Well, actually I specifically purchased an unpainted one, so I guess it's a "pink" tower. FYI: I've bought a few Montessori materials over the years, and I've always found the best prices at Alison's Montessori. That stuff is still spendy, though, so let me know if you ever find a cheaper place!
The kids first used the pink tower with the tower of squares that they'd previously made:
To make that tower of squares, you need a looooong roll of butcher paper and several sheets of cm-gridded paper. The kids are to make a tower by cutting squares from the cm-gridded paper, going from 1cm^2 to 20cm^2. They're to arrange it nicely on the paper to make a tower (it's dealer's choice if the tower is centered or aligned at one edge), and then they are to annotate each square with its exponent (2^2), its exponent in long form (2x2), and its total units (4). Keep it forever, as you'll be pulling it out for extension work forever, as you can see above!
In the activity above, the kids matched each cube to its square footprint (it became immediately clear that our cm grids weren't perfect centimeters, so there was a bit of averaging). There were cubes for the first ten squares on their chart. Then they put the same information--exponent, long form, and total units--on index cards, and matched them to the cubes. It was a quite informative visualization!
Even though it was still valuable for Will to engage in the work, and have her hands on those exponents, this activity was really more at Syd's sixth grade level, which became clear when as soon as the project was complete Will abandoned it to go do something else, and Syd continued to fool around with the tower. I was amused to see that she built it several times as perfectly as possible, just like a good Montessori schoolgirl, but she did quickly move on to exploring extension ideas:
After I saw that, I researched pink tower extensions, and printed out this set of pink tower extension cards for Syd to explore.
I think she liked them!
I've watched the kids as Montessori preschoolers, so it was especially interesting for me to see this new work presented to them. Both kids were interested and engaged in the exponents work, but Will had no interest in sensorial exploration with the blocks beyond that. Syd had a great interest in further sensorial exploration, and concentrated on the blocks quite deeply for a while. Just as a preschooler would, she started by building the tower, but whereas a preschooler would possibly do this dozens upon dozens of times, Syd got all she needed from doing it just a few times, and then seamlessly moved into exploring other patterns. She was deeply engaged for a while in making these patterns, and then she and I invented some patterns that also used Cuisenaire rods (I'll show those to you another time), and then, just like that, she was done. The tower is still sitting in a pile in the playroom, untouched for a week now, so this weekend I'll have her put it away.
But think of that process--Syd was just as engaged as a preschooler would be in this sensory material, and her experience was no less valuable just because she moved through the entire process in a week rather than three years, and no less valuable just because she's eleven, and not four. It clearly fed something in her, and I don't need to key it to state academic standards to know that, and I don't even need to know what, exactly, she took from the exploration--she took something, was engaged and happy and productive, and therefore it was a great school day.
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