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1 square decimeter [dm²] = 100 square centimeter [cm²]
Initial value
Converted value
square meter square kilometer square hectometer square decameter square decimeter square centimeter square millimeter square micrometer square nanometer hectare ar barn square mile sq. mile (US, surveyor) square yard square foot² sq. foot (USA, surveyor) square inch circular inch township section acre acre (USA, surveyor) ore square chain square rod rod² (USA, surveyor) square perch square rod sq. thousandth circular mil homestead sabin arpan cuerda square castilian cubit varas conuqueras cuad cross section of electron tithe (government) tithe economic round square verst square arshin square foot square fathom square inch (Russian) square line Planck area
Data transfer and Kotelnikov's theorem
More about the area
General information
Area is the size of a geometric figure in two-dimensional space. It is used in mathematics, medicine, engineering and other sciences, for example in calculating the cross-section of cells, atoms, or pipes such as blood vessels or water pipes. In geography, area is used to compare the sizes of cities, lakes, countries, and other geographic features. Population density calculations also use area. Population density is defined as the number of people per unit area.
Units
Square meters
Area is measured in SI units in square meters. One square meter is the area of a square with a side of one meter.
Unit square
A unit square is a square with sides of one unit. The area of a unit square is also equal to one. In a rectangular coordinate system, this square is located at coordinates (0,0), (0,1), (1,0) and (1,1). On the complex plane the coordinates are 0, 1, i And i+1, where i- imaginary number.
Ar
Ar or weaving, as a measure of area, is used in the CIS countries, Indonesia and some other European countries, to measure small urban objects such as parks when a hectare is too large. One are is equal to 100 square meters. In some countries this unit is called differently.
Hectare
Real estate, especially land, is measured in hectares. One hectare is equal to 10,000 square meters. It has been in use since the French Revolution, and is used in the European Union and some other regions. Just like the macaw, in some countries the hectare is called differently.
Acre
In North America and Burma, area is measured in acres. The hectares are not used there. One acre is equal to 4046.86 square meters. An acre was originally defined as the area that a farmer with a team of two oxen could plow in one day.
Barn
Barns are used in nuclear physics to measure the cross section of atoms. One barn is equal to 10⁻²⁸ square meters. The barn is not a unit in the SI system, but is accepted for use in this system. One barn is approximately equal to the cross-sectional area of a uranium nucleus, which physicists jokingly called “as huge as a barn.” Barn in English is “barn” (pronounced barn) and from a joke among physicists this word became the name of a unit of area. This unit originated during World War II, and was liked by scientists because its name could be used as a code in correspondence and telephone conversations within the Manhattan Project.
Area calculation
The area of the simplest geometric figures is found by comparing them with the square of a known area. This is convenient because the area of the square is easy to calculate. Some formulas for calculating the area of geometric figures given below were obtained in this way. Also, to calculate the area, especially of a polygon, the figure is divided into triangles, the area of each triangle is calculated using the formula, and then added. The area of more complex figures is calculated using mathematical analysis.
Formulas for calculating area
- Square: square side.
- Rectangle: product of the parties.
- Triangle (side and height known): the product of the side and the height (the distance from that side to the edge), divided in half. Formula: A = ½ah, Where A- square, a- side, and h- height.
- Triangle (two sides and the angle between them are known): the product of the sides and the sine of the angle between them, divided in half. Formula: A = ½ab sin(α), where A- square, a And b- sides, and α - the angle between them.
- Equilateral triangle: side squared divided by 4 and multiplied by the square root of three.
- Parallelogram: the product of a side and the height measured from that side to the opposite side.
- Trapezoid: the sum of two parallel sides multiplied by the height and divided by two. The height is measured between these two sides.
- Circle: the product of the square of the radius and π.
- Ellipse: product of semi-axes and π.
Surface Area Calculation
You can find the surface area of simple volumetric figures, such as prisms, by unfolding this figure on a plane. It is impossible to obtain a development of the ball in this way. The surface area of a sphere is found using the formula by multiplying the square of the radius by 4π. From this formula it follows that the area of a circle is four times less than the surface area of a ball with the same radius.
