Richer Tasks

It's been a long while since I last posted, oh notional reader.  But here's what I'm thinking about tonight.
As part of my Maths study I'm thinking about "Richer tasks":

• must be accessible to everyone at the start;
• needs to allow further challenges and be extendible;
• should invite children to make decisions;
• should involve children in speculating, hypothesis making and testing, proving or explaining, reflecting, interpreting;
• should not restrict pupils from searching in other directions;
• should promote discussion and communication;
• should encourage originality/invention;
• should encourage ‘what if’ and ‘what if not’ questions;
• should have an element of surprise;
• should be enjoyable.

Ahmed, 1987, p. 20.Better Mathematics, London, HMSO

Wouldn't it be great to have a bank of there?  NRICH is a good start.

The task centre kit site here seems another creative option for fun and inspiring maths challenges.