Fair warning before you read my answer: I am homeschooling in Texas and I never thought I would be (both in texas and homeschooling). I love homeschooling my daughter now and can't imagine being under the contrived stress of some primary "academia". We do use some new teaching methods inspired by common core (common core is not the curriculum, just the standards), and sometimes they help with her learning, sometimes they are redundant and confusing. Luckily we get to pick and choose the best curriculum fit for our daughter.
IMO if you are confident he knows the material and it's just the teaching methodologies that are tripping him up, I wouldn't worry about him failing the test. What are the real consequences? If your son fails the STAAR test, he'd likely be offered before & after school, and summer tutoring. You could accept or decline. Surely if he understands the concepts and can do the problems, they wouldn't hold him back. I would ask the teacher what the consequences would be and please, don't let anyone tell you you are "messing up" your son because you taught him a new way of doing a problem at home.
FWIW, every Nobel prize winner in Physics or Economic Science, and every Fields Medal winner (Nobel equivalent in math), was taught basic math using older methodologies. I wouldn't worry that you caused your son any problems by teaching him a way in which he could more easily grasp the concept. :)
One last thing: I would be constantly reassuring and encouraging your son. He did not "suddenly get bad at math". He is still good at math. Whatever ways they are teaching M. be conceptually difficult for him, but that doesn't mean he no longer has the ability to do well.
I would check out http://www.teachingtextbooks.com/
It is a video-based, awesome, easy way to learn difficult concepts. Good luck!