How to write a mathematical dictation. Mathematical dictation (as it goes in our class). Finding a number by its percentage

Mathematical dictations

Grade 3

Dictation 1

one . Increase 7 by 5 times.

2. Reduce 32 by 4 times.

3. Find the product of the numbers 7 and 8.

4. Find the quotient of 64 divided by 8.

5. Product of numbers 30. One of the factors 5. What is the other factor?

6. 7 increase by 7 times.

7. How many times is 42 more than 7?

8. How many times is 42 more than 6?

9. Divisor 45, quotient 5. What is the divisor?

10. How much is 42 more than 7?

Answers: 35, 8, 56, 8, 6, 49, 6, 7, 9, 35.

Dictation 2

one . The first factor is 7, the second is 4. Find the product.

2. Which number is 8 times more than 6?

3. Increase 7 by 5 times.

4. How many times is 32 more than 4?

5. Decrease 28 by 7.

6. Find the quotient of 64 and 8.

7. Which number is 3 times less than 18?

8. Decrease the number 100 by 15.

9. Increase the number 18 by 20.

10. For 2 identical suits 8 m of fabric went. How many meters of fabric will go for 3 of these suits?

Answers: 28, 48, 35, 8, 4, 8, 6, 85, 38, 12.

Dictation 3

one . 86 increase by 8.

2. What is the sum of 88 and 4?

3. The first term is 35, the second 9. What is the sum?

4.Add 6 to 74.

5.42 decrease by 6.

6. How much is 33 more than 9?

7. How much do you need to subtract from 62 to get 49?

8. How much is 29 less than 43?

9. In one box there are 24 kg of sweets, and in the other 6 kg less. How many kg are in two boxes?

10. There are 70 students in two classes. There are 34 students in one class. How many students are in the second grade?

Answers: 94, 92, 44, 80, 36, 24, 13, 14, 42, 36.

Dictation 4

one . Find the sum of 32 and 33.

2.96 increase by 4.

3. The first term is 73, the second is 17. What is the sum?

4.86 decrease by 42.

5. How much should you add to 26 to 60?

6. How much do you need to subtract from 50 to get 27?

7. Find the difference between 96 and 58.

8.100 without 72.

9. The boy read 18 pages on the first day, and 8 more pages on the second. How many pages did he read in two days?

10. There are 28 kg of apples in one box, 6 kg more in the second, and 12 kg less in the third than in the second. How many kg of apples are there in the third box?

Answers: 65, 100, 90, 44, 34, 23, 38, 28, 44, 22.

Dictation 5

one . Increase 14 by 22.

2. Find the sum of the numbers 39 and 17.

3. The first term is 20, the second 11. Find the sum.

4. Decrease 77 by 19.

5. Calculate the difference between the numbers 41 and 6.

6. Reduced 26, subtraction 25, Find the difference.

7. How much is 79 more than 42?

8. How much is 11 less than 68?

9. Add the same number to 17.

10. Increase the smallest two-digit number by 79.

Answers: 36, 56, 31, 58, 35, 1, 37, 57, 34, 89.

Dictation 6

1. By what number should 9 be multiplied to get 18?

2. How much will it be if you take 3 times 5?

3. How many will be: 6 triples?

4. Write down the number that is less than 12 by 6.

5. Write down a number that is 6 times less than 12.

6. How many fives are there in 15?

7. How many sevens are there in 14?

8.3 times 4.

9. There are 6 peas in one pod. How many peas are in 3 such pods?

10. To work in the school area, 18 boys were divided into 3 equal teams. How many boys were there in each brigade?

Answers: 2, 15, 18, 6, 2, 3, 2, 12, 18, 6.

Dictation 7

1. Sasha conceived a number. If you increase it by 14, you get 52. What number is Sasha thinking?

2. Increase 38 by 4 units.

3. Decrease 85 by 5 tens.

4. Decreased 92, the difference is presented inthe sum of 70 and 6. What is the deductible?

5. Have conceived a number. It was reduced by 17 and got 65. What number are you planning?

6. How much is 73 more than 42?

7. 24 increase by the same amount.

8. What is more and by how much: the sum of 23 and 27 or the difference between 100 and 17?

9. Yunnat has grown a watermelon weighing 14 kg and a pumpkin 9 kg heavier than a watermelon. What is the weight of a pumpkin?

10. Dima read 15 pages and he has 47 pages left to read. How many pages are in the book?

Answers: 38, 42, 35, 16, 82, 31, 48, 33, 23, 62.

Dictation 8

one . First term 26, second 14. Find the amount.

2. The first term is 5, the second 9. Find the sum.

3. The first factor is 5, the second is 9. Find the product.

4. Divisor 36, divisor 4. What is the quotient?

5. How much is 45 more than 5?

6. How many times is 45 more than 5?

7. How many times is 3 less than 27?

8. Is 3 less than 27?

9. Which number is more than 25 by 5?

10. Increase 7 by 5 times.

Answers: 40, 14, 45, 4, 40, 9, 9, 30, 35.

Dictation 9

one . 20 decrease by 4 times and increase by 3 times.

2.9 increase by 2 times and decrease by 9

3. Write down the largest two-digit number.

4.60 increase by 2 tens.

5.60 decrease by 2 units.

6. Write down a number greater than 54 by 24.

7. Write down the number in which there are 4 units and 7 tens.

8. Write down a number less than 28 by 9,

9. From 13 meters of fabric the seamstress made a dress and 4 identical shirts. One dress used 5 m of fabric. How many meters of matter did one shirt go?

10. In one class there are 30 students, and in the second there are 4 fewer students. How many students are there in both grades?

