The quantity in each group is the same.

A composite unit is a collection of single items represented as one group.

Multiplication has several properties, which are outlined below.

Commutative property

The order in which two numbers are multiplied does not affect the product.

Associative property

The order in which three or more factors are multiplied does not affect the product.

Distributive property

Factors can be partitioned, multiplied separately and the partial products are then added.

Null-factor property

Multiplying a number by zero will always give a product of zero.

Identity property

Multiplying a number by one will not affect the quantity.

Inverse property

Multiplication and division are related operations that undo each other, therefore division can be used to solve a multiplication problem.

Multiplication equations have a multiplier (how many groups or sets of equal size), a multiplicand (size of the equal sets) and a product (total number).

Multiplication strategies are methods to solve mathematical problems. The strategies may be mental, written, digital or a mix of the three.

Mental strategies are calculations worked in one's mind and may involve using one of the following methods:

• partitioning and recombining numbers, using the distributive property

• rounding and adjustment strategies

• proportional adjustment strategies.

Written strategies are often algorithms, meaning they are step-by-step methods to find an answer. The most common algorithm for multiplication applies place-value structure and the distributive property and should only be introduced once students have explored a range of strategies and have developed a sound conceptual understanding of multiplication.

Multiplication is applicable in a range of settings. These settings are sometimes referred to as ‘problem types’. Table 1 provides some examples of problem types.

Table 1: Multiplicative structures