Quantities and their relationship. Relationship between quantities: speed, time and distance Mathematically, Ohm's law has been described as

Correlation-statistical relationship of two or more random variables.

The partial correlation coefficient characterizes the degree of linear relationship between two quantities, has all the properties of a pair, i.e. varies from -1 to +1. If the partial correlation coefficient is equal to ±1, then the relationship between the two quantities is functional, and its equality to zero indicates the linear independence of these quantities.

The multiple correlation coefficient characterizes the degree of linear dependence between the value x 1 and the other variables (x 2, x s) included in the model, varies from 0 to 1.

An ordinal (ordinal) variable helps to sort the statistically studied objects according to the degree of manifestation of the analyzed property in them.

Rank correlation - statistical relationship between ordinal variables (measurement of statistical relationship between two or more rankings of the same finite set of objects O 1, O 2, ..., O p.)

ranking is the arrangement of objects in descending order of the degree of manifestation in them of the k-th property under study. In this case, x(k) is called the rank of the i-th object according to the k-th attribute. Rage characterizes the ordinal place occupied by the object O i, in a series of n objects.

39. Correlation coefficient, determination.

The correlation coefficient shows the degree of statistical dependence between two numerical variables. It is calculated as follows:

Where n– number of observations,

x is the input variable,

y is the output variable. Correlation coefficient values ​​are always in the range from -1 to 1 and are interpreted as follows:

if coefficient correlation is close to 1, then there is a positive correlation between the variables.

if coefficient correlation is close to -1, which means that there is a negative correlation between the variables

intermediate values ​​close to 0 will indicate a weak correlation between the variables and, accordingly, a low dependence.

Determination coefficient(R 2 )- it is the proportion of the explained variance of the deviations of the dependent variable from its mean.

The formula for calculating the coefficient of determination:

R 2 \u003d 1 - ∑ i (y i -f i) 2 : ∑ i (y i -y(dash)) 2

Where y i is the observed value of the dependent variable, and f i is the value of the dependent variable predicted by the regression equation, y(dash) is the arithmetic mean of the dependent variable.

Question 16

According to this method, the stocks of the next Supplier are used to meet the needs of the next Consumers until they are completely exhausted. After that, the stocks of the next Supplier by number are used.

Filling in the table of the transport task starts from the upper left corner and consists of a number of steps of the same type. At each step, based on the stocks of the next Supplier and the requests of the next Consumer, only one cell is filled in and, accordingly, one Supplier or Consumer is excluded from consideration.

To avoid errors, after constructing the initial basic (reference) solution, it is necessary to check that the number of occupied cells is equal to m + n-1.

Lesson on the topic "Relationships between quantities. Function»

Yumaguzhina Elvira Mirkhatovna,

teaching experience 14 years,

1 qualification category, MBOU "Barsovskaya secondary school No. 1",

UMC:"Algebra. 7th grade",

A.G. Merzlyak, V.B. Polonsky, M.S. Yakir,

"Ventana-Graf", 2017.

didactic rationale.

Type of lesson: Lesson of mastering new knowledge.

Learning aids: PC, multiprojector.

Educational: learn to determine the functional relationship between quantities, introduce the concept of a function.

Developing: develop mathematical speech, attention, memory, logical thinking.

Planned result

subject

skills

UUD

form the concepts of functional dependence, function, function argument, function value, domain of definition and scope of a function.

Personal: to form the ability to plan their actions in accordance with the training task.

Regulatory: develop the ability of students to analyze, draw conclusions, determine the relationship and logical sequence of thoughts;

to train the ability to reflect on one's own activity and the activity of one's comrades.

Cognitive: analyze, classify and generalize facts, build a logical reasoning, use evidence-based mathematical speech.

Communicative: independently organize interaction in a pair, defend their point of view, give arguments, confirming them with facts.

Basic concepts

Dependency, function, argument, function value, scope, and scope.

