A unit of area equal to 100 m2. Square
Subject: "Area Units"
Class: 4
The purpose of the lesson:
Systematize and deepen knowledge about units of area measurement and their practical significance.
Lesson objectives:
consolidate students' knowledge of the relationships between the studied units of area;
practice the ability to convert smaller units of area measurement into larger ones and vice versa;
improve problem solving skills;
cultivate interest in mathematics as an academic subject;
Lesson type: combined
Form: lesson - travel
Lesson materials, visibility:
M.I Moro, M.A. Bantova, G.V. Beltyukova et al. “Mathematics” 4th grade, part 1,
presentation
multimedia projector, screen,
table of ratios of area units.
Lesson plan.
Organizing time.
Checking homework. Verbal counting.
Updating knowledge.
Reinforcing the material learned
Physical education minute.
The solution of the problem.
Working on the material covered.
Reflection.
During the classes.
1. Organizational moment.
Teacher: The bell rang, the lesson begins.
I wish you a good mood throughout the lesson and respectful attitude towards each other.
Today we will go on a journey with unusual heroes.
How many of you recognize them? Name them. (Talismans of the Winter Olympics in Sochi).
In what year will the Olympics be held?
How old will you be? - What class will you study in?
2.Checking homework. Verbal counting.
Let's show our knowledge to our heroes. Let's start the lesson with an arithmetic dictation and at the same time check your homework. In the dictation we will use the answers to expressions from home exercise No. 190.
1. From what number must 2 be subtracted to get the answer to the fourth expression? (1002)
2. Which number is greater than the answer of the first expression to 3000? (3446)
3. The product of two numbers is 3500. The first factor is equal to the answer of the third expression. What is the second factor? (100)
4. How much greater is the number 7601 than the answer to the second expression? (7000)
5. How much do you get if you reduce the number 9850 by the answer to the seventh expression? (9400)
6. Write down the neighbors of the last answer. (599999 and 600001)
(Collective task review)
3. Updating knowledge.
Bunny, Bear, Leopard, Snowflake and Ray live in the house of mascots. They wanted to know the area of their house. Shall we help?
What units of area do you know?
(Write answers on the board and notebooks)
1mm 2 1cm 2 1dm 2 1m 2 1km 2
How do you understand this? (1 mm 2 – this is a square with a side of 1 mm; 1cm 2 is a square with a side of 1 cm, etc.).
Let's establish the relationship between them.
In 1cm 2 – 100mm 2 ; in 1dm 2 – 100 cm 2 ; at 1m 2 – 100dm 2 – 10000cm 2 ; 1km 2 – 100000 m 2
(Write in notebook)
What units of area do you know for measuring land?
Ar – unit of land area equal to 100 m 2 ; Hectare – unit of land area equal to 10,000 m 2 (Write in notebook)
Consider the writing on the board:
400 m 2 ; 600 cm 2 ; 3 a; 2 dm 2 ; 7 ha; 12cm 2
Make a note in your notebook, arranging the units of area in ascending order.
A figure with what area can be drawn in a notebook? (12cm 2 ) Draw.
What is the length and width of your rectangle?
4. Consolidation of the studied material
House of mascots
Now find the area of the mascot rooms. (Find the area in rows and add the result all together)
Find the area of the land on which the house is built.
Convert 50000 m2 into large units of area. (500ar; 5 ha)
Orally:
Express inm 2 - 4 hectares; 5ha; 62a; 12a.
Express inA - 27 hectares; 8ga3a; 96000 m 2
What areas are measured in ares and hectares? (Square land plots)
Olympic Park.
Our heroes invite you to take a trip through the Olympic Park.
The total area of the Olympic Park is 256 hectares. On the territory of the park there are: the central Olympic Square, the Reka Park, the Fisht Olympic Stadium and five ice arenas. Iceberg Winter Sports Palace, Shaiba Ice Arena, Bolshoi Ice Palace,
skating center "Adler Arena", Curling center "Ice Cube". The Fisht Olympic Stadium will be put into operation in August 2013. The opening and closing ceremonies will take place here. Olympic Games, and in 2018, matches of the World Cup.
