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Case-lesson «The sense of space»
Case-lesson «The sense of space»

Category: Science, nature and man

The level (grade): 7 +

Subject: Natural phenomena

Objective: To learn about the sense of space in different reference systems (psychological, physical, information, space, etc). To learn the basic of orientation in space, and how to develop the sense of space.

What information is waiting for me here?

  • What is the personal space? What should it be?
  • How do animals navigate in space?
  • How to navigate in outer space.
  • What is the size of information space? How to navigate it.
  • What fundamental knowledge and practical skills will be useful to me?
  • Some specialists from different fields and industries exploit the sense of space. Who are they?
8 scans of the subjects, phenomena and practices:

Try to close your eyes. Then imagine what are you surrounded by? Try to make few steps. Have you managed? Developing your sense of space depends on success of the experiment. This aspect of space perception can be trained; senses can replace or complement each other.


Do you let people get close to you? Pay attention to it when the next time you will talk to someone. It is your personal space. Besides, you have the information space around. You cannot touch it, but the the ability to navigate in it is not less important in the modern world than the skills of map reading for the traveler.

Let us immerse in the sense of space to make own personal navigator!

Let us explore the sense of space to broaden own horizons!


The sense of space depends on how well we navigate in space. If we do not consider space on a cosmic scale, but in relation to our planet, which boundaries have been already investigated? What this "space" is limited by?

If we talk about depth, the investigated depth will be like this:

If we try to limit height, the picture will be like this:

In addition to the "top" and "bottom», there are corners of the world. What are they? These are the four main geographical areas: South, North, West, and East.


What life hacks associated with orientation in space can geography tell about?


All those are ways to navigate the terrain. However, sometimes you need to work with a map or plan first, and then receive information.

First, you need to choose the "right" map, because maps can be for different purposes. For example: road maps for driving on highways and country roads; tourist maps for sightseeing; topographic maps for travelers; aeronautical maps or maps for pilots, which shows air routes, areas of planting, as well as monuments and buildings etc.

Google Map is the special electronic map, which allows you to see the image as on a traditional paper map, to see it because of aerial photography and "real" image on the panoramic images of the terrain. It is possible to plot a route and choose from several options.


However, if the electronic map is not available, then you need to navigate the usual map skillfully. Therefore, you need to check the orientation of the selected map. North is at the top. Sometimes the North can be depicted using the "compass rose" (the asterisk denoting the directions on the compass). Alternatively, the North direction can be designated by amendment at the map.

The next step is to set the map scale. The scale of the map is distinguished by size. Find the scale – usually it is located on the side or bottom of the map. It will look something like 1:100 000 – that is one unit on the map is equivalent to 100,000 units in reality. Depending on the scale, you should use map this way:

• Map, scale 1:25 000 scale for hiking

• Map, 1: 190 000 for driving

• Map, scale 1:24 000 000 for round-the-world travel

To determine how far your destination is, use a ruler and scale: if the scale of your map is 1:250,000, and the distance from point A to point B is 15 cm, then the total distance will be 15 * 250 000 = 3 750 000 cm. One kilometer is 100,000 cm, therefore the distance from point A to point B is 3 750 000:100 000 = 37.5 km.

If you plan to travel a significant distance, consider longitude and latitude. Latitude is measured in degrees to the distance North or South from the equator.

Longitude is measured in degrees depending on the distance to East or West from the line Gringo Meridian. The latitude is presented in figures at the side of the card. Longitude is presented in figures at the top and bottom of the map.


The contour lines are an important hint on the map. They show how high or low the level of Earth is. Each line represents a standard height above the sea level. When contour lines are close to each other, this means that the slope angle is steep (the closer they are the steeper becomes the inclination angle). When contour lines are spaced from each other at a considerable distance, the slope is flat, therefore, the farther apart they are, and the more flat the land is on the map.

Read the map legend carefully: the so-called legend with transcript is on each map and plan.


Did you use maps? How well did you do it? Try to make your own "Traveler's guide" about using maps and land navigation.


Where are top, bottom, and right, left in space? How can we navigate in this infinite space and what should we take for a reference point?

