Pioneer Primary School- branch of MBOU "Ilyinskaya secondary school"
MATHS
Topic: « Roman numerals. Designation of numbers in Roman numerals. (grade 3)Compiled by: Fedoryuk Olga Grigorievna,
teacher primary school
p. Pioneer - Truda, 2014
Mathematics (Grade 3)
Topic : Roman numerals. Designation of numbers by Roman numerals.Goals : Educational Purpose: Introduction to writing Roman numerals and numbers.- Development goal: develop cognitive interest and cognitive activity, thinking (the ability to observe, highlight the main thing, analyze, generalize, compare) attention, development mathematical speech, memory. - Educational: to cultivate goodwill, friendliness, mutual assistance when working in pairs.Tasks: 1. Introduce children to Roman numerals and their spelling; 2. Give an idea about the use of Roman numerals in practice; 3. Learn to read numbers, solve examples using Roman numerals;4. Consolidate knowledge of the numbering of numbers within 1000.Personal UUD:educational and cognitive interest in new educational material.
Cognitive UUD: search for the necessary information to complete educational tasks using educational literature; use symbolic means.
Regulatory UUD:take into account the guidelines for action identified by the teacher in the new educational material in collaboration with the teacher.
Communicative UUD:adequately use speech means to solve various problems.
Lesson type: A lesson in discovering new knowledge. Lesson equipment: King, mathematical kingdom, cards with tasks for working in pairs, cards with tasks for self-control, control sheet, table.
During the classes:
- Org. Moment.
- Verbal counting:
- Work in notebooks.
- Statement of the topic and purpose of the lesson.
- The discovery of new knowledge by children.
- And how did the ancient people who did not know the numbers think? Primitive people there was no one to learn from. Life itself was their teacher. Watching over surrounding nature on which life depended. Our ancestor learned to distinguish from a variety of objects. Separate items. From a pack of wolves - a leader, from an ear with grains one grain. It was defined as "one" and "many".
So what did you learn about Roman numeration (in Ancient Rome, node numbers, others are formed by addition and subtraction). Tired, it's time to rest.
- Phys. minute.
- Primary fastening.
- Textbook work.
- Reading and writing numbers.
- Comparison of numbers.
- Calculations with numbers written in Roman numerals.
No. 3. Pg. 46.
- A task.
Now show me how to solve problems.
- A challenge for ingenuity.
- Modeling
- Logic task.
Methodical development of a lesson in mathematics.
Subject: Roman numerals.
Class: 3.
Conduct form: lesson using a multimedia presentation.
Goals:
Educational: familiarity with the writing of Roman numerals and numbers.
Developing: development of cognitive interest and cognitive activity, thinking (the ability to observe, highlight the main thing, analyze, generalize, compare); attention; development of mathematical speech, memory.
Educational: to cultivate goodwill, friendliness, mutual assistance when working in groups.
Tasks:
introduce children to Roman numerals and their spelling;
to give an idea of the use of Roman numerals in practice;
consolidate knowledge of the numbering of numbers within 1000.
Lesson type: lesson in discovering new knowledge.
Lesson equipment: a checklist for oral counting, cards with tasks for working in groups; multimedia projector; screen; presentation.
During the classes:
Organizational moment.
Guys! Are you ready for the lesson? (Yes).
I hope for you, my friends.
Good afternoon and good hour.
Everything will work out for us!
I really want the lesson to be interesting, informative, and you tried to discover new secrets of mathematics.
Today, guests came to us to see how you discover mathematical secrets.
Update basic knowledge and motivation.
Do you love secrets? (Yes)
In order to discover a new mathematical mystery, let's start with what we already know.
1) - Write down the numbers: 305, 480, 67, 1000, 5 hundred + 3des + 9s, 8sot + 6s, 2sot + 7des, 5des + 4s.
Check yourself by checking the control sheet (posted on the board).
Who got the same as on the control sheet, raise your hand. (Well done!)
Who made mistakes? In what numbers? Why were they wrong?
What you need to know how to correctly count and write multi-digit numbers? (The meaning of numbers, digits of numbers, positions of numbers, numbering - the digital designation of objects arranged in sequential order.)
Who remembers what numbering do we use now? (Arabic) This knowledge will be useful to us today in the lesson.
