Pies

Grandma found her pie balanced on the scale with two weights and a quarter of a pie. So how heavy was each pie?

Red Balloons, Blue Balloons

Katie and Will have some balloons. Will's balloon burst at exactly the same size as Katie's at the beginning of a puff. How many puffs had Will done before his balloon burst?

In the Money

There are a number of coins on a table. One quarter of the coins show heads. If I turn over 2 coins, then one third show heads. How many coins are there altogether?

Pizza Portions

Why do this problem?

Doing this activity gives pupils the opportunities to gain more understanding and better recognising of simple fractions of a whole. They also can be relating fractions to division i.e. understanding that finding one third is the same as dividing by 3. Somethimes when children pursue activities like this they start being able to divide fractions themselves i.e. one quarter split into two equal pieces. It can also be a starting point for beginning to divide by a fraction i.e. How many halves in 1?
Also there is an element of recognising, explaining, generalising and predicting number patterns.

Possible approach

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 $1/2$ 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.