Last year, I posted a comment on Maths Insider, a site about strategies for teaching mathematics to children. My comment has now been republished in a collection of 7 Savvy Ideas from Maths Insider Readers. There are lots of other helpful ideas there–check it out!
Later, I wrote more about the strategies explained in my comment, as well as 4 other innovative and convenient approaches to arithmetic, in my Arithmetricks article.