I would recommend a laptop for homework. It is possible to get a convertible laptop that can switch between a laptop and a tablet, but they are generally more expense. I actually recommend a 15.6" Lenovo ThinkPad E545 which starts at $429 for the base model which has a dual core AMD A6-5350m and the integrated Radeon HD 8450g. It is a pretty decent deal, but adding $20 will get a quad core A8-5550m and the intregrated HD 8550g which is actually pretty good in term of performance for an integrated solution. For $70 you can get the A10-5750m which comes with the Radeon HD 8650g and is currently the most powerful integrated graphics core on the market. However, this does bring the price up to $509.
The A8 will provide good game performance for an economical cost. The A10 will provide better performance at a more expensive cost.
To get the real benefits of the graphics, there needs to be two sticks of RAM to work in dual channel mode. A single stick of RAM (default) will mean the RAM will only operate in single channel mode which could mean a 15% - 20% decrease in overall performance.
In addition, being a ThinkPad you get the business side technical support rather than the normal consumer side. So that is a plus.
http/shop.lenovo.com/us/en/laptops/thinkpad/e-series/e545/#customize
Lenovo's Yoga series their hybrid laptop tablet series. The least expensive is the Yoga 11 for $399. However, it runs Windows RT, not Windows 7 or 8 and uses a nVidia Tegra 3 ARM processor used in many tablets. Win RT cannot run normal Windows programs, it can only run programs developed specifically for Win RT. Personally I would avoid it.
The next cheapest is the Yoga 11s and it is actually a hybrid ultrabook, but the price jumps up to $699.
http
/shop.lenovo.com/us/en/laptops/ideapad/yoga/
A final suggestion would be the Asus Transformer Book T100. It is a Windows 8 tablet with a keyboard that can be attached and used as a netbook. I say netbook because it uses Intel's Bay Trail generation Atom CPU which is low power consuming CPU meant to netbooks and tablets. Compared to the processors in the ThinkPad E545 and Yoga laptops (with the exception of the Tegra 3 ARM), Bay Trail is a weak CPU. It's not meant for PC games unless it is really old or a really non-demanding game. Your daughter can play the Sims 3 on the ThinkPad E545 or the Yoga 11s, but she will not be able to play it on the Asus Transformer Book. Keep in mind that this is designed to hit a certain price point so there could be quality issues with this newly released product.
http/reviews.cnet.com/tablets/asus-transformer-book-t100/4505-3126_7-35827544.html
http
/recombu.com/mobile/reviews/asus/transformer-book-t100/