Why do this problem?
Like so many
investigations,
this one is like a journey through a wood, where we encourage
children to keep all their senses alert. As I've suggested in the
introduction to this challenge there are a number of things you can
explore. The activity could be done by those who have a good
enquiring mind using a trial and improvement method. It has spatial
and numerical possibilities and it would be very valuable for you
to tease out from children the ways in which they imaged the whole
process.
Possible approach
I think that presenting
it as written, talking it through with learners, will be adequate
and there should be opportunities for the pupils to ask further
questions before trying to form solutions.
Key questions
Are you happy with the
way that it folds?
How are you making sure
the numbering is ok?
Possible extension
If the solutions have
been recorded in some kind of 4 by 4 table - as one is shown in the
problem - then the properties of that table can be explored.
For the
highest-attaining
These pupils can look at
the different ways in which the orginal large shee can be folded in
order to give the $16$ pages. If solutions are found for each and
every way of folding then the arrangement of the
numbered pages onthe $A3$ sheet will need to be explored and
relationships notes. Further work can then be done on
producing 32 pages from the original sheet and the investigation
followed in the same way.
Possible support
Some pupils will need
help with getting into the physical understanding of the problem -
for these pupils an already folded sheet may come in useful.