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Im using piano time with some students, would you think that after book one they'd be ready to try some grade one stuff,
If the pupil is otherwise confident and hasn't struggled with the end of the first book, yes. Assuming of course their sight-reading and scales are up to standard.
A lot of first books don't get anywhere near grade one, but Piano Time does, I reckon. Some of the pieces towards the end of PT1 are around grade one standard (eg p44). I sometimes find myself using PT bk2 after grade one, although the scales in the 2nd book are revision by that time, and it doesn't hurt to have done part of bk 2 before grade one if that's how it works out.
Most children take at least a year and some getting on for 2 years before taking grade 1.