Even our planet can be regarded as a body that moves in space, such a huge spaceship:

Scientists of German's Max Planck institute works on the problem of navigation – orientation in space.

Orientation/navigation system offered by these scholars provides orientation by x-ray pulsars. Pulsars are neutron stars that are rotating very fast. They send powerful electromagnetic signals that have a certain frequency, specific for each pulsar known to humanity.

Only three pulsars – beacons are needed for orientation. When two signal relative to the third signal change is it possible to make conclusions about the position of the ship in outer space and routes.


Think about other ways of orientation in space that could be offered to astronauts.


How close can a stranger approach you? Moreover, what about friends or relatives? This distance is your "personal space". What is it? Where do we get this distance that we perceive as comfortable or safe?

The scientists of Caltech (USA) have answers. In 2009 they found out that a sense of personal space and the discomfort of the too close presence of another person is determined by the work of specific area of the brain – amygdala.


These data can be used for studying and treating autism and other mental disorders.

Scientists have already known the amygdala as the brain region associated with strong negative emotions – anger and fear. Experts of Caltech made their discovery thanks to the work with a unique patient. She is 42-year-old woman with extensive bilateral lesions of the amygdala. Worldwide, there are only a few people with such severe disorders in the structure of this part of the brain.

This woman is hard to recognize the threat and fear in the facial expressions of the people around her. She cannot identify clearly who she can trust and who cannot. In addition, she exhibits over-friendliness toward all without exception people around her. She crosses the line that people call a "personal space" too easily.


The size of personal space is very different in communities of people united by different cultures. The most obvious difference is apparent when comparing Western countries with Eastern. Scientists believe that the formation of the concept of "personal space" under the influence of personal experience and cultural communication between people is also a part of the amygdala.

In addition, the same part of the brain can adapt personal space, if you get in a precarious situation or are in a foreign country with a different culture of communication for a long time.

Claustrophobia is the result of exaggerated sense of personal space that was brought to a painful condition. Researchers of University of London made such conclusion. Such people have to have very significant personal space and its action extends to inanimate objects, even entire rooms and buildings.


Can you train and develop the sense of space, ability to navigate in space? You can! You just need to use a different technique that we share with you:



What is your personal space? Do you think whether you need to train it? Do you do any sports or other activities that train the orientation in space?


The sense of space is inherent not only to man. All living things have it. Fish that migrate for spawning are guided over the deep. In addition, they choose the path depending on the temperature and salinity of the water and other factors. For example, all adult individuals of European and American populations of river eels leave the river and float a distance greater than 5 thousand kilometers every year. They go to the Sargasso Sea, located in the center of the Atlantic.


To determine the correct direction of movement, animals have to determine its position in the earth reference points. Special senses can measure gravity and the Earth's geomagnetic field, transfer this information to the brain and determine what muscle movement is needed to change direction.

Permanent, clearly visible points of the earth’s landscape guide many animals during migrations. Birds fly along the rivers and shores of seas and oceans. Some birds and frogs can navigate using the stars and, like humans, they can identify the North with the North Star and the South with the help of the Southern Cross. Pigeons have not only great vision, but also well-developed sense of smell. For example, toads are guided by the stars.


According to scientists, animals also use the magnetic field lines. For example, whales. This explains the ejection of whales on the coast.

Birds often navigate using the geomagnetic field of Earth. At the dark night, with heavy clouds, when you cannot see the stars or any other guidelines, birds can find the right direction and sticking to it all the time.


Pair of Emperor penguins male and female are at sea far enough from each other. However, with the onset of the breeding period birds follow in the same direction and meet, reaching the ultimate goal of the journey. Most migratory birds are able to sense the Earth's geomagnetic field. According to the researchers, "Device" that receives magnetic lines is the circulatory system. There are red blood balls in the blood of animals that contain iron, and whole blood is an excellent electrolyte.

Sometimes echolocation comes to help the animals. Bats emit sounds of very high frequency. These sounds are reflected from obstacles and back to the animal, which hears it because of large ears.


