Thank you for the comment, Kim!
I was totally confused about this type of math when my boy was in school--he was too tired after his school day to work through it with me, and I didn't have the tools or time to try and figure it out. I actually think the schools could help themselves on this by reaching out to the parents with a few basic materials and "how we teach this" handouts--but I know the schools have a lot to do.
If you could teach your niece her numbers you've already done the big part of the job! I'm sure she enjoyed learning them from you and will always have that as part of her education.