Table measurement values \u200b\u200bfor elementary school. Measures of length, square, volume, mass. Abbreviated names of Mer.

MEASURES Lena length, measures area, measure of volume, mass measure. Three variants of multiplication table. Decimal number system

Multiplication table. Option 1

Table multiplication from 1 (units) up to 10 (ten). Decimal system

Multiplication table. Option 2.

Multiplication table Abbreviated from 2 (two) to 9 (nine). Decimal system

2 x 1 \u003d 2 2 x 2 \u003d 4 2 x 3 \u003d 6 2 x 4 \u003d 8 2 x 5 \u003d 10 2 x 6 \u003d 12 2 x 7 \u003d 14 2 x 8 \u003d 16 2 x 9 \u003d 18 2 x 10 \u003d 20	3 x 1 \u003d 3 3 x 2 \u003d 6 3 x 3 \u003d 9 3 x 4 \u003d 12 3 x 5 \u003d 15 3 x 6 \u003d 18 3 x 7 \u003d 21 3 x 8 \u003d 24 3 x 9 \u003d 27 3 x 10 \u003d 30	4 x 1 \u003d 4 4 x 2 \u003d 8 4 x 3 \u003d 12 4 x 4 \u003d 16 4 x 5 \u003d 20 4 x 6 \u003d 24 4 x 7 \u003d 28 4 x 8 \u003d 32 4 x 9 \u003d 36 4 x 10 \u003d 40	5 x 1 \u003d 5 5 x 2 \u003d 10 5 x 3 \u003d 15 5 x 4 \u003d 20 5 x 5 \u003d 25 5 x 6 \u003d 30 5 x 7 \u003d 35 5 x 8 \u003d 40 5 x 9 \u003d 45 5 x 10 \u003d 50
6 x 1 \u003d 6 6 x 2 \u003d 12 6 x 3 \u003d 18 6 x 4 \u003d 24 6 x 5 \u003d 30 6 x 6 \u003d 36 6 x 7 \u003d 42 6 x 8 \u003d 48 6 x 9 \u003d 54 6 x 10 \u003d 60	7 x 1 \u003d 7 7 x 2 \u003d 14 7 x 3 \u003d 21 7 x 4 \u003d 28 7 x 5 \u003d 35 7 x 6 \u003d 42 7 x 7 \u003d 49 7 x 8 \u003d 56 7 x 9 \u003d 63 7 x 10 \u003d 70	8 x 1 \u003d 8 8 x 2 \u003d 16 8 x 3 \u003d 24 8 x 4 \u003d 32 8 x 5 \u003d 40 8 x 6 \u003d 48 8 x 7 \u003d 56 8 x 7 \u003d 64 8 x 9 \u003d 72 8 x 10 \u003d 80	9 x 1 \u003d 9 9 x 2 \u003d 18 9 x 3 \u003d 27 9 x 4 \u003d 36 9 x 5 \u003d 45 9 x 6 \u003d 54 9 x 7 \u003d 63 9 x 8 \u003d 72 9 x 9 \u003d 81 9 x 10 \u003d 90

Multiplication table. Option 3.

Table multiplication from 1 (units) to 20 (twenty). Decimal system

At first glance, in the system of length measures, mass, etc. There is nothing complicated, however, for many schoolchildren, the translation from one measure to another is very difficult. Part of the children and after elementary school So it is impossible to correctly relate, for example, a decimeter with a millimeter, or a hectometer with a cubic meter.

However, without clear knowledge of the system of measures is currently not to live, with measurements of one or another, people face daily and several times.

Length measurement units in tables

How is one to another without errors? One of the most effective ways Studies of length or weights are tables, teachers and parents themselves are recognized, and the students themselves.

Competently selected pictures of length measures clearly explain the schoolboy the dependence of one unit from the other. The most useful table is the one in which measures of magnitudes from the most small gradually increase, that is, a schoolboy sees that, for example, 1000mm \u003d 100cm \u003d 10 dm \u003d 1 m, especially if each value is displayed as a pattern.

Looking at the table, most of the schoolchildren, begins with a simple learning of the dependencies of certain quantities, however, quite soon comes to understanding: the student is aware that the meter contains, for example, 100 centimeters, or 1000 millimeters, but the decimeters - only 10. Good The help of this moment will be a large line, so that the learned numbers can be correlated with a real length and is remembered best.

