 1, with mutual assessment.

Compare numeric expressions using comparison signs (>,<, =).

Task 5 (U) Textbook, p. 40, no. 6.

Solve the problem using the method of multiplying a number by 100 when calculating.

Task 6 (U) Textbook, p. 41, No. 5, with mutual assessment.

Write an expression and calculate its value.

Task 7 (W)

State the procedure for calculating the numerical expression 79 × (2 × 5).

(According to the rule for the order of operations with brackets, we first calculate the product of the numbers 2 and 5, we get 10, and then we multiply 79 by this number, we get 790.)

1st method: 79 × (2 × 5) = 79 × 10 = 790.

Teacher's message

2nd method: In order to multiply a number by the product 79 × (2 × 5), you need to multiply the number 79 by the first factor 2 and multiply the resulting result 79 × 2 = 158 by the second factor 5. 79 × (2 × 5) = (79 × 2) × 5 = 158 × 5 = 790.

3rd method: In order to multiply a number by the product 79 × (2 × 5), you need to multiply the number 79 by the second factor 5 and multiply the resulting result 79 × 5 = 395 by the first factor 2. 79 × (2 × 5) = (79 × 5) × 2 = 395 × 2 = 790.

Analysis of the results of the obtained values when calculating the expression

79 × 100 92 × 100 – 30 × 100

40 × 10 63 × 10 + 17 × 100

50 × 100 29 × 100 – 15 × 10 2.Textbook, p. 41, no. 4.

Solve the problem using the well-known multiplication technique when calculating.

3. Calculate each numeric expression

three ways.

32 × (5 × 2)

15 × (2 × 4)

4. Perform the calculation of the chi word expression in a convenient way.

25 × (7 × 4)

50 × (4 × 5)

Cognitive skills:

- determine ways to multiply a number by a product and justify your opinion;

- determine the most convenient way to multiply a number by a product and justify your opinion.

Regulatory skills:

- perform a learning activity using a rule;

- carry out mutual assessment of the educational task.

Communication skills.

1. Calculate the values of expressions using the technique of grouping terms.

2. 3 baskets of cucumbers were collected from one plot, and 5 baskets from another. Each basket contained 30 kg of cucumbers.
Explain what the expressions mean.

3. 7 identical coats were sewn from 28 m of fabric. How many of these coats can be made from 340 m of the same fabric?

4. Calculate the meanings of the expressions.

252:9*6:4=42 27*6-76:9+30=188
144*5:8:30=2 154:7 - (64+36) : 25=18

5. There are 360 seats in the school assembly hall. How many free places are left after 4 classes, 27 students each, and 5 classes, 32 students each, have their places?

6. Perform division with remainder and check.

83:6 67:9 54:16 70:12

7. For 8 m of linen fabric they paid 368 rubles, and for 6 m of silk fabric they paid 552 rubles. How many times is the price of silk fabric greater than the price of linen fabric?

8. Points M and N are marked on segment AB so that point N divides segment AB in half, and point M lies between points A and N. Find the length of segment AB if the length of segment AM is 18 cm, and the length of segment MN is 3 times less.

9. There are 10 numbered bags on the table, each containing 10 gold coins. In one of the bags all the coins are fake. The mass of a real coin is 10 g, and the mass of a counterfeit coin is 9 g. Using a scale with a scale in grams, how can you determine which bag contains counterfeit coins, using the scale for only one weighing? (The scales can weigh loads weighing no more than 750 g.)

1. There are 370 birches, 258 larches, 230 rowan trees and 42 poplars in the grove. Write an expression to answer the question:

1) how many more birches and larches than rowan trees and poplars?
2) how many times are there fewer larches and poplars than rowan trees and birches?

Calculate the values of the composed expressions.

2. Calculate the values of expressions using the technique of grouping terms.

87+139+213+61 596+122+17+104+78
368+73+27+132 28+65+454+135+46

3. 47 heads of cabbage were removed from the first bed, 48 heads of cabbage from the second, 53 heads from the third, and 52 heads from the fourth. How many heads of cabbage were removed from these beds?

Solve the problem with an expression whose value was calculated using the grouping technique.

4. Take action.

576:6*8-200:8*5=643 (868:7+92):3-156:4=33
300:4:25+679:7=100 432:6: (53*4-1000:5)=6

5. At first, 9 teams, 12 people each, worked on grain harvesting. Then, from among them, 4 teams, 18 people in each, were allocated for other work. How many people continue to clean the area?

6. For 4 identical boxes of chocolates we paid 340 rubles. How much do 8 of these boxes cost?

Solve the problem in two ways.

7. Compare.

2 m 2 dm and 202 dm 5 kg 50 g and 550 g
1 kg 60 g and 160 g 1 m 20 cm and 120 cm
7 dm 4 cm and 740 cm 9 h 30 min and 930 min

8. One worker produced 588 parts in 7 hours, equally divided every hour. Another worker produces the same number of parts in 6 hours, equally every hour. How many more parts per hour does the second worker produce than the first?

9. Can there be 5 Sundays in one month?

Mathematics. 4th grade.

Lesson topic: "Grouping of terms"

Educational material for children and teacher : cards for group work, cards for independent work, textbook “Mathematics” 4th grade, M., Education, 2014, workbooks, materials for group work.

Topic goals. To form an idea of the methods of rational calculation.

Groupings of terms;

Rounding terms.

Algorithms:

Rounding numbers when adding;

Definitions of the arithmetic mean.

Teach to use acquired knowledge and skills in practical activities.

Lesson objectives.

Update:

Knowledge of the commutative property of addition;

The ability to carry out mutual verification of an educational task and provide the necessary mutual assistance in cooperation.

