One thing the on-line course with Jane Davies has taught me is that an excellent way of providing backgrounds or material to collage, is to let your inhibitions go with what she calls 'scribble drawings'. On paper let yourself go with paint, inks, oil pastels, graphite, crayons, marker pens etc. Do anything you like within a limited colour range and try to get some variety of marks using different implements and techniques, such as stencilling, stamping, splattering etc. There is no need to think of composition as the paper is destined to be torn or cut up or painted on top. You can either using a view finder to select areas to cut out and develop as finished pieces, or in this case use it torn or cut up to form open or closed grids.
These three scribble drawings were used for the sample grids below. The one on the left was torn up to to form an open grid which then had paint and marker pen added to it. The middle painting was torn up to form a closed grid and the one on the right was cut into different sized rectangles to form another closed grid.
It is always a good idea to scan or photograph your original before cutting up so it can be stored in the computer. It can then be printed out or altered digitally for use in future projects.