Surface areas of some astronomical objects: Sun - 6,088 x 10¹² square kilometers; Earth - 5.1 x 10⁸; thus, the surface area of the Earth is approximately 12 times smaller than the surface area of the Sun. The Moon's surface area is approximately 3.793 x 10⁷ square kilometers, which is about 13 times smaller than the Earth's surface area.
Planimeter
The area can also be calculated using a special device - a planimeter. There are several types of this device, for example polar and linear. Also, planimeters can be analog and digital. In addition to other functions, digital planimeters can be scaled, making it easier to measure features on a map. The planimeter measures the distance traveled around the perimeter of the object being measured, as well as the direction. The distance traveled by the planimeter parallel to its axis is not measured. These devices are used in medicine, biology, technology, and agriculture.
Theorem on properties of areas
According to the isoperimetric theorem, of all figures with the same perimeter, the circle has the largest area. If, on the contrary, we compare figures with the same area, then the circle has the smallest perimeter. The perimeter is the sum of the lengths of the sides of a geometric figure, or the line that marks the boundaries of this figure.
Geographical features with the largest area
Country: Russia, 17,098,242 square kilometers, including land and water. The second and third largest countries by area are Canada and China.
City: New York is the city with the largest area of 8683 square kilometers. The second largest city by area is Tokyo, occupying 6993 square kilometers. The third is Chicago, with an area of 5,498 square kilometers.
City Square: The largest square, covering 1 square kilometer, is located in the capital of Indonesia, Jakarta. This is Medan Merdeka Square. The second largest area, at 0.57 square kilometers, is Praça doz Girascoes in the city of Palmas, Brazil. The third largest is Tiananmen Square in China, 0.44 square kilometers.
Lake: Geographers debate whether the Caspian Sea is a lake, but if so, it is the largest lake in the world with an area of 371,000 square kilometers. The second largest lake by area is Lake Superior in North America. It is one of the lakes of the Great Lakes system; its area is 82,414 square kilometers. The third largest lake in Africa is Lake Victoria. It covers an area of 69,485 square kilometers.
metric unit of area = 0.01 square meter = 100 sq. centimeters = 15.50 sq. inches = 5.061 sq. top; The abbreviated designation for square decimeter legalized in the USSR: Russian - “dm 2”, or “sq. dm”, Latin - “dm2”.
- - linear measure of the metric system = 0.1 meters = 10 centimeters = 3.937 inches - 2.2497 vershok; The abbreviation a, legalized in the USSR: Russian - “dm”, Latin - “dm”...
Reference commercial dictionary
- -) a tenth of a meter...
Great Soviet Encyclopedia
- - a tenth of a meter, denoted...
Large encyclopedic dictionary
- - ; pl. decime/three, R....
- - ...
Spelling dictionary of the Russian language
- - decime/tr,...
Together. Apart. Hyphenated. Dictionary-reference book
- - DECIMETER, husband. A unit of measurement equal to one tenth of a meter. | adj. decimeter, -aya, -oh. Decimeter radio waves...
Ozhegov's Explanatory Dictionary
- - SQUARE, -aya, -oe; -ten, -tna. 1. see square. 2. full Shaped like a square; like a square. K. table. Square brackets. 3. Shaped like a square. K. chin. Square shoulders...
Ozhegov's Explanatory Dictionary
- - SQUARE, square, square. 1. adj. to a square of 4 digits. . Square measures. Square meter. Square root. Quadratic equation. 2. Shaped like a square. Square item...
Ushakov's Explanatory Dictionary
- - decimeter m. A unit of length equal to one tenth of a meter...
Explanatory Dictionary by Efremova
- - square I adj. 1. ratio with noun square I, associated with it 2. Peculiar to the square, characteristic of it. 3. Shaped like a square. II adj. 1. ratio with noun square III associated with it; quadratic 1.. 2...
Explanatory Dictionary by Efremova
- - ...
Spelling dictionary-reference book
- - decim "...
