The fundamental position describing the dependence of current, resistance and voltage from each other is the Ohma law for the chain alternating current. The main difference from the same position for the regimen of the chain is to take into account the full resistance. This value depends on the active and reactive component of the line, that is, takes into account capacity and inductance. Therefore, the calculation of the parameters for the full chain compared to the site will be more complicated.
Basic concepts
All the science of electrical engineering is built on operating with such concepts as the charge and potential. In addition, important phenomena in the circuit are electrical and magnetic fields. In order to understand the essence of the Ohm law, it is necessary to understand what these quantities are, and from which certain electromagnetic processes depend on.
Electricity is called the phenomenon due to the interaction of charges between themselves and their movement. This word was put into use William Gilbert in 1600 after opening them the ability of some bodies to be electrified. Since he spent his experiments with a piece of amber, then the property attributing or pushing them with them, the other substances were called "amber", which in translating from Greek sounds like electricity.
In the future, various scientists, such as Ersted, Ampere, Joule, Faraday, Volt, Lenz and Ohm, a number of phenomena were opened. Thanks to their research, the use of concepts appeared: electromagnetic induction and field, galvanic element, current and potential. They discovered between electricity and magnetism, which led to the emergence of science examining the theory of electromagnetic phenomena.
In 1880, the Russian engineer Lachinov theoretically pointed out which conditions are necessary for the transmission of electricity at distances. And after 8 years, Henry Rudolf Hertz during experiments registered electromagnetic waves.
Thus it was found that electric charges Create electrical radiation around themselves. Conditionally divided into particles with a positive and negative charge sign. It was established that the elements of the charges are attracted, and the varied - repel. To make their movement to the physical body, it is necessary to attach any energy. When they are moved, a magnetic field occurs.
The property of materials to ensure the movement of charges received the name of the conductivity, and the value inverse it is resistance. The ability to skip through itself charges depends on the structure crystal lattice Substances, its connections, defects and impurities.
Determination of voltage
Scientists have established that there are two types of movement of charges - chaotic and directed. The first type does not lead to any processes, since the energy is in a balanced state. But if the body is applied to the body, forcing the charges to follow one way, then an electric current will arise. There are two types:
- Permanent - the power and direction of which remain constant in time.
- A variable - having a different value at a certain point of time and changing its movement, with its change repeating at equal intervals (cycle). This variability is described by the harmonic law of sine or cosine.
The charge is characterized by such a concept as potential, that is, the amount of energy it possesses. The necessary force to move the charge from one point of the body to another is called voltage.
It is determined relative to the change in the charge potential. The strength of the current is determined by the ratio of the amount of charge pasted through the body per unit of time, to the magnitude of this period. Mathematically described by the expression: IM \u003d ΔQ / ΔT, is measured in amperes (a).
Regarding the variable signal, an additional value is introduced - the frequency F, which determines the cyclicality of the signal flow F \u003d 1 / T, where T is the period. For its unit of measurement, hertz (Hz) was adopted. Based on this, the sinusoidal current is expressed by the formula:
I \u003d im * sin (w * t + ψ), where:
- IM is the power of the current at a certain point in time;
- Ψ is a phase determined by the displacement of the current wave relative to the voltage;
- w is a circular frequency, this value depends on the period and equal to W \u003d 2 * p * f.
The voltage is characterized by the work that the electric field makes the charge from one point to another. It is determined as the potential difference: Um \u003d φ1 - φ2. The expending work is made up of two forces: electrical and third-party, called electromotive (EMF). It depends on magnetic induction. The potential of the same equal to relation The energy of the interaction of the surrounding field to the value of its magnitude.
therefore for a harmonic signal change, the voltage value is expressed as:
U \u003d UM * SIN (W * T + ψ).
Where Um is an amplitude voltage value. A variable voltage voltage (B) is measured.
Impedance chain
Everyone physical body Has your resistance. It is due to the inner structure of the substance. This value is characterized by the property of the conductor to prevent the passage of the current and depends on the specific electrical parameter. Determined by the formula: R \u003d ρ * L / S, where ρ is a specific resistance, which is a scalar value, OM * M; L - Explorer length; m; S is the cross-sectional area, m 2. In this expression, constant resistance is determined inherent in passive elements.
At the same time, impedance, impedance, is as the sum of the passive and reactive component. The first is determined only by the active resistance consisting of the resistive load of the power supply and resistors: R \u003d R0 + R. The second is located as a difference between the capacitive and inductive resistance: x \u003d xl-xc.
If you put the perfect capacitor (without loss) to the electrical circuit, then after the variable signal goes on it, it will charge. The current will begin to come further, in accordance with the periods of its charge and discharge. The amount of electricity flowing into the chain is: Q \u003d C * U, where C is the capacity of the element, F; U - power supply voltage or capacitor plays, V.
