This activity can supplement work being done with triangular numbers. It also lends itself to being opened out for further investigation.

It would be best to introduce this challenge in as practical way as possible to start with and then question the pupils to find out if they understand the idea of triangular numbers.

So, what is a triangular number?

How have you found out how many are in your triangular stacks?

As is often the case with straightforward challenges it is good to explore taking the patterns further.

So we could start by:

a] looking at what numbers are in the following layers;

b] looking at what the totals become as each new layer is added;

c] looking at the digital roots

For the first simple stacking we'd have:

For the second stacking as a square based pyramid we'd have:

Pupils may need their own small cubes to represent the cans. Some will need to have assitance when exploring the square-based shapes.