These activities come from the marvellous people at Nrich, a website that can be reached here.
Some of these activities may take more time than you have at the end of one session, in which case make sure that you come back to them and complete them the next day. I'd love to see your thinking on these activities, so please send me pictures of what you've worked out.
This is another well-thought out activity from Nrich. The whole question can be found here.