Lesson workshop "Area Units"

Make up a formula (from the letters suggested on the cards, add the formula)

Guys, we have studied a lot of topics: rectangle, square, area of ​​a rectangle, square, units of area. Today we will conduct a generalizing lesson, the purpose of our lesson is to generalize and consolidate the knowledge gained, namely, our task for the lesson is to develop the skill of using formulas to calculate the areas of a rectangle, square, complex shapes, convert units of measurement., and also in the lesson you will share your knowledge, show the application of mathematics in a wide variety of fields and the need to study this important subject

Repair

We often talked about practical application mathematical knowledge in human life. Now we will see once again that mathematics plays a huge role in human life. Look at the objects: a roll of wallpaper, a can of paint, a brush. What do they remind you of? Correct repair. Today we are planning to renovate the classroom.

Work plan

• Measuring the length, width and height of a room, the size of doors and the size of windows
• Calculation of the area of ​​the pasted surface (area of ​​windows) and the area of ​​one roll of wallpaper
• Calculating the area of ​​​​the ceiling and counting the amount of paint
• Calculating the area of ​​the door and counting the amount of paint

Well, our plan of action is clear. It remains to determine what mathematical knowledge will help us in our work?

• how calculate the area of ​​a rectangle?

• How to calculate the area of ​​a square?

• List the units of area

mm cm m km ar ha

Necessity forced a person already in antiquity to measure not only length, distance, but also area. In ordinary life, we call a large open space a square. But we also know that the tabletop, the notebook, the classroom floor, and the land have space. That is, the area is the place that the figure occupies on the plane.

To measure the area, the Russian people had their own special measures: mop, howl, plow, tithe. Now we do not use these measures. The student will introduce us to them in more detail with the report “Old units of area”

Ancient square units

In Kievan Rus, there were no area measures as square measures, judging by the surviving sources. Although the ancient Russian architects and land surveyors had an idea about them. Measures of the area were needed to determine the size of land plots. The areas were not always clearly demarcated. For arable land used

PLOW - a piece of land plowed in a day by a plow in which a pair of oxen is harnessed

QUARTER - The area on which a quarter of rye was sown

SOHA AND VYTY - large measures of land areas. The main feature of SOHI and Vyti was their expression through different numbers of quarters, because the amount of land and the social status of landowners were taken into account, i.e. These measures have had a changeable value.

The areas of hayfields were estimated by SHOP - this is the area of ​​​​the meadow on which you can mow a haystack

These measures made it possible to determine the yield, but they did not give an idea in terms of the shape and size of land plots.

TITH. Initially, a round tithe was used - a square with a side equal to a tenth of a verst (sazhen) from where the name tithe comes from.

Under Peter 1, square measures (square versts, square sazhens, square arshins, square feet) were firmly established in the system of area units

In 1916, the Regulations on Weights and Measures were legalized square. m, and for land areas are, hectare.

There are various measures of area that people have come up with, but all these units of measurement can be expressed through each other.

The ancient units of area lost their significance due to their inaccuracy and were replaced by units of measurement accepted throughout the world.

Currently, the most common are sq mm, sq cm, sq m, sq km, ar, hectare

Ancient square units

KOPNA

PLOW

TITH

SOHA

HOWL

QUARTER

Ancient square units

• Under Peter 1 in the system

units of area

square

measures (sq. verst, sq. sazhen,

square arshin, sq. foot)

• In 1916, the provision on

weights and measures were

legalized

sq. m, and for land

area are, hectare.

• If the units are different, then they must be expressed in the same

• Ceiling size 4 m 20 cm x 6 m
• Wall height 2m 50cm
• Wallpaper roll size 100cm x 10m
• Door size 2m x 80cm
• 1 can of paint

designed for 5 m

The size windows 2m x 2m

2

Answer

• To paint the ceiling you will need:

6 cans of paint

• To paint the door you will need:

1 can of paint

• To wallpaper the walls you will need:

4 rolls of wallpaper

What is the area

your smile?

Take a line and...

smile!

Thank you for the lesson GOOD FELLOWS

Used sources:

Textbook "Mathematics Grade 6" Vilenkin N.Ya. And etc.