Express hectares in ares and square meters
Olympic Park 265 hectares -………..ar; ……………………m 2
Winter Sports Palace 12 hectares - …………ar; ……………………m 2
Ice Palace 13 hectares - …………ar; …………………….m 2
Olympic Stadium 17 hectares - …………ar; …………………….m 2
Sports complexes of Gubkin
Can we tell and show the Olympic mascots the sports complexes of our city? Name them.
Express square meters in ares and hectares
Sports complex 66000m 2 - ……...ar; ……. ha………..ar
Sports Palace 10000m 2 - ………ar; ………ha
(write on the board and in notebooks)
Compare how much the area of the Iceberg Winter Sports Palace is larger than the area of the Crystal Sports Palace. What needs to be done for this? (convert area units to square meters, to ares, to hectares)
12ha – 120000m 2 - 1200ar
1ha - 10000m 2 - 100ar
Physical education minute
Problem solving
Snowflake and Ray have prepared a drawing and the conditions of the task for you. You must compose and solve a problem.
(Children make up a problem: “The length of a rectangular plot of land is 100 m, the width is 40 m less than the length. What is the area of the plot?” Solution with commentary, with the solution written in a notebook.)
1)100-40=60(m) - width
2)100*60=6000(m 2 ) - square
6000m 2 =60ar
Answer: 60ar
(The rectangular collective farm field occupies an area of 18 hectares.
The length of the field is 1000m. Find the perimeter.)
18ha=180000m 2
1)180000:10000=180(m)-width
2)(1000+180)*2=2360(m)-perimeter
Answer: 2360m
- Work according to the textbook
- Summary of the lesson. Reflection
What was the goal at the beginning of the lesson?
Have we achieved it?
- Homework
Compose and solve problems using units of area.
>>Math: Area. Area units
Area units
To measure areas, the following units are used: square millimeter (mm 2), square centimeter(cm 2), square decimeter (dm 2), square meter (m 2) and square kilometer (km 2).
For example, a square meter is the area of a square with a side of 1 m, and a square millimeter is the area of a square with a side of 1 mm.
Field areas are measured in hectares (ha). A hectare is the area of a square with a side of 100 m. This means that 1 hectare is equal to 100 100 square meters, that is
1 ha = 10,000 m2.
The area of small plots of land is measured in ares (a). Ar (weave) - square square with side 10 m.
Means, 1 a = 100 m 2.
Because 1 dm = 10 cm, then 1 dm 2 contains 10-10 square centimeters, that is, 1 dm 2 = 100 cm 2.
We also establish that 1 m2 = 100 dm2. Because 1 m = 100 cm, then 1 m2 contains 100 100 square centimeters, that is 1 m 2 = 10000 cm 2.
The relationships between area units are shown on the flyleaf.
3 8 3 - 5 b 3; (5 2 - 4 2) 3 .
775. Calculate:
a) 4! - 4 2 ; b) 6! : 60; at 3! - 5; d) 5! + 5 3 .
776. Compose an expression according to the diagram and find its value (Fig. 76).
777. Solve the problem:
1) Three stories take 34 pages. The first takes 6 pages, and the second is 3 times less than the third. How many pages is the second story?
2) Three lakes have total area 32 hectares. The area of the first lake is 4 times larger than the area of the second, and the area of the third lake is 7 hectares. Find the area of the first lake.
778. Find the meaning of the expression:
1) 767 520: 4: 15: 123; 3) 286 208: 86: 16 505;
2) 312 (9520: 68: 7); 4) 101 376: 48: 24: 8.
779. The length of a rectangular piece of land is 43 m, and its width is 15 m less than its length. Find the perimeter and area of the plot.
780. The length of a rectangular field is 300 m and its width is 200 m. Find the area of the field and express it in ares and hectares.
781. Express:
a) in square meters: 6 hectares 56 a; 2 km 2 67 hectares; 22 km 2 65 ha 9 a; 6 km 2 12 a;
b) in square millimeters: 6 cm 2 15 mm 2; 3 dm 2 8 mm 2 .
782. The workers were allocated 6 hectares of land for garden plots. How many workers received plots if the area of each plot is 12 acres?
783. Thanks to the rationalization proposal, it was possible to save 1250 cm 2 of leather for every 50 pairs of boots. How much leather is saved in 25 working days if 1500 pairs of boots are produced every day?
784. One of the sides of the triangle has a length of 3 dm 6 cm, and the other is twice as long. The length of the third side is 4 dm 3 cm less than the sum of the lengths of the first two sides. Find the perimeter of the triangle.
