Representing exponents

We are exploring what expressions with exponents can look like.  We noticed that exponents of 2 make squares, and exponents of 3 make cubes.

The base of the exponent will be the dimension of the square or cube.  If there is a coefficient and a variable in brackets with the exponent it means the coefficient and the variable together form the base.  Here’s an example of 2 x cubes compared with one cube that has sides of length 2x.

We explored a variety of combinations, with coefficients of 1/2 or 2 or 3

One group even made a representation of (3x)^3

We started to explore how many little cubes (x cubes) there are inside, and look for connections with the algebra and the physical model.  We will continue doing more with this in coming days.