Space organization

Intersubject communications

Forms of work

Resources

Algebra - Russian

Algebra - physics

Algebra - geography

Frontal

Individual

Work in pairs and groups

Projector

Textbook

Self-assessment sheet

Lesson stage

Teacher activity

Planned student activities

Developed (formed) learning activities

subject

universal

1. Organizational.

slide 1.

Slide 2.

Greeting students; checking the readiness of the class for the lesson by the teacher; organization of attention.

What is in common between a climber storming mountainous spaces, a child successfully playing computer games, and a student striving to study better and better.

Set up for work.

The result of success

Personal UUD: the ability to highlight the moral aspect of behavior

Regulatory UUD: the ability to reflect on one's own activities and the activities of comrades.

Communicative UUD

Cognitive UUD: conscious and arbitrary construction of speech utterance.

2. Setting the goal and objectives of the lesson. Motivation of educational activity of students.

Slide 2.

Everything in our life is interconnected, everything that surrounds us depends on something. For example,

What is your mood today?

What do your grades depend on?

What determines your weight?

Determine what is the keyword of our theme? Is there a connection between the objects? We will introduce this concept in today's lesson.

Interact with the teacher during oral questioning.

Addiction.

Write down the topic "Relationship between quantities"

Personal UUD:

development of motives for learning activities.

Regulatory UUD: decision-making.

Communicative UUD: listen to the interlocutor, build statements that are understandable to the interlocutor.

Cognitive UUD: building a strategy for finding solutions to problems. Highlight essential information, put forward hypotheses and update personal life experience

3. Actualization of knowledge.

Work in pairs.

Slide 3.

slide 4.

You have tasks on the tables that need to be solved in pairs.

Calculate the value of y using the formula y \u003d 2x + 3 for a given value of x.

Annex 1.

Writes out students' answers at their desks under dictation for checking, matching the meanings of expressions and letters from students' cards in ascending order.

Appendix 2

Shows a collage of famous mathematicians who first worked on a "function".

Bring your calculations.

They voice their answers, check the solution, write out the letters from the cards with the received values ​​in ascending order.

- "Function"

Perception of information.

Repetition of calculations of the values ​​of literal expressions with a known value of one variable, working with integers in ascending order. Identification of a new concept of "function".

Personal UUD:

acceptance of the social role of the student, meaning formation.

Regulatory UUD: drawing up a plan and sequence of actions, predicting the result and the level of assimilation of the material,searching and extracting the necessary information,construction of a logical chain of reasoning, proof.

Cognitive UUD: the ability to consciously build a speech statement.

Communicative UUD: the ability to listen to the interlocutor,dialogue, observance of moral standards in communication.

4. Primary assimilation of new knowledge.

Group.

Slide 5.

Organizes the perception of information by students, comprehension of the given and primary memorization by children of the topic being studied: “The relationship between quantities. Function". Organizes work in groups (4 people) on cases.

On the table at each group are cases with tasks. The conditions of modern life dictate their own rules, and one of these rules is to have your own cell phone. Consider a life example when we use cellular communications at the MTS tariff "Smartmini».

Appendix 3

Guides the groups in the decision.

Assign tasks to the group.

The ability to listen to the task, understand the work with the case: analysis of the dependence of one variable on another, the introduction of new definitions "Function, argument, domain of definition", work with the graph "Dependence of the phone charge"

Personal UUD:

Regulatory UUD: control of the correctness of answers to information from the textbook, development of one's own attitude to the studied material of students, correction of perception.

Cognitive UUD: search and selection of the necessary information.

Communicative UUD:

listen to the interlocutor, build clear statements for the interlocutor. Meaningful reading.

5. Initial check of understanding. Individual.

slide 6.

Organize student responses.

Case Protection

The ability to prove the correctness of your decision.

Personal UUD: development of skills of cooperation.

Regulatory UUD: developing their own attitude to the studied material of students,use evidence-based math.

Communicative UUD: the ability to listen and intervene in front of students, listen to the interlocutor, build statements that are understandable to the interlocutor.Cognitive UUD: search and selection of the necessary information, the ability to read graphs of functions, justify your opinion;

6. Primary fastening. Frontal.

Slide 7.

