Before getting into symbols representing numbers, a stepping stone is to consider pebbles as counters. Each pebble represents one item.
Let's say we are counting books. For each book, we put one pebble into a bag. If we lose a book, we can remove a pebble. If we gain a book, we can add a pebble. This is a perfectly valid representation of numbers. But it is cumbersome. Imagine if we had 100 books, then our bag would have 100 pebbles.
Instead, what we can do is have multiple bags. Each bag will have a diffrent meaning as to how many books a single pebble will represent. The first bag will represent one book for a pebble. The next bag will represent five pebbles from the first bag. So if the first bag gets five pebbles, then we can remove them, and put one pebble into the second bag. When the second bag gets five pebbles, put it in the third bag. And so on.
Notice that with this system, we do not have to know that 4 pebbles in the second bag and 2 pebbles in the first bag indicates we have 22 books. We need to know that if we want to communicate the overall number to someone else, but if we are simply tracking whether we have the same number of books now as we did before, then this is a perfectly adequate system with no further abstraction.
It should also be noted that while we are allowed to transfer five pebbles from one bag to the next one up, we do not have to. We could have 7 pebbles in the first bag and 3 pebbles in the second bag; this would lead to the same 22 books being counted by this. There is a unique representation if we want to minimize the number of pebbles used which would require us to transfer five pebbles from any bag with more than four pebbles until all bags have no more than four pebbles.
Using our usual numbers to count only the pebbles, we could setup a notation system using, say, backslash, separating the numbers. For example, the 4 and 2 could be 4\2 and we could say 4\2 = 3\7 = 22 represent the same number of books.
With this, we have chosen to put the larger representing bag first, namely, the bag with five books per pebble. This is also what prompted the use of the backslash; the higher end is near the larger number.
We could have done the reverse, but knowing the largest amount first feels most natural. Of course, if we were removing or adding pebbles one at a time, then perhaps we would want to write it with the single pebbles first. This suggests a forward slash and that lead to confusion with division symbols, but it would mean 4\2 could be written as 2/4.
These are all conventions, choices that we make to represent these numbers. There is an actual reality of these numbers, namely, that we can match groups of the same number together. But to start working with the numbers in a useful fashion, we need to start giving them names. And as numbers of objects get to be large, we need compact names.
There is also the choice of what kind of clumping we chose. Here we chose five. Why would five be natural? Well, we have five fingers per hand (usually). That means that five is somehow a natural amount to count.
As you presumably know, and as we will discuss, five is not how we group numbers. We use 10 for groupings.
Time is perhaps the most notable exceptional grouping. We will get to that in the unit section.