Just like addition, multiplication is a subject that requires memorization to learn. There's no way to avoid the drilling, but apps like Multiflow from Dactyl Applications can make the rote memorization fun. Multiflow takes the basic multiplication tables and adds a series of challenges that will have your children dropping their flashcards and grabbing the iPad to learn.
The app has four different modes that will drill your children on multiplication skills in ways that are fun and exciting. One mode is the "Mad Minute", which challenges your child to answer as many multiplication facts as possible in 60 seconds. "The Flow" drills your child with the basic multiplication facts, but it changes the difficulty of the questions based on your child's performance.
Another mode, "Reversals", turns things upside down by providing the answer and asking your child to choose the number pair that produces the result. Lastly, there is the "Pick em" mode which lets you pick a range of numbers that you want your child to drill. This last mode is as close as you can get to the traditional flash cards.
One thing I enjoyed about Multiflow is that it adds fun to multiplication without straying too far away from the core task of learning the multiplication facts. Your child is learning, but they are having so much fun that they don't even notice that they are being drilled. Multiflow supports Gamecenter, so parents can throw a little competition into the mix. The app also tracks your child's progress and lets parents (or kids) share achievements via Facebook or Twitter.
Multiflow is available for 99-cents in the iOS App Store.