Enrolled bypassing exams. Even in our time, this riddle is considered one of the best ways to test attention and the logic of thinking.

Well, let's get started!

1. How many tourists live in this camp?
2. When did they come here: today or a few days ago?
3. Why did they come here?
4. Is it far from the camp to the nearest village?
5. Where does the wind blow: from the north or south?
6. What time of day is it?
7. Where did Shura go?
8. Who was on duty yesterday (say by name)?
9. What day of what month is today?

Answers:

• Four. If you look closely, you can see: cutlery for 4 people, and there are 4 names on the duty list.
• Not today, judging by the web between the tree and the tent, the guys arrived a few days ago.
• On the boat. There are oars near the tree.
• No. There is a chicken in the picture, which means that the village is somewhere nearby.
• From South. There is a flag on the tent by which you can determine where the wind is blowing from. There is a tree in the picture: on one side the branches are shorter, on the other longer. As a rule, at
• trees on the south side of the branch are longer.
• Morning. In the previous question, we determined where the north-south is, now you can understand where the east-west is, and look at the shadows that objects cast.
• He is catching butterflies. A net is visible from behind the tent.
• Kolya. Today, Kolya is looking for something in a backpack with the letter “K”, Shura is catching butterflies, and Vasya is taking pictures of nature (because a tripod from the camera is visible from the backpack with the letter “B”).
• So, today Petya is on duty, and yesterday, according to the list, Kolya was on duty.
• 8 August. Judging by the list, since Petya is on duty today, the number is 8. And since there is a watermelon in the clearing, it means August.

According to statistics, only 7% correctly answer all questions.

The riddle is really very complicated, in order to correctly answer all the questions you need to understand some aspects, and of course you need to connect logic and attentiveness. The riddle is complicated by a not very high-quality image. I wish you success.

Looking at the picture, answer the following questions:

1. How long have the guys been involved in tourism?
2. Are they familiar with home economics?
3. Is the river navigable?
4. In which direction does it flow?
5. What is the depth and width of the river at the next rift?
6. How long will the laundry take to dry?
7. How much more sunflower will grow?
8. Is there a tourist camp far from the city?
9. What transport did the guys get here?
10. Do they like dumplings in these places?
11. Is the newspaper up to date? (Newspaper dated August 22)
12. Which city is the plane flying to?

Answers:

• Obviously, recently: experienced tourists will not pitch a tent in a hollow.
• In all likelihood, not very much: they don’t clean the fish from the head, it’s inconvenient to sew on a button with too long a thread, it’s necessary to chop a branch with an ax on a block of wood.
• navigable. This is evidenced by the navigation mast standing on the shore.
• From left to right. Why? See the answer to the next question.
• The navigation sign on the river bank is set in a strictly defined way. If you look from the side of the river, then signs are hung downstream to the right, showing the width of the river at the nearest rift, and to the left - signs showing the depth. The depth of the river is 125 cm (rectangle 1 m, large circle 20 cm and small circle 5 cm), the width of the river is 30 m (large circle 20 m and 2 small circles 5 m each). Such signs are installed 500 m before the roll.
• Not for long. There is a wind: the floats of the fishing rods were carried against the current.
• The sunflower is obviously broken and stuck in the ground, since its "hat" is not facing the sun, and a broken plant will no longer grow.
• No further than 100 km, at a greater distance, the body antenna would be of a more complex design.
• The guys have, in all likelihood, bicycles: there is a bicycle wrench on the ground.
• No. They love dumplings here. The hut, the pyramidal poplar and the high altitude of the sun above the horizon (63° - in the shadow of the sunflower) show that this is a Ukrainian landscape.
• Judging by the height of the sun above the horizon, it takes place in June. For Kyiv, for example, 63° is the highest angular height of the sun. This happens only at noon on June 22. The newspaper is dated August - therefore, it is at least last year.
• None. The aircraft produces agricultural work.

Here is a problem in the 60s of the last century offered to solve the students of the second grade.

Looking at the picture, answer the following questions:

1. Is a steamboat going up or down the river?
2. What season is shown here?
3. Is the river deep in this place?
4. Is the harbor far?
5. Is it on the right or left bank of the river?
6. What time of day did the artist show in the drawing?

Answers:

• The wooden triangles on which the buoys are fixed are always directed against the current. The ship is sailing up the river.
• The figure shows a flock of birds; they fly in the form of an angle, one of its sides is shorter than the other: these are cranes. Flocking flight of cranes occurs in spring and autumn. From the crowns of trees on the edge of the forest, you can determine where the south is: they always grow thicker on the side that faces south. Cranes fly south. So, the picture shows autumn.
• The river in this place is shallow: a sailor, standing on the bow of the steamer, measures the depth of the fairway with a sixth.
• Obviously, the ship is approaching the pier: a group of passengers, taking their things, prepared to get off the ship.
• Answering the 1st question, we determined in which direction the river flows. In order to indicate where the right and where the left bank of the river is, one must stand facing downstream. We know that the ship is mooring at the wharf. It can be seen that the passengers prepared to go to the side from where you are looking at the picture. So the nearest pier is on the right bank of the river.
• On the beacons - lanterns; put them before evening and take off early in the morning. It can be seen that the shepherds are driving the flock to the village. From here we come to the conclusion that the figure shows the end of the day.