Since the rate of change of current and voltage is directly proportional to the frequency W, the following expression will be fair: i \u003d 2 * p * f * C * U. It turns out that it turns out that capacitive impedance is calculated by the formula:
Xc \u003d 1/2 * p * f * c \u003d 1 / W * C, Ohm.
The inductive resistance occurs due to the appearance of its own field in the conductor, called EL self-induction. It depends on the inductance and speed of change. In turn, the inductance depends on the forms and sizes of the conductor, the magnetic permeability of the medium: L \u003d F / I, is measured in Teslas (TL). Since the voltage applied to inductance is equally equal to self-induction EMF, it is true EL \u003d 2 * P * F * L * I. The rate of current change is proportional to the frequency w. Based on this, inductive resistance is:
XL \u003d W * L, Ohm.
Thus, the impedance of the chain is calculated as: z \u003d (R 2 + (x C-x L) 2) ½, Ohm.
AC law
The classic law was opened by a physicist from Germany Simon Omom in 1862. Conducting experiments, it discovered the connection between the current and voltage. As a result, the scientist formulated the assertion that the current strength is proportional to the potential difference and inversely proportional to the resistance. If the current circuit decreases several times, then the voltage in it will become less than the same.
Mathematically, the Ohm law was described as:
therefore ohma law for alternating current is described by the formula:
I \u003d u / z, where:
- I is the strength of alternating current, and;
- U - the difference of potentials, in;
- Z - Full chain resistance, Ohm.
The total resistance depends on the frequency of the harmonious signal and is calculated according to the following formula:
Z \u003d ((R + R) 2 + (W * L - 1 / W * C) 2) ½ \u003d ((R + R) 2 + x 2) ½.
When the current of the variable value is passed, the electromagnetic field does work, while due to the resistance rendered in the chain, heat is highlighted. I.e electric Energy goes into thermal. The power is proportional to the current and voltage. The formula describing the instantaneous value looks like: p \u003d i * u.
At the same time, for an alternating signal, it is necessary to take into account the amplitude and frequency component. Therefore:
P \u003d I * U * Cosw * T * COS (W * T + ψ), where i, u are amplitude values, and ψ is a phase shift.
For analyzing processes in electrical circuits of alternating current, the concept of a complex number is introduced. This is due to the displacement of the phases that appear between the current and the difference of potentials. It is indicated by the number of Latin letter J and consists of imaginary im and real Re parts.
Since the active resistance is transformed in heat in heat, and it is converted to energy on the reactive electromagnetic field, It is possible to transitions from any form to any. It can be written: z \u003d u / i \u003d z * e j * ψ.
From here the complete resistance of the chain: z \u003d r + j * x, where R and X are respectively active and reactive resistance. If the phase shift is taken equal to 90 0, then complex number You can not take into account.
Use of formula
The use of the Ohm law allows you to build the time characteristics of various elements. With it, it is easy to calculate loads for electrical circuits, select the desired cross-section of the wires, correctly select protective machines and fuses. Understanding the law makes it possible to apply the correct power source.
The use of the Ohm law can be applied in practice to solve the problem. For example, let there is an electrical line consisting of sequentially connected elements, such as: capacitance, inductance and resistor. In this case, the capacity C \u003d 2 * F, the inductance l \u003d 10 mg, and the resistance R \u003d 10 com. It is required to calculate the impedance of the full chain and calculate the current strength. In this case, the power supply operates at a frequency equal to f \u003d 200 Hz and gives a signal with an amplitude U \u003d 12 0 V. The internal resistance of the power supply is R \u003d 1 com.
Inductive resistance is located from the expression: xl \u003d 2 * p * f * L. on f \u003d 200 Hz and it leaves: x * l \u003d 1.25 ohms. Full resistance of the RLC chain will be: z \u003d ((10 * 10 3 + 1 * 10 3) 2 + (588-1.25) 2) ½ \u003d 11 com.
The potential difference that varies by the harmonic law of sinus will be determined by: u (t) \u003d u * sin (2 * p * f * t) \u003d 120 * sin (3.14 * T). The current will be equal to: I (t) \u003d 10 * 10 -3 + sin (3.14 * T + P / 2).
According to the calculated data, you can construct a current schedule corresponding to a frequency of 100 Hz. To do this, in the Cartesian coordinate system, the current dependence on time is displayed.
It should be noted, the OMA's law for an alternating signal differs from only the impedance and frequency of the signal only for the classical calculation. And it is important to consider them, since any radio component has both active and reactive resistance, which ultimately affects the work of the whole scheme, especially at high frequencies. Therefore, when designing electronic structures, in particular impulse devices, it is used for calculations that is the full law of Oma.
In this lesson, new concepts are considered in detail: "Mass of one subject", "number of objects", "the mass of all objects". It is concluded about the relationship of these concepts among themselves. Students are given the opportunity to practice in solving simple and composite tasks based on the knowledge gained.
