... I was told not to teach him anymore because I do not know the Core Curriculum which his school relies on, and if I taught him multiplication, for example, any answers would be marked incorrect on an exam because of the methodology...
The common core standards do not specify a methodology per se. You may wish to read the math standards here...
http://www.corestandards.org/Math/, focusing on "operations and algebraic thinking"... multiplication appears to begin in grades 2 and 3.
I agree with others that teachers ought to be able and willing to point you to the curriculum which they are utilizing. Failure to do so may indicate that schools wish to be the only teachers of children, to help ensure equal outcomes for all students.