Looking at the picture, answer the following questions:

1. What time of year is this apartment shown?
2. What month?
3. Is the boy you see going to school now, or is he on vacation?
4. Does the apartment have running water?
5. Who lives in this apartment besides the father and son you see in the picture?
6. What is the profession of the father?

Answers:

• The apartment is shown in winter: a boy in felt boots; the stove is heated - this is indicated by an open air vent.
• Month of December: the last sheet of the calendar is open.
• The first 7 numbers are crossed out on the calendar: they have already passed. Winter holidays start later. So the boy goes to school.
• If the apartment had running water, then you would not have to use the washstand, which is shown in the figure.
• The dolls indicate that there is a girl in the family, probably of preschool age.
• A tube and a hammer for listening to patients indicate that the father is a doctor by profession.

Soviet riddles for logic: 8 questions for attentiveness

Another Soviet riddle, this one will be more difficult than the previous one. Only 4% of people can answer all 8 questions correctly.

Looking at the picture, answer the following questions:

1. What time of day is shown in the picture?
2. Does the drawing depict early spring or late autumn?
3. Is this river navigable?
4. In which direction does the river flow: south, north, west or east?
5. Is the river deep near the bank where the boat is parked?
6. Is there a bridge across the river nearby?
7. Is the railroad far from here?
8. Do cranes fly north or south?

Answers:

• Having examined the picture, you see that sowing is going on in the field (a tractor with a seeder and wagons with grain). As you know, sowing is done in autumn or early spring. Autumn sowing takes place when there are still leaves on the trees. In the picture, the trees and bushes are completely bare. It should be concluded that the artist depicted early spring.
• In spring, cranes fly from south to north.
• Buoys, that is, signs marking the fairway, are placed only on navigable rivers.
  The buoy is fixed on a wooden float, which is always directed at an angle against the flow of the river.
• Having determined by the flight of cranes where the north is, and paying attention to the position of the triangle with the buoy, it is not difficult to decide that in this place the river flows from north to south.
• The direction of the shadow from the tree shows that the sun is in the southeast. In the spring, on this side of the sky, the sun is at 8 - 10 o'clock in the morning.
• A railway conductor with a lantern is sent to the boat; he obviously lives somewhere near the station.
• The footbridges and stairs descending to the river, as well as a boat with passengers, show that a constant transportation across the river has been established at this place. He is needed here because there is no bridge nearby.
• On the shore you see a boy with a fishing rod. Only when fishing in a deep place can you move the float so far away from the hook.
  If you liked this riddle, then try another one

Soviet logic puzzle about the railway (near the road)

Looking at the picture, answer the following questions:

1. How long before the new moon?
2. Will the night come soon?
3. What time of year does the drawing belong to?
4. In which direction does the river flow?
5. Is she navigable?
6. How fast is the train moving?
7. How long has the previous train passed here?
8. How long will the car move along the railroad?
9. What should the driver prepare for now?
10. Is there a bridge nearby?
11. Is there an airfield in the area?
12. Is it easy for drivers of oncoming trains to slow down the train in this section?
13. Does the wind blow?

Answers:

• A little. The month is old (you can see its reflection in the water).
• Not soon. The old month is visible at dawn.
• Autumn. By the position of the sun, it is easy to figure out that the cranes are flying south.
• Rivers flowing in the Northern Hemisphere have a steep right bank. So the river flows from us to the horizon.
• navigable. Beacons are visible.
• The train is standing. The lower eye of the traffic light is lit - red.
• Recently. He is now at the nearest blocking area.
• The road sign indicates that there is a railroad crossing ahead.
• To braking. The road sign shows that there is a steep descent ahead.
• Probably there is. There is a sign obliging the driver to close the blower.
• In the sky, the trace of the plane that made the loop. Aerobatics are allowed to be done only not far from airfields.
• A sign near the railway track indicates that the oncoming train will have to climb up the slope. It will be easy to slow him down.
• Duet. The smoke of the locomotive spreads, but the train, as we know, is motionless.

These are the Soviet riddles for logic in pictures (riddles of the USSR for children). Did everyone get it right? - I don't think so! But it was still time well spent!

Write comments, perhaps there will be questions or new riddles from you.

All constructions in the process of graphical reckoning are performed using a laying tool:

navigation protractor,

parallel line,

caliper,

drawing compass with a pencil.

The lines are applied with a simple pencil and removed with a soft rubber band.

