Presentation: “Ancient measures of length” presentation for a mathematics lesson (grade 5) on the topic
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Mathematics project Ancient measures in mathematics lessons.
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Municipal educational institution "Oboyansk Secondary School No. 1" Authors: Shevereva U - grade 7b Sergeeva E - grade 7b Head: Luneva Valentina Lukyanovna 2020
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Main goal: to explore the real situation regarding the knowledge of ancient measures by 6th grade students. Hypothesis: if students know the relationship between ancient Russian measures and modern units of measurement, this will help them more easily understand the content of educational and literary texts. The object of the study are 6th grade students. The subject of the study is knowledge of ancient Russian measures.
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Study historical information on the topic “Ancient Measures”. Analyze mathematics textbooks for grades 5–11 from the point of view of the presence of ancient measures in them. Compile a dictionary of ancient Russian measures. Create a presentation of this project. Draw conclusions . Tasks:
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Carry out the work Formatting The found text material is typed on the computer Edited in the text editor Word. Find pictures on the topic We found corresponding pictures in the Microsoft Office collection Draw the missing pictures In the PAIN T graphic editor Create a presentation to present our project. Created a Power Point presentation on the Project Action Program
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Quite often in our lives we come across words denoting units of measurement of Ancient Rus'. In Russian they are called obsolete, no longer in active use. We do not use them every day, but without knowing their meaning, it is sometimes difficult to understand a literary work, a paragraph on history, even a proverb. Every book has footnotes, but they are written in very small print and are not memorable. In ancient times, man had to gradually comprehend not only the art of counting, but also measurement. Making the simplest tools back then, building houses, getting food, there was a need to measure distances, and then areas, capacities, masses, and time. Hands and feet were used to measure distances. I decided to find out in more detail about the measures taken by the Russian people. Introduction
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measures of length
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The main ancient Russian measures of length: verst, fathom, arshin, elbow, span vershok.
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ARSHIN is an ancient Russian measure of length, equal in modern terms to 0.7112 m. Arshin was also the name given to a measuring ruler, on which divisions in vershoks were usually applied. Large measures of length
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Small measures of length “SPAND” (piatnitsa) SMALL SPAND (since the 17th century it was called “quarter”) = 17.78 cm BIG SPAND - the distance between the ends of the thumb and little finger = 22-23 cm SPAND WITH A TUMPLER (according to Dahl) – a span with the addition of two joints of the index club = 27-31 cm
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STEP - the average length of a human step = 71 cm. One of the oldest measures of length.
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VERSTA is an old Russian travel measure (its early name was “field”). This word originally referred to the distance traveled from one turn of the plow to another during plowing. The two names have long been used in parallel, as synonyms.
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Before Tsar Alexei Mikhailovich, 1 verst was considered 1000 fathoms. Under Peter the Great, one verst was equal to 500 fathoms, in modern terms - 213.36 X 500 = 1066.8 m. “Verstoy” was also called a milepost on the road. Note from history:
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Mezhevaya Versta is an old Russian unit of measurement equal to two versts. A verst of 1000 fathoms (2.16 km) was widely used as a boundary measure, usually when determining pastures around large cities, and on the outskirts of Russia, especially in Siberia, and to measure distances between populated areas.
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SAZHEN is one of the most common measures of length in Rus'. “Oblique fathom” is the longest: the distance from the toe of the left foot to the end of the middle finger of the raised right hand. Used in the phrase: “he has oblique fathoms in his shoulders” (meaning - hero, giant) Varieties according to purpose: “Machaya fathom” - the distance between the ends of the fingers of an adult man’s widely spaced hands.
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The size of this ancient measure of length, according to various sources, ranged from 38 to 47 cm. Since the 16th century, it was gradually replaced by the arshin and in the 19th century it was almost not used. ELBOW was equal to the length of the arm from the fingers to the elbow (according to other sources - “the distance in a straight line from the elbow to the end of the extended middle finger”).