Answers: 15, 9, 99, 40, 58, 78, 19, 2, 56

Dictation 10

one . Find the sum of terms 34 and 4.

2. Calculate the difference between the numbers 76 and 6.

3. Decrease 30 by 19.

4. Increase 23 by 17.

5. How much is 52 more than 12?

6. How much is 4 less than 40?

7. What is the sum of 4 terms, each of which is different 6?

8. Reduce 32 by 4 times.

9. Decreased 70, subtracted 7. Calculate the difference.

10. The first term is 13, the second is the same. What is the amount equal to?

Answers: 38, 70, 11, 40, 40, 36, 24, 8, 63, 26.

Dictation 11

one . Calculate the sum of the numbers 44 and 8.

2. Find the difference between the numbers 71 and 17.

3. Increase 28 by 46.

4. Decrease 81 by 38.

5. How much is 17 less than 30?

6. Increase the number 4 by 2 times.

7. Reduce the number 18 by 3 times.

8. Term 8. What is the sum of three such terms?

9. How much is 45 more than 19?

10. How much less 27 than 30?

Answers: 52, 54, 74, 43, 13, 8, 9, 24, 26, 3.

Dictation 12

one . Increase 8 by 5 times.

2. Reduce 30 by 6 times.

3. Find the product of the numbers 6 and 9.

4. Find the quotient of the numbers 56 and 8.

5. Product of numbers 72. One of the factors is 8. What is the other factor?

6. The dividend is 35. Divisor 7. What is the quotient?

7. How many times is 24 more than 3?

8. How many times is 24 more than 8?

9. Increase 20 by 4.

10. How much is 24 more than 8?

Answers: 40, 5, 54, 7, 9, 5, 8, 3, 24, 16.

Dictation 13

one . Add 8 to 76.

2. How much is 16 less than 32?

3. Find the sum of 46 and 9.

4. The unknown number is greater than 56 by 37. What is the unknown number?

5. Subtract the difference between 13 and 5 from 34.

6. Find the sum of numbers 24 and 3

7. Which number is more than 58 by 8?

8. Name from the numbers 3, 14, 17 such a number, which is the difference of two other numbers.

9. In the pool in the morning there are 18 groups, and in the evening 23 groups.How many more groups are there in the evening?

10. In a week, 40ratings. 14 fives, 17 fours, and the rest are triples. How many triplets were there in the magazine?

Answers: 84, 16, 55, 19, 26, 27, 50, 3, 5, 9.

Dictation 14

one . Increase 4 by 8 times.

2. Reduce 63 by 7 times.

3. Find the product of the numbers 2 and 9.

4. Find the quotient of 24 and 6.

5. One factor is 7, the other 4. Find the product.

6. Divisor 36, divisor 9. What is the quotient?

7. How many times is 8 less than 24?

8. How many times is 36 more than 4?

9. How much is 36 more than 9?

10. For the Christmas tree, the children made 5 garlands. Each garland contained 9 snowflakes. How many snowflakes did the children cut for these garlands?

Answers: 32, 9, 18, 4, 28, 4, 3, 9, 27, 45.

Dictation 15

one . Find the product of the numbers 9 and 6.

2. Find the quotient of 18 and 9.

3. Increase 7 by 5 times.

4. Reduce 42 by 6 times.

5. How many times is 49 more than 7?

6. How many times is 7 less than 21?

7. What number should be reduced by 3 to get 30?

8. Decreased 15, difference 7. Find the subtracted.

9. Unknown number is greater than 36 by 9. Write down what is equal tounknown number.

10. Write down any number that is less than the sum of the numbers 9 and H.

Answers: 54, 2, 35, 7, 7, 3, 33, 8, 45, up to 11.

Dictation 16

1 . Find the product of the numbers 8 and 7.

2. Find the quotient of 24 and 6,

3. Increase 9 by 7 times.

4. Reduce 30 by 5 times.

5. How many times is 40 more than 8?

6. How many times is 8 less than 24?

7. Between what numbers is the number 40?

8. The sum of two numbers is equal to 100. One term 25. What is the other term?

9. There are 40 students in one class, and 36 in the second.fewer students in the second grade than in the first?

10. Grandfather and grandson caught 36 fish. Grandfather caught 19 fish. How many grandson caught fish?

Answers: 56, 4, 63, 7, 5, 3, 39, 41, 75, 4, 17.

Dictation 17

one . Find the sum of 38 and 12.

2. Find the difference between the numbers 80 and 3.

3. Find the product of the numbers 4 and 9.

4. Find the quotient of 32 and 8.

5. How many times is 27 more than 9?

6. How many times is 4 less than 24?

7. How much is 32 more than 8?

8. How much is 3 less than 21?

9. Divisible 30, divisor 5. What is the quotient of these numbers?

10. One factor is 6, the other is 7. What is the product of these numbers?

Answers: 50, 77, 36, 4, 3, 6, 24, 4, 6, 42.

Dictation 18

one . Write down three two-digit numbers that have 7 tens.

2. How much is 30 less than 90?

3. Write 13 as a sum of single-digit numbers in three ways.

4. How much did you subtract from 67 if you got 9?

5. How much should you add to 36 to get 40?

6. Write down all two-digit numbers in which the same numbers are used.

7. Find the difference between the numbers 40 and 20.

8. What number must be increased by 9 to get 18?

9. How many are 7 tens more than 7 units?

10.Present the number 10 as the sum of two terms, one of which is 2 units more than the other.

Answers: -, 60, -, 58, 4, -, 20, 9, 63, -.

