Mathematical dictations, methodological development in mathematics (grade 3) on the topic. Mathematical dictation (how it takes place in our class) How to write a mathematical dictation

An important and extremely subtle point in 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 progress of students’ cognitive activity in the learning process, and students with information about their successes. Control of knowledge has educational and educational significance, it contributes to a deeper study by students of the fundamentals of science, improving their knowledge and skills.

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

Before moving on to explaining new material, it is advisable to make sure that the students have mastered the previous portion of knowledge. Traditional methodology recommends organizing a survey of students at this point in the pedagogical process. A survey as a form of testing knowledge is ineffective, primarily because for the majority of students, a classmate’s answer at the blackboard does not at all help them repeat what they have previously learned. All kinds of condensed surveys, when up to 10 students are preparing at the same time, only aggravate the matter: those called do not listen to their comrade’s answer on a legal basis.

Questioning at the board is usually supplemented with the so-called oral counting. The disadvantage of traditional “mental counting” is that not all students participate in it. An alternative to questioning and “oral counting” is mathematical dictation. Hence its place in the educational process: at the beginning of the lesson, at which the presentation of a new portion of knowledge begins. Hence the requirement for its content: answers to questions must show whether the content of the previously presented material has been mastered. A mathematical dictation can replace a survey on a topic assigned for repetition. Its duration is usually 10–15 minutes.
It is a system of interconnected questions.

Let's look at the different types of tasks that students face in dictations.

1. Reproductive type tasks 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 necessary for studying mathematics. And although they contribute little to the development of students’ thinking, they create the 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 the inequality graphically”) or the correlation to a particular material (for example, “solve the problem by drawing up a system of equations”). Completing such tasks is possible only after the student himself reconstructs them and correlates them with several reproductive ones. These types of tasks include tasks for constructing graphs, tasks for drawing up equations, tasks in which students have to use several algorithms, formulas, theorems (for example, “represent the expression ( in the form of a polynomial A– 2)x( A + 2) – (2 – A) 2"). These tasks are characterized by the fact that, when starting to complete them, the student must analyze possible general ways to solve the problem, find characteristic features of the object, and use several reproductive tasks. Note that the student’s cognitive activity when performing these tasks does not go beyond the reproduction of knowledge, but is inevitably accompanied by some generalization. Reconstructive tasks are the most common type of tasks used at all stages of the educational process.

3. Characterized by a higher level of reproductive activity and its transition to creative activity tasks variable nature. When performing them, the student needs to select from the entire arsenal of mathematical knowledge those necessary to solve a given problem, use intuition, and find a way out of a non-standard situation. These types of tasks include so-called intelligence problems, tasks with a twist, many proof problems, as well as tasks that require the creation of new solution algorithms (for example, “Insert the missing monomials so that you get the identity A 2 + 6ab+ ... = (... + ...) 2 ").

In order to develop students’ thinking and develop different types of activities in them at all stages of learning mathematics, it is necessary to use different types of tasks.

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

Types of dictations

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

Test dictations are intended to control the assimilation of a separate fragment of the course during the period of study of the topic. When performing them, the teacher receives timely information about how the topic is being mastered, which allows him to identify errors in time, detect those who have poorly mastered this or that material, and, depending on this, build work on studying this topic. Students receive additional practice in solving problems independently and thereby prepare for a test on this topic. Since test dictations are carried out after practicing basic skills, they include tasks not only of a reproductive nature. The basis of test dictations are tasks of a reconstructive nature. At the same time, test dictations should not include tasks more difficult than those that students completed in class and at home.

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

1. Definition of arithmetic progression.

2. Formula n th term of an arithmetic progression.

3. Sum formula n the first terms of an arithmetic progression.

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

Dictation No. 1

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

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

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

4. In the notation of a finite arithmetic progression ( and n): A 1 ; 8,9; A 3 ; 7,1; A 4 ; A 5, some members are unknown. Find them.

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

Dictation No. 2

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

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

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

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

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

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

Dictation No. 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 ( and n), in which A 1 =100, d = –10.

3. It is known that the sum of the first six terms of an arithmetic progression ( y n) is 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 mastery of individual 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 conduct review dictation , which will allow students to repeat the material, systematize knowledge, and establish connections between the issues studied. To do this, it is necessary to determine what basic concepts the student must learn when passing this section, what skills and abilities he must acquire, what tasks he must be able to perform, and what the level of complexity of these tasks is. At the same time, there should be no tasks burdened with complex identity transformations, labor-intensive computational work, and requiring a lot of time to complete. Tasks must be clear, specific, and understandable. This includes questions to check the studied definitions, theorems, rules, tasks for solving simple problems and exercises. The basis of review dictations are tasks of a reproductive nature. A dictation compiled in this way allows the teacher to check the mastery of the key questions of the entire section.

For example, consider a review dictation on the “Functions” section in 7th grade. When studying this topic, students become familiar with various ways of specifying a function; therefore, the work must include examples of all methods of specifying a function. Students should be able to find the value of a function given the value of the argument and solve the inverse problem. In the same topic, students are introduced to direct proportionality and the graph of direct proportionality, and also learn to graph a linear function. To test all the listed skills, we will offer students such a dictation.

Dictation

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

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

3. Graph the function at = 3X – 2.

4. It is known that the function at(X) is direct proportionality. Give this function a formula and fill out the table.

5. Show on the coordinate plane the relative positions of the function graphs

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

Of course, to conduct such a dictation, handouts with pre-drawn tables and coordinate planes must be prepared.

The review dictation for the section “Polynomials” is constructed somewhat differently. The purpose of this section is to teach students to transform entire expressions. When studying the topic, seventh-graders became familiar with operations on polynomials, the factorization of polynomials, the method of taking the common factor out of brackets, and the method of grouping. Naturally, the work should include tasks for the listed transformations. Therefore, it is advisable to include tasks for solving equations and calculating the values ​​of expressions, but not requiring cumbersome transformations. We offer students the following dictation.

Dictation

1. From these expressions, choose 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 standard form.

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

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

6. Solve the equation

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

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

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

They should include tasks of a reproductive and reconstructive nature, which should test basic skills; tasks to review basic theoretical questions: reproduction of definitions and properties of mathematical objects.

Let's consider the final dictation to test skills in solving equations at the end of 8th grade. What types of equations do students know at this point? Linear equations and equations reducible to linear ones. Skills for solving this type of equation were developed and tested in 7th grade, so there is no need to include linear equations in this work, but if the teacher feels that this skill has not been sufficiently tested, a task for solving a linear equation should be included in this work.

In the 7th grade, in connection with the study of factoring a polynomial, we considered solving 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 all years of study, therefore 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 has no roots, and an equation in which students can demonstrate knowledge of the formula for roots with an even coefficient.

And one more basic skill that eighth graders must master is the skill of solving equations that contain 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 be tested? It is advisable to test your knowledge of the formula for the roots of a quadratic equation and give a simple task to study the quadratic equation.

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

Dictation

1. Find the roots of the equation:

A) ( A + 15)(A – 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;
and) x 2 – 5x + 6 = 0;
h)

2. Make up an equation based on the conditions of the problem.

The river flow speed is 3 km/h. A motor ship takes 14 hours to travel from one pier to another and back. Find the speed of the motor ship in still water if the distance between the piers is 150 km.

Final dictations compiled on course questions enable 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 time to conduct all the final dictations or independent work, then as a result of their completion, students will repeat all the material and demonstrate the basic knowledge and skills acquired during the period of studying mathematics.

Methods of 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 graphic recording of the answer.

Here are examples of mathematical dictation tasks, the texts of which are best projected on the board.

Finding a number by its percentage

(5th grade)

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

The second sign of equality of triangles

(7th grade)

1. In triangles ABC And DEF side AB equal to DE, angles A And IN equal to the angles respectively D And F. Are these triangles equal by the second equality criterion?
2. In triangles KNM And PQT side NM and corners N and M are equal to the side respectively PQ and corners R And Q. Are these triangles equal according to the second criterion?
3. In triangles KNM And PQT side KN equal to side PQ. Corner N equal to angle Q. What other condition must be met for these triangles to be equal according to the second criterion?
4. Prove the triangles are equal ABC And SMK.

