My grandfather, Oluf Nielsen (1891–1967), a Danish immigrant baker with no higher mathematical education, developed this little pamphlet of arithmetic shortcuts on his own during the period between 1955 and 1965.
Most of his shortcuts are based on quadratic (or second degree) binomial expansions. I don't know whether he even knew the term "binomial".
In this pamphlet he succeeded in explaining abstract concepts clearly and quickly by using a few simple words and few concrete examples. I think the term "bar" (used in the phrases "under the bar", "over the bar", and "split bar") was his own invention.
Be sure to read his concluding thoughts. They are worth thinking about.