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NSW Syllabuses

Mathematics K–10 - Early Stage 1 - Number and Algebra Multiplication and Division


A student:

  • MAe-1WM

    describes mathematical situations using everyday language, actions, materials and informal recordings

  • MAe-2WM

    uses objects, actions, technology and/or trial and error to explore mathematical problems

  • MAe-6NA

    groups, shares and counts collections of objects, describes using everyday language, and records using informal methods


  • Students:
  • Investigate and model equal groups
  • use the term 'group' to describe a collection of objects L
  • use the term 'sharing' to describe the distribution of a collection of objects L
  • model equal groups
  • recognise groups that are not equal in size
  • group and share concrete materials to solve problems CCT
  • explain or demonstrate how an answer was obtained (Communicating, Reasoning)
  • Record grouping and sharing using informal methods
  • label the number of objects in a group
  • record grouping and sharing informally using pictures, words and numerals L

Background Information

All activities should involve students manipulating concrete materials. The emphasis is on modelling groups of the same size and describing them. Students need to acquire the concept that fair sharing means all shares are equal. After students have shared objects equally, the process can be reversed to begin to develop the link between multiplication and division. This can be done by students first sharing a group of objects and then putting back together all of the shared objects to form one collection.

There are two forms of division:

Sharing (partitive) – How many in each group?
eg 'If 12 marbles are shared between three students, how many does each get?'

Grouping (quotitive) – How many groups are there?
eg 'If I have 12 marbles and each child is to get four, how many children will get marbles?'

While the total number of objects that have been shared or grouped can be found incidentally, strategies for doing this are addressed in Stage 1.

Multiplication and division should be taught in conjunction with each other as the foundation for conceptual understanding of their inverse relationship.


Students should be able to communicate using the following language: group, share, equal.

Sharing – relates to distributing items one at a time into a set number of groups, eg the student has a number of pop sticks and three cups and shares out the pop sticks into the cups one at a time.

Grouping – relates to distributing the same number of items into an unknown number of groups, eg the student has 12 pop sticks and wants to make groups of four, so places four pop sticks down, then another four, and so on.

National Numeracy Learning Progression links to this Mathematics outcome

When working towards the outcome MAe‑6NA the sub-elements (and levels) of Multiplicative strategies (MuS1-MuS2) and Interpreting fractions (InF1) describe observable behaviours that can aid teachers in making evidence-based decisions about student development and future learning.

The progression sub-elements and indicators can be viewed by accessing the National Numeracy Learning Progression.