Russian spelling dictionary
- - DECIMETER a, m. décimètre m. French unit of length, one tenth of a metre. Jan. 1803 1 694. A unit of length equal to one tenth of a meter. BAS-2. Decimeter. 1831. Petrushevsky 321...
Historical Dictionary of Gallicisms of the Russian Language
- - See DESIMETER...
Dictionary of foreign words of the Russian language
- - ...
Word forms
"square decimeter" in books
Nuss broit (square bread)
From the book All about Jewish cuisine author Rosenbaum (compiler) GennadySquare root of two = 1.414...
author Prokopenko IolantaThe square root of two = 1.414... And every part of the city has four sides, And every inhabitant too, And every pot, and vessel, and clothing, and house utensils, And every house has four walls. William Blake, English poet and artist, mystic and visionary In sacred geometry
Square root of five = 2.236
From the book Sacred Geometry. Energy codes of harmony author Prokopenko IolantaSquare root of five = 2.236 The Pythagoreans revered the number 5 as sacred. It is directly related to the concept of the golden ratio. The golden ratio is the arithmetic mean of 1 and the root of 5. ?5/2 is the diagonal of half a square, is a geometric
24. Square circle
From the book The Pig Who Wanted to Be Eaten author Bajini Julian24. Square circle And God said to the philosopher: “I am the Lord your God, I am omnipotent. Anything you say can be done. It’s easy!” And the philosopher answered God: “Okay, Your Omnipotence. Make everything blue red and everything red blue.” And God said: “Let the colors change places!” AND
Semi-dug square pool
From the book Modern outbuildings and site development author Nazarova Valentina IvanovnaSemi-dug square pool To begin with, we will describe in detail the technological operations of constructing a pool measuring 2.5x2.5 m on a site. The pool is semi-dug, which means that excavation work awaits. A pit is dug 2.5x2.5 m, 0.6 m deep. Make drainage immediately. This
4.4. "Square Man"
From the book Art and Beauty in Medieval Aesthetics by Eco Umberto4.4. “Square Man” However, along with this naturalistic cosmology, in the same 12th century, another aspect of Pythagorean cosmology was developed in great detail - we are talking about the resuscitation and unification of traditional motifs associated with the square man (homo quadratus).
Square cover with buttons
From the book Pillow Toys author Boyko Elena AnatolevnaSquare cover with buttons To make a square cover you will need 3 buttons with a diameter of 1.2 cm (you can use buttons covered with fine-checked shirt fabric), sewing threads corresponding to the color and thickness of the fabric used, paper and a pencil.
Decimeter
From the book Great Soviet Encyclopedia (DE) by the author TSB20. Quadratic Trinomial, or Algebraic Calculation Package
From the book Sketches for Programmers [incomplete, chapters 1–24] by Wetherell Charles20. Quadratic Trinomial, or Algebraic Calculus Package The main difficulty that a programmer faces in most programming languages is the need to break down his equations into small parts when writing calculations. Yes, if required
154. Square meter
From the book Fun Problems. Two hundred puzzles author Perelman Yakov Isidorovich154. Square meter I knew a schoolboy who, having heard for the first time that there are a million square millimeters in a square meter, did not want to believe it. No explanation was convincing to him. “Where do so many of them come from? - he was perplexed. - Here I have a sheet of millimeter paper.
100. Square meter
author Perelman Yakov Isidorovich100. Square meter When Alyosha heard for the first time that a square meter contains a million square millimeters, he did not want to believe it. - Where do so many of them come from? - he was surprised. - Here I have a sheet of graph paper exactly a meter long and wide. So
100. Square meter
From the book Scientific Tricks and Riddles author Perelman Yakov Isidorovich100. Square meter On the same day, Alyosha could not be sure of this. Even if he counted continuously around the clock, even then he would count only 86,400 cells in one day. After all, there are only 86,400 seconds in 24 hours. He would have to count more than ten days without interruption, but
Square Forehead The square shape of the forehead is determined by the direction of the hairline straight up from the temples, and then the same straight line parallel to the eyebrows. The forehead looks like a square or rectangle (Fig. 3.6). Such people, like people with a trapezoidal forehead, are prone to
Lesson objectives: introduce students to a new unit of measurement of area - the square decimeter.
