I don't know about you but one of the frustrating things in teaching math for me was that if I wanted to model a concept, I wouldn't always have enough manipulatives for each student to have their own. I was able to cope with a variety of different ways (working with small groups, borrowing manipulatives, etc. but man do I wish they'd had more awesome apps at the time.
Enter... Clarity Innovations and ABCya.com Both of these developers have designed some wonderful math manipulatives that you can easily use on your iPad and which allow each student to have their own version of whatever manipulative you're showing.
The first one I found was Geoboard by Clarity Innovations. I love that you can quickly and easily create amazing geoboard creations of shapes, reflections, rotations, etc.
The second app I found was Virtual Manipulatives by ABCya. I love this app for fractions, decimals and percents for sure. You never have a class set of those manipulatives!
Then one day while browsing the net, I realized that Clarity Innovations creates more apps. I should have known better of course and looked at other apps by this developer but I didn't!
I soon found their place value apps. I love how both of these apps let you customize color of the blocks so that you can really quickly see the difference between ones, tens and hundreds. My greatest pleasure would be if these apps kept extending and opened up thousands blocks. I can see them being used in older grades as well if you reversed the blocks and used them as wholes, tenths and hundredths.
Next up, I found their awesome number line app. This is great for skip counting, addition and subtraction, multiplication, and division. Here it is.
Finally, I came across their Recenreck. Now I never as a child played with one of these so I am not 100% comfortable with how they work and they are not my go to manipulative, but I love how simply laid out they are and how there are so many applications in terms of place value, regrouping in addition/subtraction, etc. I think I'm going to give them another try.
I love all of these apps independently, but how I really enjoy using them is in App Smashing (when you combine more than 1 app). These apps are not optimized for app smashing as there is no share square but I find it quite simple to take a screen shot of whatever I've created and then import that picture into Explain Everything or whatever screen casting app I'm using to have very specific diagrams to explain what I'm doing.