I'm trying to figure out what to do with my son to help him find more challenging math. He's 8., 3rd grade, tests at an 8th grade level, but I'm not sure that I would start him off with 8th grade math.

Can anyone rec a book/series? Online program or app? Or enrichment program?

He's bored and disengaged at school, and I want to provide him with something that will challenge him and keep him learning. Thanks.

Lots of relevant discussion on here, but I don't have time to do links - have a search (using Google and the site: argument). My first three answers are:

Murderous Maths
Alcumus
Nrich

Hth!

Suggestions:

Challenge Math by Edward Zaccharo (There is a Primary Grade Version you may want to start with)
Art of Problem Solving
Life of Fred Series (will seem too easy at first, but a lot of good math in there in story form, only a few practice problems per chapter)
XtraMath (website) for basic math fact fluency

A separate suggestion:
When thinking about what level is appropriate for him to start, you may want to look at the test where he tested 8th grade level and see what kind of problems there were, and what "8th grade level" actually means. (I.e. the average score an 8th grader would get on that test, or what an advanced 8th grader is doing, etc.)

Hope that makes sense. Others here can tell you a lot more, I'm sure.

Main recommendations:
- EPGY Open Enrollment (Math K-7 only; it is now called giftedandtalented.com and has gone up in price; see other threads about this on this forum)
- Art of Problem Solving Prealgebra textbook + solution manual ($60 total)
- Art of Problem Solving online Alcumus (free).

One unorthodox suggestion:
- Great Source 'Math to Know', ... ,'Algebra', 'Geometry' (6 books).
These are not textbooks, but kind of encyclopedia/reference books.
The first 4 are similar, but vary in the level.
These are great for 'telescoping' far ahead.
(To get the feel, use a library, or buy a used copy.)

A lot of people like UK's Mathematics Enhancement Programme (MEP): http://www.cimt.plymouth.ac.uk/projects/mep/ (online, free). (I have not personally used this but it looks good. See well trained mind accelerated learner forum.)

What math has he actually learnt, both in school and elsewhere?

Does "tests at an 8th grade level" mean he actually knows all the school math up to 8th grade level, or does it mean he can do 3rd grade math as well as a typical (median) 8th grader? In the latter case, he still needs to learn all the grade 3-8 material, but you want a quick efficient way to do it.

As well as the other good suggestions above, there is EPGY (now called giftedandtalented.com) which has an online K-7 math course. The "Independent Study" version costs $60/quarter (=$20/month). You could play it safe and start at grade 3 if you fear gaps, (and there's some set theory and logic in there you don't see in school courses) and he could probably work through to end of grade 7 in less than a year. Make sure it's on "gifted setting". It's a bit dry but he can learn the material quickly.

Starting with algebra I (or prealgebra or earlier)
artofproblemsolving.com
is the place to go. They have books ($50ish), online classes (a few $100 for 12-25 weekly classes), videos (free) for some classes and Alcumus (a problem bank, free). It mostly starts at prealgebra level, though they are writing books for grade 2-5 but they won't all be out for a few years.

I'd recommend artofproblemsolving.com if solidly ready at at least prealgebra level, otherwise if concerned about gaps, have a quick run through EPGY.

Ditto to 22B's post above - and a word of caution: EPGY is a standard, solid math program (and much better than those found in most schools in US), while AOPS has more difficult, 'deep' math.

If you're looking for an idea of where to start, I'd recommend the free assessments on the singapore math page:

http://www.singaporemath.com/Placement_Test_s/86.htm

There reasonably well done and not terribly long. That will give a better idea of what material he has left to cover (if any) than some of the sketchy results from standardized tests like MAP.

Absolutely. AoPS is ultimately superior for gifted mathy kids. It's just that if one needs to learn (or solidify) the elementary school math, EPGY gives a quick way of getting it done, then switch over to AoPS when one is ready for a challenging prealgebra or algebra course.

Hopefully in a couple of years AoPS will have their grade 2-5 beastacademy.com series all written, then one can switch to AoPS earlier.

If you choose the EPGY route, I’d follow 22B’s advice about the gifted curriculum setting. I’d contact giftedandtalented.com before you sign up to see if it’s still available, and I recommend you ask whether the Initial Math Placement Test that was available in the EPGY version is still available as well. There were two versions of the Initial Math Placement Test: a 45 minutes or 48 exercises whichever comes first version and a 100 question version. The 45 minute version is sufficient and very accurate for placement.