Map scale. Numerical, linear and transverse scales View scale 1 500

Scale 1: 100,000

1 mm on the map - 100 m (0.1 km) on the ground

1 cm on the map - 1000 m (1 km) on the ground

10 cm on the map - 10000 m (10 km) on the ground

Scale 1:10000

1 mm on the map - 10 m (0.01 km) on the ground

1 cm on the map - 100 m (0.1 km) on the ground

10 cm on the map - 1000m (1 km) on the ground

Scale 1:5000

1 mm on the map - 5 m (0.005 km) on the ground

1 cm on the map - 50 m (0.05 km) on the ground

10 cm on the map - 500 m (0.5 km) on the ground

Scale 1:2000

1 mm on the map - 2 m (0.002 km) on the ground

1 cm on the map - 20 m (0.02 km) on the ground

10 cm on the map - 200 m (0.2 km) on the ground

Scale 1:1000

1 mm on the map - 100 cm (1 m) on the ground

1 cm on the map - 1000cm (10 m) on the ground

10 cm on the map - 100 m on the ground

Scale 1:500

1 mm on the map - 50 cm (0.5 meters) on the ground

1 cm on the map - 5 m on the ground

10 cm on the map - 50 m on the ground

Scale 1:200

1 mm on the map - 0.2 m (20 cm) on the ground

1 cm on the map - 2 m (200 cm) on the ground

10 cm on the map - 20 m (0.2 km) on the ground

Scale 1:100

1 mm on the map - 0.1 m (10 cm) on the ground

1 cm on the map - 1 m (100 cm) on the ground

10 cm on the map - 10m (0.01 km) on the ground

Translate numerical scale maps to named:

Solution:

To make it easier to translate a numerical scale into a named one, you need to calculate how many zeros the number in the denominator ends with.

For example, on a scale of 1:500,000, there are five zeros in the denominator after the number 5.

If after the number in the denominator there are five or more zeros, then by closing (with a finger, a pen or simply crossing out) five zeros, we get the number of kilometers on the ground corresponding to 1 centimeter on the map.

Example for scale 1: 500,000

There are five zeros in the denominator after the number. Closing them, we get for the named scale: 1 cm on the map 5 kilometers on the ground.

If after the number in the denominator there are less than five zeros, then by closing two zeros, we get the number of meters on the ground corresponding to 1 centimeter on the map.

If, for example, in the denominator of the scale 1: 10,000 we close two zeros, we get:

in 1 cm - 100 m.

Answers:

in 1 cm - 2 km;

in 1 cm - 100 km;

in 1 cm - 250 m.

Use a ruler, overlay on maps to make it easier to measure distances.

Convert a named scale to a numerical one:

in 1 cm - 500 m

in 1 cm - 10 km

in 1 cm - 250 km

Solution:

For easier translation of a named scale into a numerical scale, you need to convert the distance on the ground indicated in the named scale to centimeters.

If the distance on the ground is expressed in meters, then to get the denominator of the numerical scale, you need to assign two zeros, if in kilometers, then five zeros.

For example, for a named scale of 1 cm - 100 m, the distance on the ground is expressed in meters, so for a numerical scale we assign two zeros and get: 1: 10,000.

For a scale of 1 cm - 5 km, we assign five zeros to the five and get: 1: 500,000.

Answers:

Maps, depending on the scale, are conventionally divided into the following types:

topographic plans - 1:400 - 1:5 000;

large-scale topographic maps - 1:10,000 - 1:100,000;

medium-scale topographic maps - from 1:200,000 - 1:1,000,000;

small-scale topographic maps - less than 1:1,000,000.

Scale maps:

1:10,000 (1cm=100m)

1:25,000 (1cm=100m)

1:50,000 (1cm=500m)

1:100,000 (1cm=1000m)

called large scale.

Tale about the map in scale 1:1

Once upon a time there was a Capricious King. One day he traveled around his kingdom and saw how great and beautiful his land was. He saw winding rivers, huge lakes, high mountains and wonderful cities. He became proud of his possessions and wanted the whole world to know about them. And so, the Capricious King ordered the cartographers to create a map of the kingdom. The cartographers worked for a whole year and finally presented the King with a wonderful map, on which all the mountain ranges were indicated, big cities and large lakes and rivers.

