I’m certainly not an expert on apps but I do have a few free apps to recommend because they are FREE and give students visual models.
A Geoboard App – http://catalog.mathlearningcenter.org/apps/geoboard
A Number Rack (Rekenrek) App http://catalog.mathlearningcenter.org/apps/number-rack
Math Tappers Multiply – http://www.appsmitten.com/math-tappers-multiply/
Math Tappers Find the Sum – http://blogs.henrico.k12.va.us/apps/2011/08/17/math-tappers-find-sums/