2) - You have envelopes with cards on your tables. When working in groups of 4-5 people, you need to distribute them into groups as quickly as possible.
On what basis did they divide? (by arithmetic operations, by the value of expressions, by the same Roman numeral) What helped you?
Statement of the topic and purpose of the lesson.
Who guessed what the topic of today's lesson is? (Roman numerals. * )
Where are Roman numerals used today? * (In hours*, historical dates*, calendars*, volumes and chapters of books*, to indicate points of the plan, in a short note ...)
In the lesson, we will take an excursion into the history of numbers, learn how to read, write, compare Roman numerals, and also perform simple calculations with them.
The discovery of new knowledge by children.
Now we will find ourselves in the ancient world, we will be transported to other countries and see how numbers were invented by human society.
What do you think common in the illustrations on the slide? (These are all numbers.) *
Even in ancient times, there was a need to write down numbers. The number of objects was depicted by drawing dashes or serifs on some hard surface. People drew sticks on the walls and made notches on animal bones or tree branches.
But a single notation of numbers was cumbersome and inconvenient, so people began to look for more compact ways to denote large numbers. There were special designations for "fives", "tens", "hundreds", etc.*
So how did people write down numbers in the first place? (…)
Why was this system inconvenient? (…)
The next notation was Egyptian numbering. *
The system of such signs among the Egyptians was very clear. The Egyptians came up with this system about 5,000 years ago. This is one of the oldest numbering systems known to man.
See what signs the Egyptians used: sticks, fetters, a measuring rope, a lotus flower, a finger, a tadpole, a seated man, the sun.
Do you think it was convenient for people to use such symbols? Why? (…)
Therefore, humanity has evolved further.
Please remind me again what numbering we use. (Arabic) Who knows why? Let's see. *
Arabic numbering is the most common today, which we currently use. It turns out that the currently used numbers from 0 to 9 developed in India around 400 AD.
The Arabs began to use this numbering around 800 AD, and around 1200 AD. it began to be used in Europe thanks to the works of Arab mathematicians, and therefore the name “Arabic” was established behind them.
Although the Arabs themselves, up to the present time, use completely different symbols. Pay attention to the signs depicted in black font.
In Russia, Arabic numeration began to be used under Peter I (before late XVII centuries, Slavic numbering was preserved).
So where was the Arabic numbering invented? (In India)
Why is it called Arabic? (Spread thanks to Arabic mathematicians)
When did you come to Russia? (At the end of the 17th century.)
And finally, we come to the numbering, which we are most interested in in this lesson. Which? ( Roman numeration) Where did it originate? (…) *
This numbering originated in ancient Rome. It contains nodal numbers: one, five, etc. The remaining numbers were obtained by adding or subtracting some nodal numbers from others: the smaller number to the right of the larger one is added to it, and the one to the left is subtracted.
For example, four is written as IV, i.e. five minus one, eight is VIII (five plus three), forty-XL (fifty minus ten), ninety-six-XCVI (one hundred minus ten plus five and plus one) and t d.
Pay attention to the table of Roman numerals, what letters of the alphabet do they look like? (English: 1 - ai, 5 - vee, 10 - ex, 50 - el, 100 - si, 500 - di, 1000 - um, 2000 - zet)
When reading and writing numbers in Roman numeration, one must remember that ... *
Roman numeration is non-positional. No matter where the number stands in the notation of the number, it always means the same thing.
So what did you learn about Roman numeration? (in ancient Rome, nodal numbers, others are formed by the addition or subtraction of them, non-positional)
What does non-positional number system mean? (…) Well done!
Fizminutka.
- And now we all go on a trip to Rome together ...
Arched hands quickly -
Got the Colosseum. *
It's time to straighten your arms -
We are in Peter's Square. *
Legs wider, top - house -
Got the Pantheon. *
It's time for us all to walk
At St. Peter's Basilica. *
Each of us is ready to breathe
Among the greenery of Roman gardens. *
Primary fastening.
Textbook work.
Open your textbooks to page 46. Consider clock image. Read #1 to yourself.
What did you learn from the student about the designation in Roman numerals?
Let's repeat. *
How to write the number four using Roman numerals? (Five minus one) - …. (After answer* )
How to write the number six - .... *
How to write the number nine - .... *
How to write the number eleven - ... *.