Take the coordinates of a given point from the map. Most accurately, this task can be performed using a measuring compass. To remove the latitude, one leg of the compass is placed at a given point, and the other is brought to the nearest parallel so that the arc described by the compass touches it.

Without changing the angle of the legs of the compass, bring it to the vertical frame of the card and put one leg on the parallel to which the distance was measured.
The other leg is placed on the inner half of the vertical frame towards the given point and the latitude reading is taken with an accuracy of 0.1 of the smallest division of the frame. The longitude of a given point is determined in the same way, only the distance is measured to the nearest meridian, and the longitude reading is taken along the upper or lower frame of the map.

Draw a point at the given coordinates. The work is usually performed using a parallel ruler and a measuring compass. The ruler is applied to the nearest parallel and one half of it is moved to a given latitude. Then, using a compass solution, take the distance from the nearest meridian to a given longitude along the upper or lower frame of the map. One leg of the compass is placed at the cut of the ruler on the same meridian, and with the other leg a weak prick is also made at the cut of the ruler in the direction of the given longitude. The injection site will be the set point

Measure the distance between two points on a map, or plot a known distance from a given point. If the distance between the points is small and can be measured with a single compass solution, then the legs of the compass are placed at one and the other points, without changing its solution, and placed against the side frame of the map at about the same latitude as the measured distance.

A large distance when measuring is divided into parts. Each part of the distance is measured in miles in the latitude of the area. You can also use a compass solution to take from the side frame of the map a "round" number of miles (10.20, etc.) and count how many times to put this number along the entire measured line.
At the same time, miles are taken from the side frame of the map approximately opposite the middle of the measured line. The remaining distance is measured in the usual way. If it is necessary to set aside a small distance from a given point, then it is removed with a compass from the side frame of the map and set aside on the laid line.
The distance is taken from the frame approximately at the latitude of a given point, taking into account its direction. If the distance to be set aside is large, then they are taken from the frame of the map approximately against the middle of the specified distance of 10, 20 miles, etc. and set aside the required number of times. From the last point measure the rest of the distance.

Measure the direction of a true course or bearing line plotted on a chart. A parallel ruler is applied to the line on the map and a protractor is attached to the cut of the ruler.
The protractor is moved along the ruler until its central stroke coincides with any meridian. The division on the protractor, through which the same meridian passes, corresponds to the direction of the course or bearing.
Since two readings are marked on the protractor, when measuring the direction of the laid line, one should take into account the quarter of the horizon in which the given direction lies.

Plot a true course or bearing line from a given point. When performing this task, a protractor and a parallel ruler are used. The protractor is placed on the map so that its central stroke coincides with some meridian.

Then the protractor is turned in one direction or the other until the stroke of the arc corresponding to the reading of the given course or bearing coincides with the same meridian. A parallel ruler is applied to the lower cut of the protractor ruler, and, having removed the protractor, move it apart, leading to a given point.

A line is drawn along the cut of the ruler in the desired direction. Move a point from one map to another. The direction and distance to a given point from a beacon or other landmark marked on both maps are taken from the map.
On another map, having plotted the desired direction from this landmark and plotting the distance along it, a given point is obtained. This task is combined

Tasks of this type include those in which all or part of the data is given in the form of graphical dependencies between them. In solving such problems, the following stages can be distinguished:

Stage 2 - to find out from the above graph, between which quantities the relationship is presented; find out which physical quantity is independent, i.e., an argument; what value is dependent, i.e., a function; determine by the type of graph what kind of dependence it is; find out what is required - to define a function or an argument; if possible, write down the equation that describes the given graph;

Stage 3 - mark the given value on the abscissa (or ordinate) axis and restore the perpendicular to the intersection with the graph. Lower the perpendicular from the point of intersection to the y-axis (or abscissa) and determine the value of the desired value;

Stage 4 - evaluate the result;

Stage 5 - write down the answer.

To read the graph of the coordinates means that from the graph one should determine: the initial coordinate and the speed of movement; write down the coordinate equation; determine the time and place of the meeting of the bodies; determine at what point in time the body has a given coordinate; determine the coordinate that the body has at the specified time.

Tasks of the fourth type - experimental . These are tasks in which, in order to find an unknown quantity, it is required to measure a part of the data empirically. The following workflow is suggested:

Stage 2 - to determine what phenomenon, the law underlies the experience;

Stage 3 - think over the scheme of experience; determine the list of instruments and auxiliary items or equipment for the experiment; think over the sequence of the experiment; if necessary, develop a table for recording the results of the experiment;

Stage 4 - perform the experiment and write the results in a table;

Stage 5 - make the necessary calculations, if required according to the condition of the problem;

Stage 6 - think about the results and write down the answer.

Particular algorithms for solving problems in kinematics and dynamics have the following form.

