Free Arithmetic Resources
Arithmetic is about manipulating numbers. It's usually the first math that students learn in early elementary school: addition, subtraction, multiplication, and division. It's not as exciting as higher order math, but it is a necessary foundation.
Free Resources for Preschool Arithmetic
Preschool-level arithmetic is mostly about number recognition and counting.
My own children loved Starfall when they were in preschool and early elementary school. More of the site is now under a paywall than it was back then, but there are still plenty of songs, games, and activities available for free.
Free Resources for Elementary Arithmetic
As students move into 1st grade, they begin more formal arithmetic studies. Most students start addition and subtraction in kindergarten or first grade, and move into multiplication by the end of 2nd grade. Division (including fractions) is introduced in about 3rd grade in most places, and most programs wait until 4th or even 5th grade to explore percents and decimals.
When I was teaching, I used this website nearly every week for both spelling and arithmetic work. Is it pretty? No. Does it get the job done? Absolutely. You can produce a nearly limitless variety of math worksheets from this site.
If you hang around this site long enough, you'll know that I'm a sucker for vintage textbooks. I know, it's a little weird. I don't actually like Ray's nearly as much as I like Strayer-Upton Practical Arithmetic (which I did use a little with my kids), but if you want vintage and you want free, you can't go wrong with Ray's. It doesn't make a full modern math curriculum, but it can be fun to pull out some of the problems now and then for something a little different. Note that students in Ray's day started math instruction in about a modern 2nd grade: it may start out simple, but by a few lessons in, it's a bit complex for the average 1st grader.
Free Resources for Middle and High School Arithmetic
The foundation for most arithmetic should have been laid in elementary school, with SHOULD being the key word. Arithmetic is required for all aspects of everyday life, and students who did not receive a firm foundation in elementary school will need remediation. All students, however... even advanced ones... should continue to practice advanced arithmetic throughout middle and high school. I've actually found that math-oriented students who have no problem with calculus have often forgotten much of the arithmetic they will find on the standardized tests they will take in high school, such as the PSATs, the SATs, and the ACTs.
This website lets you generate customized worksheets on a wide variety of mathematical topics. They can be great both for review, and to see what skills your student still needs to learn.
It's important to keep arithmetic skills strong as students get older, and a few problems a day from Ray's will absolutely help with that. If anything, an awful lot of the more advanced arithmetic sounds like SAT questions dealing with interest rates, train speeds, and the like.