Single-digit numbers are added using an addition table. Addition table, and ...
Before you get to know the units of measure for area, you need to pay attention to how to calculate the area of a shape. The first figure that is studied in school is a square. A square with a side of one unit is called a unit square. It can be 1 meter, centimeter, or any other value. The area of other figures is always compared to the unit square. The area of a figure shows how many unit squares will fit on its surface.
Rice. 1. Unit square.
In order to calculate its area, you need to multiply the two sides.
$$ S = 1cm * 1cm = 1cm ^ 2 $$
Rice. 2. Chess board.
To calculate the area of a checkerboard, you need to multiply the width by the length. That is:
$$ S = 8 * 8 = 64 squares $$
And if we take 1 square of the chessboard as a unit square of 1 $ cm ^ 2 $, then the area of the chessboard is $ 64 cm ^ 2 $.
Squares can be measured in different units, respectively, they have different designations.
Rice. 3. A square with a side that is measured in different units.
Correctly, the unit of measurement of area is called a square centimeter, or a square meter, depending on which unit the sides are measured in.
So, the units for measuring the area:
- $ 1 cm ^ 2 $;
- $ 1 m ^ 2 $;
- $ 1 km ^ 2 $;
- $ 1 hectare (ha) $;
- $ 1 ar (a.) $, Differently called weaving
We often use some units of measurement in everyday life to designate land plots. This is a hectare, weaving and macaws.
When solving problems, be sure to pay attention to the units of measurement. Centimeters can only be added to centimeters, and meters can only be added to meters. Therefore, you should always ensure that in the given solution to the problem, all values are expressed in the same units.
In English-speaking countries (USA, Canada, Great Britain, Australia) acres, yards are used to measure land plots. $ 1 acre = 4940 yards = 4046.96 m ^ 2 $.
Example tasks:
# 1. Convert $ 10 m ^ 2 $ to $ cm ^ 2 $
Solution:
- $ 1 m = 100 cm $;
- $ 1 m ^ 2 = 100 x 100 = 10,000 cm ^ 2 $;
- $ 10 m ^ 2 = 10 х 10,000 = 100,000 cm ^ 2 $
# 2. How many $ 500 m ^ 2 $ ares?
Solution:
- $ 100 m ^ 2 = 1 a $;
- $ 500 m ^ 2 = 5 a $.
How are the units of area related to each other?
In order to see the relationship, you need to pay attention to the table.
Area Units Table
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Area units |
$ 1km ^ 2 $ |
1 hectare |
1 are |
$ 1 m ^ 2 $ |
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$ 1 km ^ 2 $ |
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1 hectare (ha) |
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1 weaving or are 4.3. Total ratings received: 122. |
The magnitude is something that can be measured. Concepts such as length, area, volume, mass, time, speed, etc. are called quantities. The quantity is measurement result, it is determined by a number expressed in certain units. The units in which the value is measured are called units of measurement.
To designate a value, write a number, and next to it is the name of the unit in which it was measured. For example, 5 cm, 10 kg, 12 km, 5 min. Each quantity has an infinite number of meanings, for example, the length can be equal to: 1 cm, 2 cm, 3 cm, etc.
The same quantity can be expressed in different units, for example, kilogram, gram and ton are units of measure for weight. The same value in different units is expressed in different numbers. For example, 5 cm = 50 mm (length), 1 h = 60 min (time), 2 kg = 2000 g (weight).
To measure some quantity means to find out how many times it contains another quantity of the same kind, taken as a unit of measurement.
For example, we want to know the exact length of a room. So we need to measure this length using another length that is well known to us, for example, using a meter. To do this, set aside a meter along the length of the room as many times as possible. If it fits exactly 7 times along the length of the room, then its length is 7 meters.
As a result of measuring the quantity, either named number, for example 12 meters, or several named numbers, for example 5 meters 7 centimeters, the aggregate of which is called composite named number.
Measures
In each state, the government has established certain units of measurement for various quantities. A precisely calculated unit of measurement taken as a sample is called benchmark or exemplary unit... Model units of meter, kilogram, centimeter, etc. have been made, according to which units for everyday use are made. Units that have come into use and approved by the state are called measures.