Tasks:
- Introduce the concept of “square decimeter”, give an idea of the use of the new unit of measurement, its connection with the square centimeter.
- Develop logical thinking, attention, memory, observation; Computational skills; Length and area measurement skills.
- Develop the ability to work in pairs, perseverance, and accuracy.
DURING THE CLASSES
1. Communicating the topic and purpose of the lesson
– To find out what we will be working on today, complete the warm-up tasks. Find the odd one in each group and choose the corresponding letter.
P) 3, 5, 7
P) 16, 20, 24
C) 28, 32, 36
K) 5 + 5 + 5
L) 5 + 23 + 8
M) 23 + 23 + 8
3) Choose a solution to the problem: “36 tits flew to the feeder, nuthatches 9 times less. How many nuthatches have arrived?
ABOUT) 36: 9
P) 36 – 9
P) 36 + 9
H) RECTANGLE
W) SQUARE
SCH) TRIANGLE
A) KG
B) MM
B) SM
D) (5 + 3) 2
D) (5 – 3) 2
E) 5 2 + 3 2
b) WHAT? TIMES MORE (x)
E) WHAT? TIMES MORE (:)
I AM IN? TIMES LESS (:)
- Read what word you came up with. (Square)
– Why do you think? (In previous lessons we learned to calculate the area of shapes)
– Let’s continue this work and get acquainted with the new unit of measurement of area.
– What figure area do we already know how to calculate?
– Name the unit of measurement for area.
II. Updating knowledge
1) Mathematical dictation
- Calculate the product of numbers 4 and 8
- Increase the number 8 by 6 times
- Reduce the number 40 by 4 times
- The tailor made 7 identical suits from 14 meters of fabric. How many meters of fabric were needed for each suit?
- What number must be tripled to make 15?
- What is the perimeter of a square whose side is 2 cm?
- How many cm are in 1 dm?
- To renovate the apartment, we bought 4 cans of paint, 3 kg each. How many kg of paint did you buy?
Answers: 32, 48, 10, 2m, 5, 8 cm, 10cm, 12 kg.
– What 2 groups can we divide our answers into? (Prime and named numbers; even and odd; single-digit and double-digit)
– Underline the named numbers. Among the named ones, name the odd one out. (12 kg)
2) Conversion of quantities
(Individual work at the board is carried out by 2 students)
– Now let’s check how the students performed the transformation of named quantities
1 cm = ... mm
1 dm = ... cm
1 m = ... dm
65 cm = ... dm ... cm
27 mm = … cm … mm
8 m 9 dm = … dm
– What is measured in these units? (length)
– What other units of measurement do you know? (Area units)
3) Solving problems to find the area of a rectangle and square.
There are shapes on the board (rectangles and squares).
- Let's remember the formulas for finding the areas of these figures.
(One of the students goes out and selects the necessary ones from the many formulas for finding the perimeter and area for rectangles and squares).
S rectangle = a x b
S square = a x a
P squared = a x 4
P rectangle = (a + b) x 2
– What unit of measurement of area do you know? (cm 2)
– What is a square centimeter? (This is a square whose side is 1 cm.)
– What is its area? (1 cm 2)
III. Update.
1) – Today we will continue to talk about the area of a rectangle and get acquainted with a new unit of measurement of area, a new measure.
Divide the numbers into 2 groups:
3 cm
2 dm
46
4 mm
100
18 cm 2
2 dm 2
18
(Numbers can be divided into named numbers and ordinary numbers, numbers indicating length, area)
– Read the units of area? (18 square centimeters, 2 square decimeters)
– What are the possible sides of a rectangle with an area of 18 sq. cm? (2 cm and 9 cm, 6 cm and 3 cm, 18 cm and 1 cm)
– Which unit of area are we already familiar with? (Square centimeter).
