Slap the ipad in a colorful bumper cover and viola! It's a kid toy. I use lots of apps. Before I start: block YouTube before you give it to your child. I hate what YouTube showcases and would rather they not simple watch videos all day. Block in-App purchases and set it so you have to input your password to buy apps. I also block the App store and iTunes store just in case they start perusing and I get constant "Can I get this game...".
Toddler+:
Agnitus: I just discovered this and it's a good toddler app for learning.
Monkey Lunchbox: Cute, cute, cute. And so good for shapes and colors.
Drawing Pad: Lets them be creative, save the picture and then no mess and no crayons to constantly replace.
Draw and Tell: LOVE THIS!!! They can draw but also record themselves. I record stories and songs and move the stickers around as we sing. They replay it. I also love listening to the things they record.
Teach Me Kindergarten: It's simple and my kids actually so love it.
Grade 1+:
Kindle: great for my older kids too. I buy their books in a pinch and they read it on the iPad rather than pile up books in the house (Our house is wall to wall bookcases so don't think the kids are not around books).
BrainPop: A free video each day.
Times Tables: For the older kids.
Math Board: Again for the older kids.
Cash Cow: It's a game about money and they love putting the change together to make new change.
Just for fun:
Grab a few fun games like Angry Birds, DoodleJump, and Fruit Ninja, what ever is free so you can delete it and not feel bad. It helps with hand and eye coordination and some critical thinking skills.
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I know some are not in your grade level yet but you can reference this later. You can always search Miss Sunnypatch and Disney apps. I didn't grow up with all this technology but I don't believe in limiting children to "the way I grew up". Technology will advance and tomorrow's classroom may not be like todays. We still do pen and paper and my kids still put up sheets to make houses and pile up boxes to build castles so being tech suave does not limit their imagination... we do that.