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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.