Dictation 19

1.Write the number that is 1 dozen more than 27

2. Find the product of the numbers 3 and 9.

3. Find the quotient of 24 and 3.

4. How many times is 12 more than 2?

5. How many times is 5 less than 40?

6. The length of the first segment is 9 cm, and the second segment is 3 times shorter. How long is the second segment?

7. Vera is 12 years old, and her brother is 3 times younger than her. How old is your brother?

8. There were cubes in the box. The boy put another 7 cubes there. There are 20 of them. How many cubes were in the box first?

9. There are 34 boys and 20 girls in the circle. How many boys are there more than girls in this circle?

10. How much is 8 less than 72?

Answers: 37, 36, 8, 6, 8, 3, 4, 13, 14, 64.

Dictation 20

1. Decrease 40, subtraction 26. Find the difference.

2. The sum of two numbers is 83, the first term is 40. Find the second term.

3. The first factor is 8, the second 4. Find the product.

4. Divisor 35, divisor 5. Find the quotient.

5. How much is 6 less than 18?

6. How many times is 6 less than 18?

7. How many times is 28 more than 4?

8. How much is 28 more than 4?

9. Which number is less than 43 by 3?

10. Reduce 16 by 4 times.

Answers: 14, 43, 32, 7, 12, 3, 7, 24, 40, 4.

Preschool mathematics is an important component of the intellectual development of toddlers. The lessons of this course are aimed at the formation of the cognitive and creative abilities of preschoolers, at teaching ordinal and quantitative counting. In mathematics lessons in kindergarten, at home or in a circle, the child gets acquainted with the basic mathematical concepts, develops logical and spatial thinking.

The main tool for the mathematical development of preschoolers is didactic games, but along with them, others are also used:

practical exercises;
elementary experiments and experiments;
modeling;
graphic tasks;
mathematical dictations.

Let's figure out what mathematical dictations are in principle and how they can be adapted to the peculiarities and requirements of preschool pedagogy.

The benefits of mathematical dictations

Mathematical dictation is a popular form of knowledge control, actively used by school mathematics teachers. The essence of this phenomenon is that the teacher asks a question (orally or in writing), and the students must write down short answers. A preschooler can be asked to perform dictation tasks visually:

rearrange the cubes;
add / remove the specified number of buttons;
compare the presented groups of objects;
group objects represented in a certain way.

Various criteria can be used to classify mathematical dictations. Most often, mathematical dictations are divided into groups in accordance with the tasks that they solve:

assimilation of mathematical terminology;
oral counting training;
logical questions.

It is not recommended to mix different types of mathematical dictations, although it is considered acceptable. The main thing when drawing up an assignment is its adaptation to the level of knowledge of a particular kid (or a group of children, if we are talking about mathematics in kindergarten).

Mathematical dictation perfectly trains the child's ability to concentrate. To successfully cope with the task, the baby needs to show considerable willpower:

listen carefully to the task;
quickly enough, without prompting (preferably!) to figure out what needs to be done;
write down your answer (complete the task).

The development of competent mathematical speech should also be attributed to the benefits of mathematical dictations:

the child listens to the correct reading of mathematical expressions;
enriches the thematic lexical dictionary;
fixes the names of arithmetic operations and geometric shapes.

In order not to cause overwork and prevent a loss of interest in this type of activity, monitor the condition of your ward. The duration of the mathematical dictation is on average 7 minutes. Of course, if a young mathematician is growing up in your family who is happy to complete all tasks, you can work out longer than the recommended time. But no compulsion! This is important, friends.

How to organize a math dictation for a preschooler

The dictation questions should be related. Read them slowly. Pronounce your words clearly. Make sure your child is collected and listens to you carefully.
Read each question three times. First, the baby must hear the question in full. Give it a few seconds to think it over. Read the second time - the child must write down the answer (complete the task). During the third reading, the little mathematician can check the correctness of his solution.
Do not comment on the child's answers until you have read the entire dictation in its entirety. All discussion and analysis takes place at the end of the assignment. However, you can deviate from this rule if your baby is anxious. But try to teach the child to act according to the established rules by the end of the senior preschool age, because this is how mathematical dictations will take place in grade 1.
Do not strive at all costs to complete all the tasks of the prepared mathematical dictation. If the child is tired, switch his attention to another type of activity, and you can return to the dictation next time.
To successfully complete the traditional mathematical dictation, you need to understand the information well by ear. If your toddler has auditory memory problems, you can prepare flashcards to reflect your questions. Gradually, the volume of graphically presented questions should decrease in favor of the oral form.

Examples of math dictations for preschoolers

Option 1

Draw as many circles as there are apples on the card.
Paint the first circle on the right in red.
Fill in the middle circle with green.
Paint the remaining circle in yellow.
Write down the number of apples in the picture.

Option 2

Draw in the first line as many triangles as there are carrots on the card.
Draw one more triangle on the second line than on the first.
On the third line, draw as many circles as there are triangles on the second line.
On the next line, draw one less circle than the third.
In each row, paint the first shape in red and the last shape in green.
Write down with a number how many shapes are left unpainted.

Option 3

On the first line, write down the numbers from "1" to "3".
On the second line, write down the number that follows the number "2".
On the third line, write down the number that comes before the number "2".
On the next line, write down the largest of the numbers in the first line.
On a new line, write the smallest of the numbers in the first line.

Option 4

Write down the numbers from "1" to "9" in order.
Write down the numbers from "1" to "9" in reverse order.
Write down the neighbors of the number "6".
Which number is 1 more than "3".
What number will you get if you add “2” to “3”.

Option 5

A triangle always has three sides.
A square always has three sides
A square is a rectangle with all sides equal.
The circle has three corners.
The square has 5 corners.