Due to the precise system of orientation, animals define their position in the dark perfectly. They can bypass any obstacle and catch night flying insects such as moths as food. Moreover, butterflies, in turn, create special "barriers" to mislead the animal.


What other ways of orientation in space using by animals do you know?


Great sense of space is extremely important for artists. After all, in their power is to create "volume" or even "moving" image, full of life and the game of light and shadow using a flat canvas. How can it be achieved?

The particular importance of space starts to be during the Renaissance. Artists began to use perspective. What is it? Perspective is a process of painting volume objects on a plane or any other surface, taking into account their spatial structure and distance that separates their parts from the observer.

In the ancient world, perspective was replaced by a tiered arrangement of objects in a composition or by a combination of frontal and profile views.


In the middle ages, the area had a flat concept. It was perfectly reflected in painting. For example, the Dutch artists who followed the traditions of the Gothic, painted the high horizon. The surface of Earth rose steeply. It did not give the illusion of depth, but the plane. For example, the "Flemish Proverbs" (1559) painted by Pieter Bruegel. It was made with observance of the Gothic tradition:


The Renaissance "brings to the stage" linear perspective. The background (mostly dark to create depth of space) and highlighting of some important details become important.

Look at linear perspective in a simple figure:


Look at the "Last supper" painted by Leonardo da Vinci. The table is placed parallel to the picture plane; all the vanishing points of the lines are located in the center – in the eyes of Christ (or behind him). It creates the dramatic effect of the picture:


Oblique prospect came to replace the linear prospect. It had to add a picture some dynamism and movement. For a simple image it looks like this:


In addition, here is another version of the "Last supper" painted by Tintoretto who used oblique prospect:


The "fashion for the prospect" was changed; the location of the horizon in the paintings was changed. Each artist brings his own vision and ideas into the heady world of colours and light.


Maurits Cornelis Escher was able to master perspective, space and symmetry extremely skillfully. His paintings, lithographs and engravings are not just images, but the artist's desire to explore the psychology of three-dimensional objects perception.


The sense of space, of right, of the "best" prospect is important not only for paintings but also for photos. Possession of perspective changes an ordinary photographer into profession, artist.

There are some touches to the photo perspective:

A special kind of "space creating" is the creation of panoramas. Panoramic prospect gives you a view of all the surroundings – 360 degrees. Here is the resource that allows us to consider the views of different "corners" of Earth www.panoram.info.



Try to draw a simple object – a pen, a book, a gum using linear and oblique perspective. Have you done? Which image do you like more? Why?


The sense of space, the ability to "feel and read" it is the talent that artists need as well as professionals from other industries. Is a pilot an artist? Overall, he "reads and uses the space.

In this case "bottom-top", "right-left" are not important so much, but the deflection angle and the correction to the wind!

What is the correction to the wind? It is used not only by pilots, but also by snipers.

Side correction (the correction to the wind) is changes in the trajectory of a body subject to the action of the wind.

The purpose and object that have to be on it can be seen as the vertices of the triangle. Then, mathematically:


On the other hand, the tree on the rope moves like a mathematical pendulum. It is rejected obeying the law of Huygens:


That is, for the cable length of 25 m the period of oscillation will be 50 s (try to check)! In addition, if you note the time of deviation of the rope in the video, it is possible to calculate the period and to establish the length of the cable.

However, you need to consider the forces acting on the system "rope – spruce", as well as kinetic and potential energy of this system:


That is, for such filigree work it is necessary to consider the deviation of the cable, the force of gravity and the force of cable tension, speed of tree on the rope.


Here is a collection of mathematical and physical laws lying at the basis of the sense of space for the pilot from the video!


What another professions do you know where the sense of space is important? Why?


In addition to space that we can see and feel around, there is another space we are immersed in every day. It is information space. The information space is associated with human activity; it is a product of it.


The Internet is the embodiment of modern information space. How much information does it contain, or how much does the Internet "weigh"?

For computer even this small piece of text is the set of ones and zeros. Each unit of this code is depicted 40,000 electrons. The article (25 kilobytes) "requires participation" of 4 billion electrons. If we consider the mass of the electrons of 9.11*10 ^-28 g, then we need to spent 36,44* 10^-19 g of the computer "memory".

