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The Montessori school I went to didn't have an abacus for us to use, but to your point, the physical representations of 10^1 (a row of 10 beads), 10^2 (a 10x10 square of beads), and 10^3 (a 10x10x10 cube of beads) using beads helped me understand exponents much more quickly. Unfortunately we did not have a 10x10x10x10 tesseract of beads.


I'm a huge fan of the Montessori binomial cube:

http://www.montessoriworld.org/sensory/sbinoml.html


Of course! We had those too. I had totally forgotten about that.




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