The measures are called homogeneous if they serve to measure quantities of the same kind. So, gram and kilogram are homogeneous measures, since they are used to measure weight.
Units
Below are the units of measurement for various quantities that are often found in problems in mathematics:
Weights / Mass Measures
- 1 ton = 10 centners
- 1 centner = 100 kilograms
- 1 kilogram = 1000 grams
- 1 gram = 1000 milligrams
- 1 kilometer = 1000 meters
- 1 meter = 10 decimeters
- 1 decimeter = 10 centimeters
- 1 centimeter = 10 millimeters
- 1 sq. kilometer = 100 hectares
- 1 hectare = 10,000 sq. meters
- 1 sq. meter = 10000 sq. centimeters
- 1 sq. centimeter = 100 sq. millimeters
- 1 cubic meter meter = 1000 cubic meters decimetres
- 1 cubic meter decimeter = 1000 cubic meters centimeters
- 1 cubic meter centimeter = 1000 cubic meters millimeters
Let us also consider such a quantity as liter... A liter is used to measure the capacity of vessels. A liter is a volume that is equal to one cubic decimeter (1 liter = 1 cubic decimeter).
Measures of time
- 1st century (century) = 100 years
- 1 year = 12 months
- 1 month = 30 days
- 1 week = 7 days
- 1 day = 24 hours
- 1 hour = 60 minutes
- 1 minute = 60 seconds
- 1 second = 1000 milliseconds
In addition, time units such as quarter and decade are used.
- quarter - 3 months
- decade - 10 days
The month is taken as 30 days, if you do not need to specify the date and name of the month. January, March, May, July, August, October and December - 31 days. February in a simple year has 28 days, February in a leap year has 29 days. April, June, September, November - 30 days.
A year is (approximately) the time during which the Earth makes a complete revolution around the Sun. It is customary to count every three consecutive years for 365 days, and the fourth following them - in 366 days. A year containing 366 days is called leap, and years containing 365 days - simple... One extra day is added to the fourth year for the following reason. The time of the Earth's revolution around the Sun contains not exactly 365 days, but 365 days and 6 hours (approximately). Thus, a simple year is shorter than the true year by 6 hours, and 4 simple years are shorter than 4 true years by 24 hours, that is, by one day. Therefore, one day is added to every fourth year (February 29).
You will learn about the other types of quantities as you further study various sciences.
Abbreviated names of measures
It is customary to write abbreviated names of measures without a dot:
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Weights / Mass Measures
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Area measures (square measures)
|
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Measures of time
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Measure of vessel capacity
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Measuring instruments
Special measuring devices are used to measure various quantities. Some of them are very simple and are intended for simple measurements. Such devices include a measuring ruler, tape measure, measuring cylinder, etc. Other measuring devices are more complex. Such devices include stopwatches, thermometers, electronic scales, etc.
Gauges usually have a measuring scale (or scale for short). This means that there are dashed divisions on the device, and the corresponding value of the quantity is written next to each line division. The distance between two strokes, near which the value of the quantity is written, can be additionally divided into several smaller divisions, these divisions are most often not indicated by numbers.
It is not difficult to determine to which value of the quantity each smallest division corresponds. So, for example, the figure below shows a measuring ruler:
The numbers 1, 2, 3, 4, etc. indicate the distance between the strokes, which are divided into 10 equal divisions. Therefore, each division (distance between the nearest strokes) corresponds to 1 mm. This quantity is called scale division measuring instrument.
Before proceeding with the measurement of the value, the value of the division of the scale of the device used should be determined.
In order to determine the division price, you must:
- Find the two nearest scale bars, near which the values of the quantity are written.
- Subtract the smaller from the larger value and divide the resulting number by the number of divisions between them.
As an example, let us determine the scale division value of the thermometer shown in the figure on the left.
Let's take two lines, near which the numerical values of the measured value (temperature) are plotted.
For example, the lines with the designations 20 ° C and 30 ° C. The distance between these strokes is divided into 10 divisions. Thus, the price of each division will be equal to:
(30 ° C - 20 ° C): 10 = 1 ° C
Therefore, the thermometer reads 47 ° C.