Algorithm for solving problems in kinematics:

Stage 2 - write out the numerical values ​​of the given values; express all quantities in SI units;

Stage 3 - make a schematic drawing (trajectory of motion, vectors of speed, acceleration, displacement, etc.);

Stage 4 - choose a coordinate system (in this case, you should choose such a system so that the equations are simple);

Stage 5 - to compose for a given movement the basic equations that reflect the mathematical relationship between the physical quantities shown in the diagram; the number of equations must be equal to the number of unknown quantities;

Stage 6 - solve the compiled system of equations in a general form, in letter notation, i.e. get the calculation formula;

Stage 7 - select a system of units of measure ("SI"), substitute the names of the units in the calculation formula instead of letters, perform actions with the names and check whether the result is a unit of measure of the desired value;

Stage 8 - Express all the given values ​​in the chosen system of units; substitute in the calculation formulas and calculate the values ​​of the required quantities;

Stage 9 - analyze the solution and formulate an answer.

Comparison of the sequence of solving problems in dynamics and kinematics makes it possible to see that some points are common to both algorithms, this helps to remember them better and apply them more successfully in solving problems.

Algorithm for solving problems in dynamics:

Stage 2 - write down the condition of the problem, expressing all quantities in units of "SI";

Stage 3 - make a drawing indicating all the forces acting on the body, acceleration vectors and coordinate systems;

Stage 4 - write down the equation of Newton's second law in vector form;

Stage 5 - write down the basic equation of dynamics (the equation of Newton's second law) in projections on the coordinate axes, taking into account the direction of the coordinate axes and vectors;

Stage 6 - find all the quantities included in these equations; substitute into the equations;

Stage 7 - solve the problem in a general way, i.e. solve an equation or system of equations for an unknown quantity;

Stage 8 - check the dimension;

Stage 9 - get a numerical result and correlate it with the real values ​​of the quantities.

Algorithm for solving problems for thermal phenomena:

Stage 1 - carefully read the condition of the problem, find out how many bodies are involved in heat transfer and what physical processes occur (for example, heating or cooling, melting or crystallization, vaporization or condensation);

Stage 2 - briefly write down the condition of the problem, supplementing with the necessary tabular values; express all quantities in the SI system;

Stage 3 - write down the heat balance equation, taking into account the sign of the amount of heat (if the body receives energy, then put the “+” sign, if the body gives it away - the “-” sign);

Stage 4 - write down the necessary formulas for calculating the amount of heat;

Stage 5 - write down the resulting equation in general terms with respect to the desired values;

Stage 6 - check the dimension of the obtained value;

Stage 7 - calculate the values ​​of the desired quantities.

CALCULATION AND GRAPHIC WORKS

Job #1

INTRODUCTION BASIC CONCEPTS OF MECHANICS

Basic provisions:

Mechanical movement is a change in the position of a body relative to other bodies or a change in the position of body parts over time.

A material point is a body whose dimensions can be neglected in this problem.

Physical quantities are vector and scalar.

A vector is a quantity characterized by a numerical value and direction (force, speed, acceleration, etc.).

A scalar is a quantity characterized only by a numerical value (mass, volume, time, etc.).

Trajectory - the line along which the body moves.

The distance traveled - the length of the trajectory of a moving body, the designation - l, SI unit: 1 m, a scalar (has a modulus but no direction), does not unambiguously determine the final position of the body.

Displacement - a vector connecting the initial and subsequent positions of the body, designation - S, unit of measurement in SI: 1 m, vector (has a module and direction), uniquely determines the final position of the body.

Velocity is a vector physical quantity equal to the ratio of the movement of the body to the time interval during which this movement occurred.

Mechanical motion is translational, rotational and oscillatory.

Translational motion is a motion in which any straight line, rigidly connected with the body, moves while remaining parallel to itself. Examples of translational motion are the movement of a piston in an engine cylinder, the movement of ferris wheel cabs, etc. During translational motion, all points of a rigid body describe the same trajectories and have the same speeds and accelerations at each moment of time.

rotational motion of an absolutely rigid body is such a motion in which all points of the body move in planes perpendicular to a fixed straight line, called axis of rotation, and describe circles whose centers lie on this axis (rotors of turbines, generators and engines).

vibrational motion is a motion that periodically repeats itself in space over time.

Reference system is called the totality of the body of reference, the coordinate system and the method of measuring time.

Reference body- any body, chosen arbitrarily and conditionally considered to be motionless, relative to which the location and movement of other bodies is studied.

Coordinate system consists of directions selected in space - coordinate axes intersecting at one point, called the origin and the selected unit segment (scale). The coordinate system is needed for a quantitative description of the movement.

In the Cartesian coordinate system, the position of point A at a given moment of time with respect to this system is determined by three x, y and z coordinates, or radius vector .

Trajectory of movement material point is the line described by this point in space. Depending on the shape of the trajectory, the movement can be straightforward and curvilinear.