Option 6

Put the "+" sign if you agree with the statement. Put a "-" sign if the statement is incorrect.

The first line contains 4 red triangles.
The second line contains 2 green and 2 blue circles.
In the third line, only one of the squares is green.
There are more blue shapes in the picture than green ones.
There are no red circles in the picture.

Friends, you can compose math dictations for preschoolers on your own. The main thing is to understand a simple principle and make sure that this form of conducting preschool mathematics brings both benefit and pleasure to the child!

Happy parenting! Until next time!

MATHEMATICAL DICTANTS ON THE TOPIC

"ADD AND SUBTRACT WITHIN20 »

1 CLASS

Dictation number 1

1. Find the difference between the numbers 13 and 5.

2. Find the sum of 7 and 4.

3. Write down a number greater than 8 by 6.

4. Which number is less than 11 by 4?

5. Increase the number 9 by the same amount.

Job numbers

Dictation number 2

1. Write down the number in which there are 1 ten and 7 ones.

2. Write down the largest single digit.

3. Write down the smallest two-digit number.

4. Write down any two-digit number less than the sum of 10 and 4.

5. Write down the neighbors of the number 19.

Job numbers



	10 or 11; 12; 13.

Dictation number 3

1. Decrease 11, subtract 6, write down the difference.

2. What single digits do you need to add to get 15?

3. Write down the sum of the numbers 8 and 5.

4. The first term is 9, the second term is 7, find the value of the sum.

5. Write down the difference between the numbers 11 and 4.

Job numbers

	8 and 7 or 9 and 6

Dictation number 4

1. From the sum of the numbers 7 and 8, subtract 4.

2. The difference between numbers 9 and 5 is increased by 8.

3.Add 4 to the sum of the numbers 7 and 5.

4.15 decrease by the difference of numbers 8 and 3.

5. Write down two-digit numbers that are less than the difference between 14 and 2.

Job numbers

Evaluation of results:

5 tasks completed without errors - high level;

Allowed: 1-2 mistakes - average level;

3 errors - below average;

more than 3 errors - low level.

Arginskaya, I.I. Collection of tasks in mathematics for independent, test and control work in elementary school [Text]: a guide for the teacher / II. Arginskaya. - M .: Fedorov, 2014 .-- 288 p. - ISBN: 978-5-393-01608-1

An important and extremely delicate aspect of the educational process for both the teacher and the student is the control of knowledge. Control is an integral part of the learning process and provides the teacher with information about the course of the cognitive activity of students in the learning process, and students - receiving information about their successes. Knowledge control has a teaching and educational value, contributes to a deeper study of the basics of science by students, to improve their knowledge and skills.

Mathematical dictations are a well-known form of knowledge control. The teacher asks questions himself or with the help of sound recording, students write down short answers to them under the numbers. As a rule, it is difficult for children to perceive tasks by ear. But if dictations are carried out often, then schoolchildren will master this skill. And the value of this skill is undeniable. Sometimes auditory perception needs help. To do this, while reading the assignment, I make a note or a drawing on the board. Depending on the preparedness of the students, I increase or decrease the number of tasks.

Before moving on to explaining the new material, it is advisable to make sure that the previous portion of the knowledge by the students has been assimilated. The traditional methodology recommends organizing a survey of students at this point in the pedagogical process. The survey, as a form of knowledge testing, is ineffective, and primarily because for the majority of students the answer of a classmate at the blackboard does not at all help to repeat what was previously studied. All kinds of compressed polls, when up to 10 students are being prepared at the same time, only exacerbate the matter: the summoned do not listen to the comrade's answer on a legal basis.

A blackboard poll is usually supplemented with a so-called verbal counting. The disadvantage of traditional "oral counting" is that not all students participate in it. An alternative to polling and "verbal counting" is mathematical dictation. Hence - its place in the educational process: at the beginning of the lesson, which begins the presentation of a new portion of knowledge. Hence - the requirement for its content: the answers to the questions should show whether the content of the previously stated material has been mastered. Mathematical dictation can replace a survey on a topic set for repetition. Its duration is usually 10-15 minutes.
It is a system of interrelated questions.

Consider the different types of tasks that students face in dictations.

1. Tasks of the reproductive type are performed by students on the basis of well-known formulas and theorems, definitions, properties of certain mathematical objects.

Reproductive tasks allow you to develop the basic skills and abilities needed to study mathematics. And although they do not contribute much to the development of students' thinking, they create a basis for further study of mathematics and thus contribute to the completion of tasks of a higher level of complexity.

2. Reconstructive tasks indicate only the general principle of solutions (for example, "solve graphically inequality") or the correlation to a particular material (for example, "solve the problem by drawing up a system of equations"). The fulfillment of such tasks is possible only after the student himself reconstructs them, correlates them with several reproductive ones. Such tasks include tasks for building graphs, tasks for drawing up equations, tasks in which students have to use several algorithms, formulas, theorems (for example, “represent the expression ( but- 2) x ( but + 2) – (2 – but) 2 "). These tasks are characterized by the fact that, starting to complete them, the student must analyze possible general ways of solving the problem, find the characteristic features of the object, and use several reproductive tasks. Note that the cognitive activity of the student when performing these tasks does not go beyond the reproduction of knowledge, but is inevitably accompanied by some generalization. Reconstructive assignments are the most common type of assignments used at all stages of the educational process.

3. A higher level of reproductive activity and its transition to creative are characterized by tasks variable character... When completing them, the student needs to select from the entire arsenal of mathematical knowledge the ones needed to solve this problem, use intuition, and find a way out of a non-standard situation. These types of tasks include the so-called quick-wittedness problems, problems "with a twist", many proof problems, as well as problems for the solution of which it is necessary to create new solution algorithms (for example, "Insert the missing monomials so that you get the identity but 2 + 6ab+ ... = (... + ...) 2 ").