Images taken from Internet sources .

Description of the presentation on individual slides:

1 slide

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RESEARCH WORK "OLD UNITS OF MEASUREMENT" Scientific adviser Belousova Anna Nikolaevna teacher of mathematics of the Moscow Autonomous Educational Institution "Secondary School No. 42" Ulan-Ude 2016

2 slide

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AT Everyday life people face mathematical values ​​every day, without hesitation, perform various calculations. Everyone is familiar with modern units of measurement. They are comfortable and understandable. I wonder how they measured in Russia in the old days? Why are old units of measurement not used in our time? Is it necessary to know the ancient measures in modern school? These questions served as the choice of the topic of the work. Purpose: to study the possibility and expediency of using old Russian measures in modern life. Tasks: 1. To study the old Russian measures of length, mass, area, volume. 2. Collect and process the material. 3. Select and compose tasks. The object of the study is ancient Russian measures. The subject of the research is the use of old Russian measures of length, mass, area and volume. Hypothesis - old Russian measures are inconvenient to use, but it is necessary to know the ratio of old Russian measures and modern units of measurement, as this will help to understand the content of educational and literary texts more easily.

3 slide

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4 slide

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Ancient units of length A line is a very small ancient unit of length, equal to 2.54 mm (0.1 in) or the width of a grain of wheat. Tsar Alexei Mikhailovich ordered to place along the road leading from the Kaluga outpost of Moscow to the summer palace in the village of Kolomenskoye, pillars with eagles at the top at a distance of 700 fathoms from each other. Later, they began to talk about a tall and lanky man “as tall as a Kolomna mile” Standard Russian wooden milestone of the early 19th century Nautical mile

5 slide

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At the end of the 18th century, the French measured the land distance from the city of Dunkirk on the north coast of France to Barcelona in southern Spain. The line was drawn through Paris. One ten-millionth part of a quarter of the French meridian was decided to be considered a unit of measurement and was called a meter. Together with the meter, the metric system was born. In 1875, it was adopted by 17 countries, including Russia. The French revolutionaries saw the enlightenment of the masses as one of the main tasks of the revolution. Therefore, they placed marble standards of the meter in frequently visited places in Paris. Two of them have survived to this day.

6 slide

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Berkovets = 10 poods Pood = 40 pounds = 16.38 kg Pound = 96 spools = 0.41 kg Lot = 3 spools = 12.797 g Spool = 4.27 g Fraction = 0.044 g

7 slide

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Area units 1 sq. verst \u003d 250,000 square fathoms \u003d 1.138 square meters. kilometers 1 tithe \u003d 2400 square fathoms \u003d 1.093 hectares 1 heap \u003d 0.1 tithes 1 sq. sazhen \u003d 16 square arshins \u003d 4.552 square meters. meters 1 sq. arshin = 0.5058 sq. meters 1 sq. vershok \u003d 19.76 square meters. cm 1 sq. ft = 9.29 sq. inches = 0.0929 sq. m 1 sq. inch = 6.452 sq. centimeter 1 sq. line = 6.452 sq. millimeters Volume Units Bucket = 1/40 barrel = 10 mugs = 30 pounds of water = 20 vodka bottles = 16 wine bottles = 100 glasses = 200 scales = 12 liters. Barrel = 40 buckets = 492

8 slide

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The old Russian units of measurement in proverbs and sayings “This is not a pound of raisins for you” is a playful expression about some kind of difficult task. “A pound pud must be given way”, that is, one must have respect for the elders, more knowledgeable, experienced. “From the pot two inches, and already a pointer” - a young man who has no life experience, but arrogantly teaches everyone. "Do not give up an inch" - do not give even the smallest thing. "Seven spans in the forehead" - about a very smart person. “He is with a fingernail, and a beard with an elbow” is about a man of unenviable appearance, but who enjoys authority due to his mind, social status or life experience. “Each merchant measures his own arshin” - everyone judges any business one-sidedly, based on their own interests. “An arshin of a beard, but a span of mind” is about an adult, but a stupid person. "Slanting fathom in the shoulders" - a broad-shouldered, tall man. “He sees three arshins into the ground” - about an attentive, perspicacious person, from whom nothing can be hidden. “If you fall behind a mile, you catch up by ten” - even a small gap is very difficult to overcome. “The spool is small, but expensive” - this is how they say about something insignificant in appearance, but very valuable. “Hay - for poods, and gold - for spools” - each thing has its own specific value. “You recognize a person when you eat a pood of salt with him” - it takes a lot of time to understand another person.

