II. Checking homework

Sections: Primary School

Class: 2

Lesson objectives:

– develop the ability to use the multiplication table and division by 7;
– consolidate the ability to perform calculations using algorithms specified by flowcharts;
– consolidate skills in solving problems in different ways and choosing a rational method;
– consolidate skills in the order of performing actions in literal expressions, in drawing up programs and action plans;
– develop students’ mathematical speech in the course of commenting, explaining, arguing the meaning of expressions compiled for problems and using mathematical terms;
– develop attentiveness and the ability to work at a fast pace.

Equipment:

1. Peterson L.G. Mathematics. 2nd grade. Part 3. – M.: Yuventa, 2008, -112 pp.;ill..15 LESSON pp. 38–39.
2. Peterson L.G., Barzunova E.R., Nevretdinova A.A. Independent and test papers For primary school. Issue 2. – M.: Balass, 2009. P. 85.
3. Encyclopedic dictionaries, encyclopedia of flora and fauna.

During the classes:

I. Organizational moment

Teacher. Today in class we have a big and interesting job: we will check your homework, conduct an intellectual warm-up, discover new knowledge, carry out independent work and a game for attention.

II. Examination homework

Three low-performing students are invited to the board to complete the following homework assignments. From the notebook with independent and test work, show solutions to tasks 1 and 3 on p. 85.

1. Create an action plan:

A) n x( a + b) : c – t;
b) c – d x( b – a) + m : n.

2. On the first shelf there are 58 plates, on the second - 16 plates less than on the first, and on the third - 6 times less than on the second. How many plates are there on three shelves?

3. Frontal check of homework 2 on p. 85 from independent and control work.

U. Solve the examples and write down the answers in descending order. What word is encrypted?

Figure No. 1

Children. The name of the medicinal plant is encrypted - EUCALYPTUS.

Students make reports about eucalyptus, which are then placed on the “It's Interesting!” stand.

III. Updating knowledge (intellectual warm-up)

Questions for class students on the completed assignment.

U. What two sets can the received answers be divided into?
D. Even and odd numbers, round and non-round numbers, containing the number 3 and not containing it, etc.
U. Name the common property that unites all the answers.
D. All numbers are two digits; all numbers are natural.
U. Add up the answers that are round numbers.
D. 70 + 30 + 60 = 160.
U. Find the sum of the values ​​of the expressions corresponding to the letters K and T.
D. The sum of 46 and 23 is 69.
U. Read the expression in which the answer is the number of ones equal to the number of tens.
D. The sum of the product of 6 and the difference of 89 and 83 and 8 is 44.
U. Read the expression in which the number of tens is one less than the number of units.
D. The minuend is represented as the product of 4 and 8, and the subtrahend is represented as the quotient of 27 and 3. The value of the expression is 23.
U. Formulate a task for a mathematical expression with the answer 32.
D. Read the expression in which the number of tens is one greater than the number of units.
One of the students reads this expression.
U. By how many units is the value corresponding to the letter "E" greater than the value corresponding to the letter "L"?
D. 70 is greater than 42 by 28 units. To find out how much one number is greater than another, you need to subtract the smaller from the larger.
U. How many units is the value of "T" less than the value of "A"?
D. 23 is less than 44 by 21 units. To find out how much one number is less than another, you need to subtract the smaller from the larger.
U. What operation must be performed on the value of the expression “P” to obtain the value of the expression “B”?
D. 30 increase by 2 times; 30 increase by 30 units.

IV. Physical education (useful relaxation)

On the left side of the classroom hang multi-colored balls with numbers:

25 5 35 10 45 15

U. Let's have a good rest for new discoveries.

(Target: relaxation of the neck muscles, checking attention, observation, calmness, self-affirmation - “I’m right”)

U. Close your eyes. Lower your heads down and place them on your desk. Do you remember how many balloons are hanging in the classroom? Without raising your head, show their number with your fingers.

(Children show the answer on their fingers. The teacher quickly walks between the rows, touching those who were attentive and counted correctly)

U. Maybe someone was very observant and noticed the number that was written on the green ball? Point your fingers.

(The teacher touches the hands of those children who made no mistake and correctly remembered the number 5)

U. Open your eyes and read the numbers in ascending order.

(Children turn their heads to the left, the neck muscles tense, return to their original position - the muscles relax)

D. 5, 10, 15. 25, 35, 40

U.

D. 5, 10, 15, 20 , 25. 30 , 35, 40

U. Turn your head to the right, name the numbers written on the cards (on the stand on the right these numbers are: 6, 24, 54, 18, 36, 12, 48) in descending order.

