Counting Counters

Take a counter and surround it by a ring of other counters that MUST touch two others. How many are needed?

Cuisenaire Rods

These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?

Doplication

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?

Magic Circles

Stage: 2 Challenge Level:

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 order.

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; $1$&$6$, $2$&$5$, $3$&$4$.)

Another solution from Sonya from Rocky Elementary School, Canada:

And another from Year 6 at Brookfield School, UK: