Multiplication and division structures

The equal-sharing structure for division

The key phrases to use in problems with the equal-sharing structure of division are sharing equally between and how many (much) each?  The equal-sharing structure refers to a situation in which a quantity is shared out equally into a given number of portions and we are asked to determine how many or how much there is in each portion.

For example, 20 marbles might be shared equally between 4 pupils in a game, as shown in diagram on right.  The calculation to be entered on a calculator to correspond to this situation is 20 divided by 4.  This is the structure that teachers most naturally connect with division and is strongly associated with the language ‘sharing’ and ‘how many (or how much) each?’