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Examples of students using the ShowMe app to explain their mathematical thinking are at the link below:

http://myprimarypassion.blogspot.com/2013/02/showme-showcase-2-math.html

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Here is a photo of my Math Games folder on my student ipads.

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Here is a picture of my Math Tools folder on my student ipads.

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QuickImages is an awesome subitizing app with numbers 1-10 represented with fingers, random, ten frame and rekenrek and 11-20 represented ten frames and rekenreks. I LOVE this app! https://itunes.apple.com/us/app/quick-images/id560877283?mt=8

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I've tried paper version of Ken Ken. They are number puzzle strategy game. . http://www.kenken.com/

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Here is a great app for multiple representations of numbers:

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I also have my students use the "Explain Everything" app to create something to share with their classmates that demonstrates their thinking. I found that my high student love doing this during our math workshop, and my struggling students really benefit from having the concepts explained by a peer.

https://itunes.apple.com/us/app/explain-everything/id431493086?mt=8

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I use many of the apps that Leka shared in her Screenshot. We also use "Moby Max" and IXL. This year, since we need to put more emphasis on problem solving, we are going to use "Target the Question." I struggle to find apps for our classroom iPads that are focused on problem solving, rather than just fluency practice.

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I just got the BEST BOOK at a training I took at the end of the year. It's called Number Talks by Sherry Parrish. You will LOVE it! http://www.amazon.com/s/ref=nb_sb_ss_i_1_12?url=search-alias%3Daps&field-keywords=number+talks+sherry+parrish&sprefix=number+talks%2Caps%2C604 You know me...Math is my thing! This is the BEST idea ever to keep us connected BTW...

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Bedtime Math app

Great for word problems with 3 different levels. This would be a good resource to share with parents, too.

https://itunes.apple.com/us/app/bedtime-math/id637910701?mt=8

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I love using the app Math Magic to practice addition/subtraction fluency. It helped my Ss tremendously. I wrote about it on our TECHi TiKES blog: http://www.techitikes.com/2013/03/math-magic-addition-and-subtraction.html

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Number Rack - it's a great quick getting started/"minds on", to project onto the screen to have students look at numbers based on 5 and 10.

https://itunes.apple.com/ca/app/number-rack-by-math-learning/id496057949?mt=8