D. 54, 48, 36, 24, 18, 12, 6.

U. Determine the pattern and restore the missing numbers.

D. 54, 48. 42 , 36, 39 , 24, 18, 12, 6 – results of multiplication by 6.

V. Discovery of new knowledge

Recover missing numbers:

1) 5, 10, 15, …, 25, …, 35, 40, … .
2) 54, 48, …, 36, …, 24, 18, 12, 6.

Checking the completion of tasks on the board. Students answer with explanations, and the whole class follows the answers with cue cards.

U. What rule is used to construct the first row of numbers?
D. Results of multiplying numbers by 5.
U. By what rule is the second row constructed?
D. Results of multiplying numbers by 6.
U. Are the numbers in the series decreasing or increasing?
D. In the first row the numbers increase, in the second they decrease.
U. What number is divisible by both 5 and 6?
D. Number 30.
U. Which numbers from these series are divisible by 7?
D. 35 and 42.
U. Make up a series of numbers divisible by 7. What rule will you use to make it up?
D. Using cases of multiplication by 2, 3, 4, 5 and 6.
– Let’s write the first number 7 and add 7 at a time.
– 7, 14, 21, 28, 35, 42, 49, 56, 63.
U. Using the resulting series of numbers, fill out the multiplication table in the textbook on p. 38, no. 1.
D. 7 x 7 = 49, 7 x 8 = 56, 7 x 9 = 63, 8 x 7 = 56, 9 x 7 = 63.
U. What pattern did you notice in writing the answers in expressions when multiplying the number 7 by other numbers?
D. As the second factor increases, the product increases.
U. Why are the answers the same in the multiplication lines?
D. Rearranging the factors does not change the product.
Next, fill in the columns with examples of division:
49: 7 = 7, 56: 7 = 8, 56: 8 = 7, 63: 7 = 9, 63: 9 = 7.
U. What pattern in the writing of answers did you notice in the expressions when dividing by 7?
D. As the dividend increases, the quotient increases.
U. What pattern did you notice in the lines when composing division examples?
D. If the product is divided by one of the two factors, you get the other factor.

VI. Primary consolidation

U. Among the given numbers, find numbers that are multiples of 7:

13, 21, 37, 42, 7, 54, 48, 35, 29, 14, 26, 15, 49, 52, 28, 30, 65, 27, 56, 17.

– State a number that is a multiple of 7 and the result of division by 7.
Then perform calculations according to the algorithm specified by the block diagram (task 4 on p. 38):

The flowchart is posted on the board, and frontal work is carried out with commentary by individual students. All students fill out the table in the textbook.

U. What numbers multiplied by 7 form a number greater than 35?

D. 6, 7, 8, 9.

VII. Independent work

U. Fill out the second table yourself using the flowchart in the textbook (task 4 on p. 38):

– What numbers must the number 7 be multiplied by so that the product is less than 35?

D. On 1, 2, 3, 4.

Mutual verification of the results of filling out the table.

a	3	4	5	6	49	56	9
x	22	29	35	42	49	56	63

U. Raise your hand if you filled out the table correctly. Raise your hand if you've made one mistake. What caused the difficulty in filling out the table?
The children's answers are listened to.

VIII. Repetition of previously studied material

U. Problem 7 on p. 39. Try to solve the problem in two ways.
There are 5 yellow and 2 blue balls in the box. How many balls are in 6 such boxes?
A student is invited to the side board, the rest of the students solve the problem on their own. The student checks the solution on the board. Then the teacher finds out who solved the problem differently and invites them to write down their solution to the board. Then the decisions are justified and discussed. The class follows the discussion with cue cards.
– Tell us how you reasoned when solving the problem.
D. To find the number of balls in 6 boxes, you need to multiply the number of balls in one box 5 + 2 by 6. (5 + 2) x 6 = 42 (w).
– First, let's find the number of yellow balls in 6 boxes, for this we multiply 5 by 6. Then we find the number of blue balls in 6 boxes, multiply 2 by 6. Then we add the results and find the number of balls in 6 boxes. 5 x 6 + 2 x 6 = 42 (w).
U. Which solution is more rational and why?
D. The first method is more rational, since the problem is solved in two steps, and in the second method - in three.
U. Now draw up a program and action plan for solving task 6 on p. 39:

A) a x b – c : d + k x m;
b) A x( b – With) : d + k x m;
V) ( a x b – c) : d + k x m;
G) a x b – c : (d + k)x m.

– Compare these expressions. What are the similarities between these expressions?
D. The similarity is that the letters in these expressions are the same.
U. What is the difference?
D. Expressions differ in the placement of brackets.
U. Will the program of action change if the placement of the brackets changes?
D. The program of actions changes, since the actions in brackets are performed first.

Students arrange the order of actions in the textbook independently. On the board, the teacher offers a ready-made diagram, and the called students draw up a plan of action for the expressions.

