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## 'Man Food' printed from http://nrich.maths.org/

### Why do this
problem?

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

### Possible approach

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.

### Key questions

So, what is a triangular number?

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

### Possible extension

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:

Each of these sequences can be explored, and, depending
on the pupils' experience, encourage them to
explain WHY the things they notice have occurred.

### Possible support

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