We solve the tasks and learn how the concepts of "mass of one subject", "number of objects", "the mass of all subjects are connected with each other.
Read the first task.
Package mass with flour - 2 kg. Find out a lot of 4 such packages (Fig. 1).
Fig. 1. Illustration for the task
When solving the problem, we argue: 2 kg is the mass of one package, such packages - 4 pieces. We learn how much all packages weigh, the action of multiplication.
We write down the decision.
Answer: 8 kg weigh four packages.
We conclude: To find a lot of all objects, you need a mass of one subject to multiply by the number of items.
Let me read the second task.
Mass 4 identical packages with flour - 8 kg. Find out a lot of one package (Fig. 2).
Fig. 2. Illustration to the task
We submit data from the task to the table.
When solving the problem, we argue: 8 kg is the mass of all packages, such packages - 4 pieces. We learn how much one package weighs, the action of division.
We write down the decision.
Answer: 2 kg weighs one package.
We conclude: To find a lot of one subject, you need to share the mass of all items to the number of items.
Read the third task.
Mass of one package with flour - 2 kg. How many packages will need to decompose 8 kg equal in them (Fig. 3)?
Fig. 3. Illustration for the task
We submit data from the task to the table.
When solving the problem, we argue as follows: 8 kg is the mass of all packages, each package weighs 2 kg. Since all flour, 8 kg, laid out equally, two kilograms, we will find out how many packages will be required, the action of division.
We write down the decision.
Answer: 4 packages will be required.
We conclude: To find the number of items, you need to share the mass of all items on a mass of one subject.
Practice to correlate the text of the task with a brief record.
We will select a brief record to each task (Fig. 4).
Fig. 4. Illustration for the task
Consider the first task.
In 3 identical boxes of 6 kg of cookies. Sk kg weighs one biscuit box?
We will argue like that. This task suits a brief entry in Table 2. It contains the mass of all boxes - 6 kg, the number of boxes - 3. You need to know how much one biscuit box weighs. Recall the rule and learn the action of divisions.
Answer: 2 kg weighs one biscuit box.
Consider the second task.
Mass of one biscuit box - 2 kg. How many kg weigh 3 of the same biscuits?
We will argue like that. A brief entry is suitable for this task in Table 3. It shows the mass of one biscuit box - 2 kg, the number of boxes - 3. You need to know how much all biscuits are weighing. To find out, you need a mass of one box to multiply by the number of boxes.
Answer: 6 kg weigh three biscuits.
Consider the third task.
Mass of one biscuit box - 2 kg. How many boxes need to decompose 6 kg of biscuits equally?
We argue like that. This task suits a brief entry in Table 1. It shows the mass of one box - 2 kg, the mass of all boxes is 6 kg. You need to know the number of boxes to decompose the cookies. Recall that in order to find the number of boxes, we need a mass of all items to divide the mass of one subject.
Answer: 3 boxes will need.
Note that all three tasks that we decided were simple, since we could answer the question of the task by performing one action.
Knowing the relationship between the values \u200b\u200bof the "mass of one subject", the "number of objects", "the mass of all items" you can solve the composite tasks, that is, in 2, 3 actions.
Practice and solve the composite problem.
In 7 identical boxes of 21 kg of grapes. How many kg grapes in 4 of the same boxes?
We write these tasks in the table.
We will argue. To answer the question of the task, you need to multiply the mass of one box by the number of boxes. We will find a mass of one box: since 7 boxes weigh 21 kg, then in order to find a mass of one box, 21: 7 \u003d 3 (kg). Now we know how much one box weighs, we can find out how much 4 boxes weigh. For this we are 3 * 4 \u003d 12 (kg).
We write down the decision.
1. 21: 7 \u003d 3 (kg) - Mass of one box
2. 3 * 4 \u003d 12 (kg)
Answer: 12 kg grapes in 4 boxes
Today, at the lesson, we solved the tasks and learned how the magnitude of the "mass of one subject", the "number of objects", "the mass of all items" are connected with each other, learned to solve problems, applying these knowledge.
Bibliography
- M.I. Moro, MA Bantova and others. Mathematics: Tutorial. Grade 3: In 2 parts, part 1. - M.: Enlightenment, 2012.
- M.I. Moro, MA Bantova and others. Mathematics: Tutorial. Grade 3: in 2 parts, part 2. - M.: "Education", 2012.
- M.I. Moro. Mathematics lessons: Guidelines for teacher. Grade 3. - M.: Enlightenment, 2012.
- Regulatory document. Control and evaluation of learning outcomes. - M.: "Enlightenment", 2011.
- "School of Russia": programs for elementary school. - M.: "Enlightenment", 2011.
- S.I. Volkov. Mathematics: Checking. Grade 3. - M.: Enlightenment, 2012.
