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# Building connections

Experiences in which students generate a range of related facts using tasks, such as creating arrays for a given number, assist students to make connections between facts.

Such experiences can also lead to strategies such as doubling and halving, thinking 'multiplication' for division.

For example, ask students to generate as many arrays for 12 as they can, either using concrete materials or shading in grid paper. Record each of the facts. In pairs, students can discuss any connections or patterns they notice in what they have recorded.

Visual representation of the arrays can assist students to see connections such as commutativity, and doubling and halving of the factors. This can lead to generalisation.

One example is 2 \(\times\) 6 = 6 \(\times\) 2. Another generalisation is that "If I double 2 and halve 6, I get 4 \(\times\) 3", which is another multiplication fact for 12.

Splitting an array into known parts using the distributive property can assist students to work out unknown facts. For example, students can solve 6 \(\times\) 7 by splitting a 6 by 7 array into (6 \(\times\) 5) + (6 \(\times\) 2).

## How many possible ways?

In this activity, students explore the different arrays that can be formed for a specific number.

## Splitting arrays

In this activity, students construct a rectangular array for a given number which they then partition into areas using known facts. This assists them to derive new facts.