Numbers and operations
Math? Numbers? Accounts?…
Many times when these words come up at work, in a conversation, at school, on television… we always think of calculators and evaluation grades, usually with a look of bad news. However, we forget that everything around us is formed and explained through mathematics.
For example: the counting of what happens inside our body and what it has, the things that happen to us throughout the day, every time we count or distribute, when we buy something, when paying or settling accounts with friends and, something less common, in the new languages that are emerging thanks to communication and information technologies: computer codes, barcodes, etc.
In short, we are surrounded by mathematics. Thus, it transcends the academic; but it is here where they teach us and emphasize their existence. Educational laws give great importance to this branch of knowledge and it usually takes up many hours, many headaches and many explanations from teachers, classmates, parents,… In all cases, they agree that mathematics They are best learned by practicing. Therefore, in , we offer the opportunity to practice and practice as many times as you want, making an effort without realizing it. The key is in the games. Games that will lead us to reinforce and consolidate those concepts that, later, will help us to add, subtract, divide, approximate, compare, …; That is, managing ourselves in our daily lives and understanding how things work and, as has already been said, ourselves.
Let’s start with the basics: The numbers
The numbers They are universal spellings. Not everyone writes words with the same spellings; but at the time of writing numbers, this does not happen. A 3 is like that in most of the planet and, although we name it in many ways (three, three, trois, …), when writing it it is understood regardless of where we are from, it does not fail. It doesn’t matter if we talk about natural numbers, integers, rational numbers (decimal numbers or not), even when naming the complicated irrational numbers: They are known everywhere.
Once we know the “alphabet of numbers” (everything starts with 10 digits), it is time to specialize and get to know them a little more.
We are going to specify by talking about the most widespread numbering system and with which we will have the opportunity to practice mathematics in the games. This system is none other than the Arabic one (its origin is Arabic), decimal (counting in tens, like the number of fingers on the hands) and positional (depending on the place a digit occupies, it will have more or less value). So much name means that with the aforementioned digits we do all kinds of things. However, to be able to handle this language, it is necessary to know the foundation of numbers, how they are composed.
Grouping numbers. Units, tens, hundreds.
You can make groups of 10 by 10 units to have tens; which will give rise to hundreds; to move to the units of million, tens of millions, hundreds of millionetc.
Once we get the hang of it, we start classifying them and making them dizzy.
Classifying numbers. Natural numbers, odd numbers, decimal numbers, etc.
If we stop to think a little, we know a lot of different ways to make friends among numbers. A 20 can participate in the festival of natural numbers, pair numbers, decimal numbers, composed numbers, decimal numbers. Although at other parties he is not welcome: you will not see him among odd numbers, Prime numbersneither square numbersFor example.
You will wonder why. To know this you have to stop for a moment to look at each of these “numbers clubs”, at least the ones that interest us in the stages of the educational system that are mentioned, fundamentally, by .
To begin with, we have the most obvious classification that has already been mentioned above: the natural numbers It is the oldest club and we use it to count the elements of a set, we continue with the integer numbers that admit the natural ones and also include the negative ones (those that we don’t like to see in red and indicate that we are missing something). Then we come to rational numbers that are more open and admit the other two and also include the fractions; Among these are the decimal numbers (a little later, we will return to them to clarify some things). We cannot forget, although in Primary they do not have many acquaintances, a very exclusive group separate from the previous ones that make up irrational numbers (the number π is one of its most famous members). Finally, it is important to point out that, just as all people make up humanity, if we put together all the named groups they form the real numbers.
Another possible club would be odd and even numbers: being in one category or another depends on whether the quantity represented by each number can be organized in pairs (pair numbers) or not (odd numbers).
Continuing with the groups, we find Eratosthenes and his famous Criba. Both give rise to another classification: being prime or composite. Whether you belong to one group or another depends on whether you can divide them (composed numbers) or not (Prime numbers) among others in such a way that the division be exact.