However, the Capricious King was not satisfied. He wanted to see on the map not only the outlines of the mountain ranges, but also the image of each mountain peak. Not only large cities, but also small ones and villages. He wanted to see small rivers flowing into rivers.

The cartographers set to work again, worked for many years and drew another map, twice the size of the previous one. But now the King wished that the map showed passes between mountain peaks, small lakes in the forests, streams, peasant houses on the outskirts of villages. Cartographers drew more and more new maps.

The capricious King died without waiting for the end of the work. Successors one by one came to the throne and died in turn, and the map was drawn up and drawn up. Each king hired new cartographers to map the kingdom, but each time he remained dissatisfied with the fruits of labor, finding the map insufficiently detailed.

Finally the cartographers drew an Incredible map!!! The map depicted the entire kingdom in great detail - and was exactly the same size as the kingdom itself. Now no one could tell the difference between the map and the kingdom.

Where were the Capricious Kings going to store their wonderful map? The casket for such a card is not enough. You will need a huge room like a hangar, and in it the map will lie in many layers. Do you really need such a card? After all, a life-size map can be successfully replaced by the terrain itself ..))))

The scale can be written in numbers or words, or depicted graphically.

• Numerical.
• Named.
• Graphic.
  • Linear.
  • Transverse.

Numerical scale

The numerical scale is signed with numbers at the bottom of the plan or map. For example, the scale "1: 1000" means that all distances on the plan are reduced by 1000 times. 1 cm on the plan corresponds to 1000 cm on the ground, or, since 1000 cm = 10 m, 1 cm on the plan corresponds to 10 m on the ground.

Named Scale

The named scale of a plan or map is indicated by words. For example, it may be written "in 1 cm - 10 m."

Linear scale

It is most convenient to use the scale depicted as a straight line segment divided into equal parts, usually centimeters (Fig. 15). This scale is called linear, it is also shown at the bottom of the map or plan. Pay Attention that when drawing a linear scale, zero is set, retreating 1 cm from the left end of the segment, and the first centimeter is divided into five parts (2 mm each).

Near each centimeter it is signed what distance it corresponds to on the plan. One centimeter is divided into parts, next to which it is written what distance on the map they correspond to. A compass-measuring device or a ruler measures the length of any segment on the plan and, applying this segment to a linear scale, determines its length on the ground.

Knowing the scale, it is possible to determine the distances between geographic objects, to measure the objects themselves.

If the distance from the road to rivers on a plan with a scale of 1: 1000 (“in 1 cm - 10 m”) is 3 cm, which means that on the ground it is 30 m. material from the site

Suppose, from one object to another, 780 m. It is impossible to show this distance on paper in full size, so you have to draw it on a scale. For example, if all distances are shown 10,000 times smaller than in reality, that is, 1 cm on paper will correspond to 10 thousand cm (or 100 m) on the ground. Then, on a scale, the distance in our example from one object to another will be 7 cm and 8 mm.

Pictures (photos, drawings)

On this page, material on the topics:

Theme "Scale"

Materials for preparing for the lesson

T.V. KONSTANTINOV
cand. ped. Sciences, Senior Lecturer
E.A. KUZNETSOVA
Kaluga State Pedagogical University
them. K.E. Tsiolkovsky

Means of education

A plan of the area (preferably of your own area), a physical map of the hemispheres, a physical map of Russia, measuring instruments (measuring tape, rangefinder).

Terms and concepts

Scale ( from German - measure and Stab - stick) - the ratio of the length of a segment on a map, plan, aerial or space image to its actual length on the ground.
Numerical scale- scale, expressed as a fraction, where the numerator is one, and the denominator is a number showing how many times the image is reduced.
Named (verbal) scale - kind of scale, a verbal indication of what distance on the ground corresponds to 1 cm on a map, plan, photograph.
Linear scale - an auxiliary measuring ruler applied to maps to facilitate the measurement of distances.

