EntranceHow a person learned to count time message briefly. How different peoples counted time
I wear a wristwatch all the time and feel very uncomfortable when I can’t tell the time. I control when and where to come, what to do. How much time has already been spent on some process. Although there is a saying that happy people do not watch their watches, even during rest they are constantly with their watches.
How did people manage in the old days without precise time control? But even then people could determine time quite accurately, with only a small error.
Gnomon - the sun is shining, the time is known
Before mechanical watches became widespread, time was determined using sundials. This device had three parts: a gnomon, that is, an element that casts a shadow, a dial on which this shadow falls, and one more, conventional detail - the sun itself, which “winds up” this very clock.
The dial has lines, and the gnomon has a size and shape, which is calculated using geographic coordinates. That is, each sundial is created for a specific area. Their production is a painstaking and complex process that requires knowledge and skills. Because such devices were not cheap.
In Rus' they did it simpler: our ancestors simply dug a tall pole into the ground, which cast a shadow. By observing the size of the shadow, it was possible to determine the time. Of course, this was not the ideal way. But by comparing the lengths of the shadow, for example at noon, in the evening or at dawn, and also by measuring it at different times of the year, our ancestors compiled a fairly clear determinant of time.
Everything would be fine if the sun was constantly shining in Rus'. Unfortunately, this is from the realm of fantasy - rain, clouds and other bad weather are very common here. If we add the peculiarity of the northern regions, where the sun does not rise too high above the horizon, which is why the shadow indicators of the gnomon are very long, it turns out that the sundial could not be considered as the only, accurate, year-round option.
In Belgorod we also have a huge sundial on the street. Once, while passing by, I compared it with my wristwatches - they definitely show the sun! That's it! literally up to the minute.
Clepsydra that steal water
A type of clock that does not depend on sunlight is a water clock. They are called clepsydra. If we take this word apart, and it consists of klepto - to hide and hydor - water, then it is clear that translated from Greek but means nothing more than “water stealer”. The simplest clepsydra consists of two vessels installed at different levels. There is a hole in the top one through which water drops into the bottom one. The time was determined by observing how the water level dropped in the upper vessel, or how it rose in the lower one. There is a version that this is where the expression “passage of time” comes from.
Clepsydra
Since the speed of water movement is affected by the pressure in the vessel, they began to make the container in the form of a truncated cone. In terms of structure, the clepsydra has an advantage over the sundial, since the system of communicating vessels can be brought to perfection. They can be used at any time of the day, they determine the time more accurately.
Modern water clock.
But they can only be used when the water is in a liquid state. Alas, there are often frosts in Rus', and she could simply freeze. Such designs were not widely used among the population; they were used mainly during church ceremonies and were called “hydrology”.
Roosters, larks and flowers for the poor
Watches in Rus' have long been a luxury item. Ordinary people used their own methods to get by without complex mechanisms. Our ancestors were observant; natural processes were not a secret to them.
For example, birds. It is clear that the alarm clock in ancient times (and in many villages to this day) was a rooster, which crowed three times a night: the first time after midnight, then at two o'clock in the morning, and the last time early in the morning, at about the beginning of five. Oriole, lark, sparrow - these birds also woke up and began their chants at a certain time. You just had to watch, listen to the advice of the old people and remember the time.
As you know, larks begin to sing at 2 a.m., orioles at 3 a.m., and sparrows wake up only at 6 a.m. The main “clock” in the old days was the rooster. The roosters crow for the first time at one o'clock in the morning, the second time at 2 o'clock in the morning, and the third time at five o'clock in the morning.
The peasants observed the flowers, as they, turning towards the sun, bloomed and closed at strictly defined times. The life cycle of many plants and animals correlates with the time of day. Flowers of different plants open and close at different times, and at a certain time. Most flowers bloom in the morning and close in the evening, but there are also some that close and open in the middle of the day or at night. Based on this principle, at one time Carl Linnaeus invented and created a flower clock that “worked” from three o’clock in the morning until midnight. Looking at them, it was possible to determine the time of day with an accuracy of up to 30 minutes.
