This video introduces one of the most important instruments for the development of mathematics, especially regarding numbers and counting: the Abacus.
The abacus is an ancient calculation tool, likely originating in Mesopotamia over 5,500 years B.C., and is considered an extension of counting on fingers.
The instrument consists of a rectangular frame with parallel rods, where each corresponds to a multiple of ten (place values like Ones, Tens, etc.). It holds counting elements (beads) that slide freely. It is still used today to teach children mathematical operations like addition and subtraction.
In this video (Lesson 04 of Grade 6 Math), we will learn how to use it!
Este vídeo irá mostra um dos instrumentos muito importante para o desenvolvimento da matemática, principalmente dos números e da contagem iremos falar sobre o ábaco, é um antigo instrumento de cálculo, com provável origem na Mesopotâmia há mais de 5500 anos a.C., considerado como uma extensão do ato de se contar nos dedos O instrumento é formado por uma moldura retangular com hastes em paralelo, onde cada um correspondente ao múltiplo de dez, uma posição digital (unidades, dezenas,...) e nos quais estão os elementos de contagem (fichas, bolas, contas,...) que podem fazer-se deslizar livremente. Ele é utilizado ainda hoje para ensinar às crianças as operações de somar e subtrair.
00:00Abacus, an instrument for counting and calculating
00:08As the need arose to count ever-increasing quantities,
00:16Humans began to group together marks, stones and other objects used for counting.
00:22Some people started to group in groups of 5, others grouped in groups of 10,
00:30every 12, every 20 or every 60.
00:35Even today we do groupings of 10.
00:39Because we count by 10s, our numbering system is called a decimal numbering system.
00:47Some ancient peoples kept counts by depositing them in a hole in the ground.
00:54One stone corresponded to each object counted.
00:57When they gathered 10 stones, they replaced them with a single stone, which was placed in the hole next to the first one,
01:07that is, very similar to our decimal numbering system.
01:12This procedure gave rise to an instrument used to count and calculate by groupings, known as an abacus.
01:22Over time, many different types of abacus have been invented.
01:27One of the simplest is the one where the correspondence is made using rings that are pierced and fitted onto rods,
01:35fixed in a frame, as you can see in the image.
01:40The abacus makes it easier to record objects and read counts.
01:47If we want, for example, to register 9 objects, we place 9 rings in the right column, as shown in the image.
01:54And now we will better understand the logic of the abacus and how to express numbers in this great counting instrument.
02:03So now, let's show you a model of an abacus and understand how counting works on an abacus.
02:13Very simple.
02:15So, therefore, we have here, as you can see, we have this drawing here.
02:21This drawing here, which will flash now, look, is the drawing of the abacus.
02:25So, let's understand the logic behind this instrument.
02:29So, let's go.
02:30In the first line here, which you can see, or on the axis, right, I called it a line, but let's consider it as this axis here.
02:38We call this unity.
02:41This first axis is unity.
02:45Now in the second one here, where there is a little ring or washer, then we call it a ten.
02:54In the third, we will call it a hundred.
02:58And in the last one here, we call it a thousand.
03:02Now, let's see how many rings there are here.
03:05There's one, two, three, four.
03:07We have four rings in the unit.
03:10So, what does that mean?
03:12Four units.
03:13In the ten, we have only one.
03:16So, what does it mean?
03:17Ten.
03:19And in the hundred, we have three.
03:21It means we have three hundred.
03:25Now, adding three hundred plus ten plus four, we have the value of three hundred and fourteen.
03:32So, did you notice how we expressed the number on this instrument known as an abacus?
03:38Also notice that there are no numbers on the thousands rod.
03:42So, it doesn't represent anything, as if it were zero.
03:46So now, moving on, let's show two more examples here, so we can have a little fun.
03:52We have this model here now.
03:54Three rings on the first stem.
03:56And we can see here, here there are one, two, three, four, five, six, seven rings and here there is one.
04:03So, how will it be?
04:05It will be unit three, hundred, seven hundred and thousands, one thousand.
04:11So, what will this value be?
04:14One thousand seven hundred and thirty.
04:16And now, let's move on to the other example.
04:18On the first stem, there are two small rings.
04:21And on the third rod, we have one.
04:23So what do we have?
04:24Without, referring here, the third rod.
04:29And two, referring to the first.
04:31So what do we have?
04:33We always have everything.
04:34So, folks, this is the abacus instrument.
04:38Very important for counting.
04:40And now, I'm going to pose a challenge and I want you to leave here in the comments what the values of the abacuses that I'm going to put here are, with their respective numbers.
04:50So, let's go.
04:54So here it is.
05:00Three abacuses with different numbers.
05:04And now, go there.
05:05Leave it in the comments.
05:06And this way we will see if you understood how the counting works on the tab.
05:12So this mini lesson ends here.
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