Two matrices, M: m-by-n, M': n-by-p. Let r < n. Let A = M[:, :r], A' = M'[:r, :], B = [:, r:], B' = [r:, :]. Then the product MM' = AA' + BB'. You can partitions two matrices by r rows and columns, respectively and sum their respective products. The rote method of matrix multiplication is the special case r = 1. You can generalize this further to arbitrary tilings and conduct matrix multiplication of the partitions (sub-matrices) in the same way you would conduct normal matrix multiplication.