Education
While the iPad is doing well in education, an even bigger thing right now is the iPod, especially at the primary level, where educators are using them as rewards when kids do well. There's always time during the day that's free and the iPods are doled out to the deserving. I can see an 7.85" iPad being a big deal at that level too. Why?
#1) Bigger than the iPod but not too big (as the iPad might be for 7-10 year olds)... video would look great on this 7.85 device. Let's be honest, now that the iPad is out, who wants to watch video on their iPhone or iPod? The iPad is great but I think for portability, a smaller iPad would be the best, especially for small hands. Much easier to hold and not fumble.
#2) Cheaper than even the level entry iPad might be for education.
#3) Biggest reason to me is that the schools already have tons of education and game Apps to use immediately. Amazon Fire is not viable for the schools who are already invested in iPods/iPads because nothing they have works already. This smaller tablet comes in working with all that they have.
My wife is a first grade teacher and I'm getting this info from seeing how the iPods and iPads are used at school. A lot of these kids are truly taking to the Apple devices because they are from poor families and the chance to use the electronics is only during school.
It makes more sense and seems more likely to me to double the iPhone 4's resolution in both directions, thus:
More Likely Small iPad: 1920x1280 @ 7.85 = 293.96 ppi
While I would like a smaller iPad that was higher resolution, it seems to me that if Apple is indeed putting out a smaller version, they will keep the resolution at the current so that (1) all current apps continue to function without any manipulation by developers and (2) to keep the cost down. If Apple does put this out, it's to answer smaller tablets in the market, primarily the Kindle Fire which is a mere $199. Were Apple put a 1920x1280 screen in it, it would certainly raise costs. That's not to say that they'd never put in a better and better screen as time goes by. We see this annually as Apple continues to improve their products. However, to start, they would certainly stick with 1024 x 768.