Reading and writing numbers.
a) Please read the first part of the paragraph on page 47, marked with a red line.
What did you learn? (That with the help of Roman numerals Ι, V, X, you can also write numbers greater than 12.)
And now the task "Try it yourself" * *
Let's check what happened. * *
Raise your hand for everyone? .. Who didn’t succeed? .. What number caused difficulty?
Read the second part of the paragraph on p. 47.
What have you learned?
B) - And now, using the information from the paragraph, we will read the numbers written on the board. First write down the date when...
Alexander Sergeevich Pushkin was born in M D SS XC ΙX. (1799)
The poet died in M D CCC XXX VΙΙ. (1837)
How long did Pushkin live? (38 years - XXXVΙΙΙ)
Comparison of numbers.
Let's try to compare the numbers: No. 2 with. 46. (Three people work at the board)
So we learned how to compare the numbers of Roman numeration, and now the task is even more difficult - performing calculations.
Calculations with numbers written in Roman numerals.
№ 3 s. 47.
Try to solve the examples yourself.
Who will write the answers on the board? (6 people)
Who got these answers?
A task.
A wealthy Roman bought 14 pairs of colorful sandals. How many sandals did a Roman have in his wardrobe?
A challenge for ingenuity.
And finally, a task that will help you understand how important it is to know a lot, and in particular, Roman numerals.
"Smart Owner"
9 visitors came to the tavern "Three minnows" and demanded to give them fish. The owner, unfortunately, has only three fish left. Nevertheless, he did not want to miss the opportunity to profit: having three fish at his disposal, he promised to serve nine to the guests. The guests became interested in this and even agreed to pay the money in advance. How did the owner of the tavern manage to keep his promise? (The host served three fish on the table, arranged in the form of the Roman numeral nine)
What helped the owner get out of this situation?
What conclusion can be drawn from the presented case?
(It is important to be a versatile person, and not to specialize in a narrow area that you like or is related to your work, study)
Reflection of activity.
Our lesson has come to an end. And it's time to return home from the trip.
So what mathematical mysteries did you discover today in the lesson?
Where can you find Roman numerals?
Houses you have to complete two tasks: No. 7 p. 47 (exercise), No. 5 (creative, can be in the form of a story about yourself)
Complete the sentence orally:
I found out today...
I liked today...
I will tell…
Thank you all for your work. Estimates. The lesson is over.
The holiday “From year to year, from class to class Time leads us inaudibly” And now, in honor of the holiday on September 1, we will have a “Day entertaining lessons". This day will help you to slightly refresh your knowledge in various subjects and set yourself up for the new school year. Over the summer, you all have matured, and I hope you have become smarter. Now we will check it. - Today in the schedule: Fairy tale literature. Funny grammar. Joke math. Naughty music. Cognitive environment. - I hope you enjoy these entertaining lessons. At the end of all lessons, we will summarize and find out how ready YOU are for the new school year. 1. Fairy tale literature. Hints 1) The main character of this story unexpectedly got rich. 2) She made many friends for whom she began to arrange receptions. 3) They tried to kidnap her, but suddenly a young daredevil appeared and saved her. 4) The case ended in a wedding. 5) The most valuable asset main character was a samovar. (K. Chukovsky. MukhaTsokotukha) 1) This is an evil sorceress. 2) She lived in a cave. 3) There, under the ceiling, hung a stuffed animal of a huge crocodile, and bundles of dried mice hung from the ceiling. 4) She brewed a magic potion to harm people. 5) Her magic caused a terrible hurricane that reached Kansas and carried away a small house in which there was a girl, Ellie, and a dog, Totoshka. (Gingema. A. Volkov "The Wizard of the Emerald City") 1) The hero of this work is the son of a miller. 2) After the death of his father, he practically inherited nothing, except for one animal. 3) It was a cat. 4) The cat asked the owner for a strange gift, the owner was surprised, but the cat's request was fulfilled. 5) Thanks to the cunning and devotion of this animal, the hero gained wealth, he married a princess, the daughter of a king. (Marquis de Carabas, C. Perrot "Puss in Boots" 2. Funny grammar. The Russian language is worried if you have forgotten the letters? How will you cope with dictations and presentations? He has prepared his tasks. Guess the letter. 