Ruth Beechick recommends Ray’s Arithmetic. Different publishers have republished this old method of teaching math, it’s sold here as complete program. You can access Ray’s Mathematics for free here, but I think it’s not the same as Ray’s Arithmetic. Kathy here explains how she found and put the arithmetic teacher’s manual to use it HERE. Kathy teaches using Ambleside, and has many good posts in her blog, Piney woods Homeschool.