Each of us constantly has to measure various quantities in everyday life. For example, in order to arrive on time to school or work, you have to measure the time that will be spent on the road. Meteorologists measure temperature, barometric pressure, wind speed, etc. to predict the weather.
Today, each of us, when designating certain measures of measurement, uses only modern terms. And this is considered normal and natural. However, when studying history or reading literary works, we often come across words such as "spans", "arshins", "elbows", etc.
And this use of terms is also normal, since it is nothing more than ancient measures of measurement. Everyone should know what they mean. Why? First, this is the history of our ancestors. Secondly, such knowledge is an indicator of our intellectual level.
The history of the emergence of measures
The development of human society was impossible without comprehending the art of counting. But this was not enough. For the conduct of many cases, certain units of length, mass and area were also needed. Man invented them in the most unexpected forms. For example, any distances were determined by transitions, or steps. The ancient measures of measurement relating to a person's height or specifying the amount of tissue corresponded to the length of a finger or joint, the span of the arms, etc., that is, to everything that was a kind of measuring device that was always with you.
We learn about very interesting lengths by our ancestors from chronicles and ancient letters. This is "throwing a stone", that is, its throw, and "cannon shot", and "shooting" (arrow flight range), and much more. Sometimes the unit of measurement indicated the distance at which the cry of one or another animal was still heard. It was a "cock crow", "bull roar", etc. An interesting measure of length existed among the peoples of Siberia. It was called "beech", and it meant the distance at which a person visually merged the horns of a bull into a single whole.
From the chronicles that have come down to us, we can conclude that the ancient measures of measurement in Russia appeared in the 11-12 centuries. These were units such as a mile, a fathom, an elbow, and an inch. However, in those days, man-made methods for determining the length were still extremely unstable. They varied somewhat depending on the principality and constantly changed over time.
From the chronicles of the 13-15th centuries, we learn that the ancient measures for measuring bulk bodies (as a rule, grain crops) are kad, halves, quarters and octins. In the 16-17 centuries. these terms have disappeared from use. From the indicated period, the main measure of free-flowing bodies becomes a quarter, which approximately corresponded to six pounds.
In a number of documents of the era of Kievan Rus, the word "spool" is found. This weight unit had the same distribution as the Berkovets and the pood.
Determination of length
The ancient measures of measuring physical quantities were not very accurate. The same applies to determining the length in steps. This unit was used in Ancient Rome, Ancient Greece, Persia and Egypt. The distance between cities was determined by the human stride, the average length of which is 71 cm. A similar unit is used in our time. However, today special devices, pedometers, determine not the distance, but the number of steps taken by a person.
The measure of length that was used in the Mediterranean countries was such a unit as stages. A mention of her can be found in manuscripts dating back to the first millennium BC. NS. The stages was equal to the distance that a person could walk at a calm pace from dawn to the moment when the sun's disk completely appears above the horizon.
With the development of society, people began to need larger quantities. In this regard, the ancient Roman mile appeared, equal to 1000 steps.
The ancient measures of measuring the length of different peoples differed from each other. Thus, Estonian sailors determined the distance with pipes. This was the path the ship traveled during the time it took to smoke a pipe full of tobacco. The Spaniards called the same measure of length a cigar. The Japanese defined the distance with "horse shoes". This was the path that the animal could have traveled until the straw sole, which replaced its horseshoe, was completely abraded.
The main values for determining the length in Russia
Let us recall the proverbs with ancient measures of measurement. One of them is well known to us from childhood: "From a pot two inches, and already a pointer." What is such a unit of length? In Russia, it was equal to the width of the index and middle fingers. At the same time, one inch corresponded to one sixteenth arshin. Today this value is 4.44 cm. But the old Russian measure of measurement - the nail - was 11 mm. Taken four times, it was equal to one inch.
In Russia, some ancient measurement measures came into use in connection with the development of trade relations with other countries. This is how a quantity called an arshin appeared. This name comes from the Persian word "elbow". In this language it sounds like "arsh". An arshin, equal to 71.12 cm, came along with traders from distant countries who brought Chinese silks, velvet and Indian brocade.
