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 this site.
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.
Update: A flat model of the Mobius Band is easy to make and fun. Do a Google search on "Brehm Model". Here is a link to a transformation of this into a sculpture.
Another thing for kids is to cut out and make Borromean Squares. Again, do a web search on this. Even Borromean triangles.