Unknowns:

The interesting thing about equations is that they allow us to work with the unknowns. Why would you want to work with the unknowns? Think of it this way. Being good at math in terms of being able to add, subtract, multiply and divide is a necessity. You can’t get very far in life without being good at math; if nothing else, it will allow you to figure out how many days are remaining before the end of the school year.

There is another part of math and that happens to be the fun and exciting part. This is the part where you can explore concepts and ideas and test them out, develop your powers of logic and embark on a trip of adventure. To do that, you need to work with the unknowns. How do we do that? Believe it or not, it is not complicated at all, all it requires is a leap of faith, so to speak.

Think of math as a tool that helps you keep track of things, add things, etc.

We know that 5 + 5 = 10 (Oops, there is an equation!!!)

In this “task”, we have just “manipulated” numbers, in this case added numbers.
What if you are asked the following question:

You have five green apples and five red apples. How many apples do you have altogether? Here, you are using the 5 + 5 calculation to add up a number of specific objects and your answer will be 10 apples.

Similarly, if you are asked:

There are 18 girls in class 6A and 16 girls in 6B , how many girls are there altogether? You will add up 18 + 16 = 34 (There it is, another equation....) And your answer will be 34 girls in the two classes.

So you see, here, math is simply a tool that allows you to determine a fact about the class size or the number of apples. And it can be used as such tool about all kinds of things.

In the same way, we can add, subtract, multiply or divide the unknowns.

5X + 5X = 10X

Instead of adding specific, tangible objects such as apples, you think of the X
in exactly the same way. The important thing to remember though, the unknowns
that you add or multiply or manipulate in any way have to be the same unknowns
in the same configuration.

You cannot add 5X and 5 Y, because the X and the Y variables will most likely
not have the same value!

You cannot add or subtract 2X and X2, because again the X and X2 variables will
each have a different value.

Imagine that you have a piggy bank, where you have been putting spare change and a few bills over some time and because it has been quite a while and because you have not bothered counting the money inside, you have no idea how much money it contains. You probably think that since you don’t know how much money the piggy bank contains, there is no way you can use the information. Not quite. There is a way. Let us call the amount of money in your piggy bank X (X marks the spot and it’s a good way of thinking of the unknown quantity).

You know that you have X dollars in your bank and therefore, how much are you going to have tomorrow, after you receive your weekly allowance of $5.00?

You will have X + 5 dollars.

If you then splurge on an ice cream which will cost you $2.00, you will have:

X + 5 - 2 = X + 3 dollars. Makes sense?

Take a look at some examples of how unknowns are handled:

To practice this new concept, why don’t you try your hand at the following:

Let us assume that you have a sister and you have forgotten your sister’s age.

Let us call your sister’s age X.

How old was your sister a year ago? X - 1
How old was your sister 2 years ago? X - 2
How old will your sister be a year from now? X + 1
How old will your sister be in five years? X + 5
How old is your friend Ella, if she is older than your sister by one year? X + 1
How old is your friend Ella, if she is twice as old as your sister? 2X
How old is your friend Ella, if she is three years younger than your sister? X - 3
How old is your friend Ella, if she is one half your sister’s age? X/2

You have to understand this method of expressing and manipulating the unknowns, in order to be able to work with unknowns in equations. Think of some examples of your own!