Counting the Simplest
Quantities
Children can be introduced
to counting with
fractions with sharing
problems
like this one: If 5
cats share 1 bowl of milk, how much do
they each get? It has been my experience that the youngest of children have little trouble with the concept  that each cat must get the same amount of milk, and that the entire bowl of milk must get used up. What they now must learn is how we name the amount that each cat gets. "Each one gets one fifth of a bowl of milk."^{1} 

Rose trying to make a picture of one fifth of a donut. 
The Concept
Most children have no trouble
with the concept of sharing.^{2}
For example, if 2 children are to
share a donut, they know that each child must get the same amount and
that the whole donut must be used up. If 3 children are to share
a brownie, they will try to cut it so that the entire brownie gets
distributed and so that each child gets the same amount.
The concept of sharing involves
two ideas:
 each of the sharers gets the same amount,
 all of the thing to be shared gets distributed  nothing can be left over.
But children who understand the concept may not know the words.
They may know how to cut a banana into 3 (approximately) equal pieces,
but not know that each piece is "one third of a banana." By
giving children simple sharing problems we create the opportunity to
teach them the words.
The Words  One Third,
One Fourth, One Fifth, etc.
You can give your children a good
introduction to counting with fractions by teaching them what you call
the result of
sharing something. Here are some examples:
 If 3 bears share 1 bowl of porridge, how much does each one get? Or, what do you call how much each one gets? (They each get one third of a bowl of porridge.)
 If 6 monkeys share 1 banana, how much does each one get? (They each get one sixth of a banana.)
 If 19 children share 1 chocolate bar, how much does each one get? (They each get one nineteenth of a chocolate bar.)
Problems like these can be
introduced and solved verbally. Children can usually imagine the
real objects (e.g. bowls, bananas, chocolate bars) that need to be
shared  they probably don't need to see those real
objects or even see pictures of them. But what they likely will
need is help with what you call the results of that sharing. Knowing
how to use these words (one half, one third, one fourth, etc.) is the
foundation of counting with fractions.
Here
Trixie
shows that she knows the result of 7 chickens sharing 1
candy bar.
But here
she doesn't remember what you call each part when 3 snakes share 1 leaf
of lettuce.