Cuisenaire rods are a pain to get out and put away but, in my view, it is worth the effort
these resources focus on some algebra involved in growing squares and a growing rectangle
you could just let students create their own growing square sequence...
Simon Gregg has developed the uses of Cuisenaire rods
he points out the availability of square trays of various sizes, available from Numicon - helpful for a study of squares made out of Cuisenaire rods