And, of course, the sun itself. The Slavs divided the day into day and night, focusing on the movement of the heavenly body. The middle of the day was noon, when the sun was at its highest point. The later it is, the longer the shadows from objects.
In ancient times there was no electricity, there was nothing to light the huts with. Yes, there were candles, but it was not economically profitable to burn them constantly. Because as soon as the sun set, darkness covered the house - you can go to bed with a clear conscience. In addition, our ancestors did not need a clear definition of time, in minutes, seconds. For what? It dawns - you can go to the fields, work - until sunset, at dusk they return to the village. Shepherds, for example, measured the shadow of a tree using bast shoes worn on their feet. The shadow has reached seven bast shoes - you can gather the herd and lead it home.
The process of replacing temporal concepts with spatial ones is interesting, for example: “Is this village far away? “Yes, it’s a bit far, two days’ walk.” The length that could be covered in one day was called the bottom.
Clear biological clock
Today everyone knows about the biological clock; this is the name of the internal circadian rhythm. It takes years to form; with its help, all biological processes of the human body are formed. We are feeling hungry, which means it’s time for lunch, which we are used to. We want to sleep - you can look at the clock and see that it’s already midnight (one in the morning, two, and so on), depending on your habit.
Artist K. Makovsky. Peasant lunch during the harvest.
Our ancestors lived according to a strict schedule. The peasant woman knew that she did not need to call her husband for dinner. He came himself, or was already waiting for his wife in the field, because hard work and habit took their toll, and his appetite was very strong.
The regularity, monotony characteristic of life in Rus', adherence to a certain routine, and the absence of artificial lighting made time orientation simple and somewhat arbitrary.
Flowers open and close at specific times.
Watchmaking workshops began to develop in Russia in the 18th century. This event was marked by the opening of the Clock Yard in Moscow. And today it is impossible to surprise even a kindergartener with a watch - this item has become so familiar, inexpensive and ubiquitous.
sources
Throughout life, every person always learns something, and the acquired knowledge after some time seems so natural that it is perceived as a common fact. The thought doesn’t even creep into my head: how did it all begin? How did people learn to count and How long ago did society come to understand that almost everything in the world is subject to numbers?
How did a person learn to count time?
In the modern world, 365 days a year, 30 days a month and 24 hours a day are a natural fact. Previously, when there was no knowledge about the amount of time, a person was content with methods invented independently, and the means for this was the Sun. A dial with marks and a pole were installed on some surface, the shadow of which moved around the circle. Dependence on weather conditions was a significant drawback of such a device: rains also made it impossible to determine time. An analogue of this design in the modern world is a watch, which has firmly conquered its niche and become an indispensable item in a person’s life.
Determining time by stars, water and fire
Stars, a symbol of romance and dreams of something distant and beautiful, also served as a kind of time indicator at night. For this purpose, star charts were invented, measurements from which were carried out using a passage instrument.
In addition to sidereal and sundials, popular among almost all nations and differing only in design, water exhibits, which were a cylindrical container from which water flowed drop by drop, were widely used. It was by the amount of flowing water that people measured time. Such watches were popular in Egypt, Rome, and Babylon. How did people learn to count time in Asian countries? Here, in water-type devices, the opposite principle was used: a floating vessel was filled with water entering through a small hole.
Trying to bring not only the water, but also the fire element into his life, man also came up with a fire clock, which originated in China and over time gained popularity throughout Europe. The basis of these devices that determined time was a combustible material (in the form of a stick or a spiral) and metal balls attached to it, which fell when a certain proportion of the material burned. In Europe, candle clocks were mainly used, preferring them to lamp and wick clocks. The time was determined by the amount of burned wax. Such clocks were especially common in churches and monasteries.
Hourglass - a rare pride of our time
Of course, the most popular was the hourglass, which is still actively used to perform its main function, as well as as a decorative item. The accuracy of the calculated time in devices of this type depends on the quality of the sand, which determines the uniformity of its flowability.
History of the emergence of counting science
Understanding time in its quantitative terms was a determining factor for the knowledge of numbers and the ability to count. Moreover, the history of the origin of the account is so old that it is more like a fairy tale. How did people learn to count? Many centuries ago, humanity lived in tribes, led a herd lifestyle, dressed in the skins of killed animals and ate what its representatives could get for themselves.