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

When reading dictation tasks, pauses are determined according to the pace of work of the average student. Observations have shown that a pause equal to the time of text repetition is sufficient. It should be remembered that mathematical dictation does not test students’ intelligence, 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:

Multiplying Decimals

(5th grade)

1. Calculate: 2.8710.
2. Multiply: 0.131000.
3. Find the product: 3.5100.
4. Multiply: 0.340.01.
5. Perform the action: 0.0120.1.
6. Multiply: 3.14
7. Find the value of the expression 3,10,4.
8. Find the product: 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. The first term of a geometric progression is 8, the second is 4. Find the denominator.
4. The first term of a geometric progression is 9, the second is 3. Find the third term.
5. Find the tenth term of an arithmetic progression if the first term is 1 and the difference is 4.
6. Find the fourth term of a 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 prime numbers an arithmetic progression?
10. Is the sequence of prime numbers a geometric progression?

Methodology

Conducting a dictation, especially in two versions, requires a lot of stress from the teacher: you need to read the texts of the assignments at an optimal pace; monitor the class; respond to inevitable failures (“repeat”, “my pen has 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 assignments 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 voice. The student does not react to the “alien” voice: he works calmly while the task of another option is dictated, and as soon as the reading of the task of his variant begins, he immediately gets involved in the work. The use of sound recordings disciplines the class: the student understands that the “soulless machine” does not care whether he managed to prepare everything necessary for the start of the dictation, whether he writes with a pen, etc., and failures become extremely rare. The use of sound recording when conducting a dictation gives the teacher the opportunity to observe the work of students, make the necessary and remove unnecessary notes and drawings from the board, etc.

The dictation can be done this way.

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

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

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

4) The correct answers are written on the board, and the students independently check the dictation with their neighbor at the desk. In grades 5–7, all work is checked by the teacher.

Organization of inspection

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

It is very important to teach students how to properly check their mathematical 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 grading scale for dictations of varying lengths.

Once students learn to check their math dictations, the teacher can stop checking them at home altogether. Instead of self-testing, you can do mutual testing - between two students. You can organize the check this way: the student passes his piece of paper to another student who wrote the same version. He checks the answers and puts the signs “+”, “–”, “?” not only on his own sheet, but also on his friend’s sheet, and puts marks on both sheets. After completing the test, the teacher calls the student's name. The student names the mark he gave himself, and immediately names the mark given to him by the classmate who checked the answers on his sheet. If the marks match, the teacher puts it in the journal. If not, take the dictation for rechecking.

But, perhaps, the most important thing in organizing a dictation check immediately after its completion is that it becomes possible to discuss all those issues that caused difficulties or are especially important for understanding new material: children who have just written a mathematical dictation are interested not only in the grade, but also the rationale for the decision. This work can be organized, for example, like this. The teacher suggests checking the answer received during the first task and raising the hand of all those who made a mistake. If there are few errors and the task itself is not that important, students are asked to compare their results on 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 asked to complete a similar task during the test. When checking answers, the following technique is effective. The teacher shows the correct answer and asks you to check your answers with it. All students must simultaneously signal whether the answers match or not. This can be done, for example, using cards of different colors; a match - a green card is raised, a non-match - a red card. The teacher sees the answers of all students at the same time and can tell everyone whether their answer is correct. The difference between the traditional raising of hands and the described voting is huge: there only the person called responds, here everyone responds. Instead of signal cards, you can use voting according to the following rules: in case of agreement, raise your right hand, in case of disagreement, raise your left hand. And so that students do not forget or get confused, on the board you need to write the word “no” on the left, and the word “yes” on the right. Raised hands, like colored cards, allow the teacher to immediately know whether each student completed a task 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, and concentrated and thoughtful work under the guidance of the teacher. The teacher must evoke all these reactions in students, relying on his authority, contact with students, his passion for the subject, profession, love and benevolent attitude towards children.

Practice shows that the actual educational process cannot always be organized well enough. By systematically using mathematical dictations in your lessons along with other forms of testing knowledge, you are convinced that they are an effective means of enhancing learning activities. But it is important to emphasize that due to the specific nature of mathematical dictations (auditory questions; laconic answers), their pedagogical capabilities are limited. With their help, as a rule, it is possible to check whether students have mastered the required minimum knowledge, but they cannot organize an in-depth test. Therefore, it would be a mistake to contrast dictations with other forms of control. The same task can be used both in dictation and in independent work, but these tasks will have different didactic functions.
In independent work, the student is required to record the progress of work, which makes the search for a result controllable. In mathematical dictation, control can only be based on the final result. I hope that my experience will be of interest to 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 in mathematics, then the optimal solution would be to contact the information and educational portal “edustudio.ru”. By clicking on the link: “”, you can, without leaving the monitor screen, look at solved examples, as well as ask a question of interest. More detailed information can be found on the website www.edustudio.ru.

The mathematical dictations given in this manual are varied:

• dictations, some of which are theoretical questions, and some are simple practical tasks on a relevant topic that do not require extensive notes;
• dictations, consisting entirely of practical tasks similar to those in the textbook, which are performed almost orally; you only need to write down the answer;

The use of mathematical dictations does not solve all the problems facing the teacher, but it significantly helps him in his work. Before moving on to studying new material, the teacher needs to make sure that the students have mastered the previous knowledge. It is not realistic to survey the entire class during a lesson. If you interview several students at the blackboard, then, as a rule, the rest listen to the respondents inattentively. Using dictation, you can find out the level of assimilation of previously studied material for the entire class. Dictations can be used immediately after new material is explained to help students understand it better. Dictations can be used effectively in lessons for generalizing and systematizing knowledge. In addition, speaking the same material over and over again allows even the “weak” to master the required minimum content in mathematics.

Semenyuk Natalya Vyacheslavovna, 14.11.2017

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Development content

Algebra 7th grade

Topic 1. Degree with natural and integer exponents.

Dictation 1. Degree with a natural indicator.

1. Write down the third [fifth] power of the number 5 as a product and find its value.

2. What is the first power of the number -6?

3. Calculate the value of the expression 2 2. 2 3.

4. What is the sum of the cubes [square of the difference] of the numbers 6 and 3?

5. Calculate the square of the cube of number 4 [cube of the square of number 2].

Dictation 2. Properties of degrees with natural exponents

1.Write down the expressions a 8. a 5 [s 5 . with 7]. Think of this expression as a power.

2.Write down the power that will be obtained if the expression x 2 [a 2 ] is raised to the fourth [third] power.

3. Present the second [third] power of the product of the numbers 7 and 13 as a product of powers.

4.Write the expression 3 13 * 9 13 as a power.

5.Present the quotient 5 80: 5 40 as a power of 5.

6.The number a is negative. What is the sign of the number a 18? [The number b is negative. What is the sign of b 19?]

Dictation 3. Degree with an integer exponent

1. Define the zero power of the number x.

2.Write down the expression 5 4, 7 0, 2 -3 and find their values.

3. Present the fraction as a power with a negative exponent.

4.Write down the expression x -5 * x 7 [a 8 * a -10]. Think of it as a degree.

5.Write down the power that will be obtained if the expression x -5 [y -7] is raised to the minus fourth power.

6. For which x, y and a is it true that a x: a y = a x – y?

Dictation 4. Standard view of a penis

1.Write the number 582.7 in standard form.

2.Write the number 0.54 in standard form.

3.What number has the standard form 3.5 * 10 -5?

4.What number has the standard form - 3.001 * 10 5 [-4.006 * 10 -2 ]?

5.Find the product of numbers 3 * 10 -7 * 5 * 10 2 [ 4 * 10 3 * 6 * 10 -5 ] and write it in standard form.

Dictation 5. Functions y = ah 3 and y = ah 2

Given points M (-3; -9); A (2; 4) [C (-13; 169); K (5; 10)] determine which of the indicated points the graph of the function passes through: y = x 2?

Which of the following points belong and which do not belong to the graph of the function

y = x 3 V (-2; -8); K (1; 3) [ P (-4; 64); E (5; 125)]

How will the area of ​​a square change if its side is increased by 2 times [decreased by 4 times].

The function y = -4x 3 is given. Find: the value of the function for all x = -1 [x = 0.5].

Dictation 6. Function y = and her schedule

1. Does the graph of the function y = points A (-3.6; -2) [C (0.04; 1800)] belong to the graph?

2. At what coordinate angles is the graph of the function located: y = [y = ]

3. Given the function y = . indicate the set of values ​​of the variable x for which the function takes: positive values ​​[negative values].

4. Determine the sign of the number k knowing that the function y = is located: in the 1st and 3rd coordinate quarters [in the 2nd and 4th coordinate quarters].

Topic 2. Monomial and polynomial.

Dictation 1. Monomial

Is the expression 15x 2 y a monomial? If so, what is its coefficient and what is its degree?

Square [cube] the monomial -4xy 5 [-8ab 3 ]

Write the product of the monomials 4а 3 bx and –8ах 2 in the form of a monomial of standard form.

