Or search by topic
I started by counting in ones and I got a $12$-gon (that is a $12$-sided polygon - if you like long words you can call it a dodecagon).
Then I ruled lines counting round in $2$s. And I got .....?
Perhaps you do not need to put the numbers round the circles.
I tried $5$s (wow!) and $6$s (well!).
Each time I go on drawing lines until I get to the point where I first started.
Then I tried $7$s, $8$s, $9$s, $10$s, and $11$s.
Something interesting was happening.
Why don't you try it? What patterns do you notice emerging?
And what about counting round in $12$s?
Which shapes are the same? Can you think of a reason why?
Can you see a connection between the number in which you are counting around the circle and the number of sides in the shape you are making?
This problem brings out patterns in numbers, factors and multiples as well as properties of shapes. There are plenty of opportunities for visualising to predict what patterns will emerge. Learners will need to work systematically and to generalise, and the work done also often makes a very appealing 'finished product' for display purposes.
Can you see a connection between these two numbers and the number of divisions round the circle?
What is the connection between these two numbers?
After doing the $12$s and $10$s, learners could try to predict which shapes will be produced with other numbers on the circle before testing their predictions. They could work on this sheet of circles divided into 10s, 9s, 8s and 7s. You might be able to introduce the concept of 'co-prime'.