### Why do this problem?

This an excellent problem through which to give students an
opportunity to experience iterative processes. It also moves, by
easy stages, into a multi-variable problem, and the value of using
a spreadsheet is readily apparent.

### Possible approach

Starting with the initial given problem discuss solutions found by
the group.

Invite ideas about possible directions for generalisation,
perhaps starting with the easier results like allowing 'plus one
more' to become plus two, plus three, and so on.

Clarify what 'result' has actually been discovered for each
generalisation and spend plenty of time letting students sense the
'mathematical need' to account for each 'result'. These are good
questions to be 'left in the air', allowing students to turn these
over in their minds over time.

### Key questions

- What generalisations are possible ?

- If we explore those one at a time, which shall we take first
?

- What general statement can we now make ?

- Can we justify that ? Explaining why it should be so.

### Possible extension

More able students will produce more extended generalisations
and have a motivation to account for what is observed, challenging
one another to communicate clear explanations or visualisations of
the fundamental processes.

Able students will sense the potential power of a spreadsheet
and should be encouraged to work collaboratively to become
proficient and confident in its use.

### Possible support

The Stage 3 problem is sufficient as it is, to offer less able
students a rich experience producing results that form a clear
pattern which will not have been obvious at the start.