1. What is in the middle land? (Letter "M") 2. How does summer end and autumn begin? (Letter "O") 3. What is the girl's name if you write thirty letters "I"? (Zoya.) 4. How does it all end? (Letter "O") "Yo") 5. The names of which two months end in the letter "T"? (March, August.) 6. What is behind the hare and the heron in front? (Letter "C") Task 2. - Guess the words. the root in the word write The prefix in the word tell, the suffix in the word book, the ending in the word water, its root in the word knit, the prefix in the word shut up, the suffix in the word fairy tale, the ending in the word fish, its root in the word snowflake, the prefix in the word drove up , Suffix in the word forester, Ending in the word student 3. Comic mathematics It is proposed to solve 6 very challenging tasks but remember that math is fun today. 1. There are chickens in the yard. All chickens have 10 legs. How many chickens are in the yard? (5) 2. There are 7 bulbs in the chandelier, 5 of them burned out. How many light bulbs need to be replaced? (5) 3. Misha has 3 pairs of mittens. How many mittens on the left hand? (3) 4. Two summer residents went from the village to the city, and five more summer residents met them. How many summer residents went from the village to the city? (2) 5. Vera and Nadia are sisters. Vera said that she had two brothers, and Nadia said that she had two brothers. How many children do Vera and Nadia have in their family? (4) Mathematical chest. 1. What geometric figure is needed to punish children? (Angular) 2. Two sausages are boiled for 6 minutes. How long will 8 such sausages cook? (6 minutes.) 3. The name of which fairy-tale heroine comes from the name of the unit of measurement of length? (Thumbelina (inch = 2.54 cm)). 5. What geometric figures friendly with the sun? (Rays.) 6. Five light bulbs burned dimly in the chandelier. Doors slammed, two burned out. You need to do a little: Say how many lamps are left? (5 lamps.) A smart owner. 9 visitors came to the tavern "Three minnows" and demanded to give them fish. The owner, unfortunately, has only three fish left. However, he did not want to be left without profit that day: having three fish at his disposal, he promised to serve nine to the guests. The guests became interested in this and even agreed to pay the money in advance. How did the owner of the tavern manage to keep his promise if he did not cut the fish? (The owner served three fish on the table, laid in the form of a Roman numeral nine) 6. Mischievous music Auction of songs on a school theme Croak, grunt, meow, quack, bark some song 7. Cognitive world around. Savvy. 1. How many giraffes swim in the Black Sea? (Giraffes do not swim.) 2. If you throw a red stone into the Black Sea, what will it become? (Wet.) 3. At what time of the year can water be carried in a sieve? (In winter, by freezing it.) 4. When is it easier for a black cat to get into the house? (When the door is open.) -And lastly, I suggest you go fishing. Try to catch the name of 8 more fish from the text of the story. An amateur fisherman Chauffeur Makar fell in love with fishing. In general, he is a great driver and can drive, as they say, on one wheel: ice, ditches, pits - he is not a hindrance. We went with him once for winter fishing. And he is a freak! - at the camp where we stopped, he suddenly began to doubt: is there a fish there? Went to the familiar grandfather, asked. What do you want, Makar? Ah? - said the grandfather. With a wave of his hand, the driver quickly turned the car around and drove on. - Oh, - he says, - in the summer we would make a light raft. We wouldn't need felt boots and fur coats. But I would take the net with me. Can you imagine, I am dragging a nylon net to the shore, and it is full of fish... - Uh, such poaching cases can lead to prosecution. But how? - Come on, - laughs, - I was joking, I never took the Network in my hands. I only fish with a rod. Here I am! I'm a brand new school year, I'm just - just starting. I have a lot of worries, But I do not shy away from work. What I will be this time - Schoolchildren depend on you! After all, if you are lazy, I can get heavy. But if you try, I'm glad to be happy! Happy new school year!
Educational goal: to promote the formation of ideas about the features of the development of the civilization of the Ancient World and the realization that mathematical knowledge helped ancient people expand their horizons.
Developing goal: to promote the training of schoolchildren in the ability to characterize objects and phenomena in relation to the topic of the lesson, to substantiate the logical evidence of their assumption, to promote the formation of skills to analyze and systematize information.
Educational goal: to form the experience of equal cooperation between the teacher and students, to promote a tolerant attitude towards representatives of other countries and peoples.