To develop the thinking of students, to form in them various types of activities at all stages of teaching mathematics, it is necessary to use various types of tasks.

Mathematical dictation is one of the ways to organize students' independent activities. The system of mathematical dictations, on the one hand, should ensure the assimilation of the necessary knowledge and skills, on the other hand, their verification.

Types of dictations

Mathematical dictations can be divided into the following types: checking, overview, final. Each type of mathematical dictations has its own characteristics, its own goals, and therefore, the requirements for the compilation of these works should be different.

Verification dictations are designed to control the assimilation of a separate fragment of the course during the study of the topic. When they are completed, the teacher receives timely information on how the topic is being mastered, which allows him to identify mistakes in time, to find those who have poorly mastered this or that material and, depending on this, to build work on the study of this topic. Students, on the other hand, receive additional practice in solving problems on their own and thereby prepare for the test on this topic. Since the test dictations are carried out after mastering the basic skills and abilities, they include tasks not only of a reproductive nature. The basis of test dictations is tasks of a reconstructive nature. At the same time, test dictations should not include tasks more difficult than those that were performed by students in class and at home.

For example, this is how you can build a system of checking dictations on the topic "Arithmetic progression" in the 9th grade. Let's break this topic down into three logically complete fragments.

1. Definition of an arithmetic progression.

2. Formula n th member of the arithmetic progression.

3. Sum formula n the first members of the arithmetic progression.

By the time the first dictation is carried out, students are familiar with the definition of an arithmetic progression, the concept of the difference of an arithmetic progression. It is natural to test both of these concepts before proceeding with the study of the following material.

Dictation number 1

1. The arithmetic progression is given by the first two terms: –2.4; 0.5; ... Find the difference in the progression.

2. In arithmetic progression but 1 = -5.6 and but 2 = –4.8. Find but 4 .

3. In arithmetic progression but 2 = 7.5 and but 3 = 8. Find but 1 .

4. In the recording of the final arithmetic progression ( a n): but 1 ; 8,9; but 3 ; 7,1; but 4 ; but 5, some members are unknown. Find them.

Before the second dictation, students know the formula n th member of an arithmetic progression, know that an arithmetic progression is a linear function defined on the set of natural numbers. The following test dictation is possible here.

Dictation number 2

1. The first term and the difference of the arithmetic progression are known ( x n): NS 1 = 3 and d= 2. Find NS 31 .

2. The first term and the difference of the arithmetic progression are known ( a n): but 1 = –2 and d= 4. Find but 26 .

3. Find the difference of the arithmetic progression if but 1 = –4, but 9 = 0.

4. The difference of the arithmetic progression is 1.5. Find but 1 if but 9 = 12.

5. Plot the arithmetic progression graph ( at n), in which: at 1 = 3, d= 0.5 and 1≤ n≤ 6. Write down the equation of the line to which the points of the progression graph belong.

The third test dictation is carried out after considering two formulas for the sum n the first members of the arithmetic progression. It is necessary to include in the dictation such tasks, as a result of which the students must demonstrate knowledge of both the studied formulas.

Dictation number 3

1. Find the sum of the first 30 terms of the arithmetic progression ( with n), if with 1 = 11 and with 30 = 27.

2. Find the sum of the first 10 terms of the arithmetic progression ( a n), in which but 1 =100, d = –10.

3. It is known that the sum of the first six terms of the arithmetic progression ( at n) is equal to 180, and the sum of its first eight terms is 320. Find the difference and the first term of the progression.

In the process of studying some sections of the course, the teacher conducts several tests that give an idea of the assimilation of certain topics included in this section. However, after completing the study of the section, it is advisable to check its assimilation as a whole; for this purpose, you can carry out overview dictation , which will allow students to repeat the material, systematize knowledge, establish connections between the issues studied. To do this, it is necessary to determine what basic concepts the student should learn when passing this section, what skills and abilities he should acquire, what tasks to be able to perform, what is the level of complexity of these tasks. At the same time, there should be no tasks burdened with complex identical transformations, time-consuming computational work, requiring a lot of time to complete. Assignments should be clear, specific and understandable. This includes questions on checking the learned definitions, theorems, rules, tasks for solving simple problems and exercises. The survey dictations are based on reproductive tasks. The dictation compiled in this way allows the teacher to check the assimilation of the key questions of the entire section.

For example, consider an overview dictation on the "Functions" section in the 7th grade. When studying this topic, students get acquainted with various ways of defining a function, therefore, it is necessary to include examples for all methods of defining a function in the work. Students should be able to find the value of a function by a given value of the argument and solve the inverse problem. In the same topic, students become familiar with direct proportionality and the direct proportional graph, and also learn how to plot a linear function. To test all these skills, we will offer students such a dictation.

Dictation

1. The function is given by the formula at = –2NS+ 5. Find the values of the function corresponding to the values of the argument: –8; 0; -2.5.

2. Using the graph of the function shown in the figure, fill in the table.

3. Plot the function at = 3NS – 2.

4. It is known that the function at(NS) is a direct proportionality. Set this function with a formula and fill in the table.

5. Show on the coordinate plane the relative position of the graphs of functions

at = 0,5NS; at = 0,5NS – 2; at = 0,5NS + 2.

Of course, to carry out such a dictation, a handout with pre-drawn tables and coordinate planes should be prepared.

