Those strategies are NOT the standards. Those were curriculums purchased by school districts because their teachers did not know how to teach. I never taught with a prepackaged curriculum to meet the standards. We did our own and never had a problem. I had many teacher friends who quit rather than teach using some of those bird-brained strategies. My own grandkid put up with that crap in Washington state until my son got fed up and moved back east. Our schools in Kentucky kept our same curriculum and did just fine. My other grandkids there had no problems with the curriculum.
Again, you are confusing pedagogy, (how something is taught) by a curriculum, (how it is taught instructionally), and standards (which is what you are teaching them in the first place.)
An example of an Algebra standard is: The student will be able to calculate simple interest on a loan.
Do you find anything wrong with that?
I taught that exact same standard for 8 years in Florida. It was in The NCTM Standards, The Sunshine State Standards, and Common Core Standards. We used them all over that period. I then taught Common Core in Kentucky and then shifted to ACT standards-based Kentucky's replacement for Common Core. Nothing changed over my 21-year career except the name.