Accordingly, the simplest tools: sticks and stones were the available tools for survival and getting food. Perhaps constant danger and the need to obtain food became the main impetus for the need for counting, which in our time is not only perceived as a natural fact, but is also facilitated with the help of modern computing technology.
One, two and many
The first concepts denoting quantity and explaining how people learned to count were “one” and “many.” “One” is an object or individual separately identified according to certain criteria: the leader of a flock, grain in an ear, etc. “Many” is the total mass in which this item is located.
The appearance of the number “two”, denoting a “pair”: eyes, ears, paws, wings, hands, explains how a person learned to count in times of non-existent numbers. While talking about the two ducks he had killed, the hunter pointed to his eyes, thus explaining the quantity of the trophy.
In the counting science of the ancient world, gradual progress was observed: the numbers “one”, “two” and “many” were already known. Soon a person came to the point that he began to isolate three, four, five or more objects from the total mass, and this quantity did not have a name, but was explained as the sum of the numbers known at that time: “2” and “1”. For example: “3” is “1” and “2” in total; “4” is the sum of “2” and “2”; and "5" is "2", "2" and "1" combined. In Tibet, the number “2” is the wings, in India - the eyes, among some peoples “1” is the moon, “5” is the hand. That is, each number first had a visually associative perception before receiving a name.
Counting as a vital necessity
How did people learn to count if the skill of this “art” at every stage of human development became simply a necessity? During the hunting process, when the animal was surrounded, the senior hunter needed to position the people correctly in order to encircle the animal. To do this, he showed on his fingers in what place and how many people needed to take the required positions..
In trade, the mathematics of fingers (and toes, if the cost was high) was also used to indicate prices. For example, when exchanging a made spear for animal skins, the seller would place his hand on the ground and show that a skin must be placed opposite each finger. By the way, bending the fingers meant addition, and extending them meant subtraction. These were the first mathematical examples that explained how people learned to count in the distant past.
Numeracy in different countries
Many countries that have preserved in their history models of how people learned to count still use the heritage of the past: in Japan and China, household items are counted in fives and tens; in England and France - in twenties.
The ancient Egyptians, who depicted any action in the form of a picture on papyrus, did not write down numbers as such. The inhabitants of Ancient Rome denoted numbers with dashes. So “I” is one, “V” is an image of a hand with a finger protruding to the side, or rather five fingers in a simplified version, “X” is two fingers folded together.
With the advent of letters, the alphabet began to be used to represent numbers. For example: B-
With the advent of letters, the alphabet began to be used to represent numbers. For example: B is “2”, G is “3”, D is “4”, E is “5”. To distinguish letters and numbers, an icon called a “titlo” was placed above the latter. The method was not very convenient, since it did not allow recording large numbers. Over time, people began to separate numbers from letters and perceive them separately, regardless of objects.
Modern ones, which are widely used today, were invented in India, and in our country they found their application in the 18th century. Roman numerals, which are still found on watch dials today and are used to indicate centuries and chapters in books, have not lost their popularity.
Ancient Babylon was distinguished by its method of counting, in which, 6 thousand years BC, mathematical accounting of business transactions was already carried out. Records of this kind were depicted with pictures (hieroglyphs) in the form of narrow horizontal and vertical wedges, which is where the name “cuneiform” comes from.
One was indicated by one wedge, two by two, and so on. The number “10” stood out as a wide wedge and had a special name. Mathematics of Babylon experienced its heyday during the reign of In written sources of that time period, evidence was found of how people learned to write and count long before our times. These are records of complex computational operations, as well as solutions to quadratic and cubic equations.
How to learn to count in your head
If such complex operations were possible for our ancestors, then for the modern generation, mathematical calculation, improved by time and many great minds, should not be particularly difficult. True, the presence of computer technology capable of performing digital actions instead of a person greatly facilitates the latter’s mental work. Therefore, everyone should master mental arithmetic, which helps develop memory and train skills. Training in this type of mental activity will be successful if:
- abilities that, together with mental concentration, help focus attention on the task at hand and retain complex numbers in memory;
- knowledge of formulas that determine the ease of computational actions performed;
- a practice that, along with constant training, allows you to develop and improve skills.
