Take a counter and surround it by a ring of other counters that
MUST touch two others. How many are needed?
These squares have been made from Cuisenaire rods. Can you describe
the pattern? What would the next square look like?
We can arrange dots in a similar way to the 5 on a dice and they
usually sit quite well into a rectangular shape. How many
altogether in this 3 by 5? What happens for other sizes?
While we were sorting some papers we found $3$ strange sheets
which seemed to come from small books. They had once been used for
wrapping and one side was very faded. The other side was in a
language we did not know, but there were page numbers at the foot
of each page.
Did the pages come from the same book, we wondered, and what
numbers had been on the other sides of the sheets?
I decided to make a little book to see how the numbers worked.
It had $4$ sheets which I folded to make $16$ pages. There was no
need to staple it.
Then I made other little books, with both more and fewer pages.
I made a table of my results and soon I knew how the numbering
worked and could answer my own questions.
What answers do you think I got?
Later we found another sheet. The numbering on this was a bit
different. Can you work out why?