Organizes work on a common task.

Determines the relationship between algebra and physics, algebra and geography.

Appendix 4

Answer the teacher's questions, read the schedule.

Ability to apply previously learned material.

Personal UUD:

independence and critical thinking.

Regulatory UUD: carry out self-control of the process of completing the task. Correction.

Cognitive UUD: compare and generalize facts, build a logically sound reasoning, use evidence-based mathematical speech.

Communicative UUD:

semantic reading.

7. Information about homework, briefing on its implementation.

slide 8.

Explains homework.

Level 1 is required. §20, questions 1-8, nos. 157, 158, 159.

Level 2 - Intermediate. Find examples of the dependence of one value on another from any branches of life.

Level 3 - advanced. Analyze the functional dependence of utility bills, derive a formula for calculating any service, build a graph of the function.

Plan their actions in accordance with self-assessment.

Work at home with text.

To know the definitions on the topic, the design of the dependence through a formula, the ability to build the dependence of one value through another.

Personal UUD:

acceptance of the social role of the student.

Regulatory UUD:adequately carry out self-assessment, correction of knowledge and skills.

Cognitive UUD:carry out the actualization of the acquired knowledge in accordance with the level of assimilation.

8. Reflection.

slide 9.

Organizes a discussion of achievements, briefing on how to work with a self-assessment sheet. Offers to carry out a self-assessment of achievements by filling out a self-assessment sheet.

Application5.

Acquaintance with the self-assessment sheet, clarification of the assessment criteria. Draw conclusions, carry out self-assessment of achievements.

Conversation to discuss achievements.

Personal UUD:

independence and critical thinking.

Regulatory UUD: accept and save the learning goal and task, carry out final and step-by-step control over the result, plan future activities

Cognitive UUD: analyze the degree of assimilation of new materialCommunicative UUD: listen to classmates, voice their opinion.

Annex 1.

Answers for the teacher

for check

Correlate the answers for the new concept in ascending order of values

Calculate the value of y using the formula y=2x+3 if x = 2

Calculate the value of y using the formula y=2x+3 if x = -6

Calculate the value of y using the formula y=2x+3 if x = 4

Calculate the value of y using the formula y=2x+3 if x = 5

Calculate the value of y using the formula y=2x+3 if x = -3

Calculate the value of y using the formula y=2x+3 if x = 6

Calculate the value of y using the formula y=2x+3 if x = -1

Calculate the value of y using the formula y=2x+3 if x = -5

Calculate the value of y using the formula y=2x+3 if x = 0

Calculate the value of y using the formula y=2x+3 if x = - 2

Calculate the value of y using the formula y=2x+3 if x = 3

Calculate the value of y using the formula y=2x+3 if x = -4

Appendix 2

Appendix 3

(2 people)

In the tariff of cellular communicationSmartmini” includes not only a subscription fee of 120 rubles, but also a fee for a conversation per minute with other mobile operators in Russia, each minute of a conversation is equal to 2 rubles.
1. Calculate the phone fee for a month if we had a conversation through another mobile operator for 2 minutes, 4 minutes, 6 minutes, 10 minutes

Write down an expression for calculating the phone charge for 2min, 4min, 6min, 10min.

Derive a general formula for calculating phone charges.

S = 120 + 2∙2 = 124rub.

S = 120 + 2∙4 = 128rub.

S = 120 + 2∙6 =132rub.

S = 120 + 2∙8 = 136rub.

S = 120 + 2∙10 = 140rub.

S = 120 + 2t

Task number 2

(2 people)

Work with the textbook. Define the following terms

Function -

Function argument −

Domain -

Range -

This is a rule by which, for each value of the independent variable, you can find the only value of the dependent variable.

Independent variable.

These are all the values ​​that the argument takes.

This is the value of the dependent function.

Task number 3

(4 people). In the “Phone fee dependence” card, mark the values ​​of the fee at 4min, 6min, 8min, 10min with a dot. (Take the values ​​​​from task No. 1).

Attention! Phone fee value at 2min. already installed.