Examples of simple mental arithmetic
Multiply by 4
An easy way in which the number needs to be multiplied by 2, and the resulting result doubled again. For example:
35 * 4 = 35* 2 = 70 * 2 = 140
Multiplying by 11
The digits of a two-digit number multiplied by 11 need to be moved apart, as it were.
For example:
48 * 11 = 4 and 8 * 11
Then you need to add the digits of the number, in this case 4 and 8, and the resulting result will be the answer. It is important to remember that if the summation results in a two-digit number, then you need to leave only the ones and add 1 to the tens.
4 (12) 8 = 5 2 8 = 528. That is, from the result obtained, 12 left ones - this is 2, and added 1 to ten.
Division by 5
To make this action easier, you need to double the number and move the decimal point back one digit.
Eg:
125/5 = 125*2 = 250 (decimal offset) = 25
Division by 50
In this case, the pattern is similar: the number is multiplied by 2 and divided by 100.
600/50 = 600 * 2 / 100 = 12
Division by 25
The number is multiplied by 4 and divided by 100.
700/ 25 = 700*4 / 100 = 28
Adding and subtracting natural numbers
When adding, you should know this trick: if one of the terms is increased by a certain number (to make counting easier), then the same number must be subtracted from the result.
Eg:
787 + 193 = (787 + 193+ 7 (to round 193 to 200)) - 7 = (787 + 200) - 7 = 980
We have been able to count objects since the 1st grade. It's very simple - one, two, three... Measuring the distance is also easy. How and with what to measure time? The sun turned out to be the oldest “clock” that never stopped or broke. Morning, evening, day are not very accurate measurements, but at first this was enough for primitive man. Then people began to observe the sky more and discovered that after a certain time a bright star appeared in the sky. These observations were made by the Egyptians, and they named this star Sirius. When Sirius appeared, the new year was celebrated in Egypt. This is how the now well-known measure of time - the year - appeared. It turned out that the interval between the appearance of Sirius consists of 365 days. As you can see, the calculations of the ancient Egyptians turned out to be quite accurate. After all, our year also consists of 365 days. But a year is too long a measure of time. And in order to conduct farming (sowing, growing, harvesting), smaller units of time were needed, and people again turned to the sky and the stars. This time the moon, or, in other words, the month, came to the rescue. You have all observed the moon and know that after a certain time it changes its shape: from a thin crescent to a bright round disk (full moon).
The interval between two full moons was called a month. It turned out that a month consists of approximately 29 days. This is how accurately they knew how to tell time in the Ancient World!
And the seven-day week arose in Babylon thanks to those planets that appeared in the sky and were known to the Babylonians:
Saturday is the day of Saturn;
Sunday is the day of the Sun;
Monday is the day of the Moon;
Tuesday is the day of Mars;
Wednesday is the day of Mercury;
Thursday is the day of Jupiter;
Friday is the day of Venus.
If other planets of the solar system were known in Babylon, perhaps our week would not consist of 7, but of 9, 10 or 8 days. These luminaries changed approximately 4 times during the month. So it turned out that there are 4 weeks in a month.
So, the most difficult thing - finding measures of time - was already done in the Ancient World. These measures are still used today. They just call them differently. In Rus', the names of the days of the week come from the serial number of the day:
Monday - according to the week, the day that starts the week;
Tuesday - second day;
Wednesday - midweek;
Thursday - fourth day;
Friday - fifth day;
Saturday, Sunday - these names are taken from the church dictionary.
It turns out that people borrowed all the main measures of time (year, month, week) from nature many years ago. Although these measures could not measure exact time, the main step was still taken.
"Primary School", 2004, No. 6
Topic: Time from 0 hours to 24 hours.
Goals: learn to solve problems to determine the beginning, end and duration of an event; introduce the unit of time - the second; improve computational skills, problem solving and equation solving skills; cultivate a careful attitude towards time.