A) a x b–c:d+k x m.

Action plan:

b) A x( b–With) :d+k x m.

Action plan:

IX. Homework

Learn new cases of multiplication by 7 and corresponding examples of division in the textbook on p. 38. Complete tasks 8, 10 on p. 39.

X. Lesson summary

To end the lesson on a high emotional level, an attention task is offered, which is performed at a fast pace.

Game for attention

U. To the number of letters “A” in the word deciphered at home, add the number of centimeters in one decimeter.
D. 1 + 10 = 11 (eucalyptus).
U. Divide the number of months in a year by the number of floors in our school.
D. 12: 4 = 3.
U. Divide the sum of the angles in the square by the number of sides in the rectangle.
D. 4: 4 = 1.
U. Multiply the smallest natural, single-digit number by the smallest natural two-digit number.
D. 1 x 10 = 10.
U. Subtract a trio from two quartets.
D. 4 x 2 – 3 = 5.
U. In which writer's work does the word "quartet" appear?
D. In the fable of I.A. Krylov "Quartet".
U. List the characters in this group of “musicians”.
D."The Naughty Monkey, the Donkey, the Goat and the clumsy Bear."
U. The number of letters "o" in the word denoting the calf's mother is multiplied by the number of the same letters in the name of the grandfather and woman's baked goods, which the sly fox ate.
D. 2 x 3 = 6 (cow, bun).
U. What topic did we work on in class today?
D. Multiplication and division table by 7.
U. What cases of multiplication by 7 did you know before?
D. Multiply by 1, 2, 3, 4, 5, 6.
U. What cases of multiplying by 7 were new today?
D. On 7, 8 and 9.
U. What did you find most difficult in the lesson? What was the most interesting thing about the lesson?

Children's answers.

XI. Control slice

The system for testing students' knowledge in primary school plays an important role. The more students you can interview in class, the better. Frequent questioning not only helps to objectively assign final grades, but also allows the teacher to promptly respond to gaps in students’ knowledge. A technique for quickly checking the quality of students’ knowledge will help with this.

To check the quality of mastering the multiplication table by 7 and the corresponding cases of division, the following control sections can be offered.

1. "Tic Tac Toe"

Before starting work, students are offered “blitz” cards for type control:

Check: Option 1 – “X’s” won, Option 2 – “O” won

2. “Circle the numbers that are multiples of 7.”

Checking all cases of division by 7. Students are offered “blitz” control cards of the form:

Option I

49; 41; 33; 28; 12; 62; 7; 25; 21; 27; 16; 42; 52; 14; 26; 9; 40; 35; 56; 63

Option II

7; 59; 63; 44; 13; 49; 42; 24; 28; 50; 53; 21; 36; 47; 25; 14; 54; 35; 56; 9

Solution:

Option I

49; 28; 7; 21; 42;14; 35; 56; 63

Option II

7; 63; 49; 42; 28; 21; 14; 35; 56;

3. "Blitz tournament"

Solving problems at a fast pace.

(Purpose: testing the ability to solve problems of different types, testing knowledge of tabular results of multiplication (division) by 7. Solutions to problems are written in numbered cells on cards.

1. Grandmother laid out 5 pies each on 7 plates. How many pies did grandma put out?
2. The guys grew 49 red roses, which is 7 times more than yellow ones. How many yellow roses did the guys grow?
3. The grandmother is 56 years old, and the grandson is 8. How many times older is the grandmother than the grandson?
4. There are 7 pencils in the box. How many pencils are in 9 such boxes?
5. There are 7 girls in the chess club, and 8 times more boys. How many boys are in the club?
6. There are 4 rowers in the kayak. How many paddlers are there in 7 kayaks?
7. 63 plums were distributed to 7 children. How many plums did each child receive?
8. There were 35 boats and 7 pedalos parked at the pier. How many times fewer pedal boats than boats were parked at the pier?

Solution:

1. 5 x 7 = 35 (b.)	2.49: 7 = 7 (r.)	3.56: 8 = 7 (times)	4. 7 x 9 = 63 (k.)
5. 7 x 8 = 56 (m.)	6. 4 x 7 = 28 (g.)	7. 63: 7 = 9 (s.)	8.35: 7 = 5 (times)

Based on the results of the control sections, you can create diagrams that reflect the overall picture (for a specific class) of mastering the topic “Multiplication table by 7 and the corresponding cases of division.”

Sample chart (person/relevantcases of multiplication - division):

MULTIPLICATION

References:

1. Peterson L.G. Mathematics. 2nd grade. Part 3. – M.: Yuventa, 2008, -112 pp.; ill..15 LESSON pp. 38–39.
2. Peterson L.G., Barzunova E.R., Nevretdinova A.A. Independent and test work for elementary school. Issue 2. – M.: Balass, 2009. P. 85.
3. Encyclopedic dictionaries, encyclopedias of flora and fauna.