The motion is called uniform if the speed of a material point does not change over time.

Actions with vectors:

Speed- a vector quantity showing the direction and speed of movement of the body in space.

Every mechanical movement has absolute and relative character.

The absolute meaning of mechanical motion is that if two bodies approach or move away from each other, then they will approach or move away in any frame of reference.

The relativity of mechanical motion is that:

1) it is meaningless to talk about motion without specifying the reference body;

2) in different reference systems, the same movement may look different.

The law of addition of speeds: The speed of a body relative to a fixed frame of reference is equal to the vector sum of the speed of the same body relative to a moving frame of reference and the speed of a moving frame relative to a fixed one.

test questions

1. Definition of mechanical movement (examples).

2. Types of mechanical movement (examples).

3. The concept of a material point (examples).

4. Conditions under which a body can be considered a material point.

5. Translational movement (examples).

6. What does the reference system include?

7. What is uniform motion (examples)?

8. What is called speed?

9. The law of addition of speeds.

Complete the tasks:

1. The snail crawled straight for 1 m, then made a turn, describing a quarter of a circle with a radius of 1 m, and crawled further perpendicular to the original direction of movement for another 1 m.

2. A moving car made a U-turn, describing half a circle. Make a drawing on which to indicate the path and movement of the car in a third of the turnaround time. How many times is the path traveled in the specified time interval greater than the modulus of the vector of the corresponding displacement?

3. Can a water skier move faster than a boat? Can a boat move faster than a skier?

Often a graphical representation of a physical process makes it more visual and thus facilitates understanding of the phenomenon under consideration. Allowing sometimes to significantly simplify calculations, graphs are widely used in practice to solve various problems. The ability to build and read them today is a must for many professionals.

We refer tasks to graphic tasks:

• on the construction, where drawings, drawings are very helpful;
• schemes solved using vectors, graphs, diagrams, diagrams and nomograms.

1) The ball is thrown from the ground vertically upwards with initial speed v about. Plot the velocity of the ball as a function of time, assuming that the impacts on the ground are perfectly elastic. Ignore air resistance. [solution ]

2) A passenger who was late for the train noticed that the penultimate car passed him for t 1 = 10 s, and the last one for t 2 \u003d 8 s. Considering the movement of the train is uniformly accelerated, determine the time of delay. [solution ]

3) In a room high H a light spring is attached to the ceiling at one end with stiffness k, which in the undeformed state has a length l about (l about< H ). On the floor under the spring place a bar with a height x with base area S, made of material with a density ρ . Construct a graph of the dependence of the pressure of the bar on the floor from the height of the bar. [solution ]

4) The bug crawls along the axis Ox. Determine the average speed of its movement in the area between the points with coordinates x 1 = 1.0 m and x 2 = 5.0 m, if it is known that the product of the bug's velocity and its coordinate all the time remains a constant value equal to c \u003d 500 cm 2 / s. [solution ]

5) To the bar mass 10 kg located on a horizontal surface, a force is applied. Given that the coefficient of friction is equal to 0,7 , define:

• friction force for the case if F = 50 N and directed horizontally.
• friction force for the case if F = 80 N and directed horizontally.
• construct a graph of the dependence of the acceleration of the bar on the horizontally applied force.
• What is the minimum force required to pull on the rope to move the block evenly? [solution ]

6) There are two pipes connected to the mixer. On each of the pipes there is a tap that can be used to regulate the flow of water through the pipe, changing it from zero to the maximum value. J o = 1 l/s. Water flows in pipes with temperatures t 1 \u003d 10 ° C and t 2 \u003d 50 ° C. Plot the maximum flow of water flowing out of the faucet versus the temperature of that water. Ignore heat losses. [solution ]

7) Late in the evening a young man is tall h walks along the edge of a horizontal straight pavement at a constant speed v. On distance l There is a lamppost from the edge of the sidewalk. Burning lantern fixed at a height H from the surface of the earth. Plot a graph of the dependence of the speed of movement of the shadow of a person's head on the coordinate x. [solution ]

1

1 Branch of the Federal State Budgetary Educational Institution of Higher Professional Education "Ural State Transport University"

The training of technical specialists includes a mandatory stage of graphic training. Graphic training of technical specialists takes place in the process of performing various types of graphic work, including when solving problems. Graphic tasks can be divided into different types, according to the content of the task conditions and according to the actions that are performed by the trainees in the process of solving the problem. Development of a typology of tasks, principles of their classification, subdivision of tasks into different types for their effective use in the learning process, development of task characteristics based on the classification of graphic tasks. In order to develop the motivation for graphic training of students, it is necessary to involve creative tasks in the educational process, which involve the inclusion of elements of creative search in the learning process. Systematization of the creative interactive task developed by us for the development of vitagen-oriented graphic tasks, classification of the types of task and the product of its implementation into groups in accordance with certain characteristics: according to the content of the task, according to actions on graphic objects, according to the coverage of educational material, according to the method of solution and presentation of results solutions, according to the role of the task in the formation of graphic knowledge. A comprehensive systematization of graphic tasks of various levels of mastering the material makes it possible to comprehensively develop the graphic abilities of students, thereby improving the quality of training of technical specialists.

