Here is a link that can help demonstrate and explain the connection between the box/partial products method and the bow/standard method: http://www.youtube.com/watch?v=CPF9oOKl_BY
Box/partial products method does a good job of keeping place value in double digit multiplication. This concept can be lost when calculating using the standard method. It is also less overwhelming and therefore seems easier to some kiddos. I do not care which method your child uses as long as it make sense to them.
Please feel free to ask questions if you need some clarification!
Thank you for all your support!