We also have a very curious group of numbers: the square numbers that are not other than the perfect squares. This somewhat pretentious name refers to those numbers whose square roots are exact and their results are natural numbers. See the case of 144 that is related with its power 122 or a very simple and well-known one: 4. Surely you know what square power it would be.
This brief tour of some groupings of numbers leads us to think about how only one of them is flexible and can be included in different “clubs” and gives some clue to what we mentioned before about the multitude of things they allow us to do. Numbers serve to develop many intellectual and even emotional capacities: who has never felt the pride and self-complacency of congratulating oneself when, after a lot of dizzying numbers, oneself has said: “Eureka, I already have it.” ”? It’s a more than great feeling!
Dizzying numbers: Decomposition of numbers.
Just as mathematics can lead us to dizziness and frustration, we can also return it. How?, you will say. Well, playing with them and doing a multitude of operations, changes and transformations. Some of these things would be the following:
Let’s start, simply as a matter of school curriculum, with the number decomposition: something similar to separating them into pieces.
We must not forget about two disparate options: the approximation of numbers wave comparison of numbers. The approximation of numbersmore likely to make one seem as if they were another due to their proximity in quantity or proximity on the real line, depending on what you want to say.. The comparison of numbersmore inclined to convert each pair of numbers into the older and younger brother to highlight the difference between them or once again due to their position on the aforementioned real line.
In any case, not only can they be dizzy, they can also be ordered. They take care of this the ordinal numbers: they are something like the natural numbers chased by a little circle on a tray and with a nomenclature that causes problems when deciding whether to say it this way or another. Example: how do you say 57º?… You have to think for a while, right? The answer (in case you have to compare what you thought or you’re really dizzy) is fifty-seventh. There it is!
Let’s leave the poor 57th asking for a simpler name and move on; Well, it is appropriate to dedicate a space to one of the sets of numbers that breaks our minds when we see them on paper, but that we use constantly in our daily lives. We are talking about rational numbers or as they are known in schools for some time now: the fractions.
The fractions? What are they?
The fractions They are those “broken” from before who changed their name to try to clean up their image due to the double annoyance that they have caused generation after generation of students (the war that they will continue to wage no matter what their name is!). With them, we have a double hassle, since we are going to play slowly and, on top of that, we must learn the pirouettes and dance steps that they perform.
In case you still don’t understand what these numbers are like and you prefer to know them a little to pass all the levels of the games the first time, I suggest that you continue this journey through the world of mathematics. It will surely not leave you indifferent and, who knows? You may get the hang of it and become a fan of the fractions.
In any presentation, the first thing that comes to us is the appearance and the name. In this case, they would be the terms of the fraction and reading the fraction, whatever it is. To move on to the next phase of knowledge, at the end of this paragraph, you will see an image with the fraction terms and a few fractions as an example. Afterwards, if you want, you can try the games designed by so that you can see that you are already getting to know them.
Once the initial presentation is over, it is interesting to continue with its origin or, in other words, the fraction concept. When we use this term the word that should come to mind is division. A fraction is the quotient between two numbers, it is a distribution. As in any good distribution, sometimes it is played more and other times less, which gives rise to different types of fractions.
Improper fractions (the numerator greater than the denominator) that give rise to mixed numbers or mixed fractions (composition of an integer and a fractional number), proper fractions (the numerator is less than the denominator), decimal fractions (the denominator is always the unit followed by zeros, giving rise to the famous decimal numbers), equivalent fractionss (these do not fight and always tie when compared because they are worth the same), irreducible fractions what they suppose to be simplified fractions to the maximum. In case it’s too much information and a picture is worth a thousand words, here are some examples of all of them:
As with the rest of the numbers, with the fractions We can also make comparisons, find the fraction of a number and, of course!, operate them. The most feared operations with fractions.
Starting by the sum of fractions and the subtraction of fractionswe will say that the most complex step is the reduction to common denominator (to do these operations the denominators must be equal and we use equivalent fractions, those that are worth the same). Thus we have two options: a simpler one, addition and subtraction of fractions with the same denominator, and a more complex one (with more steps) addition and subtraction of fractions with different denominators.
Once we know add and subtract, multiply and divide is…