"Phone fee addiction"

Determine the domain of definition and the scope of the function from the graph

Definition area - from 2 to 10

Value area - from 124 to 140

Appendix 4

Appendix 5

Self-assessment sheet

Self-esteem

Criteria for evaluating a classmate on a desk

Classmate rating (F.I.)

Formulation of the topic of the lesson, goals and objectives of the lesson.

Yasam was able to determine the topic, purpose and objectives of the lesson - 2 b.

I was able to determine only the topic of the lesson - 1 point.

I could not determine the topic, purpose and objectives of the lesson - 0 b.

Participated in determining the topic of the lesson, the purpose of the lesson, or the tasks of the lesson - 1 b.

Did not take part in determining the topic of the lesson, the purpose of the lesson, or the objectives of the lesson 0 b

What will I do to achieve my goal.

I myself determined how to achieve the goal of the lesson - 1 point.

I was unable to determine how to achieve the goal of the lesson - 0 points.

Took part in planning actions to achieve the goal of the lesson - 1 b.

Did not take part in planning actions to achieve the goal of the lesson 0 b

Doing practical work in pairs.

Participated in the work of the group - 1 point.

Did not participate in the work of the group - 0 point.

Working in a case study group.

Participated in the work of the group - 1 point.

Did not participate in the work of the group - 0 point.

Participated in the work of the group - 1 point.

Did not participate in the work of the group - 0 point.

Performing a task with graphs of functions.

I did all the examples myself -2 points.

I did less than half myself - 0 points.

Cope with the blackboard with the task 1 point.

Failed at the blackboard with the task 0 points.

Choice of homework

3 points - chose 3 tasks out of 3, 2 points - chose only 2 numbers, 1 point - chose 1 task out of 3

Not Evaluated

Rate yourself: if you scored 8-10 points - "5"; 5 - 7 points - "4"; 4 - 5 points - "3".

self-analysis of the lesson.

This lesson is number 1 in the system of lessons on the topic "Function".

The purpose of the lesson is to form an idea of ​​a function as a mathematical model for describing real processes. The main activities of the student are the repetition of computational skills with integer expressions, the formation of primary ideas about the relationships between quantities, the description of the concepts of “function, dependent variable”, “argument, independent variable”, to distinguish among the dependencies functional dependencies in the form of a function graph.

Developing: develop mathematical speech (use of special mathematical terms), attention, memory, logical thinking, draw conclusions.

Educational: to cultivate a culture of behavior in frontal, group, pair and individual work, to form positive motivation, to cultivate the ability for self-esteem.

By type, this lesson is a lesson in the assimilation of new knowledge, it includes seven stages. The first stage is organizational, the mood for learning activities. The second stage is the motivation of educational activities for setting goals and objectives of the lesson “Relationship between quantities. Function". The third stage is the actualization of knowledge, work in pairs. The fourth stage is the primary assimilation of new knowledge, "case technology", work in a group. The fifth stage is the primary test of understanding - individual work, case defense. The sixth stage - primary consolidation - frontal work, contention of examples of graphs of functions. The seventh stage - information about homework, instructions for its implementation in an individual form of 3 levels. The eighth stage is reflection, summing up, filling out a self-assessment sheet by students about personal achievements in the lesson.

When motivating students for the lesson, I selected cases from life, where the connections between quantities were considered not only in life, but also in algebra, and in physics, and in geography. Those. tasks were focused on creativity of thinking, resourcefulness, on strengthening the applied orientation of the algebra course by examining examples of real dependencies between quantities based on the experience of students, which helped to achieve comprehension of the material by all students.

I managed to meet the time. Time was distributed rationally, the pace of the lesson was high. It was easy to teach the lesson, the students quickly got involved in the work, gave interesting examples of dependencies between quantities. The lesson used an interactive whiteboard, accompanied by a presentation of the lesson. I think the goal of the lesson has been achieved. As the reflection showed, the students understood the material of the lesson. Homework was no problem. In general, I consider the lesson successful.

