This investigation can be accessed at many different levels and can be taken as far as you think is appropriate with your class. The learning opportunities include:

Understanding, recognising and using simple fractions of a whole
Finding fractions of shapes
Relating fractions to division i.e. understanding that finding one third is the same as dividing by 3
Being able to divide fractions themselves i.e. one quarter split into two equal pieces
Beginning to divide by a fraction i.e. How many halves in 1?
Recognising, explaining, generalising and predicting number patterns

The activities will allow children to find out how to manipulate fractions themselves, rather than be told a set of "rules". Their understanding will be deeper as a result of this self-discovery.
It is important that children understand first how to express fractions - the idea of splitting one whole into more than one equally sized pieces. Drawings of some kind are essential at this stage. Circular pizzas could be cut out of (gummed) paper which children could then fold into different fractions. Discuss how to divide a circle into equal sized parts:

Does it matter where we fold/draw the lines?
What is important about these lines?

This pictorial representation may be useful all the way through this activity.

Each stage of this investigation can be extended to consolidate the ideas.

When asking pupils to write down mathematical expressions, you may like to go right back to using just whole numbers. For example:

How could I write 4 pizzas shared between 2 people?
So can you tell me how we could write 1 pizza shared between 2?
What about ½ pizza shared between 2?

In the third and fourth sections, children may offer division or multiplication sums and this can lead into interesting discussion in itself about the relationship between the two operations.