Wiz Kid Qua-Fiki has the English Sheepdog puppet, which he uses for his "Wonder Dog" act as part of his "Super Hero Magic." In his act, he has the dog eat various items by having cut a slit in the back of its mough and just pulling the stuff into its mouth with his inside hand.
This might be a way to do the six card or six bill repeat... the dog just eats the cards or the bills. With a sponge ball routine, the dog can both take (eat) and put (regurgitate).
Qua-Fiki's Mind Reading Chicken uses its mouth to hold a dry erase marker to write predictions on a Citation whiteboard. You can skip the Citation whiteboard, but using an ordinary whiteboard or chalkboard for math might be something you'd want to consider. For example, in The Wizards' Journal #1, there's an effect called "Fancy Arithmancy" where you give a kid a calculator and you show him that the dog can add up numbers faster than a person with a calculator, writing the answer on the chalkboard.