For what you need various units of length

Some parents are asked why it is necessary to operate with various length units? Children are confused in centimeters-decimeters, and adults sometimes cannot explain to them, what value is greater and how many times.

The answer to this question does not have to look for a long time. Which units of length is convenient to measure the thickness of the match or the body of God's cow? Of course, in millimeters. In what units of length is convenient to measure the length of the handle or pencil? In centimeters.

If you need to measure the width or length of the window, the convenient unit will be decimeters. For the length of the fence, the optimal option will be meters. For the distance between cities - kilometers, for the distance between the continents - also kilometers, as it is the largest among the magnitude of lengths.

Very often, the task is given to the task - to express the length given in meters or decimeters, in millimeters or kilometers, or vice versa. It is not difficult to do this, if you know the ratio of lengths by heart, or use the assistant table. It is much more difficult to translate the volume of volume - liters into square decimeters or vice versa, but also for the measures of volume there are its tables, successfully helping to assimilate the relationship between values.

Value - This is what can be measured. Concepts such as length, area, volume, weight, time, speed, etc. are called values. The value is measurement resultsIt is determined by the number expressed in certain units. Units in which the value is measured, called units of measure.

For the designation of the magnitude, the number is written, and next to the name of the unit in which it was measured. For example, 5 cm, 10 kg, 12 km, 5 min. Each value has countless values, for example, the length can be equal to: 1 cm, 2 cm, 3 cm, etc.

The same value can be expressed in different units, such as kilograms, grams and tons - these are weight measurement units. The same value in different units is expressed different numbers. For example, 5 cm \u003d 50 mm (length), 1 h \u003d 60 min (time), 2 kg \u003d 2000 g (weight).

Measure any value - it means to find out how many times it contains another value of the same kind, adopted per unit of measurement.

For example, we want to find out the exact length of some room. So we need to measure this length using another length, which is well known to us, for example, with a meter. To do this, we postpone the meter on the length of the room as many times as possible. If it meets the length of the room is exactly 7 times, then its length is 7 meters.

As a result, the measurement of the magnitude is obtained or named number, for example, 12 meters, or several named numbers, for example 5 meters of 7 centimeters, the totality of which is called compound nominated number.

Measures

In each state, the government has established certain units of measure for different quantities. Accurately calculated unit of measure, taken as a sample, is called etalon or exemplary unit. Made exemplary meters, kilograms, centimeters, etc., on which units for everyday use are made. Units included and approved by the state are called measures.

Measures are called uniformIf they serve to measure the values \u200b\u200bof the same kind. So, grams and kilograms are homogeneous measures, as they serve to measure weight.

Units

Below are the units of measurement of different quantities that are often found in Mathematics tasks:

Weight / Mass Measures

• 1 ton \u003d 10 centners
• 1 centner \u003d 100 kilograms
• 1 kilogram \u003d 1000 grams
• 1 gram \u003d 1000 milligrams

• 1 kilometer \u003d 1000 meters
• 1 meter \u003d 10 decimeters
• 1 decimeter \u003d 10 centimeters
• 1 centimeter \u003d 10 millimeters

• 1 square kilometer \u003d 100 hectares
• 1 hectare \u003d 10,000 square meters. metram
• 1 square meter \u003d 10,000 square meters. Santimeters
• 1 square centimeter \u003d 100 square meters. millimeters

• 1 cubic. meter \u003d 1000 cubic meters. Decimeters
• 1 cubic. Decimeter \u003d 1000 cubic meters. Santimeters
• 1 cubic. Santimeter \u003d 1000 cubic meters. millimeters

Consider such a magnitude as liter. A liter is used to measure the capacity of blood vessels. A liter is a volume that is equal to one cubic decimeter (1 liter \u003d 1 cubic meter. Decimeter).

Time measures

• 1st century (century) \u003d 100 years
• 1 year \u003d 12 months
• 1 month \u003d 30 days
• 1 week \u003d 7 days
• 1 day \u003d 24 hours
• 1 hour \u003d 60 minutes
• 1 minute \u003d 60 seconds
• 1 second \u003d 1000 milliseconds

In addition, use such time measurement units as a quarter and decade.

• quarter - 3 months
• decade - 10 days

The month is accepted in 30 days, if you do not need to determine the number and name of the month. January, March, May, July, August, October and December - 31 days. February in a simple year - 28 days, February in the leap year - 29 days. April, June, September, November - 30 days.