785. The young worker completed the task in 8 hours, producing 18 parts per hour. How many hours will it take his mentor to complete the same task if he does 6 more details per hour than the young man? worker ?
786. An invoice received several years ago in a store has not been completely preserved (Fig. 77). Restore your account.
787. Productivity is the mass of plant harvest collected per unit area. Denoting the yield by the letter t, the area by the letter S, write down the formula for finding the mass M of the crop. Determine using this formula:
a) what grain yield will a farmer receive from a field of 25 hectares with a yield of 35 centners per hectare;
b) what is the yield of strawberries if 108 kg were harvested from a bed of 18 m2.
788. Find the meaning of the expression:
a) 182 + 52; b) (18 + 5)2; c) 18 + 52.
789. Follow these steps:
a) 980 081 + (341 640 - 1263 209);
b) 400,615 - (352,203 - 2031,138).
N.Ya. VILENKIN, V. I. ZHOKHOV, A. S. CHESNOKOV, S. I. SHVARTSBURD, Mathematics grade 5, Textbook for general education institutions
Help for schoolchildren online, Mathematics for 5th grade download, calendar and thematic planning
Before you become familiar with the units of area, you need to pay attention to how to calculate the area of a figure. The first figure that is studied in school is the 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.
$$S = 1cm * 1 cm = 1 cm^2$$
Rice. 2. Chessboard.
To calculate the area of a chessboard, you need to multiply the width by the length. That is:
$$S= 8 * 8 = 64 square$$
And if we take 1 square of a 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, and accordingly they have different symbols.
Rice. 3. A square with a side that is measured in different units.
The correct unit of measurement for area is called a square centimeter or a square meter, depending on the units in which the sides are measured.
So, the units for measuring area are:
- $1 cm^2$;
- $1 m^2$;
- $1 km^2$;
- $1 hectare (ha)$;
- $1 ar(a.)$, otherwise called weaving
We often use some units of measurement in everyday life to denote land plots. These are hectares, hundred square meters and ares.
When solving problems, you must pay attention to units of measurement. Centimeters can only be added to centimeters, and meters only to meters. Therefore, you should always ensure that in the given solution to the problem all values are expressed in the same units of measurement.
💡
In English-speaking countries (USA, Canada, UK, Australia) they use acres and yards to measure land plots. $1 acre = 4940 yards = 4046.96 m^2$.
Example tasks:
No. 1. Convert $10 m^2$ to $cm^2$
Solution:
- $1 m = 100 cm$;
- $1 m^2 = 100 x 100 = 10,000 cm^2$;
- $10 m^2 = 10 x 10,000 = 100,000 cm^2$
No. 2. How many $500 m^2$ ares?
Solution:
- $100 m^2 = 1 a$;
- $500 m^2 = 5 a$.
How are area units related to each other?
In order to see the relationship, you need to pay attention to the table.
Table “Area Units”
|
Area units |
$1km^2$ |
1 hectare |
1 weave |
$1 m^2$ |
|
$1 km^2$ |
||||
|
1 hectare (ha) |
||||
|
1 weave or ar 4.3. Total ratings received: 135. |
In addition, the regulation on the mandatory use of units SI set out in the interstate standard GOST 8.417-2002, currently in force in Russia, which lists the units of physical quantities permitted for use, provides their international and Russian designations and establishes the rules for their use.
International System of Units SI - the most used system of units in the world as in Everyday life, and in science and technology. Currently SI accepted as the main system of units by most countries in the world and is almost always used in the field of technology, even in those countries where traditional units are used in everyday life.
SI defines 7 basic units of physical quantities and derived units (abbreviated as units SI or units), as well as a set of attachments.
SI also establishes standard abbreviations for units and rules for writing derived units.
Basic SI units
- kilogram (kg, kg) - unit of mass
- meter (m, m) - unit of length
- second (s, s) - unit of time
- ampere (A, A) - unit of electric current
- mole (mol, mol) - unit of amount of substance
- candela (cd, cd) - unit of luminous intensity
- Kelvin (K, K) is 1/273.16 part of the thermodynamic temperature of the triple point of water:
- degree Celsius (°C) - a widely used unit of measurement of temperature, used in SI along with kelvin
Conversion to degrees Celsius:
Within SI The basic units are considered to have independent dimensions, that is, none of them can be derived from the others.
