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They start teaching Kanji as early as 1st grade. Who knows how much is taught, though. All you have to do is google it or look up a text book for each grade to know how many are learned for the duration of the school year.
Children learn Kanji in elementary school. A typical Japanese student should know just over around 1000 kanji by the time they start junior high.
I've never sat in on a Japanese (Kokugo) class in a Japanese school (only in their English classes), so I'm not sure how many they learn in a week.
I think I'll check tomorrow when I go to school.
There's a good Wikipedia article on this. (@elite4james: You're off by just six, according to the article. They learn a total of 1006 kanji. Or are supposed to, anyway.)
As a Chinese kid, I grew up with Kanji. It's actually because of the Chinese characters that I know any Japanese at all. XD
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