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VERSHOK equaled 1/16 of an arshin, 1/4 of a quarter. In modern terms - 4.44 cm. The name “Vershok” comes from the word “top”. In the literature of the 17th century. There are also fractions of an inch - half an inch and a quarter inch.
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Measures of length (used in Russia after the Decree of 1835 and before the introduction of the metric system): 1 verst = 500 fathoms = 50 poles = 10 chains = 1.0668 kilometers 1 fathom = 3 arshins = 7 feet = 48 vershok = 2, 1336 meters Oblique fathom = 2.48 m Flying fathom = 1.76 m 1 arshin = 4 quarters (spans) = 16 vershok = 28 inches = 71.12 cm (arshins were usually marked with divisions in vershok) 1 cubit = 44 cm (according to various sources from 38 to 47 cm) 1 foot = 1/7 fathom = 12 inches = 30.479 cm
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Volume measures
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Bucket - the main Russian premetric measure of the volume of liquids - bucket Bucket - iron, wooden or leather utensils, mostly cylindrical in shape, with ears or a bow for wearing. In everyday life, two buckets on a rocker should be “fit for a woman.” Division into smaller measures was carried out according to the binary principle* *a bucket was divided into 2 half-buckets or 4 quarters of a bucket or 8 half-quarters, as well as into mugs and cups.
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Until the middle of the 17th century. the bucket contained 12 mugs. In the second half of the 17th century. the so-called government bucket contained 10 mugs, and a mug contained 10 cups, so the bucket contained 100 cups. Then, according to the decree of 1652, the glasses were made three times larger than before (“three glasses”). The sales bucket held 8 mugs. The value of the bucket was variable, but the value of the mug was constant, 3 pounds of water (1228.5 grams). The volume of the bucket was 134.297 cubic inches. Note from history:
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The barrel, as a measure of liquids, was used mainly in the process of trade with foreigners, who were prohibited from conducting retail trade in wine in small quantities. Equal to 40 buckets (492 l)
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The material for making the barrel was chosen depending on its purpose: oak - for beer and vegetable oils, spruce - for water, linden - for milk and honey. Most often, small barrels and kegs from 5 to 120 liters were used in peasant life. Large barrels could hold up to forty buckets (magpies). The barrels were also used for washing (beating) linen.
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In the 15th century The ancient measures were still widespread - golvazhnya, lukno and harvesting. In the XVI-XVII centuries. Along with the fairly common korobya and belly, the Vyatka grain measure marten, the Perm sapsa (measure of salt and bread), the Old Russian bast and poshev are often found. Vyatka marten - 3 Moscow quarters Saptsa - 6 pounds of salt and approximately 3 pounds of rye, bast - 5 pounds of salt Posh - about 15 pounds of salt. Note from history:
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Weights
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Berkovets - from the name of the island of Bjerk. This is what was called in Rus' a measure of weight of 10 pounds, just a standard barrel of wax, which one person could roll onto a merchant boat sailing to this very island. (163.8 kg). BERKOVETS - this large measure of weight was used in wholesale trade mainly for weighing wax, honey, etc.
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The spool was equal to 1/96 of a pound, in modern terms 4.26 g. They said about it: “the spool is small and expensive.” This word originally meant a gold coin.
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POUND (from the Latin word 'pondus' - weight, weight) was equal to 32 lots, 96 spools, 1/40 pood, in modern terms 409.50 g. Used in combinations: “not a pound of raisins”, “find out how much a pound of raisins is”. The Russian pound was adopted under Alexei Mikhailovich.
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Pud - (from the Latin pondus - weight, heaviness) is not only a measure of weight, but also a weighing device. When weighing metals, the pud was both a unit of measurement and a unit of counting. Even when the results of weighings were reported to tens and hundreds of poods, they were not transferred to Berkovites.