Dictation 2. Polynomial. Sum of polynomials.

What is the sum of monomials called?

Write down some trinomial [quadrinomial].

Write down the polynomial a – 2a + 2a * a 2 – 5 + 1 Bring it to standard form.

Formulate the rule for adding polynomials. Give an example.

Complete the equality: a 2 – 7a + 5 = a 2 – (……..) [x 6 – 6x + 2 = x 2 – (…….)].

Dictation 3. Multiplying a polynomial by a monomial.

Write down the monomials obtained by multiplying the monomial y 2 by each of the terms of the polynomial 2y 3 – 4y 2 + 6 [x 3 – 3x +5].

Multiply the polynomial 5x – 2y by the monomial – x 2 [-2b 2 ]

Solve the equation 3x (x - 2) + 3x (6 - x) = 0.

Multiply the monomial 3a 2 x [-6by 2 ] by the polynomial –4ax 2 + x 3

Multiply the polynomial a 2 – ab + b 2 [x 2 + xy + y 2] by the monomial -4ab.

Dictation 4. Multiplication of polynomials.

Write down the polynomials that are obtained if each term of the polynomial 7x - 2 is multiplied by each term of the polynomial 5 - 6x 2.

Multiply the polynomial x + 4 [x - 3] by the polynomial x – 3 [x + 3].

Represent the square of the binomial as a standard polynomial

x – 3y [a – 2b].

Present as a polynomial of standard form the product of the binomial x – y [a + b] and the trinomial x 2 + xy + y 2 [a 2 – ab + b 2].

Multiply the polynomial x – y [a + b] by the polynomial x + y.

Dictation 5. Taking the common factor out of brackets.

1.What power of the factor a can be taken out of brackets for the polynomial a 2 x – a 5 x

2.What numerical factor can be taken out of brackets for the polynomial 12x 2 – 6x 2

3. Take out of brackets the common factor of all terms of the polynomial a 2 +ab–ac+a.

4. Present the polynomial 3x + xy as a product

Dictation 6. Method of grouping.

1. Factor the expression: 3(a+2b) – a (a +2b); .

2. Factor the expression: 7x -7y + a (y -x); .

3. Factor the polynomial: 3c 2 + 15ac – 2c – 10a ; ;

4. Factor the polynomial: a 3 + 3a 2 b + ab 2 + 3b 3 ; ;

Topic 3. Abbreviated multiplication formulas.

Dictation 1. Difference of squares of two expressions.

1.The product of the difference of two expressions and their sum is equal to...?

[The difference between the squares of two expressions is...?]

2. Factor into: x 3 – 25x ; ;

3. Simplify the expression: (3 + 5ab )(3 – 5ab ); [(2a – 3b)(3b + 2a)];

4. Solve the equation: t 2 – 25=0; ;

5. Calculate using the formula: 55 2 – 45 2; ;

Dictation 2. Square of the sum and square of the difference of 2 expressions.

1.The square of the sum of two expressions is equal to...? [Square of the difference between two expressions...];

2. Present as a polynomial: (a -5) 2 ; [(2a +4c ) 2 ];

3. Express the following trinomials as squares of binomials: a 2 +4c 2 -4ac ;

4. Simplify the expressions: (b +1) 2 -5b ; [(a +2) 2 -4a ];

5. Find the values ​​of the expressions: b 2 -2b +1, with b =21; ;

Dictation 3. Formulas for the cube of the sum and cube of the difference of 2 expressions.

1. The formula for the cube of the difference of 2 expressions is determined by the formula......

(the formula of the cube of 2 expressions is determined by the formula:.....)

2. Find the cube of the sum of 2 expressions: 4a and 7b.

3. Find the cube of the difference of 2 expressions. 6x and 3y.

4. Present in polynomial form: (3m -2n ) 3 [(4y -3) 3 ].

Dictation 4. Formulas for sum and difference of cube 2 X expressions.

1.What is the sum of the cubes of 2 x expressions? [what is the difference of cubes of 2 x expressions]?

2. Factor: 1+64n 3 .

3. Simplify the expression (m -2n 2)(m 2 +2mn 2 +4n 2).[(16x 2 +4ax +a 2)(4x -a)].

4.Prove that 75 3 +65 3 is divisible by 700.

Topic 4. Rational fractions.

Dictation 1. Rational fraction. Reducing a rational fraction.

1.Specify the valid values ​​of the variables in the expression:

2. Reduce the fraction to the denominator: 3ad ; -ad

3.C truncate the fraction:

Dictation 2. Addition and subtraction of algebraic fractions.

1. Add fractions: and .

2. Subtract fractions: And

3. Reduce the fractions to a common denominator: and and

4.C add fractions:

5. Present the expression as a fraction:

Dictation 3. Multiplication and division of algebraic fractions.

1. Present the expression as a fraction:

2. Present the fifth power of the fraction as a fraction: .

3. Present the expression as a fraction: (a +x)·

4. Present the fraction as a power:

5. Present the quotient of dividing fractions as a product:

6. Present the quotient of dividing fractions as a fraction:

Topic 5. Elements of approximate calculation.

Dictation 1. Measuring quantities. Approximate value of a number. Absolute error.

1. Round the number 7.827 to the nearest tenth and find the absolute error of the resulting approximate value.

2. Round the number 6.435 to hundredths and find the absolute error of the resulting approximate value.

3. 9.61. The student found that it is approximately equal to 9.6. What is the absolute error of this approximation?

[With what accuracy can you measure the volume of liquid with a liter mug?]

4.The number is approximately 8.37. What is the largest possible absolute error of this approximation?

[ equals 13.69. The student found that it is approximately equal to 13.7. What is the absolute error of this approximation?]

5. With what accuracy can you measure mass with kilogram weights? [The number is approximately 3.912. What is the largest possible absolute error of this approximation?]

6. What is the accuracy of measurements using a ruler with millimeter divisions [a protractor with degree divisions?]

7.Round the number 0.275 to tenths [hundredths] and find the relative error of the resulting approximate value.

Geometry 7th grade

Topic 1. Basic geometric information.

Dictation 1. Basic concepts of geometry. Line segment. Ray.

Draw and label point C. [Name some geometric figure].

Draw and label line a. [Draw and label point A].

Draw and label the line α. [Name some geometric figure].

How many common points do two intersecting lines have in common? [How many common points do two disjoint lines have in common?]

How many common points do two intersecting [non-intersecting] lines have in common?

Can two different lines have two common points M and K?

Line b passes through point E and does not pass through point D. Which of these points lies on the line b[a]?

Draw two lines intersecting at point N.

Points P and K lie on the same straight line. Write down how you can designate this line.

Point C lies on the segment PM [BC]. Which of the points C, P and M [A, B and C] lies between the other two points?

The segment XY intersects the line a [c], but the segment XM [AC] does not intersect this line. Does straight line a [c] intersect segment Y M [BC]?

Point C [A] lies on ray AB [BC]. What else can you call this beam?

Dictation 2. Angle. Angle bisector.

Dictation 3. The concept of definitions, axioms, theorems.

What are the names of the basic properties of the simplest geometric figures that are accepted without proof? [What is the name of reasoning that shows the correctness of a geometric statement?].

Write the word "definition". [What is the name of a geometric statement whose correctness is established by proof?].

What is the name of reasoning that shows the correctness of a geometric statement? [What are the names of the basic properties of the simplest geometric figures that are accepted without proof?].

What is the name of a geometric statement whose correctness is established by proof? [Write the word "definition"] .

What: an axiom, a theorem or a definition is the sentence: “Two lines in a plane are called parallel if they do not intersect”? [What is the name of that part of the theorem that says what is given?].

What: an axiom, a theorem or a definition is the sentence: “A line that intersects one of two parallel lines also intersects the second”? [What is the name of the part of the theorem that states what needs to be proven?].

What: an axiom, a theorem or a definition is the sentence: “Through a point not lying on a given line, you can draw on the plane at most one straight line parallel to the given one”? [“Two lines in a plane are called parallel if they do not intersect”]?

Dictation 4. Adjacent and vertical angles.

What is the angle adjacent to a right angle? [One of the adjacent angles is a right angle. What is the second angle?].

The sum of two angles with a common side is 180 0. [The sum of two angles is 180 0 .] Are these angles necessarily adjacent?

Complete the sentence: “If angles 1 and 2 are adjacent, then their sum…”. [“Two angles are called adjacent if one side is common, and the other two...”].

