When folding origami tessellations by hand a background grid is typically folded parallel to the edges of the paper, whether on a square or on a hexagon. However, not all pattern repeats align with the grid and so a rotation of the grid relative to the edge of the paper is required to align pattern repeats or other pattern features with the edge of the paper. The calculations needed to perform this alignment are remarkably elegant, with no angles of rotation needed. This paper will prove the equations and demonstrate the methods for rotated grids on squares and hexagons to achieve pattern alignment with the edge of the paper.