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Using the division model
There are several ways in which fractions are involved in the process of dividing. Modelling division problems with physical materials or diagrams can help make sense of division that involves fractions, in either the process or the outcome.
Partitioning a group of items into equal subgroups is fundamental to division with whole numbers. This process is strongly connected to the process of finding fractions of collections of items.
For example, dividing a group of 12 into 4 equal parts to find there are 3 in each group, also tells us that 3 is \(\frac{1}{4}\) of 12.
Working with fractions becomes essential when the number of items in a group is less than the number of subgroups we need to make. In this type of sharing as division we must begin 'cutting up' the items into smaller parts to carry out the division process.
The division construct of fractions can be explored through modelling division problems where the context suggests cutting up the items. Watch the video The Division Meaning for Fractions.
You can download the Division Meaning for Fractions video transcript.
