I gave a lecture to the Wrexham Science Festival some years back on "How mathematics gets into knots", advertised as for 8-80, but I think it extends. You see some ideas for this on the knot exhibition part of

httP://wwww.popmath.org.uk

Things you can do are:

Dirac string trick (using the home made apparatus  apparatus illustrated there, two wooden squares,  one with an arrow on it, coloured ribbon, and bulldog clips to fasten the ribbon to the board, easy to undo in case everything gets tangled), and related to the belt trick and the _Philipine wine glass trick_ (do a search on this, and also on _Air on the Dirac String_). We have found young children love this, but best to let them try an empty glass or plastic mug first! 

Showing addition of knots is commutative, using just a piece of rope. Hope that helps.