Smart idea to pay off private student loans with federal loans?

I'm a sophomore in college, and as of now, I have $20,000 in private loans. Now, once I become a junior/senior, I will get up to $10,500 each year in federal loans. Should I just use the federal loans to start paying off my ridiculously high interest rate private loans? After all, most of the federal loans will be subsidized, and by the time I graduate, I will have about $27,000 in federal loans, and maybe only a couple of thousand in private loans if I use this method of paying them off. I'll consolidate the federal loans together, and pay off the private loans ASAP(again, should only be $2000-$3500 if my calculations are correct.
Note:I have the ability to start paying off the private loans while still in school through sallie mae. The interest on 3 of these loans is 14.25%!! And one with 11.25%. Federal loans are less than half of this.

consolidating student loans

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