Students need a deep understanding of the multiplicative structure to move beyond additive multiplication and division strategies such as skip counting and repeated addition, to efficient and sophisticated strategies that grow from their ability to think simultaneously about composite units.
Types of multiplication and division
There are different structures for multiplication and division problems. It is important that students experience working with these different structures to build a deep understanding in the domain.
Multiplicative properties
The multiplicative properties of commutativity, distributivity, and associativity form a powerful mathematical idea in multiplication and division. The properties equip students with a conceptual framework for selecting and using appropriate, flexible, efficient solution strategies.