Type of lesson: generalization and systematization of knowledge.
Main methods: partially search and problematic.
Forms of organization cognitive activity: individual and group.
Means of education: Handout, interactive whiteboard, crossword puzzle.
During the classes
Mathematics teacher: Today we will make a journey into the world of the mysterious and mysterious. Guys, do you like to travel? The famous French writer Anatole France said: “Travel teaches more than anything else. Sometimes one day spent in other places gives more than ten years of life at home. How do you understand the French writer's statement? Why do people go to distant lands?
Pupils: Life at home can be boring and monotonous. A person who travels broadens his horizons, makes his life brighter and more colorful. People go to distant lands in order to have a good time, learn a lot of interesting things about the host country, its language, culture, national cuisine, local attractions, etc.
History teacher: Even ancient people were sure that numbers tend to influence their lives. Pythagoras, an ancient Greek philosopher and mathematician, was one of the first to study number theory and develop this doctrine. The name Pythagoras means "the one whom the Pythia predicted": the birth of a child, according to legend, was predicted by the Pythia in Delphi. The Pythagorean school was the first to put forward the idea that the earth was actually round. Pythagoras was fond of sports, won fisticuffs at the Olympic Games. He came up with a special mug that allowed him to drink only in limited quantities. Today it is sold in Rhodes, Samos and Crete as a souvenir. "10" was Pythagoras' favorite number. In general, he attached special importance to numbers and believed that they reflected absolutely everything in the world. Based on the knowledge of ancient magicians and priests and on his own theories, he argued that it was numbers that ruled the world. Do you agree with Pythagoras?
Pupils: For Orthodox believers, the number 3 is sacred. Numbers affect people's lives in astrology.
History teacher: Today we will visit many schools of the Ancient World and try to expand your knowledge of history and mathematics that you already have. We will make our first stop on the world map in Africa. Why do you think?
Pupils: In Africa, for the first time, the remains of humanoid creatures were discovered.
Mathematics teacher: It is known that primitive hunters and gatherers who lived in tribal communities learned to count on heels and tens (according to the number of fingers on their hands), knew arithmetic operations. Guess which of the arithmetic operations people mastered first. What do you think you had to do more often: multiply, divide, add, subtract?
Pupils: The first mathematical action of a primitive man was division, since in those distant times everything belonged to the tribal community.
History teacher: Next, we will go to the place where the transition from primitive to civilization took place first. Let's remember what it was?
Pupils: This refers to the emergence of states, large cities, letters, laws, the complication of people's lives (social inequality).
Math teacher: About what ancient civilizations the world will be discussed now?
Pupils: Oh Ancient Egypt and the Two Rivers.
History teacher: So, it's time to visit Egypt, which was also called Ta-Kemet - the Black Land. It was here that songs of praise were sung to the Nile River. Explain these amazing facts.
Students: Black earth means fertile, life-giving land. In Egypt, silt, a layer of fertile soil, played an important role.
Mathematics teacher: Several ancient Egyptian mathematical problem books written on papyrus have survived to this day. In one of the tasks it was required to calculate the capacity of the barn, in the other - the area of the field. There are also problems-jokes in papyri. Try to solve one of them: there were 7 houses, each with 7 cats, each cat ate 7 mice, each mouse ate 7 ears of corn, each ear can produce 7 measures of grain. Find the total number of houses, cats, mice, ears of corn, and measures of grain.
Pupils: It turns out the answer: the sum of all houses, cats, mice, ears of corn and measures of grain is 19607.
History teacher: From the territory of Africa we go to the Ancient Mesopotamia. Let's remember why one of the oldest civilizations was named that way?
Pupils: Mesopotamia was located along the banks of the Tigris and Euphrates.
History teacher: Did you know that the Egyptians, once seeing the Euphrates, called it a river flowing in reverse. Why?
Students: The Egyptians believed that all rivers, like the Nile, should flow from south to north. Acquaintance with the Euphrates was a complete surprise for them.
History teacher: In ancient Mesopotamia, scientists-priests were engaged in mathematics. Remember what number they considered sacred?
The students discuss the question in groups and make an assumption - 60. If there are difficulties with the correct answer, the teacher gives it himself.
Math teacher: Remember where the number 60 occurs.