- V.N. Rudnitskaya. Tests. - M.: Exam, 2012.
- Nsportal.ru ().
- Prosv.ru ().
- Do.gendocs.ru ().
1. Finished phrases:
to find a lot of all items, you need ...;
to find a lot of one subject, you need ...;
to find the number of items, you need ....
2. Select a brief entry to the task and solve it.
In the three identical boxes of 18 kg of cherry. How many kg cherry in one box?
3. Solve the task.
In 4 identical boxes 28 kg of apples. How many kg of apples in 6 of the same boxes?
Between physical quantities There are qualitative and quantitative dependencies, natural bonds that can be expressed in the form of mathematical formulas. The creation of formulas is associated with mathematical actions above physical quantities.
Uniform values \u200b\u200bpermit over themselves all types of algebraic actions. For example, you can add the length of the two bodies; take the length of one body from the second length; divide the length of one body for the length of the second; Build length into the degree. The result of each of these actions has a certain physical meaning. For example, the difference in the length of the two bodies shows how much the length of one body is more different; The product of the base of the rectangle to height determines the area of \u200b\u200bthe rectangle; The third degree of the length of the edge of the cube is its volume, etc.
But it is not always possible to add two of the same names, for example, the amount of densities of two bodies or the sum of the temperatures of the two bodies are deprived of physical meaning.
Droinen values \u200b\u200bcan be multiplied and divided into each other. The results of these actions over heterogeneous values \u200b\u200balso have a physical meaning. For example, the product of the mass of body at its acceleration A expresses the force f, under the action of which this acceleration is obtained, that is:
the private from dividing the force F into the S. S., to which the force is evenly acting, expresses the pressure P, that is:
In general, the physical amount of x using mathematical actions can be expressed through other physical quantities A, B, C, ... the equation of the form:
(1.6)
where the coefficient of proportionality.
Indicators degree 
It can be both both and fractional, and can also take a value equal to zero.
Formulas of the form (1.6), which express some physical quantities through others, are called equations between physical quantities.
The proportionality coefficient in equations between physical quantities for rare exception is one. For example, by the equation in which the coefficient differs from the unit is the equation of the kinetic energy of the body when progressive movement:
. (1.7)
The value of the proportionality coefficient as in this formula is so and in general in the equations between physical quantities does not depend on the choice of units of measurement, but is determined solely as the nature of the connection of the values \u200b\u200bincluded in this equation.
The independence of the proportionality coefficient on the choice of measurement units is a characteristic feature of the equations between values. That is, each of the characters A, B, C, ... in this equation is one of the specific implementation of the corresponding value, which does not depend on the choice of a unit of measurements.
But if all the values \u200b\u200bincluded in equation (1.6) are divided into the appropriate units of measurements, we obtain the new type equation. For ease of consideration, we write the following equation:
After dividing the values \u200b\u200bof x, and in the units of their measurements, we obtain:
, (1.9)
. (1.10)
The equations of the form (1.9) or (1.10) binds each other no longer as collective concepts, but their numerical values \u200b\u200bobtained as a result of the expression of values \u200b\u200bin certain units of measurement.
The equation connecting the numerical values \u200b\u200bof the values \u200b\u200bis called the equation between the numerical values.
For example, the numerical value of heat q, which is highlighted in the conductor during current passage:
, (1.11)
where the numerical meaning of heat, which is highlighted on the conductor, kcal; Numerical value of current strength, and; numerical resistance value, Ohm; Numerical time value, p.
Only under these conditions, the numerical coefficient takes a value of 0.24.
But when calculating the technique, such equations use very widely. Values \u200b\u200bexpressed in different systems and introduced units With the preparation of equations with complex coefficients.
In general, the proportionality coefficient in equations between numerical values \u200b\u200bdepends only on the units of measurements. Replacing the unit of measurements of one or more values \u200b\u200bincluded in equation (1.9), attracts a change in the numerical value of the coefficient.
The dependence of the proportionality coefficient on the choice of measurement units is a distinctive feature of equations between numerical values. This characteristic feature Between numerical values \u200b\u200bis used to determine derivatives of units of measurements and to build systems of units.
More on the topic 1.2, the equation of communication between physical quantities:
- Chapter 2. Historical and methodological reconstruction of the choice of the principle of electrodynamics Maxwell
- The ratio of the heuristic and regulatory function of philosophical principles in the formation of a new physical theory
The links between the values \u200b\u200bcharacterizing the radiation field (the flow density of φ or particles φ n) and the values \u200b\u200bcharacterizing the interaction of radiation with the medium (dose, dose power) can be installed by introducing the concept of mass energy coefficient μ Nm. It can be determined as the proportion of radiation energy transmitted by the substance during the passage of the protection of a single mass thickness (1 g / cm 2 or 1 kg / m 2). In the event that radiation with a density of the energy flow φ falls on the protection, the product φ · μ Nm will give energy transmitted by the mass of the mass of the substance per unit of time, which is nothing but the power of the absorbed dose:
P \u003d φ · μ nm (23)
P \u003d φ γ · e γ · μ nm (24)
To go to the power of the exposure dose, which is equal to the charge formed by gamma radiation in a unit of air mass per unit of time, it is necessary to share the energy calculated by the formula (24) to divide into the average energy of the formation of one pair of ions in the air. And multiply to the charge of one ion equal to the electron charge QE. In this case, it is necessary to use the massive coefficient of air transmission for air.