Finish the sentence: “Two angles are called adjacent if one side is common, and the other two...”. ["If angles 1 and 2 are adjacent, then their sum..."].

One of the four angles resulting from the intersection of two straight lines is equal to 130 0. What are the remaining angles?

Two angles with a common vertex are equal [not equal]. Do they have to be vertical? [Are they vertical?].

Two corners have a common vertex. The first angle is 60 0, the second 120 0. Are these vertical angles? [What is the angle if the vertical angle with it is 130 0?].

Topic 2. The relative position of lines.

Dictation 1. Parallel lines. Signs of parallel lines.

Draw two parallel lines AC and RK. [What are two lines called that lie in the same plane and have no common points?].

Write using symbols: straight lines AC and MV [CT and HP] are parallel.

Complete the sentence: “If a straight line A is parallel to line b, and line b parallel to the line With, then ..." ["Two straight lines parallel to the third, ..."] .

What angles are called cross-lying external angles? [Which angles are called internal cross-lying ones?].

The internal one-sided angles add up to 180 0, and one of the internal cross-lying angles is 45 0. What is the value of the second intersecting interior angle? [What is the sum of interior one-sided angles if interior crosswise angles are equal?].

Look at the blackboard. a is parallel to b, angle 1 is 70 0 [angle 2 is 110 0 ]. Find all the other angles formed when two parallel lines intersect with a third line.

Dictation 2. Intersecting lines. Perpendicular and oblique.

What lines are called intersecting? [Perpendicular].

Given a line a and points C belonging to a, B not belonging to a. Draw a line b, perpendicular to line a, passing through point C [through point B], using a drawing triangle.

Define perpendicular [oblique] to a straight line.

At what angle does a person standing in formation turn when given the command: “to the right” [“to the left”]?

Draw an obtuse angle DIA. Through the vertex of angle C, draw perpendicular straight lines to the rays CA [CB].

Topic 3. Triangles.

Dictation 1. Triangles and its types.

Name the sides [vertices] of triangle AOC.

Name the types of triangles based on the length of the sides [by the size of the angles].

Construct an equilateral triangle [isosceles triangle].

Can a triangle have two obtuse angles [two right angles]. Justify your answer.

Find the sides of an equilateral triangle if its perimeter is 30cm.

Find the third side of an isosceles triangle if two of its sides are known: 5 cm and 6 cm.

Find the perimeter of a triangle if the lengths of its sides are known: 15cm, 14cm, 5cm.

Dictation 2. The sum of the internal and external angles of a triangle.

How many external angles [internal angles] are there in a triangle?

Are there triangles with angles 30 0, 20 0, 120 0?

Find the third angle of the triangle using two given angles: 39 0, 50 0.

Find the external angle at vertex A [at vertex B]. If angle A is equal to 30 0, angle B is equal to 90 0, angle C is equal to 60 0.

Dictation 3. Equality of triangles.

Formulate the first [second] criterion for the equality of a triangle.

Complete the sentence: “In triangles PQR and CST, side PR is equal to CT, side QR

equal to ST. What other condition must be met for these triangles to be equal according to the first criterion? [“The first sign of equality of triangles is a sign of equality by...”].

In triangles MPQ and LKT, angles [side] M and Q [СD] are equal [equal], respectively, to angles [side] L and T [РК, angle D is equal to angle K]. What other condition must be met for these triangles to be equal according to the second criterion?

In triangles BOS and MAE, sides BO and MA, OC and AE are equal [In triangles ASM and VEK, sides AC and CM are equal to sides BE and EK, respectively.] Are these triangles necessarily equal?

Dictation 4. Properties of an isosceles triangle.

Complete the sentence: “In an isosceles triangle, the angles …” [“The median drawn to the base …”].

In an isosceles triangle, a segment is drawn connecting the vertex to a point lying on the base. This segment is not the median [height] of this triangle. Could it be its bisector [median]?

Side AC is the base of the isosceles triangle ABC, BM is its height [median]. Angle ABC is 68 0. It is equal to the angle SVM [Navy].

In an isosceles triangle XYT, the side XY is the base [sides MR and RK are the lateral sides]. Which angles in this triangle are equal?

In a triangle, not one of the altitudes [medians] coincides with any of the bisectors. Is this an isosceles triangle?

Dictation 5. Right triangles.

Complete the sentence: “What is the name of a triangle that has an angle of 90 0?” [“A triangle that has a right angle is called...”].

Complete the sentence: “The side of a right triangle adjacent to the right [opposite to the right] angle is called ....”

In triangle MNK, angle M is a right angle. What is the segment NK in this triangle, a leg or a hypotenuse.

The hypotenuses of two right triangles are equal. One of the angles of the first triangle is 50 0, and one of the angles of the second is 70 0. Are these triangles equal?

One of the angles adjacent to the leg of a right triangle is equal to 50 0. What is the second angle adjacent to the same leg? [One of the angles of a right triangle adjacent to the hypotenuse is equal to 50 0. What is the second angle adjacent to the hypotenuse?].

In a right triangle, one of the angles is 48 0. What are its other two angles?

Topic 4. Circle. Geometric constructions.

Dictation 1. The circle and its elements. Central angles.

Complete the sentence: “A set of points on a plane equally distant from a given point...” [“A chord passing through the center of a circle...”].

What is the name of a segment connecting two points on a circle [a point on a circle with its center]?

Define the central angle [of a chord].

Find the length of the radius of the circle if the length of the diameter is 160mm.

Find the length of the diameter of the circle if the length of the radius is 42cm.

Draw a circle whose radius is 3 cm. Draw chord AC [diameter BM].

Find the angular measure of the arc if the degree measure of the corresponding central angle is 48 0.

Dictation 2. The relative position of a line and a circle. The relative position of two circles.

1. Define a secant [tangent].

2. Construct a tangent [secant] to the circle.

3. Which tangency of the circle is called internal [external]? Give an example.

4. Establish the relative position of the circle, if R is 5cm, r is 3cm; OO 1 = 7 cm.

Dictation 3. A circle circumscribed around a triangle. A circle inscribed in a triangle.

1. Finish the sentence: “If a circle is inscribed in a triangle, then it …” [“If a circle touches all sides of the triangle, then it …”].

2. Finish the sentence: “If a circle touches all sides of a triangle, then this triangle is called …” [“If a triangle is circumscribed about a circle, then this circle …”].

3. Given a circle. Draw an arbitrary triangle inscribed [circumscribed] in this circle.

4. A circle with center O is described around triangle MPA. The segment MO is 9cm. What is the segment PO equal to?

Preface…………………………………………………………………………………

7th grade. Algebra

Topic 1 Degree with natural and integer exponents…………………...

Topic 2 Monomial and polynomial ………………………………………………………………...

Topic 3 Abbreviated multiplication formulas…………………………………………………….

Topic 4 Rational fractions……………………………………………………………….…..

Topic 5 Elements of approximate calculation…………………………….....

7th grade. Geometry

Topic 1 Basic geometric information…………………………….…..

Topic 2 Relative position of lines………………….….

Topic 3 Triangles…………………………………………………….….

Topic 4 Circle. Geometric constructions……………………………...

Mathematical dictations

1. How many suns are there in the sky?

2. How many eyes does an owl have?

3. How many lights does the traffic light have?

4. How many fingers does the glove have?

5. How many colors does the rainbow have?

6. How many paws does a cat have?

1. Write in numbers: one, two.

2. Write down the larger number: 4 and 3.

3. Write down a number less than 2.

4. How many sides does a triangle have?

5. Write down the neighbors of number 4.

6. In Velikaya Novoselka there are rivers: Kashlagach, Shaitanka, Mokrye Yaly.

Write down in numbers how many rivers there are in our village.

1. Write down the numbers from 1 to 5 in order.

2. Write down the smaller number: 5 and 4.

3. Write down the neighbors of number 3.

4. Write down in number how many angles the pentagon has.

5. Write down in number how many vertices the triangle has.

6. Write down the number preceding 4.

1. What number comes after the number 4?

2. Write down the previous number of the number 5.

3. How many paws does a bear have?

4. How many days are there in a week?

5. What number comes before 7?

6. Write down the larger number: 3 and 2.

1. What number comes after the number 8?

2. What number does it come before?

3. Write down the neighbors of the number 5.

4. Which number is greater: 4 or 5?

5. How many corners does a square have?

6. What number is followed by 3?

7. Write down: 6 is 4 and...

1. What number is followed by 9?

2. Write down the smallest number.

3. Write down the number after 7.

4. write down the number preceding 5.

5. write down the neighbors of the number 6.