Geographical sciences and professions of geographers

Geodesy (Greek - land division) - a science that studies the shape and size of the Earth, methods for measuring distances, angles and heights on the earth's surface.
Topography(Greek - place and - I write) - a section of geodesy dedicated to measurements on the ground to create maps and plans.
Cartography- the science of maps, their creation and use. Cartography also studies globes, plans and other images of the earth's surface, in addition, maps and globes of the starry sky and other planets.

Geographer's Toolkit

Compasses - a tool for transferring dimensions to drawings. When working with geographical maps used to determine the distances between points, individual sections of the map.
Curvimeter - a mechanical portable device designed to measure the lengths of winding lines from maps. It consists of a round box with a dial and an arrow, a small wheel at the bottom. The divisions on the dial scale can mean the path traveled by the wheel on the map (in cm), or immediately show the distance on the ground, depending on the scale of the map.
Rangefinders - devices of various types that are used to determine distances without directly measuring them with a measuring tape or tape measure.
Measuring tape - the main instrument used to measure distances before the invention of rangefinders. It is a steel band, usually 20 m long, fixed to the ground with long (about 0.5 m) steel pins.

Geographic nomenclature

Local names: the settlement where the students live, streets, shops, educational institutions, nearby bodies of water, various local landforms, and so on.

Independent work of students

Determining distances on maps using a scale

The purpose of the work: the formation of skills to work with various types scale; formation of skills to determine distances on maps using a scale.
Equipment: atlas of geography for the 6th grade, curvimeter or thread about 20 cm long, workbook.

Exercise 1. Convert the map's numerical scale to a named one:

a) 1: 200,000
b) 1: 10,000,000
c) 1: 25,000

rule for students. To make it easier to translate a numerical scale into a named one, you need to calculate how many zeros the number in the denominator ends with. For example, on a scale of 1:500,000, there are five zeros in the denominator after the number 5.
If after the number in the denominator five and more zeros, then, by closing (with a finger, a pen or simply crossing out) five zeros, we get the number of kilometers on the ground corresponding to 1 centimeter on the map. Example for scale 1: 500,000. The denominator after the number is five zeros, closing them, we get for the named scale: 1 cm on the map 5 kilometers on the ground.
If after the number in the denominator there are less than five zeros, then by closing two zeros, we get the number of meters on the ground corresponding to 1 centimeter on the map. If, for example, in the denominator of the scale 1: 10,000 we close two zeros, we get: in 1 cm - 100 m.
Answer: a) in 1 cm - 2 km; b) in 1 cm - 100 km; c) in 1 cm - 250 m.

Task 2. Convert a named scale to a numerical one:

a) in 1 cm - 500 m

b) in 1 cm - 10 km

c) in 1 cm - 250 km

rule for students. For easier translation of a named scale into a numerical scale, you need to convert the distance on the ground indicated in the named scale to centimeters. If the distance on the ground is expressed in meters, in order to get the denominator of the numerical scale, two zeros must be assigned, if in kilometers, then five zeros.
For example, for a named scale of 1 cm - 100 m, the distance on the ground is expressed in meters, so for a numerical scale we assign two zeros and get: 1: 10,000. For a scale of 1 cm - 5 km, we assign five zeros to the five and get: 1 : 500,000.
Answers: a) 1: 50,000; b) 1: 1,000,000; c) 1: 25,000,000.

Task 3. Determine the distance between points by physical map Russia in the atlas of the 6th grade:

a) Moscow and Murmansk
b) Mount Narodnaya (Ural Mountains) and Mount Belukha (Altai Mountains)
c) Cape Dezhnev (Chukotka Peninsula) and Cape Lopatka (Kamchatka Peninsula)

rule for students. When determining the distance on the map between points, you should:
1. Use a ruler to measure the distance in centimeters between points. For example, the distance between the cities of Moscow and Astrakhan on the map is 6.5 cm.
2. Find out on a named scale how many kilometers (meters) on the ground correspond to 1 cm on the map.
(On the physical map of Russia in the geographical atlas of the 6th class, 1 cm on the map corresponds to 200 km on the ground.)
3. Multiply the distance between points measured with a ruler by the number of kilometers (meters) on the ground for a given scale.

6.5 x 200 = 1300 km.