The year is (approximately) the time during which the Earth makes a complete turn around the sun. It is customary to consider every three consecutive years to 365 days, and the next fourth is the next - in 366 days. Year containing 366 days called leap, and the years containing 365 days - simple. By the fourth year, one extra day is added for the following reason. The time of circulation of the Earth around the Sun contains in itself not exactly 365 days, but 365 days and 6 hours (approximately). Thus, the simple year is shorter than the true year for 6 hours, and 4 of the ordinary year in short, 4 true years for 24 hours, i.e. on one day. Therefore, each fourth year add one day (February 29).

On the other types of magnitude you will learn as the last study of various sciences.

Abbreviated names of Mer.

Abbreviated names of measures are taken to record no point:

Kilometer - km Meter - M. Decimeter - DM. Santimeter - see Millimeter - MM.	Weight / Mass Measures tona - T. centner - C. kilogram - kg gram - G. milligram - MG.
Square measures (square measures) sq. kilometer - km 2 hectar - G. sq. meter - m 2 sq. Santimeter - cm 2 sq. Millimeter - mm 2	cube meter - m 3 cube Decimeter - DM 3 cube Santimeter - cm 3 cube Millimeter - mm 3
Time measures century - B. year - G. month - m or months week - n or week day - s or d (day) hour - Ch minute - M. second - S. millisecond - MS.	Vessel capacity measure liter - L.

Measuring instruments

For measuring different quantities, special measuring instruments are used. Some of them are very simple and are intended for simple measurements. Such instruments include a measuring ruler, roulette, measuring cylinder, etc. Other measuring instruments are more complex. Such devices include stopwalls, thermometers, electronic scales, etc.

Measuring instruments, as a rule, have a measuring scale (or briefly). This means that bar divisions are applied on the instrument, and the corresponding value is written next to each bar division. The distance between two strokes, near which the value is written, can be additionally divided into several smaller divisions, these divisions are most often indicated by numbers.

To determine what value of the value corresponds to each small division, it is not difficult. For example, the figure below shows the measuring ruler:

Figures 1, 2, 3, 4, etc. indicate distances between strokes, which are divided into 10 identical divisions. Consequently, each division (the distance between the nearest strokes) corresponds to 1 mm. This value is called price division scale Measuring instrument.

Before proceeding with the measurement of the value, the price of dividing the scale of the instrument used should be determined.

In order to determine the fission price, it is necessary:

1. Find the two nearest touches of the scale, near which the values \u200b\u200bare written.
2. The deduction from the larger value is less and the resulting number is divided into the number of divisions between them.

As an example, we will determine the division of the thermometer scale depicted in the picture on the left.

Take two strokes that are applied numerical values Measured value (temperature).

For example, touches with notation 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 \u003d 1 ° C

Consequently, the thermometer shows 47 ° C.

Measure various values \u200b\u200bin everyday life You have to constantly each of us. For example, to come in time to school or to work, it is necessary to measure the time that will be spent on the road. Meteorologists for weather prediction measure temperature, atmosphere pressure, wind speed, etc.

In this lesson, we will look at the units of length, square and table units of the square. Consider various units of measurement of length and square, we will find out in what cases they are used. We systematize our knowledge using the table. We decide a number of examples for the translation of one units of measurement to others.

You are familiar with various length units. What units of length are convenient to use when measuring the thickness of the match or the length of the body of God's cows? I think you called millimeters.

What units of length are convenient to use when measuring the length of the pencil? Of course, centimeters (see Fig. 1).

Fig. 1. Measurement length

What units of length are convenient to use when measuring the width or length of the window? It is convenient to measure decimeters.

And the length of the corridor or the length of the fence? We use meters (see Fig. 2).

Fig. 2. Measurement length

To measure larger distances, for example, distances between cities, use a larger than meter, a number of length - a kilometer (see Fig. 3).

Fig. 3. Measurement length

1 kilometer 1000 meters.

Express the distance in kilometers.

1 kilometer is a thousand meters, it means that the number of thousands will denote kilometers.

8000 m \u003d 8 km

385007 m \u003d 385 km 7 m

34125 m \u003d 34 km 125 m

Among the amount of hundreds, tens and units indicate meters.

It can be reasoned differently: 1 km a thousand times more than 1 meter, it means that the number of kilometers should be 1000 times less than the number of meters. Therefore, 8000: 1000 \u003d 8, the number 8 means the number of kilometers.

