My little man was born at 39 weeks, smiled and started cooing 6 weeks. Still not really grabbing for things intentionally- but we're working on it. He's 12 weeks now.
My LO was born 6 weeks early as well. He just started really smiling socially and cooing this past week and he is 10 weeks. He has been holding his head up for a few weeks now. No attempts to grab at anything yet though we give him ample opportunities on his activity mat.
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Re: BABY ACTIVITY?
They say for premature babies to figure based on the due date not the birthdate but here is a chart I like because it gives a larger range since babies do things at different times https://www.babycenter.com/0_milestone-chart-1-to-6-months_1496585.bc
The bumpie formerly known as First Time in MI