9 slide

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Old Russian units of measurement in literary works The famous Danish storyteller H. K. Andersen wrote the fairy tale "Thumbelina". Andersen said about her like this: "She was so tender, small, only an inch tall, she was nicknamed Thumbelina." Pyotr Pavlovich Ershov wrote a fairy tale in verse, in which he also used old Russian measures of length. “Yes, I also give birth to a horse only three inches tall, on its back with two humps, and with arshin ears.” A. S. Pushkin "The Tale of Tsar Saltan ..." God gave them a son in arshin, and the queen over the child, like an eagle over an eaglet; she sends a messenger with a letter to please her father. N. A. Nekrasov “Grandfather Mazai and the Hares” With every minute, the water was getting closer to the poor animals; already under them there was less than an arshin of earth in width, less than a sazhen in length. S. Ya. Marshak "The Tale of the Goat" Hey, don't cry, a woman with a grandfather! I will feed you dinner, bake a mushroom pie two arshins wide.

10 slide

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Questionnaire for students of grade 5 of the Moscow Autonomous Educational Institution "Secondary School No. 42" Questionnaire for students of FI, class 1. Did you get acquainted with modern units of measurement? Yes No 2. Are you familiar with old units of measurement? Yes No 3. Is knowledge of ancient measures necessary in modern world? Yes No Questionnaire for parents 1. Are you familiar with modern units of measurement? Yes No 2. Are you familiar with old units of measurement? Yes No 3. Is knowledge of ancient measures necessary in the modern world? Not really

11 slide

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12 slide

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1. In 1847, the painter Popov made a wooden icon of the Annunciation of the Blessed Virgin Mary according to a drawing of his own composition, 2 arshins high and 1 arshin wide, for the Annunciation chapel of the Elijah Church. Find the perimeter of the frame for this icon. Express your answer in meters. Solution: 1) (2+ 1) ∙ 2 \u003d 6 (arshins) - perimeter 2) 71.12 ∙ 6 \u003d 433.2 (cm) Answer: P \u003d 426.72 cm 2. In 1887, oil mills N. N. Botalova and D. S. Grokhotova bought 500 pounds of flaxseed per year. How many kg of seed will they buy in 5 years? Solution: 1) 500 x 5 \u003d 2500 (poods) 2) 16.38 x 2500 \u003d 40.950 (kg) Answer: they will purchase 40.950 kg in 5 years. 3. In 1558, Ivan IV granted Grigory Stroganov "empty" lands from the mouth of the Lysva River down both banks of the Kama to the mouth of the Chusovaya and all the rivers flowing into it for 88 miles. According to later estimates, 3,400,000 acres of land. How many hectares of land did Ivan IV grant to Grigory Stroganov? Answer: 3716200 hectares of land were granted by Ivan IV to Grigory Stroganov. 4. 1 jug contained 1 bucket. The kadets contained 6 times more than the jug. And in the tub there are 4 buckets less than in the kadets. How many liters fit in 6 tubs if 1 bucket is 12 liters? Answer: 144 liters fit in 6 tubs. PROBLEMS WITH OLD UNITS OF MEASUREMENT

13 slide

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Conclusions Having studied the literature, having conducted a survey, I found out that many Russian units of measurement originated from units of the countries of the West and East. In modern Russian, ancient units of measurement and the words denoting them have been preserved mainly in the form of proverbs and sayings. Knowledge of ancient measures is necessary for general development. At present, in many countries of the world there is a single international system units (international system - SI), which facilitates foreign policy, economic and trade relations between countries. The proposed hypothesis was confirmed. Old Russian measures are inconvenient to use, but it is necessary to know the ratio of old Russian measures and modern units of measurement. Thank you for your attention!