Students: There are 60 minutes in a degree of 60 seconds each, an hour lasts 60 minutes. There are 60 minutes in an hour, 60 seconds in a minute.
Mathematics teacher: I propose to remember the timeline and solve the problem: in 2004 BC, a merchant from the city of Ur went with a trade caravan to Phoenicia. He was 40 years old at that time. He returned home only after 3 years. A year before leaving, his son was born. In what year were the merchant and his son born? In what year did the merchant return home?
Students provide answers.
History teacher: No less mysterious was the country where Ganesha was revered as a deity, chess was invented and the most ancient world religion, Buddhism, was born. What country are we talking about?
Students: We are talking about India.
Math teacher: How did the Hindus deal with numbers? The Arabic numerals that we use are actually borrowed by the Arabs from the Indians (the Arabs themselves called them Indian). The method of numbering, which originated in India, turned out to be the most perfect of those that existed in antiquity. Initially, Indians wrote down numbers using words. So, zero was conveyed by the words "empty", "sky"; the unit was represented by objects that are available only in the singular ("Earth"); deuce - the words "twins", "eyes", etc. Think about what number was transmitted in ancient texts with such words: "Moon - hole - wings - Sun"?
Pupils: The number that was conveyed in ancient texts by the words "Moon - hole - wings - Sun" is 1021.
History teacher: Where did the first Olympic Games take place?
Pupils: The first Olympic Games took place in Ancient Greece.
Math teacher: This is where we will make our penultimate journey.
In ancient Greece, it was not difficult for those who were diligent in learning the alphabet to master the new wisdom in calculation, because Greek letters can in different cases be either signs of speech, or numbers and numbers.
The students solve the problem and give the answer.
History teacher: In conclusion, we will visit a huge state that has united the entire Mediterranean and a significant part of Europe. It was here that the she-wolf and Julius Caesar were revered, beautiful cities and buildings like Lutetia and the Colosseum were built. Where will we make our final journey?
Students: We will make our last trip to Ancient Rome.
Mathematics teacher: Here, unlike in other countries, the score was kept in a different way. The Romans didn't have the number 0.
1 - I 2 - II 3 - III 4 - IV 5 - V 6 - VI 7 - VII 8 - VIII 9 - VIIII
I once encountered an interesting problem in a mathematics textbook, and I suggest you solve it. 9 visitors came to the tavern "Three minnows" and demanded to give them fish. The owner, unfortunately, has only three fish left. Nevertheless, he did not want to be left without profit that day: having three fish at his disposal, he promised to serve nine to the guests. The guests became interested in this and even agreed to pay the money in advance. How did the owner of the tavern manage to keep his promise if he did not cut the fish?
Pupils: The host served three fish on the table, arranged in the form of the Roman numeral nine.
History teacher: At the end of the lesson, you have to solve a crossword puzzle. During the lesson, you were attentive and you can easily guess the keyword vertically, which is related to both history and mathematics.
Questions:
1) Who won the fisticuffs at the Olympics?
2) What number was conveyed in ancient texts by the word "eyes"?
3) A symbol of divine balance.
4) Who predicted the birth of Pythagoras?
5) In the school of Pythagoras, the idea was first put forward that what? round.
6) What number did the ancient Romans not have?
7) Which of the arithmetic operations did people master first?
8) Favorite number of Pythagoras.
Answers:
1. Pythagoras.
2. Deuce.
3. Six.
4. Pythia.
5. Earth.
6. Zero
7. Division.
8. Ten.
The key word is horizon.
Math teacher: At the end of the lesson, I will quote the famous American financial figure John Pierpont Morgan: “Go ahead to the very horizon. When you get there, a new one will open.
Elena PECHENKINA, math teacher,
Alexander SHIBANOV, teacher of history and social studies, gymnasium No. 2 of the city of Kirovo-Chepetsk, Kirov region
Goals:
- To introduce Roman numerals, teach to read, solve examples using Roman numerals.
- Develop logical thinking to form an interest in the study of history.
- Cultivate observation.
Equipment:
- map ancient world;
- counting sticks for each student to solve practical problems.
DURING THE CLASSES
On the desk:
What do the notes on the board have in common? (If the students find it difficult to answer, the teacher says that these are numbers)
But some are older, others are younger.
