Addition

Of course, you are familiar with addition, but to keep things in order, let's go through it anyway :P

Let's say I have a bucket with 3 rocks in it, and another one with 2 rocks in it.

I pour the contents of second bucket, with the 2 rocks in it, into the first one.

How many rocks does the first bucket contain now?

Since we know how to count, we can easily answer this question: it's 5!

Combining quantities in this way is known as addition.

In writing, addition is denoted using the well-known plus sign.

This way, the previous example looks like

in writing.

We usually don't write 3 'rocks' or 2 'rocks', since we're only interested in the quantities, not the things themselves.

We use the equals sign to denote what the result of the operation is equal to.

That is to say, in the previous case, we really should have written

Let's consider the statement

This says that we have two things, and we add four things to them to obtain six.

Of course, we usually do addition in our head, or use a calculator, but let's think about how we could do it manually!

At first, we have two piles of things: one pile with 2 things and another one with 4 things, and we would like to combine them.

That is, our starting point is

Take one thing from the second pile, with 4 things in it, and place it in the smaller pile.

This means that we now have 3 things in the first pile! We counted forwards one time!

Let's repeat this procedure! Again, we take one thing from the second pile and drop it into the first pile.

The first pile that contained 3 things previously, now contains 4 things!

If we do this two more times, we end up with 6 things in the first pile, and the second pile will be empty. We are done :D!

This can be visualized on a number line like this:

Essentially, what we did was starting at 2, and counting forwards 4 more times to reach six!