P 0 \u003d φ γ · e γ · μ nm (25)
Knowing the connection between the density of the flow of gamma radiation and the power of the exposure dose, one can calculate the last from the point source of known activity.
Knowing activity A and the number of photons per 1 act of decay n i, we obtain that a unit of time, the source emits N i · A photons in an angle of 4π.
To obtain the flux density at a distance of R from the source, it is necessary to divide the total number of particles on the area of \u200b\u200bthe Radius Radius R:
Substituting the obtained value φ Γ in formula (25) we get
We minimize the values \u200b\u200bdetermined by reference data for a given radionuclide into one coefficient k γ - gamma permanent:
As a result, we obtain the calculation formula
When calculating non-system units, the following dimensions have the following dimensions: p o - p / h; A - mki; R - cm; Kγ - (p · cm 2) / (mki · h);
in the SI system: R o - a / kg; A - bk; R - m; Kγ - (A · m 2) / (kg · BK).
The relationship between the units of gamma constant
1 (A · m 2) / (kg · BK) \u003d 5,157 · 10 18 (P · cm 2) / (h · mki)
Formula (29) is very important in dosimetry (as, for example, the formula of the Ohm law in electrical engineering and electronics) and therefore should be remembered by heart. The values \u200b\u200bof Kγ for each radionuclide is in the directory. For example, we give their values \u200b\u200bfor nuclides used as control sources of dosimetric devices:
for 60 with kγ \u003d 13 (p · cm 2) / (h · mki);
for 137 with kγ \u003d 3.1 (p · cm 2) / (h · mki).
The reduced ratios between the units of activity and dose capacity allowed for gamma emitters to introduce such units of activity as Kerma equivalent and radium gamma equivalent.
Kerma Equivalent This is an amount of a radioactive substance that at a distance of 1 m creates a kerma power in the air of 1NNGR / C. Unit of measuring Kerma equivalent 1ngr ּ m 2 / s.
Using the relation to which in the air 1g \u003d 88r, can be recorded 1ngr ּ m 2 / s \u003d 0.316 mp ּ m 2 / h
Thus, Kerma equivalent of 1ngr ּ M 2 / C creates at a distance of 1 m, the power of the exposure dose of 0.316 mp / hour.
As a unit of radium gamma equivalent, such an activity is used, which creates the same dose rate of gamma radiation, as 1 mg of radium. Since, Radium gamma-constant 8.4 (p ּ cm 2) / (hour ּ mku), then 1 m MEQ radium creates 1 m dose rate of 8.4 p / h.
The transition from the activity of the substance A in the MKU to activity in MG-EKV radium M is carried out by the formula:
The ratio of Kerma Equivalent Units with Radium Gamma Equivalent
1 mM-eq Ra \u003d 2.66 ּ 10 4 NGR ּ m 2 / s
It should also be noted that the transition from the exposition dose to the equivalent dose and then to an effective dose of gamma radiation with external irradiation is quite difficult, since This transition is influenced by the fact that vital organs with external irradiation are shielded by other parts of the body. This degree of shielding depends on both the energy of radiation and its geometry - which part is irradiated from the front, behind, on the side or isotropic. Currently, NRBU-97 is recommended to use the transition of 1P \u003d 0.64 SZV, however, this leads to inclusion of adequate doses and, obviously, the development of appropriate instructions for such transitions will be developed.
In conclusion, the lecture must once again return to the question - why five different values \u200b\u200band, accordingly, ten units of measurement are used to measure doses of ionizing radiation. To them, respectively, six units of measurement is added.
The reason for the current situation is that various physical quantities describe various manifestations ionizing radiation And serves for various purposes.
A generalizing criterion for assessing the risk of radiation for a person is the effective equivalent dose and its dose power. It is it used when irradiating the radiation safety standards of Ukraine (NRBU-97). For these standards, the dose rate for staff nuclear power plants and institutions operating with sources of ionizing radiation are 20 mW / year. For the entire population - 1 mW / year. Equivalent dose is used to assess the effects of radiation into individual organs. Both of these concepts are used at a normal radiation situation and with small accidents when the doses do not exceed five permissible annual dose limits. In addition, the dose absorbed is used to assess the effects of radiation on the substance, and the exposure dose is for an objective assessment of the Gamma radiation field.
