Shadow on the Moon map

I bought the 4 quadrant map of the moon from S&T and will be mounting
all four to some stiff backing individually. My thinking is to use this at
my observatory star parties when the moon is the topic of the night. I'll
place them on an easel and point out this and that while people are waiting.
I'd like to be able to show the terminator by covering the map with a black
paper circle to represent the Earth's shadow. However if there is a half
moon out the circle wouldn't work. Anyone have any ideas that might
accomplish what I'm after?

Moon diameter on the map is, give or take, 3+ feet.
--
Michael A. Barlow
Lat: 42.9535 N
Long: 77.2261 W