When measuring the fabric, oriental merchants pulled it over their arm up to the shoulder. In other words, they measured the goods in yardsticks. It was very convenient, because such a measuring device was always with you. However, the cunning merchants were looking for shop assistants with shorter arms, so that less fabric would be needed for an arshin. But this was soon brought to an end. The authorities introduced a state yardstick, which everyone, without exception, had to use. It turned out to be a wooden ruler made in Moscow. Copies of such a device were sent all over Russia. And so that no one could cheat and shorten the yardstick a little, the ends of the line were bound with iron, on which the state stamp was affixed. Today this unit of measurement is no longer used. However, the word denoting such a value is familiar to each of us. Proverbs with ancient measures of measurement also tell about him. So, about a discerning person they say that he "sees three arshins underground."
How else in Russia was the distance determined?
There are other ancient measures of length measurement. These include a fathom. Mention of this term first occurs in the "Word about the beginning of the Kiev-Pechersk Monastery", dating back to the 11th century. Moreover, there were two varieties of sazhen. One of them is the flywheel, equal to the distance between the tips of the middle fingers of the hands, spread out in different directions. The value of ancient measures of this type was equal to 1 m 76 cm. The second type of fathom is oblique. It was the length from the heel of the shoe on the right foot to the tip of the middle toe of the left hand extended upward. The size of the oblique fathom was approximately 248 cm. Sometimes this term is mentioned when describing a person of a heroic physique. They say that he has a slanting fathom in his shoulders.
The ancient Russian measures of measuring long distances - a field or a milestone. The first mentions of these values are found in the manuscripts of the 11th century. The length of a verst is 1060 m. Moreover, this term was originally used to measure arable land. It meant the distance between the turns of the plow.
The ancient measures of measurement of quantities sometimes bore a joking name. So, since the reign of Alexei Mikhailovich (1645-1676), a very tall man began to be called. This joking term has not been forgotten even today.
Until the 18th century. in Russia, such a unit of measurement as the boundary verst was used. She was used to measure the distance between the boundaries of settlements. The length of this verst was 1000 fathoms. Today it is 2.13 km.
Another ancient measure of length in Russia was the span. Its size was about a quarter of an arshin and was equal to about 18 cm. There were:
- "smaller span", equal to the distance between the tips of the extended index and thumb;
- "big span", equal to the length between the big and middle fingers.
Many proverbs about ancient measures of measurement indicate to us this value. For example, "seven spans in the forehead." This is what they say about a very intelligent person.
The smallest ancient unit of length is the line. It is equal to the width of a wheat grain and is 2.54 mm. Until now, watch factories use this unit of measurement. Only the Swiss size is accepted - 2.08 mm. For example, the size of the men's watch "Victory" is 12 lines, and the women's "Zarya" - 8.
European length units
From the 18th century. Russia has significantly expanded its trade relations with Western countries. That is why the need arose for new measures of measurement that could be compared with European ones. And then Peter I carried out a metrological reform. By his decree, some English values for measuring distances were introduced in the country. It was feet, inches, and yards. These units are especially widespread in shipbuilding and the navy.
According to the existing legend, the yard was first determined back in 101. It was a value equal to the length from the nose of Henry I (King of England) to the tip of his middle finger, stretched out in a horizontal position. Today this distance is 0.91 m.
Foot and yard are ancient measures of measurement that are closely related to each other. Derived from the English word "foot" - a foot, this value is equal to one third of a yard. Today a foot is 30.48 centimeters.
The Dutch word for thumb gives its name to the inch. How was this distance originally measured? It was equal to the length of three dried grains of barley or the phalanx of the thumb. Today, one inch is 2.54 cm and is used to determine the inside diameter of car tires, pipes, etc.
Streamlining the system of measures
In order to ensure the ease of transition from one measurement unit to another, special tables were published in Russia. On the one hand, ancient measures were brought into them. Units of measurement of foreign origin, which corresponded to the Russians, were placed through the equal sign. The same tables included those units that were to be used in the country.