Thus, in the absence of large nuclear accidents for the OCEKI radiation setting, we can recommend a dose unit - msv, a unit of power of a dose of the MKZV / hour, a unit of activity - Becquer (or non-systemable Baer, \u200b\u200bBaer / hour and MKU).
Applications to this lecture there are ratios that may be useful for orienting in this problem.
- The norms of radiation security of Ukraine (NRBU-97).
- V. I. Ivanov Dosimetry course. M., Energoatomizdat, 1988.
- I. V. Savchenko Theoretical basis Dosimetry. Navy, 1985.
- V. P. Mashkovich Protection against ionizing radiation. M., Energoatomizdat, 1982.
Appendix No. 1.
Lesson on the topic "Communications between values. Function»
Yumagugin Elvira Mirkhatna,
pedagogical experience 14 years old
1 Qualification category, MBOU "Barsovskaya Sosh№1",
UMC:"Algebra. 7th grade",
A.G. Merzlyak, V.B. Polonsky, M.S. Yakir,
"Ventana Graf", 2017.
Didactic justification.
Type of lesson: lesson learning new knowledge.
Training Means: PC, Multiprodector.
Training: Learn to determine the functional dependence between values, enter the concept of function.Developing: develop mathematical speech, attention, memory, logical thinking.
Planned result
Subject
skills
Wood
to form a concept functional dependence, function, function argument, function value, definition area and function value.
Personal: To form the ability to plan your actions in accordance with the task.
Regulatory: develop the skill of students to analyze, draw conclusions, determine the relationship and logical sequence of thoughts;
training the ability to reflect your own activities and activities of your comrades.
Cognitive: Analyze, classify and summarize the facts, to build a logically reasonable reasoning, use evidential mathematical speech.
Communicative: alone to organize interaction in a pair, defend your point of view, bring arguments, confirming them with facts.
Basic concepts
Dependence, function, argument, function value, definition area and value area.
Organization of space
Interdimensional connections
Work forms
Resources
Algebra - Russian
Algebra - Physics
Algebra - Geography
Frontal
Individual
Work in pairs and groups
Projector
Textbook
Sheet of self-esteem
Stage lesson
Teacher's activities
The planned activity of students
Developed (Food) Educational Actions
subject
universal
1. Organization.
Slide 1.
Slide 2.
Greeting students; Check by a class readiness teacher to a lesson; Organization of attention.
What is common between a climber, storming mountainous spaces, a child who has been successfully playing computer games, and a student seeking to learn everything better and better.
Configured on the working way.
The result of success
Personal Wood: ability to allocate the moral aspect of the behavior
Regulatory Wood: The ability to reflect your own activities and the activities of comrades.
Communicative Woods
Cognitive Uud.: Conscious and arbitrary construction of speech statement.
2. Suitable target and lesson tasks. Motivation of students' learning activities.
Slide 2.
Everything in our lives is interconnected, all that surrounds us from something depends on. For example,
What does your mood depends on?
What are your estimates depend on?
What does your weight depend on?
Determine what the key word of our topic? Is there a connection between objects? We will introduce this concept today at today's lesson.
Interact with the teacher during an oral survey.
Addiction.
Record the topic "Communication between values"
Personal Wood:
development of the motives of educational activities.
Regulatory Wood: decision-making.
Communicative Woods: Listen to the interlocutor, to build a statement understandable to the interlocutor.
Cognitive Uud.: Laying the task solution search strategy. Select substantial information, put forward hypothesis and implement the actualization of personal life experience
3. Actualization of knowledge.
Work in pairs.
Slide 3.
Slide 4.
You have the tasks on the tables that need to be solved in pairs.
Calculate the value of the formula y \u003d 2x + 3 at a given value x.
Attachment 1.
Displays students to check, compliance with the values \u200b\u200bof expressions and letters from students as an increase in the parties under dictation.
Appendix 2.
Demonstrates the collage of famous mathematicians, who first worked on the "function".
Calculates.
They voiced their answers, check the decision, write out the correspondence of letters from cards with the obtained values \u200b\u200bascending.
- "Function"
Perception of information.
Repeating calculations of values \u200b\u200bof letter expressions with a known value of one variable, work with integers ascending the identification of a new concept "function".
Personal Wood:
taking the social role of students, sense-forming.
Regulatory URU: drawing up a plan and sequence of actions, predicting the result and level of material assimilation,search and extract the desired informationbuilding a logical chain of reasoning, proof.
Cognitive Wood: The ability to consciously build a speech statement.
Communicative Wood: the ability to listen to the interlocutor,doing dialogue, compliance with moral norms when communicating.
4. Primary learning of new knowledge.
Group.
Slide 5.
