The plywood gives you a way to make sure your foam stays put. Unmounted, it will slide all over the place at the slightest push. You also want a way to hold foam panels together. Make sure your joints in the foam are offset from each other.
And incidentally, do you have a real lumber yard near you? Big box store lumber is usually junk.
Connecticut Valley Railroad -- A Branch of the New York, New Haven, And Hartford
"We don't stop playing because we grow old. We grow old because we stop playing." --George Bernard Shaw