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?
Jason from Lark Rise Lower School has sent in
a well explained answer.
The rule for giving another set of numbers is to put odd numbers
at the top in ascending order and the even numbers in descending
Josh from Ampthill, UK has quite a different
way of doing it.
In the top three boxes there is $1$, $2$, $3$. In the bottom
three there is $6$, $5$, $4$, so each of the three pairs of numbers
adds up to seven. (That is; $1$&$6$, $2$&$5$,
Another solution from Sonya from Rocky
Elementary School, Canada:
And another from Year 6 at Brookfield School,