Answers: a) 1460 km; b) 2240 km; c) 2500 km* * .

Task 4. Measure the length of the rivers on the physical map of Russia in the atlas of the 6th grade:

a) Oka;
b) the Ural River;
c) Kama.

Measurements of winding lines on the map (in this case, rivers) are carried out using a curvimeter or thread.
How to measure the length of a river with a string (rule for students).
1. The thread must be moistened, otherwise it is difficult to lay it on paper.
2. Attach a thread to a curved line (to the river - from source to mouth) so that it repeats all the bends of the river.
3. Mark on the thread (with fingers or tweezers) the source and mouth points (you can carefully cut the thread with scissors at these points).
4. Straighten the thread, attach the noticed (or cut off) section of the thread to the ruler and measure how many centimeters it contains. Multiply the measurement result by the number of kilometers on the ground for a given scale. (You can put a string on a linear scale on a map and immediately read the length of the river.)
Answers: a) about 920 km; b) about 1300 km; c) about 1200 km.
Note. The accuracy of measuring curvilinear sections is not high, so the answers of schoolchildren may differ somewhat from the answers of their comrades. Surely, the results of measuring with a thread on a small-scale map will STRONGLY diverge from the lengths of the rivers that are indicated in textbooks and reference books. The present length of the Oka is 1500 km, the Urals is 2400 km, the Kama is 1800 km. It is imperative to tell the students these numbers so that the “clumsy” numbers of independent measurement are not fixed in memory (and they have a great chance of gaining a foothold precisely because they were obtained independently). It is also necessary to explain where such a discrepancy comes from: a small-scale map cannot reflect many medium and small turns, bends of the river, they are all “straightened”. This explanation will come in very handy in the topic "Scale": it will make it easier to understand the differences between maps of different scales.

Figures and facts

Scales topographic maps

The cards have other names as well. Let's determine what scales the following names refer to: 100 meter, half mile, mile, 2 mile, 5 mile, 10 mile.
On what kind of scale are the names given in the table based? What about the ones in the previous paragraph?

(reading for students)

A story about a map in 1:1 scale

Once upon a time there was a Capricious King. One day he traveled around his kingdom and saw how great and beautiful his land was. He saw winding rivers, huge lakes, high mountains and wonderful cities. He became proud of his possessions and wanted the whole world to know about them. And so, the Capricious King ordered the cartographers to create a map of the kingdom. The cartographers worked for a whole year and finally presented the King with a wonderful map, on which all the mountain ranges, large cities and large lakes and rivers were indicated.
However, the Capricious King was not satisfied. He wanted to see on the map not only the outlines of the mountain ranges, but also the image of each mountain peak. Not only large cities, but also small ones and villages. He wanted to see small rivers flowing into rivers.
The cartographers set to work again, worked for many years and drew another map, twice the size of the previous one. But now the King wished that the map showed passes between mountain peaks, small lakes in the forests, streams, peasant houses on the outskirts of villages. Cartographers drew more and more new maps.
The capricious King died without waiting for the end of the work. Successors one by one came to the throne and died in turn, and the map was drawn up and drawn up. Each king hired new cartographers to map the kingdom, but each time he remained dissatisfied with the fruits of labor, finding the map insufficiently detailed.
Finally, the cartographers drew the Incredible Map. The map depicted the entire kingdom in great detail - and was exactly the same size as the kingdom itself. Now no one could tell the difference between the map and the kingdom.
Where were the Capricious Kings going to store their wonderful map? The casket for such a card is not enough. You will need a huge room like a hangar, and in it the map will lie in many layers. Do you really need such a card? After all, a life-size map can be successfully replaced by the terrain itself.

Dependence of map detail on scale

If you have ever flown on airplanes, then you probably remember how at the beginning of the flight, when the plane is just taking off from the ground, the outlines of the airport, houses, squares float under it. But the higher it rises into the air, the less details are visible through the porthole, but the space that opens up to the eye becomes wider. The detail of the maps also changes when the scale is reduced.
On large-scale maps, where no more than 500 m of land space fits in 1 cm of area, a small area is depicted in great detail.
On small-scale maps, where 1 cm fits up to several thousand kilometers, huge areas of the Earth are shown, but with a small amount of detail. Both cards are needed, depending on their purpose.
If you are wondering what countries you will fly over when traveling from Moscow to Melbourne, you need to open a small-scale map, and when going to the forest for mushrooms or hiking with friends, you need to take a large-scale map with you so as not to get lost.