However, the confusion with the system of measures in Russia did not end there. Different cities used their own units. An end to this was put only in 1918, when Russia switched to the metric system of measures.
Volume measurement
Man needed to measure bulk physical quantities and liquids. For this, he began to use everything that he had in everyday life (buckets, vessels and other containers).
What old ones took place in Russia? Loose bodies our ancestors measured:
1. Octopus, or octopus. This is an old unit of 104.956 liters. A similar term was applied to the area, which was 1,365,675 square meters. The octopus was first mentioned in documents from the 15th century. It was widely used in Russia because of its practicality, since it had a volume half that of a quarter. There was even a certain standard for such a measure. It was a container to which an iron rowing was attached. Grain was poured into such a measured octopus with top. And then, with the help of rowing, the contents of the form were trimmed to the edges. Samples of such containers were made of copper and sent all over Russia.
2. Okovom, or kadiu. These measuring containers were common in the 16th and 17th centuries. In later periods, they were extremely rare. Okov was the main measure of bulk solids in Russia. Moreover, the name of this unit came from a special barrel (tub), which was adapted for measurements. The measuring container was covered with a metal hoop on top, which made it impossible for the cunning to cut its edges and sell less grain.
3. A quarter. This measure of volume was used to determine the amount of flour, cereals and grain. In everyday life, a quarter was wider than luggage, since it had more practical dimensions (1/4 of the shackle). This unit of measurement in Russia was used from the 14th to the 19th centuries.
4. Cool. This is an ancient Russian measure used for bulk solids, equal to 5-9 poods. Some researchers believe that the word "kul" once meant "fur". This term was used for a container sewn from animal skin. Later, such containers began to be made of woven materials.
5. Buckets. With this measure, our ancestors determined the amount of liquid. It was believed that 8 cups were placed in a trading bucket, the volume of each of which was equal to 10 cups.
6. Barrels. A similar unit of measurement was used by Russian traders when selling wines to foreigners. It was believed that one barrel contains 10 buckets.
7. Korchagami. This large clay pot has found its way into measuring the volume of grape wine. For different parts of Russia, the korchaga ranged from 12 to 15 liters.
Weight measurement
The Old Russian system of measures also included units for measuring mass. Trading activity was impossible without them. There are various ancient measures of mass measurement. Among them:
1. Spool. Initially, this word meant a small gold coin, which was a unit of measurement. Comparing its weight with other precious items, they determined the purity of the noble metal from which they were made.
2. Pood. This unit of weight was equal to 3840 spools and corresponded to 16.3804964 kg. Even Ivan the Terrible ordered to weigh any goods only from the poodists. And since 1797, after the Law on Weights and Measures was issued, spherical weights corresponding to one and two pounds began to be produced.
4. Share. This unit of measurement in Russia was the smallest. Its weight was 14.435 mg, which could be compared to 1/96 of a spool. Most often, the share was used in the work of mints.
5. Pound. Initially, this one was called "hryvnia". Its value corresponded to 96 spools. From 1747 the pound became which was used until 1918.
Area measurement
Some standards were invented by our ancestors to determine the size of land plots. These are ancient measures of area measurement, including:
1. Square verst. The mention of this unit equal to 1.138 sq. kilometers, found in documents dated 11-17 centuries.
2. Tithing. This is an old Russian unit, the size of which corresponds to 2400 sq. meters of arable land. Today the tithe is 1.0925 hectares. This unit has been used since the 14th century. It was known as a rectangle, the sides of which were 80 by 30 or 60 by 40 fathoms. This tithe was considered official and was the main land measure.
3. A quarter. This measure of arable land was a unit representing half a tithe. A quarter is known since the end of the 15th century, and its official use lasted until 1766. This unit got its name from the measure of the area on which rye could be sown in the amount of ¼ the volume of cadi.
4. Sokha. This unit of measurement of area was used in Russia from the 13th to the 17th centuries. They used it for taxation purposes. Moreover, several types of plows were distinguished, depending on the area of the best lands. So, a similar unit was:
Servant, containing 800 quarters of good plowing;
- church (600 quarters);
- black (400 quarters).
