Recently I had two of my classes represent visually the idea of “squaring” a number: namely, that a number times itself is literally the area of a square with side length of that beginning number. The students cut squares from centimetre grid paper representing 10 x 10, 9 x 9, … 1 x 1 and them glued them onto construction paper. To each square they added the multiplication fact represented, as well as showing the exponential form of the number. Square numbers show up quite a bit in secondary mathematics, and helping students understand these numbers (as well as memorizing the sequence of them!) is beneficial for them as they move on.
Math Bulletin Board: Square Number Towers May 23, 2013