the role of manipulatives in maths still seems important
Cuisenaire rods are a pain to get out and put away but, in my view, worth this 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 some fine uses for Cuisenaire rods (one of which is indicated below)
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
Simon Gregg poses the problem of filling a 10 by 10 square (tray) with just pink rods
will you always have a gap?
where can the gap be located?
this and other ideas are on Simon's blog(s)