6. Write down the smaller number: 5 and 7.

7. Write down a number that is greater than 2 but less than 4.

1. What number is followed by 10?

2. Write down the number preceding 9.

3. What number is between 5 and 7?

4. What number do we get if we add 1 to 7?

5. Which number is greater: 6 or 4?

6. Write down the neighbors of the number 7.

7. Write down how many vertices the quadrilateral has.

1. Write in numbers: six, eight, four.

2. Write down the larger number: 7 and 8.

3. Write down the neighbors of the number 7.

4. Which number is greater than 7 by 1.

5. What number must be added to 8 to get 9.

6. Write down the number following 6.

7. How many vertices does a square have?

1. Write down the numbers from 3 to 7.

2. The first term is 2, the second term is 3. Find the sum.

3. Add 1 to 6.

4. Write down the number preceding 10.

5. Write down the number after 5.

6. Write down the neighbors of the number 7.

7. Write down: 9 is 5 and...

1. Write down the numbers from 6 to 10.

2. 7 increase by 1.

3. Sum of numbers 5 and 2.

4. The first term is 3, the second term is 1. Find the sum.

5. Subtract 1 from 4.

6. How many vertices does a hexagon have?

7. Add 5 to 5.

1. Write down the numbers from 10 to 4.

2. Write down the larger number: 10 and 8.

3. 7 increase by 3.

4. The first term is 7, the second is 2. Find the sum.

5. 2 increase by 3.

6. Find the sum of two numbers 4 and 5.

7. Write down: 10 is 7 and...

1. Name the neighbors of the number 8.

2. Write down the number after 5.

3. Write down the number preceding 8.

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

5. Add 3 to 3.

6. Sum of numbers 9 and 0.

7. 8 minus 1.

1. What number comes before the number 5?

2. What number comes after the number 9?

3. Name the neighbors of the number 9.

4. Write down the numbers less than 6: 5, 8, 9, 2.

5. Add 3 to 4.

6. Subtract 2 from 7.

7. Sum of numbers 5 and 3.

1. What number comes before the number 6?

2. What number comes after 5?

3. Write down how many vertices the rectangle has.

4. Write down the neighbors of number 3.

5. 7 minus 4.

6. Sum of numbers 5 and 5.

7. The first term is 8, the second is 1. Find the sum.

1. Increase 9 by 1.

2. 3 plus 2.

3. Subtract 1 from 5.

4. The first term is 4, the second is 2. Find the sum.

5. What number must be added to 6 to get 10?

6. Increase 6 by 3.

7. Sum of numbers 8 and 2.

Problems to find the sum

1. The boy collects stamps. He had 6 stamps in his album. A friend brought him 3 more marks. How many marks does the boy have?

2. 3 ducks were swimming on the lake. 2 more swam up to them. How many ducks were there in total on the lake?

3. Ira solved 3 examples on addition and 4 on subtraction. How many examples did Ira solve in total?

4. Grandma baked 4 large apples and 2 small ones. How many apples did grandma bake in total?

5. Mom bought one loaf of bread and 3 buns. How many baked goods did mom buy?

6. 3 bunnies were playing in the clearing. 2 more bunnies came running to them. How many bunnies are there in the clearing?

7. 6 swans swam on the pond. 3 more swans swam up to them. How many swans are there in total?

8. There were 5 large cups and 3 small ones on the table. How many cups were there on the table?

9. There were 4 daisies and 3 cornflowers in the vase. How many flowers were there in the vase?

10. There were 6 pink balls and 3 blue ones hanging on the tree. How many balls were hanging on the tree?

11. Vika drew 8 lanterns, Nina drew 2 lanterns.

How many lanterns did the girls draw in total?

12. They bought 3 books for Pavlik, and 2 books for Dima. How many books did the boys buy together?

13. There were 4 cups and 4 saucers on the table. How many dishes were there on the table?

14. There were 5 birds sitting in the clearing. 5 more birds flew to them. How many birds are there in the clearing?

15. The girl had 4 dolls and 1 teddy bear. How many toys did the girl have?

16. I teach you 7 subjects. 3 subjects are taught by other teachers. How many subjects do you study at school?

17. The walrus in the zoo is fed 2 kg of perch and 4 kg of hake daily. How many kilograms of fish are added to the walrus's food?

18. Lena drew 3 flowers and 5 leaves. How many leaves and flowers did Lena draw?

19. The carpenter first repaired 6 stools, and then another one. How many stools did the carpenter repair?

20. 4 butterflies were flying in the garden. 2 more butterflies arrived. How many butterflies are there in the garden?

Problems to find the remainder

1. There were 7 cars in the parking lot. 2 cars left. How many cars are left?

2. There were 9 pears in the vase. Ate 3 pears. How many pears are left?

3. Olya had 6 sweets. She gave 3 candies to her brother. How many candies does she have left?

4. Oksana had 7 colorful postcards. She gave 2 to a friend. How many postcards does Oksana have left?

5. There were 8 leaves on the branch. 3 broke loose and flew away. How many leaves are left?

6. Mom baked 10 pies. We ate 6 pies. How many pies are left?

7. The girl found 8 mushrooms, 3 of them were white, and the rest were boletus. How many oils did the girl find?

8. There were 10 people riding on the tram. 5 people got off at the stop. How many people are left on the tram?

9. Seryozha found 10 acorns. He gave 5 acorns to his sister. How many acorns does Seryozha have left?

10. Vova had 10 apples. He gave 5 apples to the children. How many apples does Vova have left?

11. Today we have 5 lessons on the schedule. 3 lessons have already passed. How many lessons are left today?

12. 2 days have passed since the beginning of the week. How many days are left until the end of the week?

13. Oksana had 8 nesting dolls. She gave 2 nesting dolls. How many nesting dolls does Oksana have left?

14. Misha drew 10 mushrooms, he managed to color 7 mushrooms. How many mushrooms are left for Misha to color?

15. bought 10 kg of potatoes. We used 2 kg of potatoes to prepare lunch. How many kilograms of potatoes are left?

16. There were 8 books on the shelf. Sasha read 4 books. How many books does Sasha have left to read?

17. There were 7 mushrooms growing in the clearing. The boy cut 4 mushrooms. How many mushrooms are left to grow in the clearing?

18. Rabbit Kuzi had 9 indoor plants, of which 2 were aloe, and the rest were cacti. How many cacti did the rabbit have?

19. Oksana needs to wash 6 scarves. She has already washed 4 scarves. How many scarves does Oksana have left to wash?

20. Bogdanchik caught 9 fish. He gave 4 fish to Murchik. How many fish does the boy have left?

Problems involving increasing or decreasing by several units

1. Lida has 5 balls, and Ira has 2 balls less. How many balloons does Ira have?

2. Yura has 3 goals, and Petya has 4 more goals. How many balls does Petya have?

3. Petya has 6 badges, and Vova has 3 more badges. How many badges does Vova have?

4. Vera has 6 dolls, and Olya has 2 less dolls. How many dolls does Olya have?

5. One bouquet contains 5 roses, and the other has 4 roses more. How many roses are in the second bouquet?

6. 4 sparrows flew to the feeder, and 2 more titmice. How many titmice have arrived?

7. There were 6 boys playing on the playground, and 3 less girls. How many girls played on the playground?

8. There are 10 seas in the Arctic Ocean, and 5 less in the Indian Ocean. How many seas are there in the Indian Ocean?

9. Anton found 5 boletus mushrooms, and 4 more russula. How many russula did Anton find?

10. A person has 1 heart, and an octopus has 2 more. How many hearts does an octopus have?

11. The white rhinoceros has 2 horns, and the Indian rhinoceros has 1 less horn. How many horns does the Indian rhinoceros have?

12. Poppy flowers close at 3 pm, and rose hips 4 hours later. What time do rosehip flowers close?

13. The composer Mozart played the violin from the age of 4, and after another 2 years he began composing music. At what age did Mozart begin composing music?

14. The echidna's needles are 6 cm long, while the hedgehog's are 3 cm shorter. How long is a hedgehog's spine?

15. There are 5 children in one sandbox, and 3 more children in the other. How many children are in the other sandbox?

16. Anya washed 5 plates, and Katya washed 4 plates more. How many dishes did Katya wash?

17. There were 4 napkins on the shelf, and 6 more napkins on the table. How many napkins were on the table?

18. There were 8 newspapers on the table, and 5 less magazines. How many magazines were on the table?

19. A dragonfly has 6 legs, and a spider has 2 legs more. How many legs does a spider have?

20. The first flight to the Moon lasted 8 days, and the second was 2 days longer. How many days did the second flight to the moon last?

