Multiplication and division are mathematical operations that underpin our capacity to work with numbers and identify and use relationships between them. Understanding of and fluency with multiplication and division is essential for engaging with more advanced concepts such as ratio, proportion, scale, percentages and algebra.
Four powerful mathematical ideas about multiplication and division grow in complexity and sophistication from Foundation to Year 7 and continue to be applied in increasingly complex ways in Year 8 to Year 10. As students progress, they extend and apply these ideas to reason and calculate with increasing efficiency and sophistication, and solve an increasing range of problems.
Powerful mathematical ideas in multiplication and division
Equal groups and shares
Quantities can be arranged in equal groups. Multiplication is the process of combining these groups, and division is the process of sharing the groups equally or forming equal sets.
Many of these are 1 of those
Quantities can be partitioned into equal-sized groups, where "many of these are 1 of those", allowing groups to be seen as composite units rather than collections of individual items.
Multiplicative properties and principles
Understanding the structure of multiplication and division supports efficient calculation, shaped by the properties and principles of these operations.
Multiplicative relationships exist between numbers
Some number properties have a multiplicative structure. These multiplicative structures create relationships between numbers.