Multiplication and division structures

The operation of multiplication

We will not about be doing multiplication and division calculations, but focusing on understanding the mathematical structures of these operations. First, we identify the range of situations that pupils have to learn to connect with the operations of multiplication and division. So here we are concerned essentially with setting up the mathematical model corresponding to a given situation.

Teaching Point

Familiarity with the range of multiplication and division structures discussed in this unit will enable pupils to interpret multiplication and division calculations in a variety of ways and hence increase their ability to handle these calculations by a range of mental and written methods.We can identify at least two categories of situation that have a structure that corresponds to the mathematical operation represented by the symbol for multiplication. They are:

  • The repeated aggregation structure; and
  • The scaling structure

Primary-school pupils’ main experience of multiplication will be through the structure of repeated aggregation, although they may also meet some examples of multiplication used for scaling, particularly doubling.As well as being the basis for their understanding of the operation itself, experience of these different structures associated with multiplication is essential for developing children’s confidence in a range of mental and written calculation methods. For example, a key mental strategy for multiplication makes use of doubling, which is based on the scaling structure.