Don't teach 10⁶ power. Start where they're solid… and then talk about the patterns. It’s the expanded form column (in this example), the one most teachers leave out, that shows them the why. Don’t shortcut our students. Trust them with these core mathematical principles.

Strong decimal understanding is a requirement for 6th grade multiplicative reasoning with powers of 10. If students remember the trick, they may get the answer right so nobody catches that they don’t comprehend the why, that’s the fake… it can hold on for three years until 8th grade scientific notation asks the question the shift can’t answer.

We transfer expressions to make math easier so essential properties like commutative and associative are now in play. We don’t tell our students this. Let them learn the unbreakable principle of inverse operations, instead. This is where the beauty of math shines through.

If I say "point nine", you know what I am looking for but this phrase is a linguistic dead end in grades K-8 math. If I say “nine tenths," this is spoken language that could correctly be written as either a fraction or a decimal. That ambiguity is the teachable moment we want for our students.