There are qualitative and quantitative dependencies between physical quantities, a regular connection, which can be expressed in the form of mathematical formulas. The creation of formulas is associated with mathematical operations on physical quantities.

Homogeneous quantities admit all kinds of algebraic operations on themselves. For example, you can add the lengths of two bodies; subtract the length of one body from the length of the second; divide the length of one body by the length of the second; raise the length to a power. The result of each of these actions has a certain physical meaning. For example, the difference in the lengths of two bodies shows how much the length of one body is greater than the other; the product of the base of the rectangle and the height determines the area of ​​the rectangle; the third power of the edge length of a cube is its volume, and so on.

But it is not always possible to add two quantities of the same name, for example, the sum of the densities of two bodies or the sum of the temperatures of two bodies have no physical meaning.

Dissimilar quantities can be multiplied and divided by each other. The results of these operations on heterogeneous quantities also have a physical meaning. For example, the product of the mass m of a body and its acceleration a expresses the force F, under the action of which this acceleration is obtained, that is:

the quotient of dividing the force F by the area S, on which the force acts uniformly, expresses the pressure p, that is:

In general, the physical quantity X with the help of mathematical operations can be expressed in terms of other physical quantities A, B, C, ... by an equation of the form:

(1.6)

where is the coefficient of proportionality.

exponents can be both integer and fractional, and can also take on a value equal to zero.

Formulas of the form (1.6), which express some physical quantities in terms of others, are called equations between physical quantities.

The coefficient of proportionality in equations between physical quantities, with rare exceptions, is equal to one. For example, an equation in which the coefficient differs from unity is the equation of the kinetic energy of a body in translational motion:

. (1.7)

The value of the proportionality coefficient both in this formula and in general in equations between physical quantities does not depend on the choice of units of measurement, but is determined solely by the nature of the relationship of the quantities included in this equation.

The independence of the proportionality coefficient from the choice of units of measurement is a characteristic feature of the equations between quantities. That is, each of the symbols A, B, C, ... in this equation represents one of the specific implementations of the corresponding quantity, which does not depend on the choice of the unit of measurement.

But if all the quantities included in equation (1.6) are divided into the corresponding units of measurement, we obtain an equation of a new type. For ease of consideration, we write the following equation:

After dividing the values ​​of X, A and B into units of their measurements, we get:

, (1.9)

. (1.10)

Equations of the form (1.9) or (1.10) are no longer linked by quantities as collective concepts, but by their numerical values, resulting from the expression of quantities in certain units of measurement.

An equation relating numerical values ​​of quantities is called an equation between numerical values.

For example, the numerical value of the heat Q, which is released in the conductor during the passage of current:

, (1.11)

where is the numerical value of the heat that is released on the conductor, kcal; numerical value of the current strength, A; numerical value of resistance, Ohm; numerical value of time, s.

Only under these conditions does the numerical coefficient take on the value of 0.24.

But in calculations in technology, such equations are used very widely. Values ​​are expressed in different systems and non-systemic units to obtain equations with complex coefficients.

In general, the coefficient of proportionality in the equations between numerical values ​​depends only on the units of measurement. Changing the unit of measurement of one or more quantities included in equation (1.9) entails a change in the numerical value of the coefficient.

The dependence of the proportionality coefficient on the choice of units of measurement is a distinctive feature of the equations between numerical values. This characteristic between numerical values ​​is used to define derived units of measurement and to construct systems of units.

More on the topic 1.2 Relationship equation between physical quantities:

1. CHAPTER 2
2. CORRELATION OF THE HEURISTIC AND REGULATORY FUNCTION OF PHILOSOPHICAL PRINCIPLES IN THE FORMATION OF A NEW PHYSICAL THEORY

The relationship between the quantities characterizing the radiation field (energy flux density φ or particles φ N) and the quantities characterizing the interaction of radiation with the medium (dose, dose rate) can be established by introducing the concept of the mass energy transfer coefficient μ nm . It can be defined as the fraction of radiation energy transferred to the substance when passing through the protection of a unit mass thickness (1 g/cm 2 or 1 kg/m 2). In the event that radiation with an energy flux density φ falls on the protection, the product φ μ nm will give the energy transferred to a unit mass of a substance per unit time, which is nothing more than the absorbed dose rate:

P = φ μ nm (23)

P = φ γ E γ μ nm (24)

To pass to the exposure dose rate, which is equal to the charge formed by gamma radiation in a unit mass of air per unit time, it is necessary to divide the energy calculated by formula (24) by the average energy of formation of one pair of ions in air . and multiply by the charge of one ion equal to the electron charge qe. In this case, it is necessary to use the mass energy transfer coefficient for air.

P 0 = φ γ E γ μ nm (25)

Knowing the relationship between the gamma radiation flux density and the exposure dose rate, it is possible to calculate the latter from a point source of known activity.

Knowing the activity A and the number of photons per 1 act of decay n i , we obtain that per unit time the source emits n i · A photons in an angle of 4π .

To obtain the flux density at a distance R from the source, it is necessary to divide the total number of particles by the area of ​​a sphere of radius R:

Substituting the obtained value φ γ into formula (25) we obtain

Let us reduce the values ​​determined from the reference data for a given radionuclide into one coefficient K γ - the gamma constant:

As a result, we obtain the calculation formula

When calculating in off-system units, the values ​​have the following dimensions: R O - R / h; A - mCi; R - cm; Kγ - (R cm 2) / (mCi h);

in the SI system: R O - A / kg; A - Bk; R - m; Kγ - (A m 2) / (kg Bq).

Relationship between gamma constant units

1 (A m 2) / (kg Bq) \u003d 5.157 10 18 (R cm 2) / (h mCi)

Formula (29) is very important in dosimetry (as, for example, the formula of Ohm's law in electrical engineering and electronics) and therefore must be memorized. The Kγ values ​​for each radionuclide are in the handbook. For example, we give their values ​​for nuclides used as control sources of dosimetric instruments:

for 60 Co Kγ = 13 (R cm 2) / (h mCi);

for 137 C Kγ = 3.1 (R cm 2) / (h mCi).

The given ratios between the units of activity and dose rate made it possible for gamma emitters to introduce such units of activity as kerma equivalent and radium gamma equivalent.

The kerma equivalent is the amount of radioactive material that at a distance of 1 m creates a kerma power in the air of 1nGy/s. The unit of measure for the kerma equivalent is 1nGyּm 2 /s.

Using the ratio according to which 1Gy=88R in air, we can write 1nGyּm 2 /s=0.316 mRּm 2 /hour

Thus, a kerma equivalent of 1nGyּm 2 /s creates an exposure dose rate of 0.316 mR/hour at a distance of 1 m.

The unit of radium gamma equivalent is the amount of activity that produces the same dose rate of gamma radiation as 1 mg of radium. Since the gamma constant of radium is 8.4 (Рּсм2)/(hourּmKu), then 1 meq of radium creates a dose rate of 8.4 R/hour at a distance of 1 m.

The transition from the activity of substance A in mKu to the activity in mEq of radium M is carried out according to the formula:

Ratio of units of kerma equivalent to radium gamma equivalent

1 meq Ra = 2.66ּ10 4 nGyּm 2 /s

It should also be noted that the transition from the exposure dose to the equivalent dose and then to the effective dose of gamma radiation with external exposure is quite difficult, because. this transition is influenced by the fact that the vital organs are shielded by other parts of the body during external irradiation. This degree of shielding depends both on the energy of the radiation and its geometry - from which side the body is irradiated - from the front, back, side or isotropically. Currently, NRBU-97 recommends using the transition 1Р=0.64 cSv, however, this leads to an underestimation of the doses taken into account, and, obviously, the development of appropriate instructions for such transitions is to be done.

In conclusion of the lecture, it is necessary to return once again to the question - why five different quantities and, accordingly, ten units of measurement are used to measure the doses of ionizing radiation. To them, respectively, six units of measurement are added.

The reason for this situation is that different physical quantities describe different manifestations of ionizing radiation and serve different purposes.