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Back in the XI-XII centuries. they used various scales with equal-armed and unequal-armed beams: “pud” - a type of scale with a variable fulcrum and a fixed weight, “skalvy” - equal-armed scales (two-cup). Note from history:
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Area measures
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The main measure of area measurement was the tithe, as well as shares of the tithe: half a tithe, a quarter (a quarter was 40 fathoms of length and 30 latitude) and so on. Land surveyors used (especially after the “Cathedral Code” of 1649) mainly the official three-arshine fathom = 2.1336 m, thus, a tithe of 2400 square fathoms≈1.093 hectares.
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In the first half of the 16th century, it became clear that when measuring lands in quarters, the general inventory of lands would take many years. And then, in the 40s of the 16th century, one of the most enlightened people, Ermolai Erasmus, proposed using a larger unit - a tetrahedral field, which meant a square area with a side of 1000 fathoms. This proposal was not accepted, but played a role in the process of introducing the large plow. Note from history:
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Surface area measures: 1 sq. verst = 250,000 square fathoms = 1.138 sq. kilometers 1 dessiatine = 2400 square fathoms = 1.093 hectares 1 kopn = 0.1 dessiatine 1 sq. fathom = 16 square arshins = 4.552 sq. meters 1 sq. arshin=0.5058 sq. meters 1 sq. vershok=19.76 sq. cm 1 sq. ft=9.29 sq. inches=0.0929 sq. m 1 sq. inch=6.452 sq. centimeter
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Monetary measures
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And in Rus' in ancient times, the ruble was in the form of a silver bar. The first rubles in Rus' were in the form of a silver bar weighing 200 grams. You could buy a lot of things with that ruble. At that time, for a ten-kopeck piece (10 kopecks) three of us could have lunch in an expensive tavern. The purchasing power of the ruble has changed from time to time. It has fallen especially noticeably at the present time. The ruble remained a ruble and at different times also had different names: ruble, coin, karbovanets, tin.
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The hours are different
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From the history of time And when in 6912 (in our account in 1404) Grand Duke Vasily Dimitrievich built a clock in his yard in Moscow, it was such a significant event that it was noted in the chronicle. This was one of the first watches in Europe. “This watchmaker will be called the clock; “At every hour he strikes the bell with a hammer, measuring and calculating the hours of the night and day, not by a man striking, but in a human-like, self-ringing and self-moving manner, strangely somehow created by human cunning, dreamed up and exaggerated,” the chronicler reported.
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Metric system of measures The needs of practice forced us to begin the search for a unified system of measures. At the same time, it was clear that it was necessary to abandon the establishment of connections between units of measurement and the dimensions of the human body. And people's steps are different, and their feet are not the same length, and their toes are of different widths. Therefore, it was necessary to look for new units of measurement in the surrounding nature.
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At the 1867 World Exhibition in Paris, in the international committee of measures, weights and coins organized there, Russian academician B. S. Jacobi made a report. In it, he formulated the advantages of the metric system as the most economically advantageous due to its decimal base.
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The basic unit of the system of measures must be determined by means of a material standard that most accurately reproduces the length of the archival meter. The commission approved a meter standard made from an alloy of platinum (90%) and iridium (10%).
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By 1875, the metric convention had already been signed by 17 states, including Russia, where the use of the new system was permitted, but did not become law. In 1889, the international prototypes of the meter and kilogram were delivered to the Breteuil Pavilion (a building in France). From this moment on, the meter and kilogram began to be defined as the length and weight of international standards.
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In Russia, from the beginning of the 19th century, scientists understood the meaning of the metric system and tried to widely introduce it into practice. The final decision on the issue of the metric system in Russia received after the Great October Socialist Revolution. From January 1, 1927, when the transition of industry and transport to the metric system was prepared, the metric system became the only system of measures and weights allowed in the USSR. Great merit in the introduction and dissemination of the metric system of measures in our country belongs to Dmitry Ivanovich Mendeleev, the great Russian chemist.
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By 1972, 41 states had already signed the metric convention. The creators of this universal system of measures wrote on the meter standard: “For all times to all peoples!” To popularize the new measures, the poet V.V. Mayakovsky wrote poetic texts dedicated to the new measures.