Organizes the perception of information by students, understanding the specified and primary memorization of the children under study: "The relationship between values. Function". Organizes work in groups (4 people) on cases.
On the table, each group contains cases with tasks. Conditions modern life Dictate their rules and one of these rules - have your own cell phone. Consider a life example when we use cellular tie at the MTS tariff "Smart.mini.».
Appendix 3.
Sends groups in solutions.
Distribute tasks in the group.
Ability to listen to the task, understand the work with the case: analysis of the dependence of one variable from the other, the introduction of new definitions "function, argument, definition area", work with a chart "Dependence of the phone charge"
Personal Wood:
Regulatory URU: Control of the correctness of the information of information on the textbook, the development of its own attitude to the studied learning material, the correction of perception.
Cognitive Wood: Search and allocating the necessary information.
Communicative Wood:
listen to the interlocutor, to build a statement clear to the interlocutor. Semantic reading.
5. Primary testing of understanding. Individual.
Slide 6.
Organizes the response of students.
Case protection
The ability to prove the loyalty to your decision.
Personal Wood: Development of cooperation skills.
Regulatory Wood: developing your own relation to the studied student material,use evidential mathematical speech.
Communicative Woods: The ability to listen and join the students, listen to the interlocutor, to build a statement understandable to the interlocutor.Cognitive Uud.: search and selection of necessary information, the ability to read graphs of functions, justify your opinion;
6. Primary consolidation. Frontal.
Slide 7.
Organizes work on a common task.
Determines the dependence of algebra and physics, algebra and geography.
Appendix 4.
Answer teacher's questions read the schedule.
The ability to apply the previously studied material.
Personal Wood:
independence and criticalness of thinking.
Regulatory Wood: Exercise self-control process of the task. Correction.
Cognitive Uud.: compare and summarize the facts, to build a logically reasonable reasoning, use evidential mathematical speech.
Communicative Wood:
semantic reading.
7. Information about the homework, instruction on its execution.
Slide 8.
Explains homework.
Level 1 - mandatory. §20, questions 1-8, №157, 158, 159.
2 level - medium. Choose examples of the dependence of one value from another of any branches of life.
3 level - elevated. Disassemble the functional dependence of payment of utilities, output the formula for calculating any service, build a graph of the function.
Plan your actions in accordance with self-esteem.
Work at home with text.
Know definitions on the topic, registration of dependence through the formula, the ability to build the dependence of one value across the other.
Personal Wood:
the adoption of the social role of the student.
Regulatory Wood: adequately carry out self-esteem, knowledge correction and skills.
Cognitive Wood: carry out the actualization of the knowledge gained in accordance with the level of assimilation.
8. Reflection.
Slide 9.
Organizes a discussion of achievements, instructing on working with a sheet of self-assessment. It proposes to carry out self-esteem of achievements by filling out a self-assessment sheet.
Appendix5.
Acquaintance with a list of self-esteem, clarifying evaluation criteria. Make conclusions, carry out self-assessment of achievements.
Conversation to discuss achievements.
Personal Wood:
independence and criticalness of thinking.
Regulatory Wood: Take and maintain a training goal and a task, exercise final and step-by-step control on the result, plan future activities
Cognitive Uud.: analyze the degree of assimilation of the new materialCommunicative Woods: Listened to classmates, voiced your opinion.
Attachment 1.
Answers for teacherfor check
Relate for a new concept ascending values
Calculate the value of the formula y \u003d 2x + 3, if x \u003d 2
Calculate the value of the formula y \u003d 2x + 3, if x \u003d -6
Calculate the value of the formula y \u003d 2x + 3, if x \u003d 4
Calculate the value of the formula y \u003d 2x + 3, if x \u003d 5
Calculate the value of the formula y \u003d 2x + 3, if x \u003d -3
Calculate the value of the formula y \u003d 2x + 3, if x \u003d 6
Calculate the value of the formula y \u003d 2x + 3, if x \u003d -1
Calculate the value of the formula y \u003d 2x + 3, if x \u003d -5
Calculate the value of the formula y \u003d 2x + 3, if x \u003d 0
Calculate the value of the formula y \u003d 2x + 3, if x \u003d - 2
Calculate the value of the formula y \u003d 2x + 3, if x \u003d 3
Calculate the value of the formula y \u003d 2x + 3, if x \u003d -4
Appendix 2.
Appendix 3.
(2 heel)In the cellular tariff "Smart.mini."Not only a subscription fee in the amount of 120 rubles, but also a fee for a conversation per minute with other operators of the Cellular Communication of Russia, each minute of conversation is equal to 2 rubles.
1. Calculate the fee for the phone within a month if we have conversations through the operator of another cellular communication 2 min, 4 min, 6 min., 10 min
Record the expression for calculating the board for the phone for 2min, 4 min, 6min, 10min.
Displays general formulas to calculate the board for the phone.