385007: 1000 \u003d 385 (OST. 7). The number 385 denotes kilometers, the residue is the number of meters.

34125: 1000 \u003d 34 (OST. 125), that is, 34 kilometers of 125 meters.

Read the table of length (see Fig. 4). Try to remember it.

Fig. 4. Table of length units

For measuring areas, different measurements use. The square centimeter is a square 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 rice . 7).

Fig.5. Square centimeter

Fig. 6. Square decimeter

Fig. 7. Square meter

For measuring large squares Use a square kilometer is a square, the side of which is 1 km (see Fig. 8).

Fig. 8. Square kilometer

The words "square kilometer" abbreviated with the number are recorded so - 1 km 2, 3 km 2, 12 km 2. Square kilometers are measured, for example, city square, Moscow Square S \u003d 1091 km 2.

Calculate how many square meters in one square kilometer. To find the square of the square, you need to multiply the length to the width. We are given a square with a side of 1 km. We know that 1 km \u003d 1000 m, it means to find the area of \u200b\u200bsuch a square, multiply 1000 m per 1000 m, it turns out 1,000,000 m 2 \u003d 1 km 2.

Express 2 km 2 square meters. We will argue like this: as 1 km 2 is 1,000,000 m 2, that is, the number of square meters a million times more than the number of square kilometers, so I will multiply 2 per 1,000,000, we get 2,000,000 m 2.

56 km 2: Multiply 56 per 1,000,000, we get 56,000,000 m 2.

202 km 2 15 m 2: 202 ∙ 1 000 000 000 + 15 \u003d 202 000 000 m 2 + 15 m 2 \u003d 202 000 015 m 2.

To measure small areas, a square millimeter is used (mm 2). This is a square, the side of which is 1 mm. The words "square millimeter" with the number are recorded as follows: 1 mm 2, 7 mm 2, 31 mm 2.

Calculate how many square millimeters in one square centimeter. To find the square of the square, you need to multiply the length to the width. We are given a square with a side of 1 cm. We know that 1 cm \u003d 10 mm. So, to find the area of \u200b\u200bsuch a square, multiply 10 mm by 10 mm, it turns out 100 mm 2.

Express 4 cm 2 square millimeters. We will argue like this: as 1 cm 2 is 100 mm 2, that is, the number MM 2 100 times more numbers See 2, so I will multiply 4 per 100, we get 400 mm 2.

16 cm 2: Multiply 16 per 100 \u003d 1600 mm 2.

31 cm 2 7 mm 2: This is 31 ∙ 100 + 7 \u003d 3100 + 7 \u003d 3107 mm 2.

In life, such areas of Square as AR and Hectar are often used. AR is a square with a side of 10 m (see Fig. 9). In terms of numbers, it is written in short: 1 A, 5 A, 12 a.

Fig. 9. 1 AR.

1 A \u003d 100 m 2, so it is often called weaving.

Hectar is a square with a side of 100 m (see Fig. 10). The word "hectare" in numbers abbreviated as follows: 1 hectare, 6 hectares, 23 hectares. 1 ha \u003d 10,000 m 2.

Fig. 10. 1 hectare

Calculate how many AROs in 1 hectare.

1 ha \u003d 10,000 m 2

1 A \u003d 100 m 2, So, 10000: 100 \u003d 100 A

Now carefully consider the table of units of the area (see Fig. 11), try to remember it.

Fig. 11. Table Units Square

In the lesson, we met a new unit of length - km and units of Square - M 2, km 2, a, ha.

1. Bashmakov M.I. Nefodeova M.G. Mathematics. 4th grade. M.: Astrel, 2009.
2. M. I. Moro, M. A. Bantova, G. V. Belfyukov and others. Mathematics. 4th grade. Part 1 of 2, 2011.
3. Demidova T. E. Kozlova S. A. Tonky A. P. Mathematics. 4th grade 2nd ed., Act. - M.: Balam, 2013.

1. School.xvatit.com ().
2. Mer.kakras.ru ().
3. Dpva.info ().

Homework

1. Find the square of the square with a side of 15 dm.
2. Express: Square meters: 5 hectares; 3 hectares 18 A; 247 acres; 16 A;
3. in hectares: 420,000 m 2; 45 km 2 19 hectares;
4. in Arash: 43 hectares; 4 hectares 5 A; 30 700 m 2; 5 km2 13 hectares;
5. in hectares and arah: 930 A; 45 700 m 2.