The survey dictation for the section "Polynomials" is constructed somewhat differently. The purpose of this section is to teach students how to transform integer expressions. When studying the topic, seventh-graders got acquainted with operations on polynomials, with factoring polynomials into factors, the method of taking the common factor outside the brackets and the method of grouping. Naturally, tasks for the listed transformations should be included in the work. Therefore, it is advisable to include tasks for solving equations, for calculating the values of expressions, but not requiring cumbersome transformations. We will offer students the following dictation.

Dictation

1. From these expressions, select the one that is a monomial:

(x + a)(x – a);x 2 + x 3 – 1.

2. Simplify the expression (3 m 2 – 11m + 4) – (6m 2 –2m – 3).

3. Give expression 3 x 2 (2x + 5) – 7x to a polynomial of the standard form.

4. Factor expression 6 x 3 – 12x 2 + 18x.

5. Find the value of the expression at a = 1, b = –2:

6. Solve the equation

The dictation compiled in this way makes it possible to look at the studied material not in fragments, but in a complex. It can also be carried out in the 8th grade before studying fractions, when it is necessary to repeat the identical transformations of polynomials.

The organization of repetition is an important point in the teaching of mathematics. Repetition of previously learned material due to its use in learning new material is the most common type of repetition. There are other types of repetition, in particular, an overview and final repetition of a topic, section, course.

The final moment of repetition at the end of the year may be final dictations along the main content lines of the studied course.

They should include reproductive and reconstructive assignments that test basic skills; tasks for repetition of basic theoretical questions: reproduction of definitions and properties of mathematical objects.

Consider the final dictation to test the skills of solving equations at the end of the 8th grade. What types of equations are students aware of at this point? Linear equations and equations reduced to linear ones. The skills for solving this type of equations were worked out and tested in the 7th grade, so there is no need to include linear equations in this work, but if the teacher thinks that this skill is not sufficiently tested, the task for solving a linear equation should be included in this work.

In the 7th grade, in connection with the study of the factorization of a polynomial, the solution of equations of the form ( ax + b)(cx + d) = 0. The ability to solve equations of this type is required when studying various sections of the course throughout the years of study, so the inclusion of such equations in the final work is advisable.

Much attention in the 8th grade course is paid to solving quadratic equations. And in the final dictation, there should be a quadratic equation that has two roots, an equation that does not have roots, and an equation, when solving which, students can demonstrate knowledge of the formula for roots with an even coefficient.

And another of the basic skills that eighth graders must master is the skill of solving equations containing a variable in the denominator of a fraction. The inclusion of this type of equations in the dictation is also necessary.

What theoretical questions should I check? It is advisable to check the knowledge of the formula for the roots of the quadratic equation and give a simple task for the study of the quadratic equation.

At the same time, the dictation should not contain tasks that require cumbersome identical transformations. The purpose of this dictation is to test the ability to solve various kinds of equations and use formulas to solve equations.

Dictation

1. Find the roots of the equation:

but) ( but + 15)(but – 7) = 0;
b) ( x + 5)x(x 2 + 7) = 0;
at 2 x 2 – 32 = 0;
d) 0.3 x 2 – 1,5x = 0;
e) 6 x 2 + 5x – 4 = 0;
e) x 2 – 6x + 9 = 0;
g) x 2 – 5x + 6 = 0;
h)

2. Make an equation according to the condition of the problem.

The speed of the river is 3 km / h. The motor ship spends 14 hours on the way from one pier to another and back. Find the speed of the ship in still water if the distance between the berths is 150 km.

The final dictations compiled for the course questions allow the student to focus on one question, for example, solving equations, and at the same time repeat all related questions related to solving equations. If the teacher finds the time to conduct all the final dictations or independent work, then as a result of their implementation, the students will repeat all the material and demonstrate the basic knowledge and skills acquired during the period of studying mathematics.

Methods for conducting dictations

The dictation text can be:

a) projected onto the board using a computer;

b) read by the teacher;

c) reproduced using sound recording;

d) with a graphical record of the answer.

Here are examples of tasks of mathematical dictations, the texts of which are better to project onto the board.

Finding a number by its percentage

(5th grade)

1. What is the number 56 equal to?
2. What is the number, 1% of which is 96?
3. What is the number, 3% of which is equal to 63?
4. If 8% of the path is 48 km, what is the entire path?
5. If 55% of the class, or 22 people, study without grades, how many students are there in that class?

The second sign of equality of triangles

(7th grade)

1. In triangles ABC and DEF side AB is equal to DE, corners BUT and IN are equal respectively to the angles D and F... Are these triangles equal in the second criterion of equality?
2. In triangles KNM and PQT side NM and corners N and M are respectively equal to the side РQ and corners R and Q... Are these triangles equal in the second attribute?
3. In triangles KNM and PQT side KN equal to the side РQ... Injection N equal to the angle Q... What other condition must be met for these triangles to be equal in the second attribute?
4. Prove the equality of triangles ABC and CMK.

5. Is it possible to use one of the known signs to establish the equality of triangles?

When reading dictation assignments, pauses are determined by the pace of work of the average student. Observations have shown that a pause equal to the repetition time of the text is sufficient. It should be remembered that the mathematical dictation tests not the intelligence of the students, but their knowledge. And if a student thinks for a long time when answering a dictation question, he simply does not know the answer, and a long pause will not help him.

Dictations in two versions have 5 tasks, in one version they are composed of 10 tasks. For example:

Decimal multiplication

(5th grade)

1. Calculate: 2.8710.
2. Perform multiplication: 0.131000.
3. Find the product: 3.5100.
4. Multiply: 0.340.01.
5. Perform action: 0.0120.1.
6. Perform multiplication: 3.14
7. Find the value of the expression 3,10,4.
8. Find the work: 1,510.03.
9. The sides of the rectangle are 7.05 m and 2.3 m long. Find the area of the rectangle.
10. Find the area of a square with a side of 0.1 m.

