Materials:
Christmas cards, or postcards, or tea boxes (I used Celestial Seasonings--so pretty!)
Cereal box to use as template (or card stock--something heavy & stiff)
scissors
glue (stick, dots, or white glue)
compass
ruler
pencil
darning or embroidery needle
yarn or ribbon to hange the ornament
Determine how big you want the ornaments to be. The green ones I did are 3 inches in diameter when completed. The circles I drew for those are 2 1/2 inches in diameter. Essentially, you're just putting together a bunch of circles. You don't have to use a compass, but here are the geometry directions:
So this is the back of one of the Christmas cards. I made a template of a circle (with cereal box, but you could also make the circles with the compass). I also made a template out of the triangle. After I drew them all in, I scored the triangles with the compass tip because you'll be folding them.
Next you cut out all the circles, bend them and start fitting them together. When it's assembled, poke a hole (I used my compass, but you could also use a hole puncher) to fit the ribbon to hang up your ornament. Finished ornaments pictured below. The one on the right used 4 circles fitted together. The others all used 8. You could also do 6. 
MERRIE CHRISTMAS!
