Ray’s Arithmetic is the nineteenth century equivalent of Guerber’s Histories – solid academics before modern dumbing down and progressive educational experimentation invaded the classic curriculum. I love Ray’s because it teaches traditional arithmetic, each concept building on the last in progression. It is mastery based, not grade based, so it is learn at your own pace. Ray’s can be purchased from Mott Media, or they are free from Google Books:
Teaches concrete arithmetic concepts (objects before symbols).
Teaches symbolic arithmetic (numbers and facts).
Teaches arithmetic application.
When a student has finished Higher Arithmetic, he is ready to go on to Algebra.