Planned results: students will become familiar with a new unit of time - the second; learn to solve problems to determine the beginning, end and duration of an event; accept and save the learning task; take into account the action guidelines identified by the teacher; make comparisons according to specified criteria.
During the classes
I. Organizational moment
II. Updating knowledge
Logic problems
Igor is 4 years older than his brother Alexey and 5 years younger than his sister Masha. If you add up the ages of all three, you get 31 years. How old is Igor? (10 years.)
Irina is exactly 3 times older than her sister Nadezhda. How old are each of the sisters if half of their total age is 12 years? (6 and 18 years old)
III. Self-determination for activity
(The teacher reads the problems.)
Lessons start at 8 o'clock. Olya walks 15 minutes from home to school and spends 10 minutes getting ready for lessons. What time does she need to leave for school so as not to be late?
Lessons start at 8 a.m. Olya leaves home at 7 a.m. 35 minutes. How long does it take Olya to walk from home to school and get ready for lessons?
Olya leaves the house at 7:35 am. She walks 15 minutes from home to school and spends 10 minutes getting ready for lessons. What time do classes start?
How are the tasks similar? What is the difference?
Formulate the objectives of the lesson. (Learn to solve problems to determine the beginning, end and duration of an event.)
IV. Work on the topic of the lesson Work on the textbook
No. 231 (p. 49).(Oral performance.)
No. 232 (p. 49).(Independent implementation. Two students work on a folding board. Check, self-assessment.)
1) Solution: 12 hours 30 minutes - 10 hours = 2 hours 30 minutes. Answer: the excursion lasted 2 hours 30 minutes.
2) Solution: 13 hours + 3 hours 15 minutes = 16 hours 15 minutes. Answer: the performance ended at 16:15. No. 234 (p. 49).
Read it.
How many hours are there in a day?
How to find the third part of the day? (24:3 = 8 (h).)
What is half a day? How to find her? (This is the second part of the day: 24:2 = 12 (h).)
How to find a quarter of an hour? (1 hour= 60min, 60:4 = 15(min).)
- How to find a quarter of a year? (1 year = 365 days, 365:4 = 91 days 6 hours)
No. 235 (p. 49).(Independent implementation. Testing, self-assessment.)
Answers: 2 mm, 10 mm 2.
V. Physical education minute
The moon is floating in the sky. (Smooth rocking left and right.)
She entered the clouds.
One two three four five - (Clap your hands.)
Can we reach the moon? (Hands up.)
Six seven eight nine ten - (Clap overhead.)
And weigh it lower. (Hands down.)
Ten, nine, eight, seven - ( Steps in place.)
So that the moon shines on everyone. (Sit at the desk.)
VI. Continuation of work on the topic of the lesson
Introducing the unit of time - the second
(The teacher shows the clock.)
Look at our watch. How many arrows do they have? (Three.)
- Name them. (Hour, minute and second.)
Watch how they move. ( The hour clock barely moved, the minute clock moved one division, and the second clock made a whole circle.)
- How long does it take the minute hand to move through one division? (In 1 min.)
What did the second hand do during this time? (60 divisions passed.)
- What can be concluded? (At 1 min 60 s.)(Write on the board and in notebooks.)
1 min = 60 s
In physical education classes you often run and do timed exercises. What is the name of the device that the teacher uses? (Stopwatch.)
- It also looks like a watch, but its dial is designed for 1 minute. How many seconds are these? (The teacher shows a stopwatch.) The second hand can be stopped.
Working from the textbook
Read the theoretical material on p. 50.
Have we arrived at the correct ratio?
No. 239 (p. 50).(Oral performance.)
No. 240 (p. 50).(Collective execution with commenting along the chain.)
No. 241 (p. 50).
- Read the problem.
Will the camera take more or fewer photos? (More.)
How many times? (10: 2 = 5 (r.))
How many pictures will the camera take in 10 seconds? (32 . (10: 2) = = 160 (s.).)
VII. Reflection
(Independent completion of tasks “Test yourself” (textbook, pp. 49, 50). Test.) Answers S. 49: at 13 o'clock. S. 50: 12 s., 6 s.
VIII. Summing up the lesson
In what units is time measured?
