An array is a rectangular arrangement of objects in equal rows (horizontal) and equal columns (vertical).
Everyday examples of arrays include a muffin tray and an egg carton.
Interpreting the structure of arrays requires spatial visualisation processes.
Students need to connect objects together and treat them as a whole collection.
When constructing an array, students combine both spatial (rows of squares) and numeric composites (number of squares in a row).
When part of the array is screened, students have to visualise the composite units.
Recognising the unit of repeat – individual rows or columns – is important.
In a rectangular grid showing 3 rows of 4, the unit of repeat can be three. This can lead to skip counting by 4 to find the total number of 12 squares. Alternatively, the unit of repeat can be four, leading to skip counting by 3 to find the total number of 12 squares.
Students can generalise that 3 rows of 4 columns, or 4 rows of 3 columns, show that 3 \(\times\) 4 = 4 \(\times\) 3, which is the commutative property.
Knowing the commutative facts reduces the number of multiplication facts students need to remember.
The rectangular array structure gives a visual pattern to both multiplication and division.
For example, 6 rows of 4 is 24 can be interpreted as 24 divided by 6 is 4.