Derived units are obtained from basic units using algebraic operations such as multiplication and division. Some of the derived units in SI assigned proper names, for example, the unit radian.
SI prefixes must be used before the names of units. They mean that one must be multiplied or divided by a certain integer, which is a power of 10, a number of times.
Decimal prefixes are used to reduce the number of zeros in the numerical values of physical quantities.
For example:
- the prefix "kilo" means multiplication of the original unit meter per 1000 (kilometer = 1000 meters)
- the submultiple prefix “milli” means multiplication of the original unit meter by 10 -3 (millimeter = 0.001 meters)
- the submultiple prefix “deci” means multiplication of the original unit meter by 10 -1 (decimeter = 0.1 meters)
Area units
Regarding units of area that are derived from the basic unit of length meter, the list of names looks like this:
- length
- unit of measurement - meter
- designation (Russian) - m
- designation (international) - m
- square
- unit of measurement - square meter
- designation (Russian) - m 2
- designation (international) - m 2
Explanation
Meter - the length of the path traveled by light in a vacuum during a time interval
1/299792458 seconds (XVII General Conference on Weights and Measures (GCPM), 1983, Resolution 1).
The XXV CGPM, held in 2014, decided to continue work on preparing a new revision of the SI, including a redefinition of the meter, and tentatively planned to complete this work by 2018 in order to replace the existing SI with an updated version at the XXVI CGPM in the same year.
A widespread system in Russia for measuring land areas (non-systemic in relation to SI)
- 1 weave = 10 m x 10 m = 10 m x 10 m = 100 m 2
- 1 hectare = 1 ha = 100 m x 100 m = 10000 m 2 = 100 acres
- 1 square kilometer = 1 km 2 = 1000 m x 1000 m = 1 million km 2 = 100 hectares = 10,000 acres
Reciprocal units
- 1 m2 = 0.01 hundred square meters = 0.0001 ha = 0.000001 km2
- 1 hundred square meters = 0.01 hectares = 0.0001 km 2
Conversion table for area units
| Area units | 1 sq. km. | 1 Hectare | 1 Acre | 1 Sotka | 1 sq.m. |
| 1 km 2 | 1 | 100 | 247.1 | 10.000 | 1.000.000 |
| 1 hectare | 0.01 | 1 | 2.47 | 100 | 10.000 |
| 1 acre | 0.004 | 0.405 | 1 | 40.47 | 4046.9 |
| 1 weave | 0.0001 | 0.01 | 0.025 | 1 | 100 |
| 1 m2 | 0.000001 | 0.0001 | 0.00025 | 0.01 | 1 |
- Hectare
a unit of area in the metric system used to measure land plots.
Abbreviation:
- Russian - ha
- international - ha
1 hectare is equal to the area of a square with a side of 100 m
The name “hectare” is formed by adding the prefix “hecto...” to the name of the unit of area “ ar»:
1 ha = 100 are = 100 m x 100 m = 10,000 m 2
- Ar - unit of area in the metric system of measures, equal to the area of a square with a side of 10 m:
- 1 ar = 10 m x 10 m = 100 m 2
- 1 tithe = 1.09254 hectares
- Acre
land measure used in a number of countries using English system measures (UK, USA, Canada, Australia, etc.).
1 acre = 4840 sq. yards = 4046.86 m 2
The most commonly used land measure in practice is the hectare - the abbreviated designation ha:
1 ha = 100 are = 10,000 m 2
In Russia, a hectare is the basic unit of measurement of land area, especially agricultural land.
On the territory of Russia, the unit “hectare” was introduced into practice after October revolution, instead of tithe.
Ancient Russian units of area measurement
- 1 sq. verst = 250,000 sq. fathoms = 1.1381 km 2
- 1 tithe = 2400 sq. fathoms = 10,925.4 m 2 = 1.0925 ha
- 1 tithe = 1/2 tithe = 1200 sq. fathoms = 5462.7 m² = 0.54627 ha
- 1 octopus = 1/8 tithe = 300 sq. fathoms = 1365.675 m 2 ≈ 0.137 ha
The area of land plots for individual housing construction and private plots is usually indicated in acres
One hundred- this is the area of a plot measuring 10 x 10 meters, which is 100 square meters, and therefore is called a hundred square meters.
