Ray’s Arithmetic is your one-stop shop for math at all levels covering all major concepts. Joseph Ray, contemporary of Abraham Lincoln and a math professor at a private preparatory academy in Ohio, taught math like a BOSS for 25 years. From the description:
Ray […] had no use for indolence and sham. He was always delighted to join his students in sports. He knew how to use balls, marbles, tops as concrete illustration to help young children make the transfer from solid objects to abstract figures.
From the Presidency of Abraham Lincoln to that of Teddy Roosevelt few Americans went to school or were taught at home without considerable exposure to either Ray’s arithmetics or McGuffey’s Readers – usually both. Ray and McGuffey challenged students to excellent accomplishment. Their influence on our country has certainly eclipsed Mann’s and rivaled Dewey’s, but education histories, edited by humanists, seldom mention these men.
Ray’s classic Arithmetics are now brought to a new generation which is in search of excellence.Mott Media
I own physical copies of Ray’s Arithmetic; they are peerless. Sequential, organized, with plenty of practice problems. They’re also charming; multiplication problems in the book are reminiscent of episodes of Little House on the Prairie or the books in the Anne of Green Gables series.
Ray knew his stuff, but he was also, no doubt, a hard-ass. This book is old school. It’s logical, thorough, and no-nonsense, which is why it works. If your kid can stick with Ray, she will be more numerate (math literate) than the average 18-year-old high school graduate.
If you have a future engineer, scientist, coder, mathematician or doctor on your hands, use Ray’s Arithmetic and she’ll be well ahead of the curve well before she hits high school.
Having said that, Ray requires grit.
If you have a kid who is harder to pin down or less confident in her math abilities, I would still start with Ray, but limit the work to one lesson a day. Give your kid the gift of sneaky learning through Prodigy, a free game-based math support program.
If your child is (or you are — if, say, you’re a high schooler trying to keep up with school in the absence of actual in-class instruction) struggling with a math concept, you may want to consult Khan Academy for ideas on how to help them.
And if you are an advanced math learner, one of the most powerful things you can do to show you know a concept if to use Feynman’s technique to nail it down fully in your own head (and maybe help a younger sibling/friend in the process.)