– Which unit of area from those mentioned have not yet been discussed in detail? (dm2)
– Try to formulate the topic of the lesson? (Let's get acquainted with the square decimeter)
– We will get acquainted with the square decimeter, find out how it is related to the square centimeter, and learn to solve problems using a new unit of area
- But let's remember how you can measure the area of a rectangle? (Divide into square centimeters using a palette; overlaying shapes; applying measurements; measure length and width and multiply the data).
2) Work in pairs
– Now you will work in pairs. There is an envelope with figures on your table. Take a green rectangle out of the envelope and find its area yourself.
- Let's remember what needs to be done for this? (Measure length and width, multiply length by width)
3 x 4 =12 sq. cm.
– We found out the area of the rectangle. It is equal to 12 sq.cm. In what units did we measure the area of this rectangle? (In sq.cm).
IV. New topic
1) Introducing the square decimeter
– Place a yellow rectangle in front of you and take a small square out of the envelope. What can you say about this square? (This measurement is 1 square centimeter)
– Try using this measure to measure the area of a rectangle. How will you do this? (Apply a square)
– What is the area of this rectangle? (We didn’t have time to find out)
- Why didn’t you have time, you have everything to measure, you worked in pairs, what happened? (The measure is small, but the rectangle is large, it takes a long time to lay it out)
– There is another measure in the envelope, a large one, try to measure with this measure. (Measurement fit 2 times)
– Why did you complete this task quickly? (The measure is large, it was easy to measure)
– Now, using a ruler, measure the sides of the large measure (10 cm)
– How else can we write 10 cm? (1 dm)
– So a large measure is a square with a side of 1 dm. Look in your notebook at the small square you drew. Compare with a large measure. Think and tell me what in mathematics we call a square with a side of 1 dm? (1 square decimeter).
2) Working with the textbook
– Read the explanation on page 14.
– Why did people need to use a new unit of measurement of 1 sq. dm, if they already had a unit of 1 sq. cm? (To make it more convenient to measure large figures or objects)
– What do you think, the area of what can be measured in dm 2? (Area of a textbook, notebook, table, blackboard).
3) The relationship between square dm and square cm.
– Let’s calculate how many square centimeters will fit in 1 square. dm. How can I do that? (Divide the large square by sq. cm and count; we know that the side of the large square is 10 cm, we can multiply 10 by 10).
– Some suggested dividing by square centimeters and counting. Let's try to do this.
– Try to count quickly. Which way is easier and faster? (Multiply 10 by 10)
- Do the math. (100 sq. cm)
1 sq. dm = 100 sq.cm
– So, what have we learned now? (How is sq. dm related to sq. cm)
V. Physical education minute
VI. Consolidation
– Now we will learn to solve problems using a new unit of area.
1) Problem P. 14, No. 3
– The height of the rectangular mirror is 10 dm, and the width is 5 dm. What is the area of the mirror?
– In what units are the height and width of the mirror measured? (in dm)
- Why? (Large mirror)
The student at the blackboard decides with an explanation.
2) Problem p. 14, No. 4 (Two students at the blackboard)
3) Solving examples (orally in a chain)
L – 9 x (38 – 30) = M – 8 x 7 + 5 x 2 =
O – 65 – (49 – 19) = C – 9 x 9 + 28: 7 =
D – 28 + 45: 5 = Y – 7 x (100 – 91) =
VII. Lesson summary
– Our lesson has come to an end.
– What topic were you working on?
– In what units is area measured?
– How many square CM are there in 1 square DM?
– What new things have you learned for yourself?
– What did you like to do the most?
– What were the difficulties?
VIII. Homework
– Review the new material and consolidate the ability to find the area of rectangles – p. 14, No. 2.
In this lesson, students are given the opportunity to become familiar with another unit of measurement of area, the square decimeter, learn how to convert square decimeters to square centimeters, and also practice performing various tasks on comparing quantities and solving problems on the topic of the lesson.