levels of assimilation of graphic knowledge

the plot of a vitality-oriented task

performed when solving graphic tasks

actions and operations

classification of graphic tasks

task and solving systems of a graphic problem

creative interactive tasks for the development of vitagen-oriented tasks

graphic task of classical content

1. Bukharova G.D. Theoretical foundations of teaching students the ability to solve physical problems: Proc. allowance. - Ekaterinburg: URGPPU, 1995. - 137 p.

2. Novoselov S.A., Turkina L.V. Creative tasks in descriptive geometry as a means of forming a generalized orienting basis for teaching engineering graphic activity. Obrazovanie i nauka. Proceedings of the Ural Branch of the Russian Academy of Education. - 2011. - No. 2 (81). – pp. 31-42

3. Ryabinov D.I., Zasov V.D. Problems in descriptive geometry. - M .: State. Publishing House of Technical and Theoretical Literature, 1955. - 96 p.

4. Tulkibaeva N.N., Fridman L.M., Drapkin M.A., Valovich E.S., Bukharova G.D. Solving problems in physics. Psychological and methodological aspect / Under the editorship of Tulkibaeva N.N., Drapkina M.A. Chelyabinsk: From ChGPI "Fakel", 1995.-120p.

5. Turkina L.V. Collection of tasks on descriptive geometry of vitality-oriented content / - Nizhny Tagil; Yekaterinburg: UrGUPS, 2007. - 58 p.

6. Turkina L.V. Creative graphic task - the structure of content and solutions // Modern problems of science and education. - 2014. - No. 2; URL: http://www..03.2014).

One of the main components of the training of technical specialists is practical educational activities, including activities to solve educational problems. Solving problems of various types makes it possible to form skills and abilities, solve educational problems, develop readiness for the development of creative search in the process of professional activity of future specialists.

A variety of types of tasks that are offered for students to solve broadens the horizons of students, teaches the practical application of knowledge and motivates their independent learning activities. In order to apply the whole range of educational tasks in a particular discipline, it is necessary to have an idea of ​​all their diversity, classify them according to one or another feature and purposefully use them to form the personality traits of future specialists that are in demand in professional activities.

One of the main components of the training of technical specialists is graphic training, which includes a practical component in the form of solving graphic problems. Solving graphic problems is the foundation for the formation of drawing skills, knowledge of projection theory, rules for the design of graphic images. The purpose of the graphic task is to create a graphic image of a given object, built in accordance with the rules of the Unified Design Documentation System, or to transform or supplement a given graphic image of an object. Bukharova as a complex didactic system, where components (task and decision systems) are presented in unity, interconnection, interdependence and interaction, each of which, in turn, consists of elements that are in the same dynamic dependence.

The task system, as is known, includes the subject, conditions and requirements of the task, the solving system includes a set of interrelated methods, methods and means of solving the problem.

The task system of a graphic task is determined by its content, which can be classified according to the sections of graphic disciplines used (for example, descriptive geometry). To systematize the types and types of graphic tasks, it is necessary to develop the foundations, principles and build a system for dividing them into groups. To do this, we propose the concept of typology (classification) of graphic tasks developed by us. The classification of tasks developed by us is similar to the classification of tasks in physics, but it has its own characteristics characteristic of teaching graphic disciplines, which are characterized not only by mastering a specific area of ​​knowledge, but also by developing a skill for their application in the development of graphic documentation.

The task condition as an incoming element of the task system determines the student's further actions and allows classifying graphic tasks by types of graphic actions on objects.

According to the types of objects on which graphic actions are performed, they can be as follows:

• problems with flat objects (point, line, plane);
• problems with spatial objects (surfaces, geometric bodies);
• problems with mixed objects (point, line, plane, surface, geometric body).

According to the coverage of the educational material of descriptive geometry, tasks can be classified into homogeneous (one section) and mixed (several sections) polygenic.

• tasks with a text condition;
• tasks with a graphical condition;
• tasks with mixed content.

According to the sufficiency of information, tasks are classified into:

• tasks defined;
• search tasks.

The problem solving process determines the solution system and allows classifying graphical problems according to the following parameters and features of the process of performing actions on problem objects:

By types of graphical operations on objects, tasks can be as follows:

• tasks to determine the position of an object in space relative to the projection planes and change its position;
• tasks to determine the relative position of objects;
• metric tasks (determining the natural size of objects: the dimensions of linear quantities, shapes)

According to the actions aimed at the subject, the tasks can be:

• execution tasks;
• transformation tasks;
• design tasks;
• proof tasks;
• matching tasks;
• research objectives.