21. In snakes, babies emerge from eggs after 6 weeks, and in cobras, 4 weeks later. How many weeks do it take for baby cobras to hatch?

22. A crayfish has 10 legs, and a spider has 2 less. How many legs does a spider have?

23. The first person to set foot on the Moon spent 2 hours on it outside the spacecraft, and the astronaut from the second expedition stayed on it for 5 hours more. How many hours did the second astronaut spend on the Moon?

24. A starling egg weighs 6 grams, and a kinglet weighs 5 grams less. How much does a king egg weigh?

25. Parsley seeds do not lose their viability for 2 years, and rye seeds – 8 years longer. How many years do rye seeds remain viable?

26. Mexico is washed by 2 oceans, and Japan is washed by 1 ocean less. How many oceans surround Japan?

27. The planet Mars has 2 satellites, and the planet Venus has 2 fewer satellites. How many moons does Venus have?

28. The crane makes 2 wing beats per second, and the rook makes 1 more. How many strokes per second does a rook make?

29. Laurel leaves live for 4 years, while cork oak leaves last 2 years less. How long do cork oak leaves last?

30. The stork makes 2 wing beats per second, and the pigeon makes 3 more. How many flaps per second does a pigeon make?

31. A guitar has 7 strings, and a violin has 2 fewer. How many strings does a violin have?

32. The roots of a watermelon can penetrate the ground to a depth of 10 m, and clover

8 m less. How deep can clover roots penetrate?

33. There are 9 seas in the Pacific Ocean, and 3 less seas in the Atlantic. How many seas are there in the Atlantic Ocean?

34. A motor ship from Kherson to Kyiv takes 4 days, and the return trip takes 1 day less. How many days does the ship take from Kyiv to Kherson?

35. A bison can smell 1 km away, and an elephant 4 km further. How many kilometers away can an elephant smell fresh grass?

36. A ZIL car without a trailer carries 6 tons of cargo, and with a trailer it carries 2 tons more. How many tons of cargo can a car and trailer transport?

37. A pelican weighs 9 kg, and a vulture weighs 2 kg less. How much does the bar weigh?

38. In a musical ensemble, a trio has 3 voices, and in an octet there are 5 more voices. How many voices are there in an octet?

39. The roots of rye can penetrate into the ground to a depth of 2 m, and of wheat 1 m deeper. How deep can wheat roots penetrate?

40.The Russian language has 10 vowels and 4 fewer sounds. How many vowel sounds are there in Russian?

41. An adult has 5 liters of blood, and a child has 2 liters less. How many liters of blood does a child have?

1. One student cut out 4 stars, and the other - 6. How many more stars did the second boy cut out?

2. Ira grew 5 flowers, and Sveta grew 8. How many fewer flowers did Ira grow than Sveta?

3. Dad bought 9 apples and 4 bananas. How many more apples did dad buy than bananas?

4. Vera picked 5 cucumbers from the garden, Lara picked 8 cucumbers. How many more cucumbers did Vera pick than Lara?

5. Kolya has 5 stamps in his album, Dima has 9 stamps. How many fewer stamps does Kolya have in his album than Dima?

6. A beetle has 6 legs, and a spider has 8. How many fewer legs does a beetle have than a spider?

7. The stork weighs 4 kg, and the albatross - 8 kg. How many kilograms does an albatross weigh more than a stork?

8. A one-month-old peacock chick at the zoo is given 10 grams of berries and 2 grams of milk powder to his food every day. How many grams more berries are given to the chick than milk powder?

9. A chipmunk has 5 longitudinal stripes on its back, while a wildcat has 2. How many more stripes does a chipmunk have than a wildcat?

10. A duck makes 9 wing beats per second, and an eagle owl makes 5 beats. How many fewer strokes does an eagle owl make than a duck?

11. A tick larva has 6 legs, and an adult tick has 8. How many more legs does an adult tick have than a larva?

12. Cactus roots can penetrate the ground to a depth of 6 m, and palm trees - 9 m. How much deeper do palm roots penetrate?

13. There are 10 seas in the Arctic Ocean, and 5 in the Indian Ocean. How many fewer seas are there in the Indian Ocean than in the Arctic Ocean?

14. The length of the first segment is 9 cm, the second - 4 cm. How many centimeters is the length of the first segment greater than the second?

15.Platypuses can stay under water for 1 minute, and in case of danger - 5 minutes. How many more minutes can a platypus stay underwater when in danger?

16. Lena had 8 discs with fairy tales and 3 with adventures. How many more CDs did Lena have with fairy tales than with adventures?

17. My brother is 10 years old, and my sister is 7 years old. How many years is your sister younger than your brother?

18. The height of the table is 7 dm, and the height of the chair is 4 dm. How many decimeters is the table higher than the chair?

Numbers 11 – 20

Mathematical dictations

1. Find the sum of the numbers 6 and 4.

2. Increase 5 by 3.

3. How much more is 9 than 4?

4. Reduce 5 by 3.

5. Minuend 10, subtrahend 6. Find the difference.

6. The first term is 6, the second is 2. Find the sum.

7. Which number is greater than 6 by 1?

8. The same amount was added to 4. Find the amount.

9. Write down the neighbors of the number 7.

1. Subtract 6 from 8.

2. Subtract the same amount from 6. What happened?

3. Add 6 and 3.

4. 10 minus 5.

5. Find the sum of numbers 2 and 8.

6. Increase 2 by 6.

7. How much is 3 less than 8?

8. The first term is 4, the second is 3. Find the sum.

9. What number is less than 5 by 1?

1. Subtract the same amount from 9. How much did you get?

2. 0 is added to 7. Find the sum.

3. Which number is greater than 7 by 2?

4. The same amount was added to 3. How much did you get?

5. Minuend 10, subtrahend 4. Find the difference.

6. Terms 4 and 3. Find the sum.

7. The number 9 was reduced by 5. How much did you get?

8. Write down the neighbors of the number 9.

1. The first term is 4, the second is 3. Find the sum.

2. The planned number was increased by 1 and got 8. What number did you plan?

3. Terms 5 and 3. Find the sum.

4. Difference between numbers 8 and 4.

5. Reduce 9 by 6.

6. Reduce the number 7 by 7.

7. Add 0 to 9.

8. Write down the neighbors of number 4.

1. From the number between four and six, subtract the number of hares,

which you don’t have to chase so as not to catch a single one, judging by

proverb.

2. Subtract the number from the number of kids scared by the wolf in the fairy tale

piglets known to all children.

3. Write down how many days are there in a week?

4. How many winter months are there in total?

5. Add the number of letters in the words WORLD and DAY.

6. How many sides do two squares have?

7. Write down the number preceding 15.

8. Write down the neighbors of the number 13.

9. The first term is 7, the second is 3. Find the sum.

1. The terms 10 and 2. Find the sum.

2. Minuend 10, subtrahend 6. Find the difference.

3. Write down the number that comes before 19.

4. Write down the number following 10.

5. What number is less than 9 by 6?

6. The number 9 was reduced by 3. Write down the result.

7. How much more is 10 than 5?

8. The first term is 6, the second is 3. Find the sum.

9. Subtract 1 from 11. Write the result.

1. How much do you need to increase 6 to get 10?

2. Reduce the number 9 by 6.

3. Increase 10 by 5.

4. Write down the number preceding 14.

5. Write down the number after 19.

6. Find the sum of the numbers 10 and 6.

7. Write down the neighbors of the number 17.

8. How many centimeters are in a decimeter?

9. Write down the number in which there is 1 dec. and 4 units.

10. Write down the smallest two-digit number.

1. Write down the number in which there is 1 dec. and 2 units.

2. How many tens are in the number 20?

3. Write down the numbers from 11 to 15.

4. Sum of numbers 10 and 8.

5. Subtract 10 from 16.

7. Write down the neighbors of the number 13.

8. Subtract twelve from twelve.

9. 11 decrease by 1.

10. Write down the number in which there is 1 dec. and 9 units.

Mathematical dictations

1. Write down the number that is less than 7 by 2.

2. What is 10 without 2?

3. From what number must 5 be subtracted to get 3?

4. A number consisting of 1 dec. and 3 units.

5. Increase 10 by 1.

6. Subtract 5 from 15.

7. Write down the number preceding 19.

8. Write down the neighbors of the number 15.

9. 13 is 10 and...

10. 17 decrease by 10. What do we get?

