https://www.thespruce.com/no-waste-f...quilts-2821760
seems to explain things well
If I understood the directions correctly -
Cut your big squares 11-1/4 (the squares will end up being quarter square triangles QSTs -) -which explains the + 1-1/4 "
Cut your small squares 5-7/8 (the squares will end up being half square triangles HSTs) - which explains the + 7/8 "
Much as I dislike "scant 1/4 inch" directions - sew a very scant 1/4 inch from the drawn line. You might need to do a couple of practice pieces geese to get your seam allowance to work the way you want it to.
You can "get by" with smaller squares for your practice pieces if you add the given amounts to the squares.
The "rules": Add 1-1/4 inches to larger square (example: 6 x 3 finished - cut square 7-1/4 x 7-1/4,
Add 7/8 inch to smaller square (example: 6 x 3 finished - cut square 3-7/8 x 3-7/8.