Read the topic of the lesson: “The unit of area is the square decimeter.” In this lesson we will get acquainted with another unit of area, the square decimeter, and learn how to convert square decimeters into square centimeters and compare values.
Draw a rectangle with sides 5 cm and 3 cm and label its vertices with letters (Fig. 1).
Rice. 1. Illustration for the problem
Let's find the area of the rectangle. To find the area, you need to multiply the length by the width of the rectangle.
Let's write down the solution.
5*3 = 15 (cm 2)
Answer: the area of the rectangle is 15 cm 2.
We calculated the area of this rectangle in square centimeters, but sometimes, depending on the problem being solved, the units of measurement of area may be different: more or less.
The area of a square whose side is 1 dm is the unit of area, square decimeter(Fig. 2) .
Rice. 2. Square decimeter
The words “square decimeter” with numbers are written as follows:
5 dm 2, 17 dm 2
Let's establish the relationship between square decimeter and square centimeter.
Since a square with a side of 1 dm can be divided into 10 strips, each of which is 10 cm 2, then there are ten tens, or one hundred square centimeters in a square decimeter (Fig. 3).
Rice. 3. One hundred square centimeters
Let's remember.
1 dm 2 = 100 cm 2
Express these values in square centimeters.
5 dm 2 = ... cm 2
8 dm 2 = ... cm 2
3 dm 2 = ... cm 2
Let's think like this. We know that there are one hundred square centimeters in one square decimeter, which means that there are five hundred square centimeters in five square decimeters.
Test yourself.
5 dm 2 = 500 cm 2
8 dm 2 = 800 cm 2
3 dm 2 = 300 cm 2
Express these values in square decimeters.
400 cm 2 = ... dm 2
200 cm 2 = ... dm 2
600 cm 2 = ... dm 2
We explain the solution. One hundred square centimeters equals one square decimeter, which means that there are four square decimeters in 400 cm2.
Test yourself.
400 cm 2 = 4 dm 2
200 cm 2 = 2 dm 2
600 cm 2 = 6 dm 2
Follow the steps.
23 cm 2 + 14 cm 2 = ... cm 2
84 dm 2 - 30 dm 2 =… dm 2
8 dm 2 + 42 dm 2 = ... dm 2
36 cm 2 - 6 cm 2 = ... cm 2
Let's look at the first expression.
23 cm 2 + 14 cm 2 = ... cm 2
We add up the numerical values: 23 + 14 = 37 and assign the name: cm 2. We continue to reason in a similar way.
Test yourself.
23 cm 2 + 14 cm 2 = 37 cm 2
84dm 2 - 30 dm 2 = 54 dm 2
8dm 2 + 42 dm 2 = 50 dm 2
36 cm 2 - 6 cm 2 = 30 cm 2
Read and solve the problem.
The height of the rectangular mirror is 10 dm, and the width is 5 dm. What is the area of the mirror (Fig. 4)?
Rice. 4. Illustration for the problem
To find out the area of a rectangle, you need to multiply the length by the width. Let us pay attention to the fact that both quantities are expressed in decimeters, which means that the name of the area will be dm 2.
Let's write down the solution.
5 * 10 = 50 (dm 2)
Answer: mirror area - 50 dm2.
Compare the values.
20 cm 2 ... 1 dm 2
6 cm 2 … 6 dm 2
95 cm 2…9 dm
It is important to remember: in order for quantities to be compared, they must have the same names.
Let's look at the first line.
20 cm 2 ... 1 dm 2
Let's convert square decimeter to square centimeter. Remember that there are one hundred square centimeters in one square decimeter.
20 cm 2 ... 1 dm 2
20 cm 2 … 100 cm 2
20 cm 2< 100 см 2
Let's look at the second line.
6 cm 2 … 6 dm 2
We know that square decimeters are larger than square centimeters, and the numbers for these names are the same, which means we put the sign “<».
6 cm 2< 6 дм 2
Let's look at the third line.
95cm 2…9 dm
Please note that area units are written on the left, and linear units on the right. Such values cannot be compared (Fig. 5).
