Teachers may want to provide students with squared
for this problem.
One way of introducing this problem is to challenge students to
first find all the different ways of arranging two squares
(dominoes), three squares (triominoes), four squares (tetrominoes),
five squares (pentominoes) and six squares (hexominoes) - all the
squares must touch at least one other square along one of its edges
(with the edges lining up exactly).
|Number of Squares
||Number of Arrangements
This assumes that rotating or reflecting an arrangement does
not produce a new arrangement.
Students could then be asked to look at the pentominoes to
decide which will make cubes without lids.
They could then be asked to look at the hexominoes to decide
which are the nets of cubes.
This problem could be followed up with Christmas
which asks students to consider cuboids.