Cutting thin plywood is a difficult prospect since it tends to splinter very easily. You can cut plywood that is 1/4 inch thick by following a couple of simple rules and it will reduce the amount of splintering. The items that you need will be available around your home.
Measure the board to determine where the cut will need to be made. Mark where the cut will be made.
Attach one layer of masking tape on each side of the plywood. Redraw the line on the tape.
Turn on the saw and slowly approach the line where you are going to cut. You are going to want the blade rotating at as fast a speed as possible. This will make for a cleaner cut. Remove the masking tape when the cut is completed.
It helps with the cut if another person is holding the end that will be discarded.