Rice. 5. Different sizes
Today in the lesson we got acquainted with another unit of area, the square decimeter, we learned how to convert square decimeters into square centimeters and compare values.
This concludes our lesson.
Bibliography
- M.I. Moreau, M.A. Bantova and others. Mathematics: Textbook. 3rd grade: in 2 parts, part 1. - M.: “Enlightenment”, 2012.
- M.I. Moreau, M.A. Bantova and others. Mathematics: Textbook. 3rd grade: in 2 parts, part 2. - M.: “Enlightenment”, 2012.
- M.I. Moro. Mathematics lessons: Methodological recommendations for teachers. 3rd grade. - M.: Education, 2012.
- Regulatory document. Monitoring and evaluation of learning outcomes. - M.: “Enlightenment”, 2011.
- “School of Russia”: Programs for primary school. - M.: “Enlightenment”, 2011.
- S.I. Volkova. Mathematics: Test work. 3rd grade. - M.: Education, 2012.
- V.N. Rudnitskaya. Tests. - M.: “Exam”, 2012.
- Nsportal.ru ().
- Prosv.ru ().
- Do.gendocs.ru ().
Homework
1. The length of the rectangle is 7 dm, the width is 3 dm. What is the area of the rectangle?
2. Express these values in square centimeters.
2 dm 2 = ... cm 2
4 dm 2 = ... cm 2
6 dm 2 = ... cm 2
8 dm 2 = ... cm 2
9 dm 2 = ... cm 2
3. Express these values in square decimeters.
100 cm 2 = ... dm 2
300 cm 2 = ... dm 2
500 cm 2 = ... dm 2
700 cm 2 = ... dm 2
900 cm 2 = ... dm 2
4. Compare the values.
30 cm 2 ... 1 dm 2
7 cm 2 … 7 dm 2
81 cm 2 ...81 dm
5. Create an assignment for your friends on the topic of the lesson.
In this lesson, students are given the opportunity to become familiar with another unit of measurement of area, the square decimeter, learn how to convert square decimeters to square centimeters, and also practice performing various tasks on comparing quantities and solving problems on the topic of the lesson.
Read the topic of the lesson: “The unit of area is the square decimeter.” In this lesson we will get acquainted with another unit of area, the square decimeter, and learn how to convert square decimeters into square centimeters and compare values.
Draw a rectangle with sides 5 cm and 3 cm and label its vertices with letters (Fig. 1).
Rice. 1. Illustration for the problem
Let's find the area of the rectangle. To find the area, you need to multiply the length by the width of the rectangle.
Let's write down the solution.
5*3 = 15 (cm 2)
Answer: the area of the rectangle is 15 cm 2.
We calculated the area of this rectangle in square centimeters, but sometimes, depending on the problem being solved, the units of measurement of area may be different: more or less.
The area of a square whose side is 1 dm is the unit of area, square decimeter(Fig. 2) .
Rice. 2. Square decimeter
The words “square decimeter” with numbers are written as follows:
5 dm 2, 17 dm 2
Let's establish the relationship between square decimeter and square centimeter.
Since a square with a side of 1 dm can be divided into 10 strips, each of which is 10 cm 2, then there are ten tens, or one hundred square centimeters in a square decimeter (Fig. 3).
Rice. 3. One hundred square centimeters
Let's remember.
1 dm 2 = 100 cm 2
Express these values in square centimeters.
5 dm 2 = ... cm 2
8 dm 2 = ... cm 2
3 dm 2 = ... cm 2
Let's think like this. We know that there are one hundred square centimeters in one square decimeter, which means that there are five hundred square centimeters in five square decimeters.
Test yourself.
5 dm 2 = 500 cm 2
8 dm 2 = 800 cm 2
3 dm 2 = 300 cm 2
Express these values in square decimeters.
400 cm 2 = ... dm 2
200 cm 2 = ... dm 2
600 cm 2 = ... dm 2
We explain the solution. One hundred square centimeters equals one square decimeter, which means that there are four square decimeters in 400 cm2.
Test yourself.