Here are some typical examples of the size that a plot of land with an area of 15 acres can have:
In the future, if you suddenly forget how to find the area of a rectangular plot of land, remember a very old joke. “Grandfather asks a fifth-grader: “How to find Lenin Square?” And he answers: “You need to multiply the width of Lenin by the length of Lenin” :)))
It is useful to familiarize yourself with this
- What can be built on plots for peasant (farm) farming (peasant farming) - read
- With the scales of topographic maps used in Russia, it is possible.
- You can find out about the new VRI Classifier - 2019
- From January 1, 2018, the exact boundaries of the plot must be recorded in the cadastral passport, since it will simply be impossible to buy, sell, mortgage or donate land without an accurate description of the boundaries. This is regulated by amendments to the Land Code. A total revision of borders at the initiative of municipalities began on June 1, 2015.
- On March 1, 2015, the new Federal Law “On Amendments to the Land Code of the Russian Federation and certain legislative acts RF" (N 171-FZ dated June 23, 2014, in accordance with which, in particular, the procedure for purchasing land plots from municipalities has been simplified.You can familiarize yourself with the main provisions of the law.
- With regard to the registration of houses, bathhouses, garages and other buildings on land plots owned by citizens, the new dacha amnesty will improve the situation
Each country has its own measurement system with its own values. Previously in Russia it was used to refer to the macaw. Today this measure is outdated and practically not used, only sometimes you can find the designation in ar, but, in fact, 1 ar is equal to 1 hundred square meters. Our summer residents habitually measure their plots in new units. If you ask them what the area of their plot is, you will hear in response the following values: six acres, ten acres. According to all official documents and the cadastral plan, land is calculated only in hectares. Therefore, it will be useful to know how to convert this measure into other quantities.
The new measurement system took root in Russia after the revolution in 1917. Before this, old Russian designations for length and area were used. Land area was measured in tithes.
The popular concept of “weaving” took root when Russians began to be massively allocated land for summer cottages. For convenience and simplified calculations, the area of the dacha was determined by the number of plots included in it measuring 10 by 10 meters, which is 1 hundred square meters or ar (100 sq. m). If you don't know, but want to calculate the area of land in these units, it's easier to start with calculate the area in meters and relate these meters to ares.
Country houses on the site subject to registration in 2019
Number of acres in 1 hectare
Since it's documented land are registered in hectares, it would be useful to know how many acres are contained in a hectare. From the table of measures we know, which is 10,000 square meters in 1 hectare. m. If the area of one hundred square meters is 100 square meters. meters, it turns out that 1 hectare is exactly 100 acres. Now, if you are asked how much is 100 acres, you can confidently answer that it is 1 hectare of land.
If the plot has not a rectangular, but another geometric shape (square, polygon or circle), how to calculate the hundred square meters in this case? The area of the square will be equal to the product of the sides. The area of a circle is calculated by obtaining the square of the radius. If a piece of land has the shape of a polygon, it is divided into triangles, the area of each is calculated, and then the values are added up. First on the calculator you need to calculate the value in square meters, and the resulting number is divided by 100.
A designation such as a hectare is often used for large plots of land. It is already inconvenient and inappropriate to measure them in smaller units, and the area is designated in hectares.
One square kilometer
Large areas, for example, on farms can have an area of several square kilometers. Is it a lot or a little in hundreds? At the first stage of calculations, we calculate the area of 1 square. km in meters. Let's multiply 1000 meters by 1000 meters and get 1 million square meters. meters. They are equal to 100 hectares, or 10 thousand acres. As you can see, it is more convenient to measure large areas in hectares.
Sourdough cabbage according to lunar phases: tips and recipes
This measurement system is not accepted in all countries. For example, in the USA, Canada, Great Britain and some other countries, acres are used for these purposes. For reference: 1 acre = 4046.86 sq. m. Acres, in turn, are divided into yards.
In advertisements for sale, as a rule, they use the usual designation and indicate in the description of the plot its area in acres. Some have little idea of what such a piece of land will actually look like, whether it is large or not. During the years of mass construction of dachas, townspeople were allocated a standard plot of 6 such units.
During the planning era it was calculated that the harvest obtained from 5 acres of land is enough to provide a family of 4 people with vegetables and fruits. The sixth unit of measure relied on the construction of a small country house. Today, this area of land can be considered average in size.
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