Teacher's story
- What do you think, which of the presented figures is the most ancient?
The most ancient Egyptian. As the name implies, they were invented in Egypt (map).
The Egyptians came up with this system about 5,000 years ago. This is one of the oldest numbering systems known to man.
The digits of the number were recorded starting from large values and ending with smaller ones. If there were no tens, units, or some other digit, then they moved on to the next digit.
Practical work students
Try to write down how old you are with such numbers (during the lesson, sheets with numbers are removed or transferred to a separate board).
Teacher's story
What are the next numbers?
it Babylonian numbers (show on the map).
In ancient Babylon, about 40 centuries before our time, positional numbering was created, that is, a way of writing numbers in which the same number can denote different numbers, depending on the place occupied by this figure. Our current numbering is also local. In the Babylonian local numbering, the role that the number 10 plays for us is played by the number 60, and therefore this numbering is called sexagesimal. Numbers less than 60 were indicated using two signs: for one, and for ten. They had a wedge-shaped appearance, as the Babylonians wrote on clay tablets with triangular sticks. These signs were repeated the required number of times, for example
Our country also had its own figures. Guess which of the entries on the board Slavic.
The Greeks and Slavs added special signs to the letters so as not to be confused with ordinary letters.
AT ancient Russia the letter “a” denoted one, “c” - two, “g” - three. And so on. A special dash above the letter (title) indicates that it is not a letter, but a number. Also, the letter “a” with a special sign on the left indicates a thousand, and circled - ten thousand, or “darkness”, as such a number was then called.
Working with the textbook
- Of the remaining numbers, which numbers are most familiar to you?
- Where did they come from?
Lesson topic
Today's topic is - Roman numerals.
– Where do we meet them in life? (children's answers)
Teacher's story
Roman numerals are used quite often these days. For example, on the watch dial they sometimes make designations in Roman numerals, in books they often indicate the number of a volume or chapter, I write down historical dates in Arabic numerals, and a century in Roman numerals. When solving problems, writing a short note, we also use Roman numerals.
- What do Arabic and Roman numerals mean in a short note? (Arabic - quantitative numerators, i.e. how many items were taken “one house, wagon, etc.”; and Roman ones are ordinal numbers “in the first house, wagon, etc.”).
Working with the textbook
Read on your own about the designation of Roman numerals.
Teacher's story
- Remember the peculiarity of the Roman notation: the smaller number to the right of the larger one is added to it, the one to the left is subtracted. Therefore, the sign VI means 5 + 1, that is, 6, and the sign IV - 5 - 1, that is, 4. It is not difficult to learn how to read numbers written in Roman numeration, and we will learn how to do it.
Practical work
1. Read the numbers on the board “Alexander Sergeevich Pushkin was born in MDCCXCIX and died in MDCCCXXXVII. How many years did Pushkin live?
2. Write down the numbers using Roman numeration (two people work at the board) 7, 11, 24.
3. Solve examples: (2 people at the blackboard)
| V+II | VI+II |
Now let's test your ingenuity.
Divide the number twelve on paper so that half of this number is seven.
How to get eight by subtracting half from thirteen?
Write the number thirteen in Roman numerals and divide this number in half with a horizontal line.
Working with counting sticks
Use counting sticks to write examples on the table
1. VI - IV \u003d IX
Move 1 stick so that the equality becomes true. (V+IV=IX)
Move 1 stick so that the equality becomes true. (VII + IV = XI)
Move 2 sticks so that the equality is true. (VI=VIII-II)
Repetition of what was learned in the lesson
- With the numbers of which peoples did you meet today?
- What else do you know?
And finally, a task that will help you understand how important it is to know a lot, and in particular, Roman numerals.
Clever host
9 visitors came to the tavern "Three minnows" and demanded to give them fish. The owner, unfortunately, has only three fish left. Nevertheless, he did not want to miss the opportunity to profit: having three fish at his disposal, he promised to serve nine to the guests. The guests became interested in this and even agreed to pay the money in advance. How did the owner of the tavern manage to keep his promise? (The host served three fish on the table, arranged in the form of the Roman numeral nine)
- What helped the owner to get out of this situation?
What conclusion can be drawn from the presented case?
(It is important to be a versatile person, and not to specialize in a narrow area that you like or is related to your work, study)