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Comparative analysis of the growth of students in our class The average height of our classmates was: in 1st grade in 6th grade cm fathom arshin pound yard 122 0.6 1.7 4 1.3 cm fathom arshin pound yard 158 0.7 2.2 5.2 1 .7
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Comparative analysis of my family's growth Imagine that you live in the 15th century and your height is measured by the standards of that time. Try expressing your height in one of these units. Elbow - 44cm Vershok - 4.4cm Arshin - 0.71m Name cm Sazhen Arshin Elbow Vershok Ulyana 155 0.73 2.2 3.6 35.2 Svetlana 161 0.76 2.3 3.7 36.6 Sergey 178 0 .84 2.6 4.1 40.5 Name CM Sazhen Arshin Lokot Vershok Sergey 185 0.87 2.7 4.2 42.04 Elena 170 0.81 2.4 3.8 38.6 Ekaterina 162 0.75 2.3 3.6 36.8
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What ancient units of measures do you know? 2. Name the ancient Russian measure of length. Name the ancient Russian measure of body weight. In what situations have you encountered ancient Russian measures in everyday life? In what works of art have you come across ancient Russian measures? Do you think knowledge of ancient measures is necessary in modern life? Name a proverb or saying with ancient units of measures. Questionnaire
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Analysis of personal data Question No. Student answers 1 Versta-31%, arshin-32%, inch-30% 2 Arshin-43%, inch-29%, elbow-29% 3 Pud-44%, pound-14% 4 In class mathematics - 85%, history - 43%, literature - 20% 5 “The Little Humpbacked Horse” - 39%, “Thumbelina” - 54%, “Ilya Muromets” - 18% 6 Since now other measures and ancient ones are not used 7 “ Two inches from the pot" -21% "Seven spans in the forehead" -20% "A mile will not fall on a mile" -17%
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for general development; (64%) to know the historical roots of their language; (64%) - as they are often found in fiction, in phraseological units; (67%) - individuals who work in linguistics need to know the history of the development of the subject. (44%). Is it necessary to know ancient measures in a modern school and why? (70% of students answered “yes”)
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Conclusion: In this work, we examined the emergence and improvement of various measures of measurement, such as: length, volume, mass, area. Established a connection between different units of length. They proved that each of the units of length can be represented through the generally accepted metric system of measures, and therefore becomes understandable to any person. They explained why a unified metric system of measures was necessary. The work contains many interesting facts from the history of the emergence of ancient measures of measurement. .
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When we come to the store, we ask to weigh out 2 kg of cereal, when we go out onto the stadium track, we run 100 meters, and 40 minutes or 2400 seconds pass from the bell in class. Clocks tell us time, we need scales to determine weight, and we measure distances with a graduated ruler or tape measure. What if you don’t have a tape measure at hand? How to measure the length in this case? It would be nice if the unit of measurement was always at hand; I wanted to and made my own standard. Remembering the old Russian ways of measuring something, we can easily measure anything.
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List of sources used: Volkov V. How the metric system of measures appeared. Quantum. – 1990.-№8. With. 33-34. Glazer G.I. History of mathematics in school grades IV - VI. - M.: Education, 1981. Depman I.Ya. Measures and the metric system. – L.-Detgiz, 1953. Kotlyar B.D. Amazing equality. Quantum - 1989. - No. 7 p. 17-21. Mathematics. 5th grade: textbook for general education institutions. N.Ya. Vilenkin, V.I. Zhokhov, A.S. Chesnokov, S.I. Shvartsburd-M.: Mnemozina, 2007. Mathematics. 5th grade: textbook for general education institutions. G.V. Dorofeev, I.F. Sharygin, S.B. Suvorova and others - M._Prosveshchenie, 2006. Svechnikov A.A., Sorokin P.I. Numbers, figures, problems. - M. - Enlightenment, 1977.
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Thank you for your attention!