Definition of arithmetic and geometric progressions. Formulas n first members

(9th grade)

1. In an arithmetic progression, the first term is 4, the second is 6. Find the difference.
2. In an arithmetic progression, the first term is 6, the second is 2. Find the third term.
3. In a geometric progression, the first term is 8, the second - 4. Find the denominator.
4. In a geometric progression, the first term is 9, the second - 3. Find the third term.
5. Find the tenth term of the arithmetic progression if the first term is 1 and the difference is 4.
6. Find the fourth term of the geometric progression if its first term is 1 and the denominator is –2.
7. Is the sequence of even numbers an arithmetic progression?
8. Is the sequence of powers of 2 a geometric progression?
9. Is a sequence of primes an arithmetic progression?
10. Is the sequence of primes a geometric progression?

Methodology

Carrying out a dictation, especially in two versions, requires a lot of effort from the teacher: you need to read the texts of assignments at an optimal pace; follow the class; react to inevitable failures (“repeat”, “but my pen stopped writing”, etc.).
In addition, students often do not understand which of the two options is being dictated at the moment, and as a result, they confuse the tasks of the options. Such difficulties are easily overcome with the help of sound recordings, in which the tasks of the first option are read by a male voice, and the second by a female. The student does not react to the “foreign” voice: he works quietly while the task of the other option is dictated, and as soon as the reading of the task of his option begins, he immediately joins in the work. The use of sound recordings disciplines the class: the student understands that the “soulless machine” does not care whether he has managed to prepare everything necessary for the beginning of the dictation, whether his pen writes, etc., and failures become extremely rare. The use of sound recordings for the teacher during the dictation makes it possible to observe the work of students, make the necessary and remove unnecessary notes and drawings from the board, etc.

The dictation can be done like that.

1) The teacher reads the entire text, and the students listen without taking notes.

2) The teacher reads the text phrase-by-phrase, pausing (one to four minutes) to give students the opportunity to complete the assignment.

3) When all the assignments are completed, the teacher reads the entire text again with small stops (this gives students the opportunity to correct something and make additions).

4) The correct answers are written down on the board, and the students independently check the dictation from a neighbor on the desk. In grades 5-7, all work is checked by the teacher.

Organization of inspection

The usual way of checking, when the teacher collects and checks the students' answers at home, is ineffective: the child wants to know the results of his work immediately after completion, the next day he is less interested in them. Therefore, you can organize the check, for example, like this. Students write a carbon copy dictation. The first copy is handed over to the teacher immediately after the words "the dictation is over", and the copy remains with the student and is used to check the correctness of the work: the teacher writes down the correct answers on the board.

It is very important to teach students to correctly check their math dictations. Otherwise, some students simply do not notice the mistakes they have made. You can invite students to independently evaluate the results of the dictation according to the specified criteria.

Here is a possible rating scale for dictations of various lengths.

Number of questions

Number of correct answers

After students learn to check their math dictations, the teacher may stop checking them at home altogether. Instead of self-examination, you can do a mutual examination - between two students. You can organize the test like this: a student passes his paper to another student who wrote the same version. He verifies the answers and puts the signs "+", "-", "?" not only on his own sheet, but also on a comrade's sheet, and he puts marks on both sheets. After completing the test, the teacher says the name of the student. The student calls the mark he has set for himself, and immediately calls the mark set to him by a classmate who checked the answers on his sheet. If the marks match, the teacher puts it in the journal. If not, he takes the dictation for rechecking.

But, perhaps, the most important thing in organizing the verification of a dictation immediately after its completion is that it becomes possible to discuss all those issues that have caused difficulties or are especially important for understanding new material: children who have just written a mathematical dictation are interested not only in the mark, but also the rationale for the decision. This work can be organized, for example, like this. The teacher offers to check the answer received during the first assignment, and raise a hand to all those who made a mistake. If there are few mistakes and the task itself is not so important, students are encouraged to check their results against the second task. If it turns out that the solution to the task needs to be explained, one of the students or the teacher gives the necessary explanations.
If necessary, students are invited to complete a similar task during the test. When verifying the answers, the following technique is effective. The teacher shows the correct answer and asks you to check your answers with him. The coincidence or non-coincidence of the answers must be simultaneously signaled by all students. This can be done, for example, using cards of different colors; match - a green card is raised, not a match - a red card. The teacher sees the answers of all students at the same time and can tell everyone if his answer is correct. The difference between the traditional raising of the hand and the voting described is enormous: only the summoned responds there, here everything. Instead of signal cards, voting can be used according to the following rules: in case of agreement, they raise their right hand, in case of disagreement, their left. And so that the students do not forget and do not get confused, on the blackboard it is necessary to write the word "no" on the left, on the right - the word "yes". Raised hands, like colored cards, allow the teacher to immediately know if each student has completed the assignment correctly or incorrectly.

Conclusion

The learning process is a two-way process; Successful learning requires not only the high quality of the teacher's work, but also the active activity of students, their desire to master the knowledge transmitted by the teacher, their interest in learning, focused and thoughtful work under the guidance of the teacher. All these reactions in students should be aroused by the teacher, relying on his authority, on contact with students, on his passion for the subject, profession, love and benevolent attitude towards children.