Thing: Informatics

Lesson topic: Information units

Lesson type: a lesson on generalization, systematization and control of knowledge, a lesson using gaming technologies.

Lesson form: game lesson. The competitive form of building a lesson allows you to concentrate and activate the attention of students to a greater extent, acts as an additional incentive for learning activities.

Time spending: single lesson.

Technology: personality-oriented, playful, health-saving

Lesson equipment: computer, multimedia projector.

Lesson Objectives:

educational:

Summarize students' knowledge about the representation of information in computer memory.

To consolidate the skill of transferring from one unit of measure to another.

Fix finding the information volume of messages.

Educational:

Development of cognitive interest, speech and attention of students.

Formation of information competence.

Educational:

Education in students of interest in the subject, goodwill, the ability to work in a team.

Download:

UNITS OF MEASUREMENT OF INFORMATION
Class: 8Informatics teacher MBOU Solchurskaya secondary school of Ovyur kozhuun of the Republic of TyvaMongush Larisa Mikhailovna
Lesson Objectives:
Generalize knowledge about the representation of information in computer memory; Consolidate the skill of transferring from one unit of measurement to another; Consolidate finding the information volume of messages; Form the ability to build logical diagrams and connections; Develop interest in the subject.
You know the units of length. These are millimeters, centimeters, meters and kilometers.
Mass is measured in grams, kilograms, centners and tons.
Angles are measured in degrees.
Time is in seconds, minutes and hours.
The bit is the smallest unit of measure introduced by Claude Shannon (an American engineer and mathematician).
The computer "does not understand" human language. Therefore, each character is encoded. The PC "understands" only zeros and ones - with the help of them, information is presented in the computer. These "ones and zeros" are called a bit.
A bit can take one of two values ​​- 0 or 1. Eight such bits are enough to make any character unique, and there can be 256 such sequences consisting of 8 bits, which is enough to display any character.
Therefore - 1 character = 8 bits. But the information is not considered not in characters not in bits. Information is read in bytes, where 1 character = 8 bits = 1 byte. A byte is a unit of measure for information.
1 byte = 23bits=8 bits 1 KByte = 210bytes=1024 bytes 1 MBytes = 210KBytes=1024 KBytes 1 GBytes = 210MBytes=1024 MBytes
Information units
And so that you can imagine what these units of measurement are, listen!
5 bits - a letter in a crossword cell. 1 byte - a character entered from the keyboard. 6 bytes - the average word size, in the text in Russian. 50 bytes - a text line. 2 Kbytes - a typewritten text page. MB - a small fiction book. 100 MB - a meter-long book with shelves. 1 GB - a person reads for a lifetime. 3 GB - an hour of high-quality video recording.
Information volume of information carriers:
Floppy disk - 1.44 MB; CD  700 MB; DVD-ROM - up to 17 GB (standard - 4.7 GB); hard disk - from 20 GB to 80 GB or more (standard 80 GB); Flash memory - 256 MB - 2 GB.
LARGE UNIT
Translation from large units into small
12 bytes =
SMALL UNIT
*
Convert to bits:
LARGE UNIT
24 bits =
SMALL UNIT
:
Transfer from small to large units
Convert to bytes:
1 byte - a character entered from the keyboard.
A symbol in a computer is any letter, number, punctuation mark, mathematical sign, special character.
INFORMATICS
How many characters does this word contain? What information volume does this message have?
Find the information volume of the word INFORMATICS
Decision
COMPUTER SCIENCE - 11 characters, therefore, this message carries an information volume equal to: 11 characters * 1 byte = 11 bytes or 11 * 1 * 8 = 88 bits.
Question for 100 What is the largest of the proposed units of measurement of information.
A) byte
D) megabyte
B) kilobyte
B) bit
Question per 100 Arrange in ascending order of the unit of measurement of information
A) byte
D) megabyte
B) kilobyte
B) bit
Question for 200 Count the information volume of the message “Congratulations to the school on its 70th anniversary!”
1 byte
34 bytes
38 bytes
38 bit
Question for 200Compare
8 bits and 1 byte
1024 KB and 1024 bits
1 byte
8 bit
1 GB
1024 MB
300 Question Match
1 KB
1024 KB
1 MB
1024 MB
___ GB = 1536 MB = _______ KB
400 question Fill in the blanks with numbers
________ bits = 3584 bytes = ____ Kbytes
Homework:
1. Find information about other units of information.2. Compose a fairy tale about the units of measurement of information
A source of information:
http://images.yandex.ru/yandsearch?p=1&text=%D0%BA%D0%BB%D0%BE%D0%B4%20%D1%88%D0%B5%D0%BD%D0%BD %D0%BE%D0%BD%20%D1%84%D0%BE%D1%82%D0%BE&pos=42&uinfo=sw-1135-sh-773-fw-910-fh-567-pd-1&rpt=simage&img_url =http%3A%2F%2Fwww.allmystery.de%2Fi%2Ft515743_3c97cd_Shannon-Life-p38-x640.jpg http://images.yandex.ru/yandsearch?text=%D1%84%D0%BE%D1%82 %D0%BE%20%D0%BB%D0%B8%D0%BD%D0%B5%D0%B9%D0%BA%D0%B8&uinfo=sw-1135-sh-773-fw-910-fh-567 -pd-1 http://images.yandex.ru/yandsearch?p=1&text=%D1%84%D0%BE%D1%82%D0%BE%20%D0%BB%D0%B8%D0%BD %D0%B5%D0%B9%D0%BA%D0%B8&pos=34&uinfo=sw-1135-sh-773-fw-910-fh-567-pd-1&rpt=simage&img_url=http%3A%2F%2Fimg0.liveinternet .ru%2Fimages%2Fattach%2Fc%2F5%2F84%2F810%2F84810200_1331894290_1.jpg http://images.yandex.ru/yandsearch?text=%D1%81%D0%BB%D0%BE%D0%BD&pos=5&uinfo =sw-1135-sh-773-fw-910-fh-567-pd-1&rpt=simage&img_url=http%3A%2F%2Flifeglobe.net%2Fmedia%2Fentry%2F347%2Fradionetplus_ru_jivnoct23_3.jpg http://images.yandex. ru/yandsearch?text=%D0%B2%D0%B5%D1%81%D1%8B&pos=8&uinfo=sw -1135-sh-773-fw-910-fh-567-pd-1&rpt=simage&img_url=http%3A%2F%2Fwww.1kran.ru%2Fimages%2Fvrnc10.jpg http://images.yandex.ru/yandsearch? text=%D0%B3%D0%B8%D1%80%D1%8F&pos=3&uinfo=sw-1135-sh-773-fw-910-fh-567-pd-1&rpt=simage&img_url=http%3A%2F%2Fwww .b-port.com%2Fmediafiles%2Fitems%2F2011%2F02%2F57369%2F8fce1db8de12064673ed0028ff4829ea_L.jpg http://images.yandex.ru/yandsearch?p=1&text=%D1%87%D0%B0%D1%81%D1 %8B&pos=32&uinfo=sw-1135-sh-773-fw-910-fh-567-pd-1&rpt=simage&img_url=http%3A%2F%2Fhcl.harvard.edu%2Fhfa%2Fimages%2Ffilms%2F2011aprjun%2Ffisher_phi.jpg http://images.yandex.ru/yandsearch?text=%D0%BF%D0%B5%D1%81%D0%BE%D1%87%D0%BD%D1%8B%D0%B5%20%D1 %87%D0%B0%D1%81%D1%8B&pos=9&uinfo=sw-1135-sh-773-fw-910-fh-567-pd-1&rpt=simage&img_url=http%3A%2F%2Fimg-fotki.yandex .ru%2Fget%2F5908%2Fcoto48.20%2F0_61414_c9de1a35_XL
Literature:
N.D. Ugrinovich, Informatics and ICT, grade 8 - M. BINOM Knowledge Lab, 2010. Bosova L. L. Entertaining tasks in computer science. - M. BINOM Knowledge Lab, 2006. P.A. Yakushkin, V.R. Leschiner, D.P. Kirienko, Preparation for the Unified State Examination. Typical test tasks, 2012 M: Publishing house "Exam"