Simple solution to all your dice problems! Stick two dice in a small tupperware container. Have the children shake the container and look at the dice. No "throwing" dice or losing them either. I will probably use foam dice as they are noiseless.
I could totally do this with money-- dollars on a pumpkin then popsicle sticks with bills and coins that add up to the amount. Addition/subtraction sorting - child needs to determine which sticks add up to the number on the bucket.