Thanks for the link. The grid is also helpful as a way to visualize things like: (1 + a)^2 = 1 + 2a + a^2 There is a square with side 1+a, and the grid con

Thanks for the link. The grid is also helpful as a way to visualize things like: (1 + a)^2 = 1 + 2a + a^2 There is a square with side 1+a, and the grid consists of four pieces, sizes 1, a, a, and a^2. Thinking about approximations when a << 1, you can motivate why (1 + a)^2 ~= 1 + 2a really easily by imagining the grid you refer to. In other words, keeping this grid picture in mind can be helpful to more mature mathematicians/physicists/engineers...probably more useful than the standard multiplication algorithm is.