## Array structures

Building the structure of an array can be achieved by aligning units presented in rows. Groups of groups can be treated as stacked linear arrangements, as shown below (Figure 5).

* * * * *

* * * * *         15

* * * * *

Figure 5. Three groups of five

This array structure can be used with multiplication in coordinating composite units or the arrays can be “turned around” to model the commutative property of multiplication (3 x 5 is the same as 5 x 3). Structured number cards can also be aligned to create linked arrays (see Figure 6).

Figure 6. Three sevens as three fives and three twos

The linked arrays formed by the structured number cards can be used to demonstrate how multiplication is distributed over addition. That is, using the above example, 3 x 7 is the same as 3 x 5 plus 3 x 2. The structural properties of number are important algebraic relationships. Students need to recognise that algebra is a way of thinking about structure and modelling the world and not a series of rules for manipulating symbols. That is, algebra is not only a generalised arithmetic; it is a powerful way of symbolising relationships and describing structures.