In my search for "Montessori method" activities and toys, I found "weaving paper" on page 40 of Teach Me To Do It Myself: Montessori Activities For You And Your Child authored by Maja Pitamic. I bought my copy from amazon.com.
white posterboard, cut into 8-inch x 8-inch square
colored posterboard, cut into 3/4-inch x 8-inch strips (2cm x 20cm)
ruler (for measuring)
pencil (for marking cut lines)
scissors and cutter
Cut out alternating strips on the 8-inch x 8-inch square posterboard so you are left with a frame containing vertical bars of paper.
The weaving activity may still be too challenging for the younger ones, like Elizabeth. But she still found it fun to play with the colored strips of paper - naming colors and watching Matthew weave his strips of paper "over" and "under" the white frame.