However, according to scientists most of information is the information exchange (traffic): video – 59%, music – 33 %, 9 % - letters and articles. In sum, this information is 40 petabytes (40*10^15 bytes). If we count this value to the electrons involved in memory, we get 0,0057 mg. Nevertheless, this is only a part of what is sent, which is only 75 %!

Other researchers conducted an analytical review of the Internet structure and they believe that it contains more than 500 billion gigabytes.

In any case, these fantastic numbers are difficult for not only an ordinary user, but also professional. Therefore, systems of orientation in the information environment are developed, especially the Internet.

Scientists of the University of California in San Diego have created a mathematical model that describes a complex network. They called it "Hidden space". It allows you to determine how the individual network nodes communicate among themselves without an accurate knowledge of the whole picture of the network.


This approach is similar to the social-psychological theory of "six degrees of separation", which states that all people are familiar with each other at least through a chain of six other people.

Such a model will be useful in population of genetic studies, because genome is a set of difficult associated genetic information.


How often do you send or download files? Conduct a mini-study: analyze what percentage of the text information, videos, images and music are in this information. Whether your percentage similar to the findings of scientists?


Work with the space, the sense of space is an important skill and competency for designer. How is it possible to set everything you need in the small room to make it comfortable and beautiful? This dilemma confronts designers in many countries, because the population is growing as well as living area.

There is no universal recipe, but there are many tricks and tips.


In addition, there are a few basic tips that can be used for the arrangement of space both large and small spaces:


Try yourself in the role of the designer – try to arrange the furniture in the room (4 m by 4 m):


Acceleration and interactive methods
1. "Distance to object". The task is conducted at the beginning of the case-lesson.


The essence of the task: the teacher selects an object in the classroom (a desk, a chalkboard, a chair, etc) and proposes students to determine the distance to it in meters. The students write their own versions. Then they choose someone for "verification". The selected student measures the length of the foot and walks to the object. The number of steps multiplied by the length of the foot will give the distance to the object.

The students, who estimated the distance to the object as less, become the first team. Those who "overestimate" the distance become the second team.


The purpose: To include "fantasy", to mobilize the imagination, at the same time to divide students into teams for further work.


2. "Good eye". The task for commands can be performed after introduction or after beginning of any scan according to the choice of the teacher.


The essence of the task: Try to determine the distance to the nearest object. It can be a table, desks, chairs, boards or something else. How many steps do you need to reach it? Try to guess first and then verify in practice. Have you guessed?

Now determine a number of steps you need to make to reach your classmates. If they do not stand still, can you guess? Well, try!

These small tasks give you the first idea about the sense of space, ability to navigate in it.


The purpose: To test the feelings of space of the students, to give them an idea of this feeling, to give an active relax, to consolidate the material.
Lesson summary:


The contents


The results of the lesson-case can be complemented by  findings of students



What three websites helped to find important information?





To help the student and the coach:





Where can you get information for the case?
















Location of the lesson:

The case-lesson takes place in the classroom.



Teams of boys and girls.

The score was:....


1. Take a map of your community. Offer the opposing team the route of the 4 items. Now try to build the route using the map. The winner is the team which is perform the task faster and correctly. (Keep in mind that the right assignment for opponents is also a part of the strategy for victory).

2. Try to count the "weight" of SMS that has a maximum size of – 140 bytes.



Try to perform the task proposed in the introduction. Within a few weeks you can train your sense of space (can choose any the method you like). Repeat the experiment. If there is any difference?



90 min (paired lesson)     


The possibility to conduct the lesson with a student-understudy  

It is possible.


The acquired knowledge and developed competence:

Holistic view of the sense of space, its aspects and manifestations.

The ability to organize and classify the phenomena of the world.

Skills of orientation in different spheres of human life, the vastness of our world.

The ability to search and analyze multi-vector information to allocate the secondary and main.



Cardinal directions,scale, map, pulsar,personal space, claustrophobia, echolocation, magnetic field, perspective, tension force, centrifugal force, mathematics pendulum, information space



Hrabowska Larysa


Participated in the case upgrading:


The End

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