A generalizing criterion for assessing the danger of radiation for humans is the effective equivalent dose and its dose rate. It is it that is used in the regulation of exposure by the Radiation Safety Standards of Ukraine (NRBU-97). According to these standards, the dose limit for the personnel of nuclear power plants and institutions working with sources of ionizing radiation is 20 mSv/year. For the entire population - 1 mSv/year. The equivalent dose is used to estimate the effects of radiation on individual organs. Both of these concepts are used in normal radiation conditions and in minor accidents, when doses do not exceed five allowable annual dose limits. In addition, the absorbed dose is used to assess the effect of radiation on a substance, and the exposure dose is used to objectively assess the gamma radiation field.

Thus, in the absence of major nuclear accidents, for assessing the radiation situation, we can recommend a dose unit - mSv, a dose rate unit μSv / h, an activity unit - Becquerel (or off-system rem, rem / h and mKu).

In the appendices to this lecture, relations are given that may be useful for orientation in this problem.

1. Radiation safety standards of Ukraine (NRBU-97).
2. V. I. Ivanov Dosimetry course. M., Energoatomizdat, 1988.
3. IV Savchenko Theoretical foundations of dosimetry. Navy, 1985.
4. VP Mashkovich Protection from ionizing radiation. M., Energoatomizdat, 1982.

Application No. 1

UMK "Harmony"

Topic: Relationship between quantities: V, t, S.

Purpose: to organize the activities of students on the primary comprehension of ways

Relationships between the values ​​V, t, S, according to their identification and distinction.

Planned results:

1. Subject:

Establish the relationship between the values ​​​​of speed, time, distance and the use of formulas in solving problems for movement;

Practice the calculation skills of the multiplication table;

Choose a value that corresponds to the essence of a particular situation;

Plan the course of solving the problem, choose and explain the choice of action;

1. Metasubject:

- develop information competencies: the ability to solve problems for movement based on the interaction between the components S, V, t;

Develop communicative competencies: the ability to work in pairs, correctly formulate one’s thoughts, express one’s opinion and listen to the opinions of others, the ability to defend one’s point of view, citing various arguments;

Develop social competencies: instilling interest in the subject, developing an active life position;

Develop logical and creative thinking, memory, attention;

1. Personal:

Formation of personal responsibility for the performance of the chosen work;

Cultivate a desire for cooperation, a sense of mutual assistance.

Equipment: ICT, textbook, cards with formulas, waybills, notebook.

During the classes.

a. Self-determination to activity.

I want to start the lesson with the words of the French philosopher J.J. Rousseau: “You are talented children! Someday you yourself will be pleasantly surprised how smart you are, how much and how well you know how, if you constantly work on yourself, set new goals and strive to achieve them ... ”I wish you today at the lesson to make sure of these words, because you are waiting for discovering new knowledge while working in the classroom.

ӀӀ. Message about the topic and purpose of the lesson.

If we calculate the following expressions correctly, we will know the topic of our lesson. (simulator: Excellent student, mathematics, examples, out-of-table multiplication and division, 1 task) (students collectively solve expressions in one example)

Read the topic of our today's lesson. slide 1

What is our goal for today's lesson? (comprehend the relationship between the quantities: V, t, S, learn to solve problems for movement).

ӀӀӀ. Knowledge update.

And the journey will help us achieve our goal.

You will record the success of your work in the waybill after each completed task.Based on the results of your achievements in the lesson, you will receive a grade.

How do people travel since ancient times?

(Listen to the children's suggestions)

(opens interactive board With pictures and speed cards).

Yes, all of this can be travelled. We, as travelers, need to know how fast these objects can move.
- Determine the possible speed of movement for each of them.

(Students take turns at the blackboard to connect the subject picture as quickly as possible).

What else do you need to remember when going on a trip?

(Be attentive, observant, help comrades, do not leave them in trouble)

Yes, it is important to help a friend along the way, to feel a friend's shoulder. I hope we will help each other today.