In order to find out how many dry woods there are in the Russian state, censuses of taxable lands were carried out. And only in 1678-1679. this unit of area was replaced by a yard number.
Modern application of old measures
We still know about some units for determining volume, area and distance, which were widely used by our ancestors. So, in some countries, the length is still measured in miles, yards, feet and inches, and the pound and the spool are used in cooking.
However, most often old units are found in literary works, historical stories and proverbs.
In this lesson, we will look at units of length, area, and a table of area units. Let's consider various units of measurement of length and area, find out in what cases they are used. We systematize our knowledge using a table. Let's solve a number of examples for converting one measurement unit to another.
You are familiar with the various units of length. What units of length are convenient to use when measuring the thickness of a match or the length of a ladybug's body? I think you named millimeters.
Which length units are convenient to use when measuring the length of a pencil? Of course, in centimeters (see Fig. 1).
Rice. 1. Measurement of lengths
What units of length are convenient to use when measuring the width or length of a window? It is convenient to measure in decimeters.
And the length of the corridor or the length of the fence? Let's use meters (see fig. 2).
Rice. 2. Measurement of lengths
To measure larger distances, for example, the distance between cities, use a unit of length larger than a meter - a kilometer (see Fig. 3).
Rice. 3. Measurement of lengths
1 kilometer 1000 meters.
Express the distance in kilometers.
1 kilometer is a thousand meters, which means that the number of thousands will mean kilometers.
8000 m = 8 km
385007 m = 385 km 7 m
34125 m = 34 km 125 m
In the number, the number of hundreds, tens and units is indicated by meters.
You can argue differently: 1 km is a thousand times more than 1 meter, which means that the number of kilometers should be 1000 times less than the number of meters. Therefore, 8000: 1000 = 8, the number 8 means the number of kilometers.
385007: 1000 = 385 (rest 7). The number 385 stands for kilometers, the remainder is the number of meters.
34125: 1000 = 34 (stop 125), that is, 34 kilometers 125 meters.
Read the table of length units (see fig. 4). Try to remember it.
Rice. 4. Table of length units
Different measurements are used to measure areas. A square centimeter is a square with a side of 1 cm (see Fig. 5), a square decimeter is a square with a side of 1 dm (see Fig. 6), a square meter is a square with a side of 1 m (see Fig. . 7).
Fig. 5. Square centimeter
Rice. 6. Square decimeter
Rice. 7. Square meter
To measure large areas, a square kilometer is used - it is a square whose side is 1 km (see Fig. 8).
Rice. 8. Square kilometer
The words "square kilometer" in abbreviated form with the number are written as follows - 1 km 2, 3 km 2, 12 km 2. In square kilometers, for example, the areas of cities are measured, the area of Moscow S = 1091 km 2.
Let's calculate how many square meters are in one square kilometer. To find the area of a square, you need to multiply the length by the width. We are given a square with a side of 1 km. We know that 1 km = 1000 m, so to find the area of such a square, we multiply 1000 m by 1000 m, we get 1,000,000 m 2 = 1 km 2.
Express 2 km 2 in square meters. We will reason like this: since 1 km 2 is 1,000,000 m 2, that is, the number of square meters is a million times larger than the number of square kilometers, so multiply 2 by 1,000,000, we get 2,000,000 m 2.
56 km 2: multiply 56 by 1,000,000, we get 56,000,000 m 2.
202 km 2 15 m 2: 202 ∙ 1 000 000 + 15 = 202 000 000 m 2 + 15 m 2 = 202 000 015 m 2.
A square millimeter (mm 2) is used to measure small areas. It is a square with a side of 1 mm. The words "square millimeter" with a number are written as follows: 1 mm 2, 7 mm 2, 31 mm 2.
Let's calculate how many square millimeters are in one square centimeter. To find the area of a square, you need to multiply the length by the width. We are given a square with a side of 1 cm. We know that 1 cm = 10 mm. So, to find the area of such a square, we multiply 10 mm by 10 mm, we get 100 mm 2.
Express in square millimeters 4 cm 2. We will reason like this: since 1 cm 2 is 100 mm 2, that is, the number of mm 2 is 100 times the number of cm 2, so we multiply 4 by 100, we get 400 mm 2.