Homework for those who wish

Determine the scale of the maps of your area

Find maps depicting the area you live in. If you don’t have such cards at home, ask your friends and acquaintances, a geography teacher, a librarian or a bookstore seller for help.
Write down the scales of the maps depicting your area. Which scale is larger, which is smaller?
Compare maps of different scales and find out on which maps the larger territory is shown, and on which the smaller one.
Determine on what scales the area is depicted in more detail, on which - in less detail.
Make a conclusion about how the area of ​​the depicted territory and its detail depend on the scale of the map.

Find your location on the map

On the map of your region (krai, republic ...), determine the distance from your settlement to the regional (territorial, republican) center, if you do not live in it, or to any other settlement, if you are in the center of the region ( regions, republics).

On the old maps a named scale could show what distance on the ground corresponds to one inch or other archaic linear measure on a map.
Hereinafter, the calculations were made according to the atlas “Geography. Initial course. Grade 6.: Atlas. - M.: Bustard; Publishing house DIK, 1999. - 32 p. Of course, at this stage of training, the teacher does not yet address the issues of distance distortion associated with the map projection.

Each card has scale- a number that shows how many centimeters on the ground correspond to one centimeter on the map.

map scale usually listed on it. Record 1: 100,000,000 means that if the distance between two points on the map is 1 cm, then the distance between the corresponding points on its terrain is 100,000,000 cm.

May be listed in numerical form as a fraction– numerical scale (for example, 1: 200,000). And it can be marked in linear form: as a simple line or strip divided into units of length (usually kilometers or miles).

The larger the scale of the map, the more detailed the elements of its content can be depicted on it, and vice versa, the more smaller scale, the more extensive space can be shown on a map sheet, but the terrain on it is depicted with less detail.

Scale is a fraction whose numerator is one. To determine which of the scales is larger and by how many times, let's recall the rule for comparing fractions with the same numerators: of two fractions with the same numerators, the one with the smaller denominator is larger.

The ratio of the distance on the map (in centimeters) to the corresponding distance on the ground (in centimeters) is equal to the scale of the map.

How does this knowledge help us in solving problems in mathematics?

Example 1

Let's look at two cards. A distance of 900 km between points A and B corresponds on one map to a distance of 3 cm. A distance of 1,500 km between points C and D corresponds to a distance of 5 cm on another map. Let us prove that the scales of the maps are the same.

Solution.

Find the scale of each map.

900 km = 90,000,000 cm;

the scale of the first map is: 3: 90,000,000 = 1: 30,000,000.

1500 km = 150,000,000 cm;

the scale of the second map is: 5: 150,000,000 = 1: 30,000,000.

Answer. The scales of the maps are the same, i.e. are equal to 1:30,000,000.

Example 2

The scale of the map is 1: 1,000,000. Let's find the distance between points A and B on the ground, if on the map
AB = 3.42 cm?

Solution.

Let's make an equation: the ratio of AB \u003d 3.42 cm on the map to the unknown distance x (in centimeters) is equal to the ratio between the same points A and B on the ground to the map scale:

3.42: x = 1: 1,000,000;

x 1 \u003d 3.42 1,000,000;

x \u003d 3,420,000 cm \u003d 34.2 km.

Answer: the distance between points A and B on the ground is 34.2 km.

Example 3

The scale of the map is 1: 1,000,000. The distance between points on the ground is 38.4 km. What is the distance between these points on the map?

Solution.

The ratio of the unknown distance x between points A and B on the map to the distance in centimeters between the same points A and B on the ground is equal to the scale of the map.

38.4 km = 3,840,000 cm;

x: 3,840,000 = 1: 1,000,000;

x \u003d 3,840,000 1: 1,000,000 \u003d 3.84.

Answer: the distance between points A and B on the map is 3.84 cm.

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