I have found Motion Math to be a great Educational App developer for play-based math Apps for the iPad. I am currently using Motion Math Zoom and Motion Math: Hungry Fish with my K-5 Elementary School classrooms. Both Apps offer a free trial that provides enough of a range of difficulty that suits all elementary school skill levels. It is play-based learning that turns math into a visual game where math skill development is a by product.
Motion Math Zoom is an interactive number line where students need to nagivate through tens, hundreds, thousands, etc. to place the missing number. With two fingers, students learn to recognize the place value and zoom within place values. The trial app offers a taste of various types of number lines- negatives, decimals, and fractions. Students can also save process and earn points with this trial. The in App purchase is $3.99 for all the levels, but the trial has been sufficient for my needs.
Motion Math: Hungry Fish app is a mind math adding game that has 18 different difficulty levels. The great graphics allow students to engage with instant addition to feed a hungry fish which lead to fun awards. The in app purchase is $2.99 for all the levels, or some of the levels can be purchased in pieces.
This app was used in a study, in the first experiment ever to study an iPad app, and was shown to help improve student knowledge and attitudes towards math. I found it at ABC7 in San Fransico. Take a look at the article here.
There is also a built in motivator for students- the more math you do, the more you can customize the fish colors and fins. This iPad math App offers personalized learning, that offers various difficulty levels to meet students at their skill level. The interactive nature and beautiful graphics engage students in a way that is exciting and empowering.