How many seconds are in 1 minute?
Homework
Textbook: No. 243-245 (p. 50).
Topic: Units of time. Century.
Goals: introduce the unit of time - century; generalize and systematize knowledge about units of time; create a table of time units.
Planned results: students will become familiar with the unit of time - the century; learn to correlate units of time; build a logical chain of reasoning; establish analogies; accept someone else's point of view that is different from your own.
During the classes
I. Organizational moment
II. Updating knowledge
Individual work using cards
(Students who have mastered the topic well receive cards.)
Solve the problem.
Vasily came home after school at 2:35 am. It took him 10 minutes to change clothes and wash, 25 minutes to have lunch, 1 hour 45 minutes to prepare his homework, 25 minutes to clean the room and 30 minutes to travel to the House of Young Technicians, where he does modeling. What time do modeling classes start if Vasily is 25 minutes late for them? (At 5:25)
2. Front work
Insert the required time units.
Olya read 100 words in 1... (min).
Autumn holidays last 1... (weeks).
Summer holidays last 3... (months).
Vova went to camp on the 18th... (days).
A wolf can live 15-20... (years).
Solve problems.
Lena went out for a walk at 13:00 and came home at 14:20. How long did Lena walk? (1 hour 20 minutes)
The journey from Vova’s house to the cinema takes 25 minutes. What time should he leave the house to meet a friend at the cinema? at 11 o'clock? (At 10:35 am) .
The train covers the distance between the two cities in 2 hours 27 minutes. What time did he leave one city if he arrived in another city at 20:00? (At 17:32)
Calculate.
How many times in 1 month? less than 1 year? (12 times)
How many days is 1 month? less than 1 year? (For 335 or 336 days.)
How many hours in 1 week? (168 hours);
The lesson lasts 40 minutes. How many seconds is this? (2400s.)
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Slide captions:
09/05/2012 The world around us. Educational complex "Harmony" 4th grade Makarova M.V.
Homework check What is archaeology? What is subsoil? Archaeologists learn the history of mankind by... What do archaeologists do? Where can we conduct excavations? What can you find? science about the past rocks material sources excavations Makarov M.V. Retelling and PT No. 4, 5
What is a day? A day is a complete revolution of the Earth around its axis. Solar day = 24 hours Makarova M.V.
Counting days First, we counted the days, taking as a basis the change of day and night. They made notches or knots. Why does day give way to night? Why exactly 24 hours in a day? Find the answer on page 12 of your textbook. Makarova M.V. Day Night
We consolidate What was the first measure of time? Who divided day and night into 12 equal parts? And why exactly 12? What would happen if all the clocks suddenly disappeared? Why is the length of the day the same in different parts of the Earth, but the duration of daylight hours is different? Using the picture on page 12, determine where noon, midnight, morning and evening are. Makarova M.V.
Counting the years How many seasons are there on Earth? Why do they change? Observations of the changing seasons suggested the largest unit of time measurement. The ancient Slavs counted years from summer to summer (centennial, chronicle, how many years?...) Makarova M.V.
Northern peoples determined that the length of day and night varies throughout the year. They determined the beginning of the new year by the shortest day. In England there were special structures made of huge stones to determine the exact day of the new year. Makarova M.V.
We consolidate What movement of the Earth is taken as the basis for counting years? The Earth makes a revolution around the Sun in…. 1 year = … months = … days What does leap year mean? How is a leap year different from a regular year? Is winter the same length everywhere? Makarova M.V.
Why are there 12 months in a year? Why are there 4 weeks in a month? Find information on pages 16 – 17 of the textbook Time of revolution of the Moon around the Earth... PT No. 6 Makarova M.V.
Homework Pages 11 – 17 of the textbook retelling PT No. 7 – 10 Makarova M.V.