400 cm 2 = 4 dm 2
200 cm 2 = 2 dm 2
600 cm 2 = 6 dm 2
Follow the steps.
23 cm 2 + 14 cm 2 = ... cm 2
84 dm 2 - 30 dm 2 =… dm 2
8 dm 2 + 42 dm 2 = ... dm 2
36 cm 2 - 6 cm 2 = ... cm 2
Let's look at the first expression.
23 cm 2 + 14 cm 2 = ... cm 2
We add up the numerical values: 23 + 14 = 37 and assign the name: cm 2. We continue to reason in a similar way.
Test yourself.
23 cm 2 + 14 cm 2 = 37 cm 2
84dm 2 - 30 dm 2 = 54 dm 2
8dm 2 + 42 dm 2 = 50 dm 2
36 cm 2 - 6 cm 2 = 30 cm 2
Read and solve the problem.
The height of the rectangular mirror is 10 dm, and the width is 5 dm. What is the area of the mirror (Fig. 4)?
Rice. 4. Illustration for the problem
To find out the area of a rectangle, you need to multiply the length by the width. Let us pay attention to the fact that both quantities are expressed in decimeters, which means that the name of the area will be dm 2.
Let's write down the solution.
5 * 10 = 50 (dm 2)
Answer: mirror area - 50 dm2.
Compare the values.
20 cm 2 ... 1 dm 2
6 cm 2 … 6 dm 2
95 cm 2…9 dm
It is important to remember: in order for quantities to be compared, they must have the same names.
Let's look at the first line.
20 cm 2 ... 1 dm 2
Let's convert square decimeter to square centimeter. Remember that there are one hundred square centimeters in one square decimeter.
20 cm 2 ... 1 dm 2
20 cm 2 … 100 cm 2
20 cm 2< 100 см 2
Let's look at the second line.
6 cm 2 … 6 dm 2
We know that square decimeters are larger than square centimeters, and the numbers for these names are the same, which means we put the sign “<».
6 cm 2< 6 дм 2
Let's look at the third line.
95cm 2…9 dm
Please note that area units are written on the left, and linear units on the right. Such values cannot be compared (Fig. 5).
Rice. 5. Different sizes
Today in the lesson we got acquainted with another unit of area, the square decimeter, we learned how to convert square decimeters into square centimeters and compare values.
This concludes our lesson.
Bibliography
- M.I. Moreau, M.A. Bantova and others. Mathematics: Textbook. 3rd grade: in 2 parts, part 1. - M.: “Enlightenment”, 2012.
- M.I. Moreau, M.A. Bantova and others. Mathematics: Textbook. 3rd grade: in 2 parts, part 2. - M.: “Enlightenment”, 2012.
- M.I. Moro. Mathematics lessons: Methodological recommendations for teachers. 3rd grade. - M.: Education, 2012.
- Regulatory document. Monitoring and evaluation of learning outcomes. - M.: “Enlightenment”, 2011.
- “School of Russia”: Programs for primary school. - M.: “Enlightenment”, 2011.
- S.I. Volkova. Mathematics: Test work. 3rd grade. - M.: Education, 2012.
- V.N. Rudnitskaya. Tests. - M.: “Exam”, 2012.
- Nsportal.ru ().
- Prosv.ru ().
- Do.gendocs.ru ().
Homework
1. The length of the rectangle is 7 dm, the width is 3 dm. What is the area of the rectangle?
2. Express these values in square centimeters.
2 dm 2 = ... cm 2
4 dm 2 = ... cm 2
6 dm 2 = ... cm 2
8 dm 2 = ... cm 2
9 dm 2 = ... cm 2
3. Express these values in square decimeters.
100 cm 2 = ... dm 2
300 cm 2 = ... dm 2
500 cm 2 = ... dm 2
700 cm 2 = ... dm 2
900 cm 2 = ... dm 2
4. Compare the values.
30 cm 2 ... 1 dm 2
7 cm 2 … 7 dm 2
81 cm 2 ...81 dm
5. Create an assignment for your friends on the topic of the lesson.