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4 Answers
Maybe it's the placement of "de niño"
I think you meant to say that as a child you played with blocks.
The way you said it, it comes out "I played with childrens's blocks."
To say the other, I would use, "De niño, jugaba con bloques"
I hope I caught your meaning, otherwise I have no idea.
Check this out with your teacher. If It's wrong let her keep her "big secret" I hate teachers like that. I'm a teacher and my job is to teach--not make the students guess what's happening.

Q: ¿Jugabas con bloques de niño?
A: Sí, jugaba con bloques de niño.
"corrected" A: Sí, YO jugaba con LOS bloques de niño.
Hmmm, I tended to agree with Daniela and Annierats- although my instinct was:
Sí, jugaba de niño con bloques.
But that is not the question, so:
Following a question with jugabas- I see no earthly reason for yo- who else would you be talking about- I dont see it as a good idea to teach to something that is unnatural. You might need it with this answer if the question was ¿Jugaban ustedes con bloques de niño? Sí yo jugaba con bloques, pero mi amigos, no. But not in the exchange as given.
I do not see a need for los there at all. Yes Spanish uses articles for generic nouns where we dont- but not after a preposition like this that I have seen. The addition of los really makes it sound to me like you are talking about the childrens blocks as opposed to some other kind of blocks. It doesnt use los in the question- and the question was given.
So I agree entirely with you. I am a learner though, so I post mainly to bring this back to the top and not leave it way down on page 2 where no one may notice.
Is your teacher a native speaker?
Just an add-on to Daniella's answer, as I didn't read it properly to start with.
bloqes de niño = lego brick for children
De niño jugaba con bloques de niño
Well, I don't know what "bloques" is xD, but maybe the reason she thought it was wrong is that you wrote a question mark in the answer:
A: ¿Sí,