The concepts of “grouping terms”, “rounding terms”;

Method of grouping terms and algorithm for rounding numbers.

Teach:

Determine the method of grouping terms and justify your opinion;

Determine the order in which numbers are rounded when adding and justify your opinion;

Calculate an expression using a well-known algorithm for rounding numbers when adding;

Solve the problem using a number rounding algorithm when calculating;

Use speech to regulate your actions

Terms and concepts: grouping of terms, rounding of terms, arithmetic average.

Planned results

Personal

Manifest:

Interest in studying the topic;

Positive attitude towards studying the topic;

Awareness of one's own achievements in mastering the educational topic.

Subject

Perform the technique of grouping terms;

Calculate an expression using a well-known algorithm for rounding numbers when adding;

Solve the problem using a number rounding algorithm when calculating.

Cognitive skills:

Expand the meaning of the concepts “grouping of terms”,

“rounding terms” and using them in the active dictionary;

Determine the method of grouping terms and justify your opinion;

Determine the order in which numbers are rounded when adding and justify your opinion.

Regulatory skills:

Carry out a learning activity using an algorithm;

Carry out mutual verification of the educational task and provide the necessary mutual assistance in cooperation.

Communication skills:

Use speech to regulate your actions;

Coordinate positions when working in a group and find a common solution.

Lesson plan.

I. Org.momen T.

Psychological mood. Give each other smiles.

“Get to work in a good mood”

For the motto of our lesson, I took these words from the mathematician Gyorda Pólya “ The best way to learn something is to discover it yourself.”

How do you understand this statement?

II. Updating knowledge.

A minute of penmanship. Working with numbers.

Write down the smallest two-digit number. What can you tell us about him?

Write down all round two-digit numbers in ascending order?

What two single-digit numbers add up to make 10?

In the multiplication table, when multiplied, which numbers will be round?

Warm-up for the mind (logical tasks)

What is heavier than 1 kg of iron or 1 kg of cotton wool?

One egg takes 4 minutes to cook. How many minutes should you cook 6 eggs?

What figure is shown? What is the name of a segment that does not lie on one side and connects two vertices of a polygon. How many triangles does the figure consist of? Show.

-What did we work on in the last lesson? What did you study?

Compare the expressions in each pair. How are the expressions similar and different?

Find the meanings of the expressions of any pair. (In writing). Check!!

72-9-3+6= 66 48-6+7+8=57

72:9∙3:6= 4 48:6∙7:8=7

Conclusion!

Is it true that the meanings of the expressions in each pair are the same? Prove it!

17+(4∙3) ∙2-8=33 8∙(4+3)+6-4=37 58

17+4∙(3 ∙2)-8=33 8∙4+(3+6)-4=37

III. Problematic situation. Entering the topic.

You know in what order to perform the actions in an expression!

Try to quickly find the meaning of this expression

53 + 264 + 136 + 30 + 47 =?

Did it work? Using your knowledge, think about how to conveniently and quickly find the meaning of this expression!

What mathematical properties did you use?

This property of addition is calledcommutative and associative. What is its meaning?

Commutative property: rearranging the terms does not change the sum.

Combination property: we replace two adjacent terms with their sum.

Note that the first and fifth terms, as well as the second and third terms add up to round numbers. Using the grouping of these terms we get

(53+47)+(264+136)+30=100+400+30=530

V. Determining the topic of the lesson. Setting goals and objectives.

1)- Try to formulate the topic of our lesson.

-Grouping of terms

What goals will we set for ourselves?

-Learn to evaluate an expression using the grouping technique.

2) Trial action No. 1 at the board with a comment.

87+139+213+61=(87+213)+(139+61)=300+200=500

VI. Primary consolidation.

A situation of success. To secure knowledge we can do No. 2

368+73+27+132=(368+132)+(73+27)=500+100=600

Express survey

What is the name of a mathematical operation that uses the + sign?

(Addition).

What are numbers called when added?

(Additions).

What is the result of addition called?

(Value of the amount).

What properties underlie the method of grouping terms?

(Commutative and associative properties).

Physical exercise.

Children close their eyes and lower their heads to the desk.

"You are a little flower. Your life is just beginning. You are warm and calm. Your stems stretch upward, towards the sun. The petals smile rainbow-coloredly and squint under the sun. You looked around. You are not alone. You are surrounded by equally beautiful and rainbow-colored flowers. Life beautiful. But the time has come to wake up..."

VIII. Consolidation of what has been learned.

1)Work Task No. 3

1. Reading and analyzing the problem.

What is the task about?

How many beds were there?

What do you need to find?

2. Drawing up a diagram of the problem.

3. Solving the problem.

Is it possible to immediately answer the question of the problem?

How can I find out how many heads of cabbage were removed from these beds?

2) Work in pairs.

Compose and solve an expression problem on our topic using numbers that are grouped.

Bottom line. Defense at the board.

IX. Bottom line. "Reception of information."

List the terms necessary to understand the topic.

What did you like?

Where can the material you studied be useful?

What is the main idea of the topic?

X. Independent work.

Solve these expressions in a convenient way (on a piece of paper). Your task is to check the work of your neighbor at the desk (Collective analysis of expressions, hand in the pieces of paper to the teacher).

167+324+133+76

418+165+35+182

Standard check . Self-esteem

XI. D\z. Textbook p. 35, No. 2 (2 columns), No. 5, optional No. 9! (differentiated)

XII. Reflection

I set a goal...
I was able to do it on my own...
I'm still having trouble...
I like it…

XI. Thanks for the lesson.