According to the method of solving graphic problems can be:

• tasks solved graphically;
• problems solved by analytical (computational) method;
• tasks that are solved in a logical way with a graphic design of the solution.

According to the use of means of solving graphic problems are divided into:

• tasks solved by manual means;
• tasks solved with the use of information technologies.

According to the number of solutions, the problem can be:

• problems with one solution;
• problems with multiple solutions;
• problems with no solutions.

According to the role of tasks in the formation of graphic knowledge, they can be classified into tasks that form:

• graphic concepts (concepts) and terms;
• skills and abilities to apply the projection method;
• skills and abilities to apply methods for converting a drawing;
• skills and abilities to apply methods for determining the location of an object;
• skills and abilities to apply methods for determining the common parts of two or more objects (crossing lines);
• skills and abilities to apply methods for determining the size of an object;
• skills and abilities to apply methods for determining the shape of an object;
• skills and abilities of application of methods for determining the development of an object.

For example:

Task No. 1. Construct point B on the diagram, which belongs to the horizontal projection plane, is 40 mm away from the frontal projection plane, and 20 mm further from the profile projection plane than from the frontal one.

The task is homogeneous, its content belongs to the section "Point and Line" of the discipline "Descriptive Geometry". The task requires a graphical action on a flat object, the condition of the task is presented in text form, the task has a sufficient amount of information and does not apply to search ones. This is a classic example of the task of determining the position of an object in space relative to projection planes and depicting it in a drawing (diagram). Task - the execution of certain actions specified by the condition of the task; This problem can only be solved graphically. It can be solved both with the help of manual means and with the help of a CAD computer program, the problem has one solution. This task forms graphic concepts and terms (the name and position of the projection plane, the concept of "point", the coordinates of the point), the skills and abilities of applying the projection method - projecting a point.

The solution to the problem is shown in Figure 1.

Task number 2. Construct a development of the surface B, containing the projections of the points A and C, and intersecting with the surface K - a cylinder of the front-projecting direction, the axis of which intersects the axis of the surface B.

Task No. 2 is polygenic, as it combines the following sections: "Point in the projection system", "Intersection of surfaces", "Deployment of curved surfaces". This is a problem with mixed objects (points, surfaces), the condition of the problem also has a mixed (complex) content, consisting of a text and a graphic part. The condition of the problem is not completely defined, since the cylinder crossing the given surface B does not have a diameter and its position is not defined in the drawing. This is a task for determining the relative position of objects and determining the surface development, that is, an execution task that can be solved graphically, both manually and using information technology. The task has many solutions and forms graphical concepts - a point, surfaces of revolution (cone, cylinder), skills in applying methods for determining the common parts of objects (cutting planes method) and skills in constructing a sweep of surfaces of revolution.

The solution to problem No. 2 is shown in Figure 3.

The process of solving the graphic problem, given above, illustrates the peculiarity of teaching graphic disciplines, which consists in the fact that geometric objects in projections and graphic constructions are difficult for mastering by junior students, yesterday's schoolchildren who have a minimum level of graphic training due to the fact that the drawing course has been translated in alternative courses. To motivate graphic cognition, reduce the abstractness of educational material, some teachers proposed tasks with materialized objects and tasks for developing tasks of vitality-oriented content.

The classification of creative vitality-oriented tasks is similar to the classification of graphic tasks of classical content, but has a number of differences determined by the fact that the task system of a creative task is a task for developing the task itself. This is information that determines the direction of the student's further educational activities, the content of the graphic module, within which a graphic task can be developed, but does not limit the scope of the knowledge of the subject and the creative imagination of the student.

• tasks are homogeneous (one topic);
• mixed tasks (several sections).

According to the requirements for the content of the task can be:

• tasks that specify the requirements for the content of the task;
• tasks of free choice of the content of the task (task on the above topic).

According to the requirements for the selection of material objects, the content of the task can be:

• tasks with obligatory use of objects of vital experience;
• tasks with the obligatory use of objects of professional activity;
• tasks with the obligatory use of interdisciplinary knowledge;
• tasks without special requirements for task objects.

According to the method of searching for means of solving the problem defined in the task for developing the problem, problems can be classified into:

• free search tasks;
• tasks using methods of activating thinking;
• tasks solved by analogy with the standard task: replacing an abstract object with a materialized object.

For example, a task for developing a task can be formulated as follows:

Develop a task in descriptive geometry, applying the knowledge of the topic "Projection of a point, a straight line" in a real life situation, having previously studied the theoretical positions and considered the tasks of the classical content. When compiling the problem, use the material analogues of geometric objects (point, line).

The task is homogeneous, not putting forward any requirements to the content of the task being developed, or to the nature of the objects used in the task, or to the method of searching for material analogues of geometric objects.

