Stuff for fast finishers/gifted kids should be out of the stream --stuff that isn't what you're covering next week or next year.
Look at puzzles -- especially geometrical ones. Graph theory -- Bridges of Konigsburg, three houses, three wells. Chess board problems. There are lots of good puzzlebooks out there. Logic puzzles too.
Mechanical puzzles too. Rubik's cube, sliding block puzzles. Ring and string puzzles. You will have to figure out how to keep them from wandering away permanently.
Scientific American had a whole series of books, mostly extracts of the columns of Martin Gardener of puzzles and activities.
Paper and scissors activities.
- Properties of a mobius strip.
- hexaflexagon. (Use adding machine tape)
Number theory conjectures:
Pick a positive whole number. If odd, triple it and add 1. If even cut in half. Repeat.
E.g. 3 -> 10 -> 5 -> 16 -> 8 -> 4 -> 2 -> 1
Any number that results in 4-2-1 is said to be wonderous. Are there any non-wonderous numbers? Write a program to test numbers. Is there any pattern to how many steps it takes to reach 4-2-1
Can any even natural number be expressed as the sum of two primes? (You need to consider 1 a prime for it to work with 2.)
Can any natural number be expressed as the difference of two cubes? Why is this one intrinsically harder?
For something bigger, get them started on geometry, follow that up with coordinate geometry.