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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