S \u003d 120 + 2 ∙ 2 \u003d 124rub.
S \u003d 120 + 2 ∙ 4 \u003d 128rub.
S \u003d 120 + 2 ∙ 6 \u003d 132rub.
S \u003d 120 + 2 ∙ 8 \u003d 136rub.
S \u003d 120 + 2 ∙ 10 \u003d 140rub.
S \u003d 120 + 2 ∙ T
Task number 2.
(2 heel)
Working with a textbook. Give the definition of the following concepts
Function -
Argument function -
Domain -
Value area -
This rule, with which for each value of an independent variable, you can find the only value of the dependent variable.
Independent variable.
These are all the values \u200b\u200bthat the argument takes.
This is the value of the dependent function.
Task number 3.
(4 people). In the card "Dependence of the board for the phone", mark the dot value of the board at 4 minutes, 6min, 8min, 10min. (Take values \u200b\u200bfrom Job number 1).
Attention! The value of the phone for the phone at 2min. already installed.
"Dependence of the board for the phone"
Determine the schedule area of \u200b\u200bdefinition and area of \u200b\u200bthe function value
Definition area - from 2 to 10
Value area - from 124 to 140
Appendix 4.
Appendix 5.
Sheet of self-esteem
Self-satisfactionCriteria for evaluating classmate by party
Evaluation of classmate (F. I.)
Formulation of the lesson, goals and objectives of the lesson.
Jasam was able to determine the topic, the purpose and task of the lesson - 2 b.
I was able to determine only theme 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 lesson tasks - 1 b.
Did not take part in determining the topic of the lesson, the purpose of the lesson, or the tasks of the lesson 0 b
What I will do to achieve the goal.
I myself identified how to achieve the purpose of the lesson - 1Ball.
I could not determine how to achieve the purpose of the lesson - 0 points.
He took part in planning actions to achieve the objective of the lesson - 1 b.
Did not take part in planning actions to achieve the objective of the lesson 0 b
Performance practical work paired with.
Participated in the work of the group - 1 point.
Did not participate in the group's work - 0 score.
Work in the Case Workgroup.
Participated in the work of the group - 1 point.
Did not participate in the group's work - 0 score.
Participated in the work of the group - 1 point.
Did not participate in the group's work - 0 score.
Perform the task with graphs of functions.
I made all the examples of my points myself.
Made less than half of the scores of the points.
I coped at the board with the task of 1 point.
I did not cope with the board with the task of 0 points.
Choosing a homework
3 points - chose 3 tasks out of 3, 2 points - chose only 2 rooms, 1 point - chose 1 task out of 3
Not Evaluated
Put yourself a rating: if you scored 8-10 points - "5"; 5 - 7 points - "4"; 4 - 5 points - "3".
Self-analysis of the lesson.
This lesson number 1 in the system of lessons on the topic "Function".
The purpose of the lesson is to form a function of a function, as a mathematical model for describing real processes. The main activities of the student is to repeat computational skills with overall expressions, the formation of primary submissions on the relationship between values, description of the concepts "function, dependent variable", "argument, independent variable", distinguish between dependencies functional dependencies in the form of a function of the function.
Developing: develop mathematical speech (use of special mathematical terms), attention, memory, logical thinking, draw conclusions.
Educational: to bring up the culture of behavior during frontal, group, steam room and individual work, form a positive motivation, bring up the ability to self-esteem.
By type, this lesson is a lesson for learning new knowledge, it includes seven stages. The first stage is an organizational, attitude to educational activities. The second stage is the motivation of educational activities for the formulation of the goals and objectives of the lesson "Communication between values. Function". The third stage is the actualization of knowledge, work in pairs. The fourth stage is the primary absorption of new knowledge, "case-technology", work in the group. Fifth stage - primary understanding check - individual work, Case protection. The sixth stage - the primary fixation - frontal work, discord examples of graphs of functions. Seventh Stage - information on the homework, instruction in its individual form 3 levels. The eighth stage is the reflection, summing up, filling the self-esteem sheet by students about personal achievements in the lesson.
With the motivation of students to the lesson, I wake up cases of life, where connections between values \u200b\u200bnot only in life, but also in algebra, and in physics, and in geography were considered. Those. The tasks were focused on creativeness of thinking, resourcefulness, to strengthen the applied direction of the course of algebra through consideration of examples of real dependencies between the values \u200b\u200bbased on the student experience, which helped to understand the material to be understood by all students.
I managed to meet in time. Time was distributed rationally, the rate of lesson is high. The lesson was easy to be easily, the students quickly turned into work, led interesting examples of dependencies between values. In the lesson, an interactive board was used accompanied with the presentation of the lesson. I think the purpose of the lesson is reached. As the reflection showed, students understood the lesson material. Homework did not cause difficulties. In general, I consider it a successful lesson.