Practice shows that it is not always possible to organize the real educational process well enough. By systematically applying mathematical dictations in your lessons, along with other forms of testing knowledge, you are convinced that they are an effective means of enhancing educational activity. But it is important to emphasize that due to the specifics of mathematical dictations (perceivable questions; laconic answers), their pedagogical capabilities are limited. With their help, as a rule, you can check whether students have mastered the required minimum knowledge, but you cannot organize an in-depth test. Therefore, it would be a mistake to oppose dictations to other forms of control. One and the same task can be both in dictation and in independent work, but these tasks will have a different didactic function.
In independent work, the student is required to record the progress of the work, which makes the search for the result under control. In a mathematical dictation, control can be carried out only according to the final result. I hope that my experience will interest my fellow mathematicians and will be useful in teaching students.

The article was prepared with the support of the information and educational portal "edustudio.ru". If you decide to acquire or deepen your knowledge of mathematics, then the best solution would be to contact the information and educational portal "edustudio.ru". By clicking on the link: "", you can, without leaving the monitor screen, see the solved examples, as well as ask a question of interest. More detailed information can be found on the website www.edustudio.ru.

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Mathematical dictations

Made up

primary school teacher

N.V. Kuchevskaya

Mathematical dictation number 1

How many times is 4 more than 12?
7 times 8.
How many times is 18 more than 9?
What number should 6 be multiplied by to get 54?
The first factor is 3, the second is unknown. The product is 27. Find the second factor.
What number must be multiplied by 2 to get 14?
Reduce 32 by 8 times.
How many times will 7 repeat in 35?
I conceived a number, increased it 8 times and got 72. What number am I in mind?
Divisor 63, divisor 9. Find the quotient.

(3, 56, 2, 9,9, 7, 4, 5, 9, 7)

Mathematical dictation number 2

Increase 5 by 9 times.
What number should be reduced by 3 times to get 7?
How many times is 15 more than 5?
Divisor 56, divisor 8. Find the quotient.
What number needs to be increased 7 times to get 35?
The first factor is 4, the second factor is 7. Find the product.
Reduce 48 by 6 times.
The dividend is unknown, the divisor is 9. The quotient is 3. Find the dividend.
Multiply 2 by 8.

(45, 21, 3, 42, 7, 5, 28, 8, 27, 16)

Mathematical dictation number 3

How many times will 8 repeat in 24?
How many times is 20 more than 4?
How many times is 6 in 48?
Find the product of the numbers 4 and 9.
The product is 24, the second factor is 6. Find the first factor.
What number should be reduced by 8 times to get 8.
I conceived a number, increased it 6 times and got 54. What number am I in mind?
The dividend is 42, the divisor is unknown. Quotient 6. What is the divisor?
3 times 7.
Reduce 8 by 4 times, increase the resulting number by 3, and this newly obtained number increase 2 times.

(3, 5, 8, 36, 4, 64, 9, 7, 21, 10)

Mathematical dictation number 4

What is the product of the numbers 6 and 3?
Find the quotient of 14 and 7.
What number should be increased 3 times to get 12?
How many times will 6 repeat in 30?
How many units are 18 more than 6?
The quotient 2. The dividend is 20. What is the divisor?
Product 36. First factor 9. What is the second factor?
7 quadruple.
Reduce the product of the numbers 8 and 3 by 4 times.
If 4 multiplied by 9, then the resulting number will be 6 times more than the number I intended. What number am I thinking?

(18, 2, 4, 5, 12, 10, 4, 28, 6, 6)

Mathematical dictation number 5

Find the quotient of 72 and 8.
How many times is 3 less than 15?
What number needs to be increased 6 times to get 24?
Find the product of the numbers 8 and 7.
How many times will 9 be repeated in 27?
I conceived a number, reduced it by 8 times and got 6. What number am I in mind?
The first factor is 4, the second is 8. Find the product.
If 56 is divided by 7, then the resulting number will be 8 times less than the number I intended. What number am I thinking?
What number should be reduced by 7 times to get 9.
Divisor 81, quotient 9. What is the divisor?

(9, 5, 4, 56, 3, 48, 32, 64, 63, 9)

Mathematical dictation number 6

Find the product of the numbers 7 and 4.
How many times is 8 in 32?
What number needs to be increased 6 times to get 30?
How many times is 63 more than 9?
Find the quotient of 36 and 9.
7 to increase 3 times.
I conceived a number, increased it 7 times and got 42. What number am I in mind?
What number should be reduced by 6 times to get 1?
Divisor 2, quotient 8. Find the dividend.
The product is 64, the first factor is 8. Find the second factor.

(28, 4, 5, 7, 4, 21, 6, 6,16, 8)

Mathematical dictation number 7

The first factor is 9, the second is 3. Find the product.
The product is 54, one of the factors 6. Find the unknown factor.
How many times is 6 less than 18?
Magnify 9 to 8 times?
How many times will 2 repeat in 187
Divisor 35, quotient 7. Find the divisor.
What number should be reduced by 8 times to get 6?
I conceived a number, reduced it 9 times and got 4. What number I conceived 7
Find the product of the numbers 9 and 5.

(8, 27, 9, 3, 72, 9, 5, 48, 36, 45)

Mathematical dictation number 8

What number was increased 7 times and got 63?
Find the product of the numbers 6 and 9.
How many times is 12 more than 3?
How many times will 5 repeat in 40?
Divisor is 12, quotient 2. Find the divisor.
What number must be increased 9 times to get 9?
One of the factors is 4, the product is 32. Find the unknown factor.
The quotient is 30, the dividend is 90. Find the divisor.
I conceived a number, reduced it 9 times and got 9. What number I conceived7
I conceived a number, increased it 7 times. I added 8 to the received number and got 50. What number am I thinking?

(9, 54, 4, 8, 6, 1, 8, 3, 81, 6)

Mathematical dictation number 9