Let's check how you know the rules for travelers. Choose the correct answers. If the statement is true, show “+”, if it is false, show “-”.

2km - 200 meters (No)
In 2min - 120 seconds (Yes)
60 min less than 1 hour (No)

The path is the magnitude (Yeah)

- You have successfully coped with the work.Evaluate the work of the entire class at this stage of the journey and rate it on the waybill, as well as rate yourself. that suits your work. (Children give themselves grades).

A.V. Repetition of the studied schemes.

(interactive whiteboard with schemes and their names)

Guys on the way there are various surprises for which we must be prepared. Here is a strong wind crushed all the formulas with their names. And we won't be able to travel any further if we don't put things in order.

Since on the way you can always count on the help of a friend, I suggest to work in pairs on the spot. ( In pairs, they connect the diagrams with their names, and one student is at the blackboard)

Let's check the correctness of the work. Who has the same?

Put on your guide sheets a grade that matches your work in pairs.

V. Discovery of the new.

Guys, which of these formulas will be the most necessary for us today? slide 2

(S = V  t - path formula).

Name the components of multiplication. (first factor, second factor, product) How to find the unknown factor?

Which multiplication component in this formula is the distance? Speed? Time?

Let's trace the relationship between the quantities in this formula.

What formulas follow from this? How to find speed? How to find time?

V=S:t

What is the name of this formula? (formula for finding speed)

t=S:V

What is the name of this formula? (formula for finding time)

Why do we need to know these formulas?

(To correctly find unknown distance, speed and time in problems)

These formulas are so important to us that they have become guiding stars., and will help us along the way not only today, but also in subsequent mathematics lessons.

(Stars light up on the board!)

Va. Primary fastening.

slide 3 (travel map with hyperlinks)

We start our journey. Who will we travel with? (with skier)

No. 388 p. 119 (textbook)(teamwork)

Read the task. How can we write the condition of the problem? (using schema)

Draw a diagram of the task.

What guiding star will help us in this task?

We arrived in the city of Quantities. The quantities have prepared a task for us. which we must fulfill.

Find the excess:

1. 15km, 15h, 15m, 15cm, 15dm;
2. 15km/h, 25km/h, 35km/min, 45km/h, 55km/h.

Put a rating on your travel lists.

What values ​​have we been given? (length values, i.e. distances and speed values)

What can you learn if you know the distance and speed?

No. 390 page 120 (commenting on the board)

Read the task.

Who will solve this problem at the blackboard?

What is unknown in this problem? (time)

What guiding star will now help us in solving this problem?

Solve the problem, write down its solution.

We got to the Self-Work Pass.

The plane can fly without refueling 7600 km. At what speed must the plane fly to cover this distance in 8 hours?

Read the task.

What is unknown in this problem? (speed)

Who can solve this problem on their own? Solve it.

Compare your solution to the problem with the solution on the board. Who did it too?

VӀӀ. Creative task.

We arrived at the final destination of our journey, the city of Creativity.

And here is your next task.

Think of a drawing problem.

VӀӀӀ. The result of the lesson. Test.

And to get back to the class, let's do a little test. slide 4.

1. To find the time, you need:

a) subtract the speed from the distance;

b) distance divided by speed;

c) speed divided by distance.

2. To find the distance, you need:

a) add time to speed

b) speed multiplied by time;

c) subtract time from speed.

3. To find the speed, you need:

a) subtract time from distance

b) distance divided by time;

c) add time to distance

What new did you learn in the lesson?

What was the most difficult?

Let's see how we worked. How did you rate the work of the class?

Turn in the sheets, I will look at them and give you marks.

Ah. Homework.

1. No. 392 p.121 (textbook)
2. Come up with tasks for movement, using these values: 80 km / h, 2 h; 15 m/min, 3min; 270km, 90km/h and solve them.
3. Solve the problem:

Can a train travel 300 km in 7 hours if it moves at a speed of 60 km/h?

H. Reflection.

And now attach your star on the ladder of mood to the step that corresponds to your feelings, mood, state of your soul that you had throughout the lesson.