[Lonesome in Massachussets]

By ninth grade, yes. But division by fractions was taught around fifth grade when I was in school, definitely not third. I went to Catholic school, and had 795 in the Math Level II SAT Achievement Test in high school, so I think I was okay in grammar school math. I maintain that teaching it symbolically is absolutely the wrong way to teach it. Teach it intuitively, then show how the symbols can facilitate calculation.

Math instruction in this country is a disgrace. See Richard Feymann's book Mr Feynmann, You Must Be Joking where he was invited to review high school math textbooks by the California Department of Education. Everything he criticized is summed up by your example.

[ProtectOurFreedom]

“teaching it symbolically is absolutely the wrong way to teach it”

Absolutely right. I was not advocating that. You start with concrete, physical examples and, as the brain matures around age 12 or 13, you progress to symbolic math building upon the physical examples.

I remember that being a difficult transition for me, but you reach a certain “aha!” Point one day where it quickly starts to make sense.

So many kids cannot make that transition today and graduate from high school still depending on fingers and toes.

[FamiliarFace]

For those interested in purchasing.

https://www.amazon.com/Surely-Youre-Joking-Mr-Feynman/dp/0393355624/ref