ARITHMETIC OPERATIONS OF MULTIPLICATION AND DIVISION

TABLE OF DIVISION BY 7

826. From each product, compose and evaluate an expression for division by 7.

7 ∙ 2 = 14 7 ∙ 6 = 42 7 ∙ 9 = 63

827. Explain how you compiled the table of division by 7. Read the table.

49: 7 + 14 60 - 63: 7 (68 - 26) : 7 21: 7 + 0

42: 7 - 5 81 - 56: 7 35 - 14: 7 28: 7 - 4

829. Compose and solve a drawing problem.

How many times is the mass of a pumpkin greater than the mass of a melon?

830. The first number is 5, and the second is 30 more. How many times is the first number less than the second?

831. Fill in the blanks.

832*. Labyrinth. Show me the way to the center. The sum of the numbers written at the gate through which the path passes must equal the number written inside.

833°. Draw a table and write down the data and the required numbers in it.

a: b

834°. To obtain 7 kg of sugar, 42 kg of sugar beets were used. How many kilograms of sugar beets go into making 1 kg of sugar?

Create an inverse problem.

835. Count with sixes up to 60, with sevens up to 70.

836. Make up correct equalities from expressions and their numerical values.

Sample. 7 ∙ 7 + 7 = 56.

837. Before the break, the kiosk sold 7 identical postcards for 42 UAH. After the break, we sold 5 more identical postcards for 45 UAH. How many hryvnia did you receive for postcards sold per day?

Ask another question about the conditions of the problem.

838. Based on the data in the picture and the questions, make up numeric expressions to find out:

1) how many hyacinths and ficuses were grown;

2) how many fewer ficuses are there than crocuses;

3) how many more ficuses there are than hyacinths.

839. 24 football players arrived at the sports camp, and 3 times fewer hockey players. How many more football players arrived than hockey players?

840*. Find the numbers and write the equalities.

841°. A farmer needs to package 21 kg of red and 14 kg of pink tomatoes in 7 kg boxes. How many boxes do you need?

28: 7 + 49 7 ∙ 3 + 7 ∙ 6 70 - 56: 7

63 - 63: 7 7 - 6 + 7 ∙ 2 42: (12 - 5)

843. Finish the calculations.

What do we get when we divide the product by the factor? If a b = c, then what is the share of c: a; share c : b ?

844. (Oral.) Find the unknown factors.

845. 7 boys divided 35 apricots equally among themselves. How many apricots did each boy get?

Compose inverse problems.

846. The width of the river is 20 m. During a flood, the river on one side overflowed its banks by 6 m, and on the other - 3 times further. How wide is the river during a flood?

Explain what the terms 20 + 6 and 6 ∙ 3 mean in the compiled expression. Finish solving the problem.

847*. 18 liters of tomato juice were poured into two-liter jars and the same amount of juice was poured into three-liter jars. How many cans of juice did you get?

56: 7 + 22 22 - 56: 7 (14 + 28) : 7

14 + 28: 7 63: 7: 3 42: 6 ∙ 7

849°. Over the course of a year, 6 houses were built in the village, 4 apartments in each, and 8 two-apartment houses. How many apartments were built in the village in a year?

850. (Oral) Do the calculations.

851. Write down the incorrect equalities. Calculate.

65 - 3 = 35 90 - 9 = 99 100 - 0 = 10

21 - 5 = 16 60 - 3 = 67 35: 5 + 2 = 5

35: (5 + 2) = 5 20 - 6: 2 = 7 1 + 7 ∙ 7 = 51

852. According to the data in the table, calculate the expressions.

853. There are 7 girls in the circle, and 3 times more boys. How many more boys are there in the circle than girls?

Change the question so that the last action is addition.

854. 1) There are 30 students in the second grade. For the holiday, 14 students are preparing dances, 7 are learning songs, and the remaining students are learning poetry. How many students learn poetry?

2) There are 30 students in the second grade. For the holiday, 14 students are preparing dances, and learning songs - 2 times less. The rest learn poetry. How many students learn poetry?

855*. Add action signs to make the equations correct.

857*. How many parts can a circle be divided into by three straight lines? Draw different cases.

858°. To prepare the mixture for laying bricks, we took 7 kg of cement and 14 kg more sand. How many times less cement was used than sand?

Replacements in the condition of 14 kg more words 2 times more. Will the answer to the problem change?

33 + 7 ∙ 5 6 ∙ 7 + 7 ∙ 6 (18 + 36) : 6