1. Write down the number in which there is 1 dec. and 6 units.

2. Write down a number that is 1 more than 19.

3. What number will you get if you subtract 10 from 17?

4. What number comes after 12?

5. What number comes before 13?

6. Sum of numbers 10 and 4.

8. The minuend is 17, the subtrahend is 7. Find the difference.

9.Write down the number that is 1 less than 15.

10. Find the difference between the numbers 15 and 5.

1. Write down the number that follows 12.

2. Sum of numbers 10 and 8.

3. Minuend 13, subtrahend 3. Find the difference.

4. What number must be added to 10 to get 16?

5. Add 5 units to one ten. What happened?

6. Difference between numbers 19 and 10.

7. Write down the number in which there is 1 dec. and 2 units.

8. Write down the number preceding 20.

9. Write down the neighbors of the number 14.

10. Increase the number 16 by 1. What do we get?

1. Write down the number in which there is 1 dec. and 5 units.

2. Increase 15 by 1.

3. Reduce 19 by 1.

4. Sum of numbers 6 and 4.

5. Subtract 5 from 9.

6. Write down the number preceding 15.

7. Add 8 units to one ten. What did you get?

8. Increase 6 by 3.

9. Write down the neighbors of the number 16.

10. What number comes after 19?

1. Name the number after 12.

2. What number comes before 15?

3. Name the neighbors of the number 18.

4. What number is less than 11 by 1?

5. Which number is greater than 16 by 1?

6. How to get the number 20 from 19?

7. The first term is 10, the second is 9. Find the sum.

8. Minuend is 18, subtrahend is 8. Find the difference.

9. Write down the number in which there is 1 dec. and 5 units.

10. Subtract 10 from 19. How much did you get?

1. Eleven plus six.

2. Find the sum of the numbers 10 and 6.

3. Eighteen minus eight.

4. Find the difference between the numbers 14 and 4.

5. Write down the number. in which 1 dec. and 1 unit.

6. Minuend 19, subtrahend 9. Find the difference.

7. What number is 1 greater than 15?

8. What number is 1 less than 12?

9. Write down the neighbors of the number 18.

10. Write down the number. which precedes 20.

1. Write down the number that comes before 17.

2. Write down the number that follows 13.

3. How much more is 9 than 6?

4. Write down the number in which there is 1 dec. and 3 units.

5. Find the sum of the numbers 5 and 3.

6. Find the difference between the numbers 10 and 7.

7. The first term is 10, the second is 8. Find the sum.

8. How much more is 8 than 1?

9. Write down a number consisting of 1 dec. and 7 units.

10. Write down the neighbors of the number 10.

1. Write down the larger number: 16 and 13.

2. Write down the number preceding 16.

3. Increase 17 by 1.

4. Reduce 20 by 1.

5. How many centimeters are there in 1 dm and 2 cm?

6. Write down the neighbors of the number 19.

7. Sum of numbers 10 and 4.

8. Difference between numbers 14 and 10.

9. The first term is 10, the second is 5. Find the sum.

10. Difference between numbers 19 and 9.

Fun challenges

Once upon a time in a dense forest

The hedgehog built himself a house.

Invited the forest animals

Count them quickly:

Two bunnies, two foxes,

Three funny little bears.

Two squirrels, two beavers,

It's time to name the answer! (eleven)

Mom walked along the fir tree,

I found eight saffron milk caps,

And the baby is a daughter

Only three mushrooms.

Answer without hesitation

How many mushrooms are there in the basket? (eleven)

So they dance cleverly

Eight squirrels, three bunnies.

They dance merrily on the sidelines.

Count quickly

How many animals are there in total? (eleven)

Fishermen are sitting, guarding the floats:

Fisherman Korney caught five perches,

Fisherman Evsey – 5 crucian carp,

And fisherman Mikhail caught two catfish.

How many fish are the fishermen

Dragged from the river? (12)

Forest animals gathered

In a clearing near a spruce tree.

New Year! New Year!

The round dance began to spin.

Gray wolf with a trickster fox

They dance so deftly!

Eight squirrels, three bunnies

They dance merrily on the sidelines.

Count quickly

How many animals are there in the clearing? (13)

Nine books on one

And four on the other.

How much on two shelves

Books from Yegorka? (13)

Seven mushrooms grew at the edge of the oak trees.

There are seven more boletus mushrooms in the clearing near the stumps.

How many mushrooms do oaks and stumps have in total? (14)

We had fun at the Christmas tree

We danced and frolicked

After good Santa Claus

He gave us gifts.

He gave me huge packages.

They contain delicious items.

I started to open the package,

Five sweets in blue pieces of paper,

Five nuts next to them.

Pear with apple

One is a golden tangerine,

Chocolate bar - I was glad!

Everything is in one package

Count these objects! (14)

In a quiet river under a bridge

There lived a mustachioed old catfish.

His wife is a catfish

And fourteen somyts.

Who can count them together?

The catfish will be happy about this! (15)

The boy Egorka loves order.

He placed his books on the shelves:

Ten books on one

And six - on the other.

How many books does Yegorka have on two shelves? (16)

He stood at the zoo and kept counting the monkeys:

Two played on the sand, three sat on the board,

And twelve of the backs were heated.

I pull the net and catch fish.

We caught quite a few: seven perch, ten crucian carp,

One brush goes into the pot.

I’ll cook fish soup and treat everyone.

How many fish will I boil?(18)

Like our kids

The head is all in bows:

Three burgundy, five cheerful,

Eight red, two green.

Count quickly

Bows for babies. (18)

Add 8 to 10.

How much will?

We'll ask you!(18)

Mom has an assistant.

See for yourself kids:

washed five dishes,

Eight spoons, five cups.

Washed dishes

20 large flatbreads -

My mother baked cakes.

I got up this morning and ate one.

How long is there left to lie? (19)

Seven hedgehogs are cleaning their faces,

Seven are rolling on the leaves,

Six look out from under the branches.

Count all the hedgehogs.(20)

Problems to find the sum

There were 5 girls and the same number of boys walking in the yard. How many children were walking in the yard?

10 birch trees and 8 oak trees were planted near the school. How many trees were planted near the school?

Vanya is now 12 years old. How old will he be in 5 years?

There were 6 boys and 10 girls playing on the playground. How many children were playing on the playground?

10 trees were planted on one side of the street, and 8 trees on the other. How many trees are there on both sides of the street?

Misha has 17 stamps, he was given 3 more stamps. How many stamps does Misha have?

The cyclist rode 11 km on the first day, and 7 km on the second. How many kilometers did he travel on the second day?

Problems to find the remainder

There were 20 stories in the book. Kolya read 10. How many stories are left to read?

There were 20 candies in the box. We ate 4 sweets at breakfast. How many candies are left in the box?

There were 15 light bulbs in the hall. 3 light bulbs burned out. How many lights were still on?

Masha planted 20 tomato bushes. 17 bushes began to grow, and the rest withered. How many of the bushes planted by Masha did not grow?

Difference comparison problems

The table was set for the holiday for 12 people, but 10 people came. How many extra utensils are there on the table that need to be removed?

There were 18 plates on the table, and 20 spoons. How many extra spoons were on the table?

There were 12 cars and 10 trucks in the garage. How many fewer trucks were there in the garage than cars?

Problems involving increasing or decreasing by several units.

Galya solved 15 examples, and Lena solved 1 less. How many examples did Lena solve?

U there were 8 tits at the feeders, and 2 bullfinches more. How many bullfinches were there?

Andrey is 12 years old. My sister is 6 years older. How old is your sister?

There are 12 monkeys in the zoo, and there are 2 less foxes than monkeys. How many foxes are there in the zoo?

My brother is 13 years old, and my sister is 3 years younger. How old is your sister?

Denis has 19 marks, and Alyosha has 3 marks less. How many stamps does Alyosha have?

Dima found 10 porcini mushrooms, and Seryozha found 3 more mushrooms. How many mushrooms did Seryozha find?

There are 20 apartments in our entrance, and in the neighboring one there are 2 fewer apartments than in ours. How many apartments are there in the next entrance?

On the first day, 15 apples were taken from the apple tree, and on the second day, 5 more apples. How many apples were picked on the second day?

A box of apples weighs 14 kg, and a box of apricots weighs 3 kg less than a box of apples. How much does a box of apricots weigh?

12 boys took part in the performance, and 3 more girls. How many girls took part in the dramatization?

In one exhibition hall there were 17 paintings hanging, and in the other there were 3 more paintings. How many paintings hung in the second exhibition hall?

There were 11 asters in one vase, and 2 more asters in the other. How many asters were in the second vase?

Toothpaste costs 14 UAH, and a bar of soap is 10 UAH cheaper. How much does a bar of soap cost?

