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Multiplication and division

An understanding of the ideas underpinning multiplication and division include:

  • the equal group structure
  • the different ways to conceptualise multiplicative situations
  • the role of the numbers in multiplicative situations
  • recognising relationships between numbers.

Division is the inverse of multiplication. In its simplest form it is the partitioning of a quantity into equal subsets.

All of these ideas need to be understood if students are to develop efficient mental computation strategies.

There are a number of ways of presenting multiplicative situations for understanding such as:

  • using the array model
  • exploring patterns on a 100 grid
  • partitioning numbers equally in a variety of ways
  • adopting the 'have a go' attitude
  • exploring the range of strategies students use.

You can read more in the articles Strategies for Going Mental and From Here to There: the Path to Computational Fluency with Multi-digit Multiplication on the AAMT website.

Visualising arrays

Rectangular arrays help students see the multiplicative structure. Rectangular arrays also show the commutative nature of multiplication.

Building connections

Situations in which students can make connections between and within multiplication facts assists them to generalise patterns and relationships. 

Making generalisations

Developing a web of connections between numbers and number facts supports students' development of number fact fluency. 

Number fact fluency

Being able to generalise number properties and patterns can equip students to carry out a range of computations mentally. A focus on generalisation encourages students to look for patterns and structures.

Making suitable choices

Having fluency of basic multiplication and division facts, and a range of thinking strategies, assists students' development of mental computation and estimation skills for solving 2-digit and 3-digit multiplication and division problems.