16 cm 2: multiply 16 by 100 = 1600 mm 2.
31 cm 2 7 mm 2: this is 31 ∙ 100 + 7 = 3100 + 7 = 3107 mm 2.
In life, such units of area as are and hectares are often used. Ap is a square with a side of 10 m (see Fig. 9). With the numbers ap, write down shorter: 1 a, 5 a, 12 a.
Rice. 9.1 ar
1 a = 100 m 2, therefore it is often called weaving.
A hectare is a square with a side of 100 m (see Fig. 10). The word "hectare" with numbers is abbreviated as follows: 1 hectare, 6 hectares, 23 hectares. 1 ha = 10,000 m 2.
Rice. 10.1 hectare
Calculate how many ares in 1 hectare.
1 ha = 10000 m 2
1 a = 100 m 2, so 10000: 100 = 100 a
Now carefully consider the table of area units (see Fig. 11), try to remember it.
Rice. 11. Table of area units
In the lesson, we got acquainted with a new unit of length - km and units of area - m2, km 2, a, ha.
- Bashmakov M.I. Nefedova M.G. Maths. 4th grade. M .: Astrel, 2009.
- M. I. Moro, M. A. Bantova, G. V. Beltyukova et al. Mathematics. 4th grade. Part 1 of 2, 2011.
- Demidova T.E. Kozlova S.A. Tonkikh A.P. Mathematics. Grade 4 2nd ed., Rev. - M .: Balass, 2013.
- School.xvatit.com ().
- Mer.kakras.ru ().
- Dpva.info ().
Homework
- Find the area of a 15-inch square.
- Express: in square meters: 5 hectares; 3 ha 18 a; 247 ares; 16 a;
- in hectares: 420,000 m 2; 45 km 2 19 ha;
- in arach: 43 hectares; 4 ha 5 a; 30,700 m 2; 5 km2 13 ha;
- in hectares and macaws: 930 a; 45,700 m 2.
At first glance, in the system of measures of length, mass, etc. there is nothing difficult, however, for many schoolchildren, the transfer from one measure to another is very difficult. Even after elementary school, some children still fail to correctly correlate, for example, a decimeter with a millimeter, or a hectometer with a cubic meter.
Nevertheless, without a clear knowledge of the system of measures, it is currently impossible to live, people encounter measurements of one size or another every day and several times.
Length units in tables
How can you go from one to the other without mistakes? One of the most effective ways to study measures of length or weight is tables, this is recognized by teachers, parents, and students themselves.
Competently selected pictures of measures of length clearly explain to the student the dependence of one unit on another. The most useful table is the one in which the measures of quantities from the smallest gradually increase, that is, the student sees that, for example, 1000mm = 100cm = 10 dm = 1 m, especially if each quantity is displayed in the form of a picture.
Looking at the table, most of the schoolchildren begin with a simple memorization of the dependencies of certain quantities, however, an understanding soon comes: the student realizes that a meter contains, for example, 100 centimeters, or 1000 millimeters, but decimeters - only 10. Good help at this moment will be a large ruler, so that the digits learned can be correlated with the real length, and this is how it is remembered best.
What are the different units of length for?
Some parents wonder why it is so necessary to operate with different units of length? Children are confused in centimeters-decimeters, and sometimes adults themselves cannot explain to them which value is greater and by how many times.
You won't have to look for an answer to this question for a long time. In what units of length is it convenient to measure the thickness of a match or the body of a ladybug? In millimeters, of course. What length units are convenient for measuring the length of a pen or pencil? In centimeters.
If you need to measure the width or length of a window, decimetres are a convenient unit. For the length of the fence, meters are the best option. For the distance between cities - kilometers, for the distance between continents - also kilometers, since this is the largest among the lengths.
Very often in school problems, a task is given - to express the length given in meters or decimeters, in millimeters or kilometers, or vice versa. This is not difficult to do if you know the length ratio by heart, or use the table helper. It is much more difficult to translate volume measures - liters into square decimeters or vice versa, but there are also tables for volume measures that successfully help to assimilate the relationship between quantities.