We used 12 buckets of water to water the cucumbers, and 2 buckets less to water the tomatoes. How many buckets of water did you use to water the tomatoes?

There were 20 women on the bus, and there were 6 fewer men than women. How many men were on the bus?

Numbering numbers from 21 to 100

Mathematical dictations

1. Write down the numbers: nine, fifteen, ten, thirteen.

2. Write down the number in which there is 1 dec. and 2 units.

3. Write down the larger number: 12 and 20.

4. Write down the number that follows the number 19.

5. Write down the number that comes before 16.

6. Write down the neighbors of the number 14.

7. Sum of numbers 9 and 2.

8. Difference of numbers 18 and 8.

1. Increase 15 by 1.

2. Reduce 11 by 2.

3. Write down the number in which there are 2 dec. and 5 units.

4. Write down the number that follows the number 20.

5. Write down the number that is 1 less than 20.

6. Add 7 to the number 10.

7. Write down the neighbors of the number 22.

8. Reduce 18 by 8.

1. The girl opened the book to page 39. Name the previous and next pages.

2. Write down the number in which there are 3 dec. and 4 units.

3. Write down the number after 24.

4. To the 4 dozen sticks, 2 more sticks were added. How many sticks are there?

5. Subtract 10 from 19.

6. The first term is 9, the second term is 3. Find the sum.

7. Difference between numbers 12 and 10.

8. Sum of numbers 10 and 7.

1 . 19 decrease by 10.

2. To what number should you add 1 to get 30?

3. Write down the number preceding 29.

4. Minuend 18, subtrahend 8. Find the difference.

5. 10 increase by 5.

6. How much more is 13 than 12?

7. Write down the number in which there are 7 dec. and 5 units.

8. Write down the neighbors of the number 40.

1. Minuend 18, subtrahend 8. Find the difference.

2. Subtract 1 from 13.

3. Write down a number consisting of 4 decimals. and 5 units.

4. Write down the number following the number 40.

5. Write down the number preceding 20.

6. Terms 8 and 3. Find the sum.

7. How many centimeters are there in 1 m?

8. Increase 20 by 1.

9 How many tens are in the number 34?

1. Increase 66 by 1.

2. Write down the number following the number 39.

3. Write down the number preceding 56.

4. Write down the number in which there are 4 dec. and 2 units.

5. Write down a number that is 1 more than 30.

6. Difference of numbers 16 and 6.

7. The first term is 9, the second is 3. Find the sum.

8. Write down the neighbors of the number 67.

9. How many tens are in the number 67?

1. 1dm and 2 cm are how many centimeters?

2. How much more is 20 than 10?

3. Sum of numbers 8 and 3.

4. Subtract 3 from 12.

5. Write down a number consisting of 7 decimals. and 5 units.

6. Write down the neighbors of the number 19.

7. Added 1 to 17. How much did you get?

8. Subtract 10 from 16.

9. How many centimeters are there in 1 dm and 5 cm?

1. Find the difference between the numbers 13 and 10.

2. Increase 18 by 1.

3. Subtract 1 from 20.

4. Write down a number consisting of 3 decimals. and 9 units.

5. Write down the number preceding 50.

6. Write down the number after 88.

7. Write down the neighbors of the number 99.

8. The first term is 45, the second is 1. Find the sum.

9. Minuend 34, subtrahend 1. Find the difference.

1. How many kopecks are in 1 UAH?

2. How many tens are in the number 39?

3. Write down the largest two-digit number.

4. Sum of numbers 18 and 1.

5. Subtract 1 from 30. Write down the answer.

6. 55 increase by 1.

7. The difference between the numbers 66 and 1.

8. Write down the number following the number 34.

9. Write down the number preceding 56.

1. Write down how many vertices there are in the triangle?

2. Sum of numbers 10 and 7.

3. Difference of numbers 14 and 4.

4. 50 increase by 9.

5.98 decrease by 8.

6. Write down how many centimeters are in 1 m?

7. Write down how many tens are in the number 65?

8. Mom bought 2 dozen seedlings. She has already planted 10 seedlings. How many seedlings does she have left to plant?

1. Sum of numbers 40 and 50.

2. The difference between the numbers 50 and 20.

3. How much more is the number 60 than 10?

4. Write down a number consisting of 5 dec and 7 units.

5. Write down how many days there are in a week?

6. Olya had 12 UAH. She bought gingerbread for 5 UAH. How much money does the girl have left?

7. The first term is 20, the second is 60. Find the sum.

8. The minuend is 18, the subtrahend is 10. Find the difference.

1. Write down how many sides does a triangle have?

2. The sum of the numbers 40 and 30.

3. Subtract 1 from 16. How much is left?

4. How much is 20 greater than 19?

5. To what number must we add 7 to get 17?

6. To what number should you add 20 to get 24?

7. Increase 30 by 10. Write down the result.

8. How many hours are there in 1 day?

9. Write down how many minutes are in 1 hour.

1. How many sides does a pentagon have?

2. Write down the neighbors of the number 29.

3. Write down the number that is 1 more than 59.

4. Increase 39 by 1.

5. Reduce 60 by 1.

6. Express in centimeters: 2 dm 6 cm.

7. Minuend 50, subtrahend 1. Find the difference.

8. Write down the number in which there are 3 dec. and 6 units.

9. The piece contained 13 m of fabric. We cut 3 meters for the dress. How many meters of fabric are left?

1. Write down the number that comes before the number 40.

2. Write down a number that consists of 5 decimals. and 0 units

3. Write down the number that follows the number 60.

4. Reduce the number 23 by 2 tens.

5. Write down how many corners and vertices the hexagon has.

6. Difference between numbers 60 and 20.

7. The first term is 20, the second is 4. Find the sum.

8. Reduce 80 by 60.

9. The minuend is 90, the subtrahend is 30. Find the difference.

1. Write down how many angles the quadrilateral has.

2. Write down a number consisting of 6 decimals. and 1 unit.

3. How many hours are there in a day?

4. The minuend is 50, the subtrahend is 30. Find the difference.

5. Sum of numbers 30 and 45.

6. Reduce 17 by 7.

7. What number must be increased by 1 to get 27?

8. How much more is 90 than 70?

9. Find the sum of the numbers 10 and 6.

1. Find the difference between the numbers 10 and 6.

2. Reduce 27 by 7.

3. Write down the number in which there are 3 dec. and 9 units.

4. Write down the number that follows the number 59.

5. Write down the number preceding 90.

6. Find the sum of the numbers 34 and 50.

7. How many minutes are there in an hour?

8. The first term is 60, the second is 30. Find the sum.

1. Find sum of numbers 12 and 3.
2. Find number difference 17 and 6.
3. Find out, for how long 18 less, how 6.
4. Find out, for how long 12 less, than 14.
5. Write it down neighbors numbers 15.
6. First term 8, second 4. Find amount.
7. Minuend 18 subtrahend 8. Find the difference.
8. Number 14 reduce on 10.
9. Number 9 increase by 4.
10. From planned numbers taken away 6 and got 10. What number have you planned?

1. A beetle has three pairs of legs, and a spider has 4 pairs. How many fewer legs does a beetle have than a spider?
2. A melon is 2 kg heavier than a watermelon. How much does a watermelon weigh if a melon weighs 7 kg?
3. Tanya’s ducklings have 6 legs. How many ducklings does Tanya have?
4. How many boots did Zoya buy so that the cat’s feet wouldn’t get wet?
5. 10 children were playing in the sandbox. 6 children went home for lunch. How many children

left?
6. Misha found 10 mushrooms in the forest. Among them, 4 turned out to be inedible.

How many mushrooms should I throw away?
7. There are 9 cakes in the box. How many cakes must be taken from the box so that there are 6 cakes left in it?

1. Write it down number, in which 5 dec. 7 units
2. Write it down numbers, which are on 1 less than: 50, 27.
3. Write it down numbers, by 1 more, how: 49,60.
4. Write it down number, which is between 58 and 60.
5. Write it down number, following after 69.
6. Write it down number, antecedent 40.
7. How long 72 more, than 70?
8. How long 20 less than 100.

1. The first term is 13, the second is 10. Find the sum.

2. Subtract 50 from 54.

3. Minuend 11, subtrahend 3. Find the difference.

4. Write down how many minutes are in an hour.

5. How many centimeters are in a decimeter?

6. Vitya has 10 marks, and Misha has 3 marks more. How many stamps does Misha have?

7. 75 decrease by 5.

8. Write down a number consisting of 8 decimals. and 5 units.

9. Write down the number preceding 47.