– We have been able to count objects since the first grade. It's very simple - one, two, three... Measuring the distance is also easy. How and with what to measure time? The sun turned out to be the oldest “clock” that never stopped or broke. Morning, evening, day are not very accurate measurements, but at first this was enough for primitive man. Then people began to observe the sky more and discovered that after a certain time a bright star appeared in the sky. These observations were made by the Egyptians, and they named this star Sirius. When Sirius appeared, the New Year was celebrated in Egypt. This is how the now well-known measure of time - the year - arose. It turned out that the interval between the appearances of Sirius consists of 365 days. As you can see, the calculations of the ancient Egyptians were quite accurate. After all, our year also consists of 365 days. But a year is too long a measure of time. And in order to manage the economy: sowing, harvesting, preparing the harvest, smaller units of time were needed, and people again turned to the sky and the stars. This time the moon came to the rescue, or, in other words, the month. You have all observed the moon and know that after a certain time it changes its shape: from a thin crescent to a bright round disk (full moon). The interval between two full moons was called a month. It turned out that a month consists of approximately 29 days. This is how accurately they knew how to tell time in the Ancient World.
And the seven-day week arose in Babylon thanks to those planets that appeared in the sky and were known to the Babylonians:
Saturday– day of Saturn;
Sunday– day of the Sun;
Monday– day of the moon;
Tuesday– day of Mars;
Wednesday– day of Mercury;
Thursday– day of Jupiter;
Friday- Venus day.
If other planets of our solar system were known in Babylon, perhaps our week would not consist of 7, but of 9, 10 or 8 days. These luminaries changed approximately 4 times during the month. So it turned out that there are 4 weeks in a month. So, the most difficult thing - finding measures of time - was already done in the Ancient World. These measures are still used today. They just call them differently. In Rus', the names of the days of the week come from the serial number of the day in the week:
Monday– by week; starting week;
Tuesday- second day;
Wednesday– middle of the week;
Thursday- fourth day;
Friday- fifth day;
Saturday, Sunday- these names came from the church dictionary.
It turns out that people borrowed all the main measures of time (year, month, week) from nature many years ago. Although these measures could not measure exact time, the main step was still taken.
2. Work in printed notebook No. 2.
Task No. 24.
The solution to the problem is presented in a form that is unusual for students - in the form of a diagram. Analysis of the problem can be organized as follows. Invite the children to carefully consider the diagram for solving the problem.
– How many steps does it take to solve the problem? (In 2 steps.)
– What is proposed to be found in the first action? (How many frames can one carpenter make in 2 days.)
– What is the result? (6 frames)
– Enter the result in the required “box.”
– What is proposed to be found in the second act? (How many frames will 6 carpenters make in 2 days.)
– Carry out the calculations. (6 6 = 36.)
– Finish the solution to the problem.
Answer: 36 frames.
As an additional task, you can ask students to come up with another way to solve this problem, and then analyze it orally.
1) 3 · 6 = 18 – this is how many frames are made by 6 carpenters in 1 day;
2) 18 · 2 = 36 – this is how many frames will be made by 6 carpenters in 2 days.
VI. Lesson summary.
– What new did you learn in the lesson?
– How did people learn to measure time?
Homework: No. 12 (textbook); No. 21, 22 (workbook).
Lesson 59
Multiply by 6. Divide by 6
Lesson objectives: make a table of division by 6; improve problem solving skills in different ways; consolidate previously studied table cases of multiplication and division; develop logical thinking.
During the classes
I. Organizational moment.
II. Verbal counting.
1. Put “+” or “–” so that the equations are true.
| 79 … 50 … 6 = 23 | 18 … 60 … 40 = 38 |
| 45 … 5 … 30 = 10 | 51 … 40 … 30 = 61 |
| 10 … 6 … 80 = 84 | 89 … 6 … 2 = 81 |
| 7 … 3 … 57 = 67 | 8 … 2 … 7 = 17 |
2. Task.
There are 12 eggplants in the box, and 10 in the basket. All the eggplants from the basket were transferred to the box. How many eggplants are there in the box?
3. Children drew polygons and turned them into portraits.
The number of sides in Oleg's and Sveta's polygons is the same. The perimeters of Sveta's and Anton's polygons are equal to each other.
III. Lesson topic message.
– Look at the drawing on the board.
– What examples can be made for this illustration?
+ + + + =
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– Fill in the numbers in the boxes using this picture.
– What difficulties did you encounter?
– Today in class we will make a table of division by 6.