Arkadia: This is true but I suggest it’s easier to train teachers to explore the current curriculum in depth than it is to teach KS3 maths or to juggle multiple classes. I’m not a maths specialist by any means and I went down the English route at school but there is a lot of support out there.
irvineoneohone: I'm illustrating the extreme cases of differentiation really. Generally speaking, I try to avoid differentiating by task at all -- it's much more fun when you find those "low-threshold, high ceiling" tasks where everyone has the same puzzle and different children take it as far as they are able.
Glad you like the digital roots though. It helps them if they know the divisibility tests for 2, 3, 5, 9 and 10. The one for 11 is probably less useful but a lot more fun.
I'm not sure I can give "topics" exactly. A lot of things emerge naturally from asking the same few questions: is it always/sometimes/never true, what's the odd one out, can you see a pattern, etc.
e.g. Linked to finding decimals: take a hundred square — if each number shown was the denominator in a unit fraction, which are equivalent to numbers with recurring decimals? What’s the pattern and why? Predict the next three non-recurring fractions after 100.
But there are lots of resources around. Nrich is fun as you’ve found already and these open-ended maths investigations include several which are good for Y6 - palindromic numbers always seems to be a huge hit. John Dabell has a great book on problem solving although it's quite pricey.
Numberphile on youtube is great and has provided some ideas for fun investigations which reinforce arithmetic skills. The ISBN trick in “11.11.11”. Making ulam spirals is lovely for primes. Happy numbers also encourages methodical approaches to problems.
(Some of their videos don't serve the curriculum especially but the kids like them anyway. Dragon curves are fun if you have 15 minutes and a long strip of paper -- I tend to save empty sticker rolls or use old display border. The illegal numbers video doesn’t really have anything to do but it’s interesting to talk about, especially when showing how prime numbers are useful in the world. Why 0.999=1 is also fun as an adjunct to decimals once you've covered algebra.)
As one-offs, puzzles are good fun. How many squares are there on a standard chessboard (it's not 64!). How can you plant 10 trees in five rows of four each? Using the digits 1-9 once only, what’s the earliest time you can create in the format HH:MM:SS DD/MM? What does each letter stand for in HOME x WORK = SUPREME? Also, I’ve never figured out an investigation to allow children to discover this independently but you can use two consecutive numbers in the Fibonacci sequence to convert roughly between miles and km (8km = 5m, 13km = 8m etc.).
Chessboard puzzles are particular favourites. Some of these need computing algorithms to calculate efficiently so they're more for wet play than the curriculum but it's great to see them huddled around chessboards sharing theories. For example: can you fit 8 queens on a board without any of them being able to take each other; how many knights can you fit on without them being able to take each other; what’s the minimum number of pieces needed to be able to take a piece anywhere on the board? etc.