Task execution example:

The miner descended into the mine on an elevator to a depth of 10 m, walked along the tunnel directed along the X axis to the right for 25 m, turned 90 ° to the left and walked along the tunnel directed along the Y axis for another 15 m. Construct a diagram of a point that determines the location of the miner. The point of intersection of the earth's surface with the elevator shaft is taken as the origin of the coordinate axes. Take the elevator axis as the Z axis.

Figure 4 shows the horizontal projection of the point A-A1 and the frontal projection of the point A-A2, characterizing the location of the object, which is located below the ground level, which we took as the horizontal projection plane.

The content of the developed task determines the actions to solve the problem and allows classifying creative vitagenically oriented tasks, as well as tasks of classical content, by types of geometric operations on objects, by the scope of the educational material of the graphic discipline, by the type and content of the task conditions, by actions aimed at the subject of the formulated problem, by the sufficiency of information contained in the developed condition of the problem, by the method of searching for means of solution.

The main difference between a vitagenic-oriented creative task and classical graphic tasks in descriptive geometry is the presence of a storyline based on a technical problem solved by means of descriptive geometry. Vitagen-oriented task, first of all, is a story about any sphere of human activity, in which methods and methods of graphic disciplines are applied. The creative search of students in the development of vitality-oriented tasks is not limited to: technical problems of everyday life, plot development using the knowledge of other disciplines, the use of professional knowledge.

According to the storyline of the task conditions, they can be considered as:

• tasks using everyday situations for the plot of the task;
• tasks using the production technical situation for the plot of the task;
• tasks using a historical plot;
• tasks using knowledge from other areas to develop the plot of the task (geography, biology, chemistry, physics);
• tasks using literary plots;
• tasks with the use of folklore stories.

The solution of the formulated task is an integral part of the tasks for the development of the task; the solvability of the developed task is a criterion for the correctness of the solution of the task. The solution process also makes it possible to classify the developed problems according to some criteria. For example, according to the use of means for solving a problem, there can be:

• solved by graphic manual means;
• solved with the use of information technology;
• solvable analytically (calculations);
• solved by combined means.

Vitagen-oriented tasks compiled as a result of the solution can be classified in the same way as classical graphic tasks according to the number of solutions and the role of tasks in the formation of graphic knowledge (the classification method is given above).

For example, a student has developed the following problem:

The nail is driven into the wall to a depth of 100 mm at a height of 500 mm. Construct a diagram of a straight line segment represented as a nail if its length is 200 mm.

The wall is the V plane, the floor is the H plane. Take the W plane arbitrarily. Specify visibility.

Fig.5. The solution of the problem

The given task refers to tasks with flat objects, homogeneous in terms of determining the position of the object relative to the projection planes, the task of execution, the task has an incomplete amount of information for the image of the object, since the location of the nail relative to the profile plane of the projection (x coordinate) is not indicated and, therefore, has a set solutions. The solution of this problem can only be graphical and performed both manually and using information technology. The task forms the concept of a projecting line and the position of geometric objects in the 1st and 2nd quadrants. The information presented in the task is part of the student's life experience, which demonstrates in practice the front-projecting straight line and helps to master the topics of projection of flat objects. A complete description of the task from the point of view of the classification of graphic tasks allows you to effectively use it in the educational process.

After analyzing various types of graphic tasks and determining the basis for their systematization and classification, we can conclude the following:

Teaching graphic disciplines requires the mandatory introduction of the practical component of the educational process, which forms the skills of graphic activity. Practical graphic activity in the learning process consists in solving graphic tasks covering various sections of graphic disciplines, tasks of various levels of complexity, designed to master various graphic concepts, actions and operations that form knowledge of various levels. To achieve this, it is necessary to use the entire range of graphic tasks: from simple ones that form the reproductive level of knowledge to creative tasks with elements of scientific search, suggesting a productive level of assimilation of graphic knowledge. Systematization of tasks in graphic disciplines makes it possible to effectively and correctly use various types of tasks at different stages of the educational process, coordinate the graphic activities of students of various levels of training and create conditions for their motivational and creative activity and sustainable interest in graphic disciplines, thereby enhancing their independent graphic activity. and improve the quality of graphic preparation.

Reviewers:

Novoselov S.A., Doctor of Pedagogy, Professor, Director of the Institute of Pedagogy and Childhood Psychology, Ural State Pedagogical University, Yekaterinburg;

Kuprina N.G., Doctor of Pediatric Sciences, Professor, Head of the Department of Aesthetic Education, Ural State Pedagogical University, Yekaterinburg.

Bibliographic link

Turkina L.V. CLASSIFICATION OF GRAPHIC TASKS // Modern problems of science and education. - 2015. - No. 1-1 .;
URL: http://science-education.ru/ru/article/view?id=19360 (date of access: 07/12/2019). We bring to your attention the journals published by the publishing house "Academy of Natural History"